Dissertation References
Updated April 2009
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Active Teaching/Learning (10 Refs)
Cooper, J., & Robinson, P. (1998). Small group instruction in science, mathematics, engineering, and technology. Journal of College Science Teaching, 27(6), 383-388.
Cooper & Robinson, 1998.
Level: College
Small-Group instruction (Research - Quantitative)
Davidson, N. (1997). Small-group learning and teaching in mathematics: A selective review of research. In E. Dubinsky, D. Mathews, & B. E. Reynolds (Eds.), Readings in cooperative learning for undergraduate mathematics (pp. 59-68). Washington, D.C.: Mathematical Association of America.
Davidson, 1997.
Level: K-12
Review of Small-Group Learning Research (Research - Mixed Methods)
Davidson summarizes the findings of research prior to 1985 related to the effectiveness of several small-group methods of instruction and a number of dynamics of small-group methods of instruction that effect performance and cognition. Particular attention is payed to control-group studies that tested possible performance differences between small-group instruction again individual instruction on common measures of mathematical achievement. Some of the small-group methods of instruction for which he reviews studies include small-group discovery-based, laboratory and data collection, computer assisted instruction (CAI), goal structure-based, and group rewards for individual learning. Davidson presents research findings surrounding group-processes and aptitude*treatment interactions, as well as group-testing, brainstorming, and cognitive development implications of small-group learning according to Perry's scheme. The summary is followed by a list of 12 recommendations for future research, many of which are probably still open areas for research into small-group learning at the collegiate level.
Johnson, D. W., Maruyama, G., Johnson, R., Nelson, D., & Skon, L. (1981). Effects of cooperative, competitive, and individualistic goal structures on achievement: A meta-analysis. Psychological Bulletin, 89(1), 47-62.
Johnson, Maruyama, Johnson, Nelson, & Skon, 1981.
Level: Secondary
Types of Classroom Cooperative Learning Structures (Research - Quantitative)
Meta analysis of goal structures research.
Johnson, R. T., & Johnson, D. W. (1994). An overview of cooperative learning. In J. Thousand, A. Villa, & A. Nevin (Eds.), Creativity and collaborative learning (chap. 3). Baltimore: Brookes Press.
Johnson & Johnson, 1994.
Level: K-12
Cooperative Learning (Practice)
Keppell, M., Au, E., Ma, A., & Chan, C. (2006). Peer learning and learning-oriented assessment in technology-enhanced environments. Special issue: Learning-oriented assessment: Principles and practice. Assessment & Evaluation in Higher Education, 31(4), 453-464. Retrieved November 14, 2006, from ERIC database (EJ 736098).
Keppell, Au, Ma, & Chan, 2006.
Level: College
Technology and Assessment (Practice)
Leikin, R., & Zaslavsky, O. (1999). Connecting research to teaching: Cooperative learning in mathematics. The Mathematics Teacher, 92(3), 240-246.
Leikin & Zaslavsky, 1999.
Level: K-12
Cooperative Learning (Practice)
Lists 4 conditions for cooperative learning. describes the "exchange-of-knowledge" method and lists conclusions.
Rosenthal, J. S. (1995). Active learning strategies in advanced mathematics classes. Studies in Higher Education, 20 (2), 223-229.
Rosenthal, 1995.
Reform Teaching in Advanced Mathematics (Practice)
Savery, J. R., & Duffy, T. M. (1995). Problem Based Learning: An instructional model and its constructivist framework. Educational Technology, (35), 31-38.
Savery & Duffy, 1995.
Level: K-12
Problem-Based Learning (Practice)
The Calculus Development Team. (1996). Models of automobile velocities. Retrieved June 10, 2007, from http://www.geom.uiuc.edu/
The Calculus Development Team, 1996.
Level: College
Example of Reform Calculus Project (Practice)
Wilson, P. S., Cooney, T. J., & Stinson, D. W. (2005). What constitutes good mathematics teaching and how it develops: Nine high school teachers’ perspectives. Journal of Mathematics Teacher Education, 8 (2), 83-111.
Wilson, Cooney, & Stinson, 2005.
Good Mathematics Teaching in High School (Practice - Qualitative)
Feedback and Formative Assessment (20 Refs)
Black, P., & Wiliam, D. (1998, October). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 139-148.
Black & Wiliam, 1998.
Level: Secondary
Formative Assessment (Practice)
Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41-62.
Boaler, 1998.
Level: Secondary Learning Theory: Situated Cognition Methodology: Comparative Case Study
Reform Curriculum and Transfer (Research - Mixed Methods)
Using a mixed methods approach, Boaler (1998) investigated the nature of learning of students (ranging in age from 13 to 16) at two British schools, one process-based school where students focused on projects and applications problems and one content-based school where students focused on algorithms and memorization of concepts. Data collection included student and teacher interviews, student questionnaires, open ended tests, short answer tests, student demographic information, lesson observations, and standardized exam grades. The results showed that the students who learned mathematical processes (process-based) scored higher on open ended questions and performed as well as students who learned mathematical procedures (content-based) on procedural questions. In addition, the content-based students have worse attitudes toward mathematics than the other students do. Implications for teaching consist of the idea that students who learn through activity based instruction (process-based) perform better on applied problems and as well as students taught using algorithms on short answer, content-based problems. [by Ann Wheeler]
Bransford, J. D., Brown, A. L., &Cocking, R. R. (Eds.). (1999). Learning and transfer. In How people learn: Brain, mind, experience, and school (pp. 51-78). Washington, D.C.: National Research Council.
Bransford, Brown, &Cocking, 1999.
Learning Theory: General Learning Theory
Research Insights into Transfer and Learning (Theory - Mixed Methods)
This chapter includes in depth insights into transfer of learning. Starting with Thorndike's work in 1913 suggesting the likelihood of transfer depends on the similarities in elements between the learned task and novel task, the authors list a number of results. In particular, they point to (1) inital learning/astery is necessary for transfer, (2) overly contextualized knowledge can reduce transfer while abstract representations of knowledge can promote transfer, (3) transfer is best viewed as an active, dynamic processes rather than a passive end-product, and (4) the fact that all new learning involves transfer has implications for designing instruction. Some additional information includes examples of negative transfer, the role of learning for understanding vs. memorizing facts, time-spent initially learning material, motivation, and context-tied knowledge. The authors suggest that a major goal of schooling is to promote flexible transfer, and that transfer is best defined as an improvement in the time it takes someone to learn new material, rather than the dichotomous question of whether someone is able to "make the connection".
Doerr, H. M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41(2), 143-163.
Doerr & Zangor, 2000.
Level: Secondary Learning Theory: Social Constructivism Methodology: Basic
Qualitative Study of Graphing Calculators (Research - Qualitative)
Qualitative study on issues surrounding the graphing calc., including its negative effects on cooperative learning.
Erlwanger, S. H. (1973). Benny's conception of rules and answers in IPI mathematics. Journal of Children's Mathematical Behavior, 1(2), 7-25.
Erlwanger, 1973.
Level: Primary Learning Theory: Behaviorism Methodology: Case Study
Individual Programmed Instruction (Research - Qualitative)
Benny is a student who develops incomplete understanding of mathematics by working for several years in a individualized programmed instruction curriculum. Benny "learns" that mathematics is sometimes like magic and that there are multiple answers for a given mathematical problem, but that equivalent answers may be incorrect because they do not follow the form on the answer sheet. This early example of a qualitative study was influential in mathematics education because it provided a counterexample to the benefits that behavioral researchers attributed to programmed instruction that was founded on Skinner's principles of conditioned responses. Though Benny was excelling in his program, Erlwanger was able to gain insight into Benny's many misconceptions through tasked-based interviews with qualitative follow-up questions. Benny had invented many "rules" to fit the feedback he received from the answer keys, but understood very little mathematics. Poor Benny.
Friedberg, S., Ash, A., Brown, E., Hughes Hallet, D., Kasman, R., Kenney, M., et al. (2001). Study habits. In Teaching mathematics in colleges and universities: Case studies for today's classroom: Faculty edition (pp. 49-54,141-143). Providence, RI: American Mathematical Society.
Friedberg, Ash, Brown, Hughes Hallet, Kasman, Kenney, et al, 2001.
Level: College
Teaching with Quizzes in Calc II (Practice)
This short vignette describes the efforts of Angelica, a fictional teaching assistant in a large mathematics department, to introduce regular quizzes as part of assessment in a Calculus II course.
Gijbels, D., & Dochy, F. (2006). Students' assessment preferences and approaches to learning: Can formative assessment make a difference. Educational Studies, 32(4), 399-409.
Gijbels & Dochy, 2006.
Level: College
Change in College Students' Preferences (Research - Quantitative)
Greer, B., & Harel, G. (1998). The role of isomorphisms in mathematical cognition. Journal of Mathematical Behavior, 17(1), 5-24.
Greer & Harel, 1998.
Level: College Methodology: Basic
Types of Isomorphism during Problem Solving Transfer (Research - Qualitative)
In the context of mathematical cognition, isomorphism refers to when an individual recognizes a surface-level or structural-level correspondence between two mathematical problems or statements. Greer and Harel set isomorphism within the larger context of knowledge transfer, which was extensively researched in the 1970's and 80's (summarized by Lave, 1988). A primary goal of this theoretical article was to propose three models for cognitive isomorphism: surface-level isomorphim, deep isomorphism, and mediated isomorphism. Examples of each proposed model distinguish them from each other. Considerable effort is spent discussing teaching implications of isomorphism research, including the use of analogies, manipulatives, and teacher-imposed isomorphisms as solution aids.
Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66(1), 64-74.
Hake, 1998.
Level: College
Reform in College Physics (Research - Quantitative)
Herzig, A. H. (2002). Where have all the students gone? Participation of doctoral students in authentic mathematical activity as a necessary condition for persistence toward the Ph.D. Educational Studies in Mathematics, 50(2), 177-212.
Herzig, 2002.
Level: College Learning Theory: Situated Cognition Methodology: Basic
Why Doctoral Math Students Leave and Stay (Research - Qualitative)
Herzig (2002) summarizes her dissertation investigation into graduate students in mathematics and faculty members at a large doctoral mathematics program. Using a situated learning perspective, and focusing on participating in mathematics communities and authentic activities, Herzig found that some students left the program due in part to a lack of positive experiences with faculty members. Herzig also relates the importance of how graduate students and faculty viewed qualifying exams and mentorship opportunities.
Husman, J., Brem, S., & Duggan, M. A. (2005). Student goal orientation and formative assessment. Academic Exchange Quarterly, 9 (3), 355–359.
Husman, Brem, & Duggan, 2005.
Level: Primary
Relationship between Formative Assessments and Goal Orientations (Research - Quantitative)
Abstract: This study examined the role of formative assessment in the development of student goal orientations. Students in one elementary school were examined over the course of a school year as they participated in a reading program using continuous formative assessment. Mastery orientation remained consistently high and performance orientation decreased. Students’ personal goal orientations were significantly related to their perceptions of their teachers’ goals for reading.
Lobato, J. (2003). How design experiments can inform a rethinking of transfer and vice versa. Educational Researcher, 32(1), 17-20.
Lobato, 2003.
Actor-Oriented Transfer Research (Theory)
Paschal, C. B. (2002). Formative assessment in physiology teaching using a wireless classroom communication system. Teaching with Technology, 26(4), 299-308.
Paschal, 2002.
Level: College
Clickers and Formative Assessment (Research - Quantitative)
Rietz, H. L. (1910). The teaching of college algebra. The American Mathematical Monthly, 17(3), 51-55.
Rietz, 1910.
Level: College
College Algebra in 1910 (Practice)
Rietz (1910), from the University of Illinois, presents his thoughts on some important aspects of teaching college algebra. The historical nature of the think piece provides historical context for college algebra reform. Rietz defines College Algebra to be a freshman mathematics course for students who successfully completed 1 1/ears of algebra in secondary school. He points out that College Algebra is a difficult course to successfully teach in college because 1) professors from many branches of mathematics would like students to be familiar with a variety of algebraic methods used in the specializations, 2) there is difficulty identifying unifying elements among the many topics, 3) instructors differ on the appropriate role of proof, limits, and series in a first year college mathematics course. In much the way that geometry is unified by logic and proof, Rietz argues that College Algebra should be unified by two key concepts: a) the concept that an equation is a relation to be satisfied (rather than a condition with an unknown that needs to be found), and b) the idea of tracking the changes of a function and its close connection to plotting graphs. Even in 1910, Rietz points out that "the view has been frequently expressed by writers on mathematical education that the mathematics of of the college is not well correlated with the mathematics as taught at present in the secondary schools, and that the ideas of the best trained mathematicians have little influence on school instruction" (p. 52). In terms of appropriate topics in College Algebra, Rietz suggests that 1) theory of equations be treated lightly and primarily as a method to introduce methods of approximation, 2) logarithms can be a useful tool in plotting graphs of functions, and 3) limits and infinite series are appropriate for College Algebra if they are introduced as examples of functions "whose changes in value concern us". He reiterates that graphing should be increasingly used to help understand functions and that exercises and problems should include "illustrative problems so connected with the experience of the pupil as to make the principle appear of real value on account of its applications" (p. 53).
Segers, M., Nijhuis, J., & Gijselaers, W. (2006). Redesigning a learning and assessment environment: The influence on students' perceptions of assessment demands and their learning strategies. Studies in Educational Evaluation, (32), 223-242.
Segers, Nijhuis, & Gijselaers, 2006.
Level: College
Change in College Students' Preferences (Research - Quantitative)
Struyven, K., Dochy, F., & Janssens, S. (2005). Students' perceptions about evaluation and assessment in higher education: A review. Assessment & Evaluation in Higher Education, 30(4), 325-341.
Struyven, Dochy, & Janssens, 2005.
Level: College
Students' Perceptions of Evaluations (Research - Quantitative)
Thompson, A. G. (1984). The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice. In T. Carpenter, J. Dossey, & J. Koehler, Classics in mathematics education research (pp. 173-184). Reston, VA: National Council of Teachers of Mathematics.
Thompson, 1984.
Level: Middle Methodology: Comparative Case Study
Teachers' Views of Mathematics (Research - Qualitative)
Ulmer, M. B. (2000). Self-grading: A simple strategy for formative assessment in activity-based instruction. Spartanburg, SC: Author. Retrieved November 14, 2006, from ERIC database (ED 444433).
Ulmer, 2000.
Level: College
Self-Grading and Formative Assessment (Practice)
van Zee, E., & Minstrell, J. (1997). Using questioning to guide student thinking. The Journal of the Learning Sciences, 6(2), 227-269.
van Zee & Minstrell, 1997.
Level: Secondary
Questioning (Practice)
Wiliam, D., Lee, C., Harrison, C., & Black, P. (2004). Teachers developing assessment for learning: Impact on student achievement. Assessment in Education, 11(1), 49-65.
Wiliam, Lee, Harrison, & Black, 2004.
Level: Secondary
Formative Assessment and Achievement (Research - Quantitative)
Learning Theory (12 Refs)
Bandura, A. (1995). Comments on the crusade against the causal efficacy of human thought. Journal of Behavioral Therapy and Experimental Psychology, 26(3), 179-190.
Bandura, 1995.
Learning Theory: Social Cognitive Theory
Social Cognitive Theory as Anti-Behaviorist (Theory)
Bandura gives the philosophical argument for Social Cognitive Theory as an anti-behaviorist approach to the question of whether there is a causal relationship between cognition and behavior.
Bandura, A., Ross, D., & Ross, S. A. (1963). Imitation of film-mediated aggresive models. Journal of Abnormal and Social Psychology, 66 (1), 3-11.
Bandura, Ross, & Ross, 1963.
Level: Primary Learning Theory: Social Cognitive Theory
Imitative Aggression in Children (Research - Quantitative)
Important early study of observation learning-- children exhibited aggresive behaviors after observing aggressive cartoons as well as after observing peer models. The term “imitation” is used to refer to the learned behavior.
Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school (Expanded ed.). Washington, DC: National Academy Press.
Bransford, Brown, & Cocking, 2000.
Learning Theory: General Learning Theory
Results of Learning Research (including Transfer) (Theory)
Reports recent research in teaching and learning in the context of learner, knowledge, assessment, and community centeredness principles. Includes mentions to classroom communication systems, evaluation of learning environments, and teacher development programs. Owens et al. (2002) used HPL as their theoretical perspective. Good quote: "New tools of technology have the potential of enhancing learning in many ways. The tools of technology are creating new learning environments, which need to be assessed carefully."
Debowski, S., Wood, R. E., & Bandura, A. (2001). Impact of guided exploration and enactive exploration on self-regulatory mechanisms and information acquisition through electronic search. Journal of Applied Psychology, 86(6), 1129-1141.
Debowski, Wood, & Bandura, 2001.
Level: College Learning Theory: Social Cognitive Theory
Guided Exploration and Learning to Search (Research - Quantitative)
Driscoll, M. P. (2000). Introduction to theories of learning and instruction. In Psychology of learning for instruction (2nd ed., pp. 11-17). Boston, MA: Allyn & Bacon.
Driscoll, 2000.
Basics of Learning (Theory)
Following a brief history of learning, Driscoll dives into epistemological considerations in the philosophy of knowledge and learning. Perspectives on what is considered valuable knowledge (empiricism, nativism, rationalism) are combined with what is considered to be knowable (skepticism, idealism, realism, pragmatism) to give a vocabulary for discussing the three major epistemological traditions: objectivism, interpretivism, and pragmatism. The introduction is brief but includes helpful diagrams and tables that I've referred to many times in trying to grapple with the philosophical assumptions of various learning theories.
Driscoll, M. P. (2004). Self-regulation. In Psychology of learning for instruction (3rd ed., pp. 328-332). Boston, MA: Allyn & Bacon.
Driscoll, 2004.
Learning Theory: Social Cognitive Theory
Overview of Self-Regulation (Theory)
This brief portion of Driscoll's text summarizes the work of Zimmerman and Schunk in self-regulation. As a concept in social cognitive theory, a large amount of research has looked into the dimensions of academic self-regulation and possible instructional interventions that might help students improve their self-regulatory behavior. Monitoring progress toward goals is described as being fundamental to what Zimmerman and Schunk call enactive feedback loops, which include three strategies: (1) observing one's performance, (2) comparing one's performance to a standard or goal, and (3) reacting and responding to the perceived differences. Thus, planning/orethought, monitoring of performance, and self-reflection contribute to a three-phased cycle of self-regulation. A point is made that self-regulation may or may not be "teachable" through modeling strategies that have been shown to be effective tools for self-regulation.
Dubinsky, E. (2001, May). Using a theory of learning in college mathematics courses. MSOR Connections, 10-16. Retrieved April 30, 2007, from http://mathstore.ac.uk/
Dubinsky, 2001.
Learning Theory: APOS
APOS Theory in College Math (Theory)
Dubinsky starts by describing what he believe constitutes an acceptable theory in education. A theory should (1) support prediction, (2) possess explanatory power, (3) be applicable to a broad range of phenomena, (4) help organize thinking about learning phenomena, (5) serve as a tool for analyzing data, and (6) provide a language for communication about learning. He goes on to describe APOS theory in mathematics education. In APOS theory, a hierarchy of understanding is established for mathematical concepts: action, process, object, schema. Similar to Van Heile levels, APOS theory provides a framework for describing students' understanding while simultaneously acknowledging the constructivist viewpoint that understanding can exist on multiple levels and is unique to individuals. Interestingly, Dubinsky (the inventor of APOS) suggests that the most important instructional strategies for helping students construct internal representations of mathematics are cooperative learning and "having students write computer code to implement mathematical concepts" p. 13. The driving example of the article is a study into the genetic decomposition and related teaching of the mathematical concept of cosets in abstract algebra.
Martin, J. (2004). Self-regulated learning, social cognitive theory, and agency. Educational Psychologist, 39(2), 135-145.
Martin, 2004.
Learning Theory: Social Cognitive Theory
Overview of Social Cognitive Theory (Theory)
Schraw, G. (1998). Promoting general metacognitive awareness. Instructional Science, 26, 113-125.
Schraw, 1998.
Level: Secondary Learning Theory: Social Cognitive Theory
Metacognition (Practice)
This article describes metacognition (or thinking about thinking) as existing through knowledge about one's own cognition and regulation of cognition. Knowledge of cognition can be considered from the perspective of (1) declarative knowledge (what I know about myself and the factors that influence my learning), (2) procedural knowledge (heuristics and strategies for doing things), and (3) conditional knowledge (ways that I know when and how to use declarative and procedural knowledge). The other aspect of metacognition is regulation, which is the means by which an individual controls their learning. Included in regulation are the subprocesses of planning, monitoring, and evaluation. Metacognition is domain general and can be learned when instructors employ classroom strategies that promote awareness, regulation, and support for evaluating progress and the effectiveness of problem-solving approaches.
Schunk, D. H. (2004). Learning theories: An educational perspective (pp. 285-289, 447-451). Upper Saddle River, NJ: Pearson Education.
Schunk, 2004.
Learning Theory: General Learning Theory
Overview of Learning Theories (Theory)
Schunk, D. H. (2004). Social cognitive theory. In Learning theories: an educational perspective (pp. 83-134). Upper Saddle River, NJ: Pearson Education.
Schunk, 2004.
Learning Theory: Social Cognitive Theory
Overview of Social Cognitive Theory (Theory)
Teong, S.-K., Threlfall, J., & Monaghan, J. (2000). The effects of metacognitive training in mathematical word problem solving in a computer environment. Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education, 4, 193-200.
Teong, Threlfall, & Monaghan, 2000.
Level: College Learning Theory: Social Cognitive Theory
Metacognition and Problem Solving (Research - Quantitative)
This short proceedings article summarizes a mixed methods study into the effects of metacognitive training for twelve-year-olds in Singapore who are engaged in computer-assisted word problem instruction. The software, WordMath, uses a cognitive apprenticeship approach to teaching problem solving skills. Results of the study indicated that metacognitive training delivered through WordMath significantly improved problem solving performance and the use of problem solving strategies.
The study's short qualitative component employed Schoenfeld's (1985) episode analysis technique for evaluating think-aloud task interviews. Pairs of students from each of the conditions completed a word problem, with only the MAC students successfully solving the problem. The MAC pair appeared to spend about the same amount of time in the Reading and Analysis phases of problem solving, but was the only group to move on to Planning, Implementation, and Verification. Transcript data supports the belief that metacognitive training improved the MAC students' strategic thinking.
Methods (28 Refs)
Byrne, B. M. (1998). Structural equation modeling with LISREL, PRELIS, and SIMPLIS: Basic concepts, applications, and programming. Mahwah, NJ: Lawrence Erlbaum Associates.
Byrne, 1998.
SEM with LISREL (Theory - Quantitative)
Good book on SEM with LISREL
College Board. (2008). ACT-SAT Concordance Tables. Retrieved January 15,, 2009, from http://www.act.org/aap/concordance/pdf/report.pdf
College Board, 2008.
ACT-SAT conversion (Practice)
Colosi, L. (1997). Reliability and validity: What's the difference? In The layman's guide to social research methods. Retrieved November 5, 2006, from http://www.socialresearchmethods.net/
Colosi, 1997.
Reliability and Validity (Theory)
Economic and Social Data Service. (2006, June 22). Qualitative data types. Retrieved October 25, 2006, from http://www.esds.ac.uk/
Economic and Social Data Service, 2006.
Qualitative Data Types (Theory)
Evans, S. W. (2006). Differential performance of items in mathematics assesment materials for 7-year-old pupils in English-medium and Welsh-medium versions. Educational Studies in Mathematics, 64(2), 145-168.
Evans, 2006.
Level: Primary
DIF: Testing Items (Research - Quantitative)
Foster, J., Barkus, E., & Yavorsky, C. (2006). Path analysis. In Understanding and using advanced statistics. (pp. 89-102). London: Sage Publications.
Foster, Barkus, & Yavorsky, 2006.
Path Analysis in Correlational Studies (Theory)
Fowler, F. J. (2002). Survey research methods (3rd ed.). Thousand Oaks, CA: Sage.
Fowler, 2002.
Designing and Carrying-out Surveys (Theory)
Fowler gives a number of tips and tricks for designing surveys, administering such instruments, and analyzing data. The author focuses on validity and reliability of survey items, alignment of items with constructs and research questions, and assessing survey results.
Frankfort-Nachmias, C., & Nachmias, D. (2000). Research methods in the social sciences. (6th ed.). New York: Worth Publishers.
Frankfort-Nachmias & Nachmias, 2000.
Overview of Quantitative Research Methods (Theory)
Garson, D. (2006). Path analysis. Retrieved February 26, 2007, from North Carolina State University Web site: http://www2.chass.ncsu.edu/
Garson, 2006.
Path Analysis in Correlational Studies (Theory)
Guion, L. A. (2002, September). Triangulation: Establishing the validity of qualitative studies. Retrieved November 4, 2006, from University of Florida Extension Web site: http://edis.ifas.ufl.edu/
Guion, 2002.
Triangulation (Theory)
Hair, J. F., Jr., Anderson, R. E., Tatham, R. L., & Black, W. C. (1998). Multivariate data analysis (5th ed.). Upper Saddle River, NJ: Prentice Hall.
Hair, Jr, Anderson, Tatham, & Black, 1998.
Structural Equation Modeling (Theory - Quantitative)
Chapter 12 is AWESOME… includes 7-stage process for SEM and two examples
Harwell, M. R., Post, T. R., Maeda, Y., Davis, J. D., Cutler, A. L., Andersen, E., et al. (2007). Standards-based mathematics curricula and secondary students' performance on standardized achievement tests. Journal for Research in Mathematics Education, 38(1), 71-101.
Harwell, Post, Maeda, Davis, Cutler, Andersen, et al, 2007.
Level: Secondary
Reformed Curriculum and Achievement (Research - Quantitative)
Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31 (4), 396-428.
Healy & Hoyles, 2000.
Level: Middle
Students Conceptions of Algebraic Proof (Research - Mixed Methods)
Healy and Hoyles aimed to investigate the impact of the new proof component in England’s National Curriculum using mixed methods. The authors used hierarchical linear modeling (students at Level 1, class, school, teacher, and curriculum at Level 2). Students and teachers were asked separately to choose proofs of number theoretic statements based on the one that most resembled a proof they might give as well as the proof they thought would receive the best marks. The most popular choice for “own method” was the least popular choice for “get the best mark”; however, this could be due to the survey instrument because the task of “List the one proof that most closely resembles the method you prefer” was IMMEDIATELY followed by “List one that might receive the best mark”. The authors point to evidence that students “transported” (or transferred) the investigations approach in their curriculum when trying to construct proofs of number conjectures. Students used techniques like the ones they were taught. Students tended to use empirical arguments, but were aware that they were not considered valid for their teachers (“they knew more was expected of them”). The students' viewed the purpose of proof to be verification, explanation, examples, or ritual (p. 417) Moreover, the study found gender differences: “Higher general mathematics competence is associated with better constructed proofs, with girls performing better than boys” (p. 421) The study originally aimed to compare schools and teachers, but found no differences in students’ choices associated with teacher effects-- found more unexplained variation within schools than between schools.
Howell, J. T. (1973). Hard Living on Clay Street. Prospect Heights, IL: Waveland Press.
Howell, 1973.
Level: Adult Methodology: Ethnography
Ethnography of Blue Collar Families in Washington, D.C. (Research - Qualitative)
Joreskog, K., & Sorbom, D. (2008). LISREL for Windows (Version 8.8) [Computer software]. Lincolnwood, IL: Scientific Software International.
Joreskog & Sorbom, 2008.
LISREL (Research - Quantitative)
Common Structural Equation Modeling Software
Loehlin, J. C. (1987). Latent variable models: An introduction to factor, path, and structural analysis. Hillsdale, NJ: Lawrence Erlbaum Associates.
Loehlin, 1987.
SEM with LISREL (Theory - Quantitative)
Relies heavily on that Norwegian guy's view of SEM. Some good examples.
Mels, G. (2006). LISREL for Windows: Getting started guide. Lincolnwood, IL: Scientific Software International.
Mels, 2006.
Intro to LISREL and Path Analysis (Theory)
pages 4-7 explain how to fit a path model
Milner, H. R. (2007). Race, culture, and researcher positionality: Working through dangers seen, unseen, and unforeseen. Educational Researcher, 36(7), 388-400.
Milner, 2007.
Positionality and Voice (Theory - Qualitative)
Milner cautions educational researchers that avoidance of racial and cultural influences in research comes with many dangers. After reviewing the negative impact of color- and culture-blind research and policy, Milner presents contrasting tenets of educational research based on critical race theory and argues for a framework of researcher positionality which affords educators and researchers opportunities to examine race and culture at personal, interpersonal, representational, and systemic levels. The basic thesis of this theory-based article is that researchers have historically failed to adequately address racial concerns in their practice. By engagement, raised consciousness of racial concerns, and critical self-reflection, Milner suggests issues of race and culture can become a central and positive component in educational research.
O'Callaghan, B. R. (1998). Computer-intensive algebra and students' conceptual knowledge of functions. Journal for Research in Mathematics Education, 29(1), 21-40.
O'Callaghan, 1998.
Level: College
Conceptual Understanding of Functions (Research - Mixed Methods)
Tested if a reformed College Algebra curriculum improved students' understanding of functions. The author defined understanding of function as consisting of modeling, interpreting, translating, reifying, and procedural skills. O'Callaghan taught two classes (one traditional, one experimental) and also included another traditional section. The study is an example of mixed methods, with a pre-post design for the quantitative measures (attitudes and understanding of functions) and an in-depth task-based interview design for the concurrent qualitative component.
Osborne, J. W., & Waters, E. (2002). Four assumptions of multiple linear regression that researchers should always test. Practical Assessment, Research, & Evaluation, 8(2). Retrieved January 15, 2009 from http://PAREonline.net
Osborne & Waters, 2002.
Assumptions of Multiple Linear Regressions (Research - Quantitative)
Lists assumptions and gives preactical reasons for testing for them.
Schwandt, T. A. (2001). Dictionary of qualitative inquiry (2nd ed.). Thousand Oaks, CA: Sage.
Schwandt, 2001.
Dictionary of Qualitative Terminology (Theory)
Defines all/ost of the terms in qualitative research.
Seidman, I. (1998). Interviewing as qualitative research (2nd ed.). New York: Teachers College Press.
Seidman, 1998.
Interviewing (Theory)
Senger, E. S. (1999). Reflective reform in mathematics: The recursive nature of teacher change. Educational Studies in Mathematics, 37(3), 199-221.
Senger, 1999.
Level: K-12 Methodology: Comparative Case Study
Teacher Change (Research - Qualitative)
Snedecor, G. W., & Cochran, W. G. (1989). Statistical methods (8th ed.). Ames, IA: Iowa State University Press.
Snedecor & Cochran, 1989.
Statistics of all Types (Theory - Quantitative)
Basic data analysis and statistics for social sciences, lots of examples involve physical sciences though.
Stage, F. K., Carter, H. C., & Nora, A. (2004). Path analysis: An introduction and analysis of a decade of research. The Journal of Educational Research, 98(1), 5-12.
Stage, Carter, & Nora, 2004.
Path Analysis Guidelines (Research - Quantitative)
contains criteria for path analysis and reporting... VERY GOOD
Stevens, J. (1996). Applied Multivariate Statistics for the Social Sciences, 3rd Ed. Mahwah, NJ: Lawrence Erlbaum Associates.
Stevens, 1996.
Statistical Methods (Theory)
Thorough treatment of statistical methods with SPSS. Particularly good for validating models.
Suhr, D. (2008). Step your way through path analysis. Western Users of SAS Software Conference Proceedings. Retrieved January 13, 2009, from http://www.wuss.org/
Suhr, 2008.
Path Analysis Step-by-Step (Research - Quantitative)
Some procedural steps for path analysis.
Timm, N. H. (2002). Applied multivariate analysis. New York: Springer-Verlag.
Timm, 2002.
Multivariate data analysis and statistics. (Theory - Quantitative)
High-level treatment of multivariate statistics. Lots of equations.
Motivational Constructs (14 Refs)
Alderman, M. K. (1999). Motivation for achievement. Mahwah, NJ: Lawrence Erlbaum Associates.
Alderman, 1999.
Learning Theory: Social Cognitive Theory
Motivation in Education (Theory)
See chapter 3 for "concepts of ability and motivation", including self-perceptions of ability from an SCT perspective. Also, chapter 6 has info on teacher efficacy and motivation.
Bong, M., & Clark, R. E. (1999). Comparison between self-concept and self-efficacy in academic motivation research. Educational Psychologist, 34(3), 139-153.
Bong & Clark, 1999.
Learning Theory: Social Cognitive Theory
Self-Concept Vs. Self-Efficacy (Research - Quantitative)
Bong and Clark (1999) compare and contrast self-concept and self-efficacy along theoretical and empirical dimensions. They cite Shavelson et al’s (1976) definition of self-concept as the “perceptions of one’s self” that develop through an interplay of experiences, cognition, and affect. Self-concept is characterized as organized, multifaceted, hierarchical, stable, developmental, evaluative, and differentiable. The cognitive aspect of self-concept includes descriptive and evaluative components, and that the evaluative components often relate to comparisons to others (inferiority and superiority). Self-esteem refers to one’s general feelings of self-worth in which one is treated as a global entity. Self-efficacy, by focusing on one’s perception of capability to complete a given task in a specific context, is conceptually different, but often confused with self-concept. Some research suggests self-efficacy predicts self-concept. Self-concept effect sizes on achievement are often not definitive (average correlation of .21), while self-efficacy is a better predictor of both performance (.38) and persistence (.34). Self-concept has stronger relationships to anxiety, apprehension, intrinsic motivation, and value than self-efficacy. There is strong research evidence that self-concept and self-efficacy influences achievement more than the reverse effect, especially for older students (after 4th grade). The authors suggest that self-concept research could benefit from assessing cognitive components (self-concept of ability) and affective components separately, thus improving predictive power of the construct.
Davenport, E. C., Davison, M. L., Kuang, H., Ding, S., Kim, S. K., & Kwak, N. (1998). High school mathematics course-taking by gender and ethnicity. American Educational Research Journal, 35(3), 497-514.
Davenport, Davison, Kuang, Ding, Kim, & Kwak, 1998.
Level: Secondary
Gender and Ethnicity Differences in Course Taking (Research - Quantitative)
Very small sex differences in mathematics course taking found in the 1990 NAEP data.
Dowling, D. M. (1978). The development of a mathematics confidence scale and its application in the study of confidence in women college students. Dissertation Abstracts, 39. (UMI No. AAT 7902111)
Dowling, 1978.
Level: College
Mathematics Confidence Scale (Research - Quantitative)
Dissertation addresses the reliability and validity of a mathematics confidence scale for college women.
Elliot, A. J., & Moller, A. C. (2003). Performance-approach goals: Good or bad forms of regulation? International Journal of Educational Research, 39, 339-356.
Elliot & Moller, 2003.
Are Performance Approach Goals Good or Bad? (Theory)
Abstract: At present, there is disagreement among achievement goal theorists regarding the beneficial or inimical nature of performance-approach goals. This article evaluates performance approach goals using three criteria: empirical, theoretical, and meta-theoretical (values/? beliefs). On the basis of these criteria, we conclude that performance-approach goals may be construed in both positive and negative terms, and that one’s opinion of these goals is likely to be based in which evaluative criteria one highlights. At the end of the article, we offer our own opinion of how educators should view performance-approach goals.
Hansford, B. C., & Hattie, J. A. (1982). The relationship between self and achievement/?performance measures. Review of Educational Research, 52 (1), 123-142.
Hansford & Hattie, 1982.
Level: K-12
Inconsistent Relationship between Self-Esteem and Performance (Research - Quantitative)
Abstract: This meta-analysis examines the relationship between the various self-measures and measures of performance and achievement. The statistical results of 128 studies are transformed to a common measure, namely, correlation coefficients. These studies represent a total sample of 202,823 persons and produce a data base of 1,136 correlations between self-ratings and performance measures. A range in the relationship of -.77 to .96 was reported with an “average” correlation of.21. It was found that this average relationship was modified by a number of variables. The more significant modifiers of the average relation- ship were the grade-level of subjects, socioeconomic status, ethnicity, ability of subjects, self-term used in the study, name of self-test used, type and name of performance/?achievement measures, and the reliability of both the self-ratings and performance/?achievement measures.
McMillan, J. H., Singh, J., & Simonetta, L. G. (2001, Winter). The tyranny of self-oriented self-esteem. Educational Horizons, 92-95.
McMillan, Singh, & Simonetta, 2001.
Self-Focused Self-Esteem is Bad (Theory)
Suggests that the common misconception of self-esteem as a self-focused concept should be replaced by “earned self-esteem”, which can only be gained through accomplishments in outwardly-focused activities with external standards.
Midgley, C., & Urdan, T. (2001). Academic self-handicapping and achievement goals: A further examination. Contemporary Educational Psychology, 26, 61-75.
Midgley & Urdan, 2001.
Level: Middle
Performance Avoid=Bad, Mastery=Good, Performance Approach=? (Research - Quantitative)
Abstract: This study extends previous research on the relations among students’ personal achievement goals, perceptions of the classroom goal structure, and reports of the use of self-handicapping strategies. Surveys, specific to the math domain, were given to 484 7th-grade students in nine middle schools. Personal performance-avoid goals positively predicted handicapping, whereas personal performance-approach goals did not. Personal task goals negatively predicted handicapping. Perceptions of a performance goal structure positively predicted handicapping, and perceptions of a task goal structure negatively predicted handicapping, independent of personal goals. Median splits used to examine multiple goal profiles revealed that students high in performance-avoid goals used handicapping more than did those low in performance-avoid goals regardless of the level of task goals. Students low in performance- avoid goals and high in task goals handicapped less than those low in both goals. Level of performance-approach goals had little effect on the relation between task goals and handicapping.
Moore, D. A., & Small, D. A. (2007). Error and bias in comparative judgment: On being better and worse than we think we are. Journal of Personality and Social Psychology, 92 (6), 972-989.
Moore & Small, 2007.
Error, bias, and Social/ormative Comparisons (Theory)
Moore and Small (2007) discuss individual’s self-beliefs regarding social comparisons, including the primary tendency of people to judge themselves as better than average in most domains (e.g., driving, investing) and contrasting tendency to judge themselves as worse than average in very difficult domains (e.g., juggling, living past 100). The authors suggest these social comparisons, because of the ambiguous nature of “other people” and the comparative lack of information individuals have about others, really reflect self-evaluations. This suggests normative evaluations, as in those used in self-concept measures, reflect response bias toward self-evaluations. (Additional evidence for self-efficacy over self-concept.)
Pajares, F., & Graham, L. (1999). Self-efficacy, motivation constructs, and mathematics performance of entering middle school students. Contemporary Educational Psychology, 24, 124-139.
Pajares & Graham, 1999.
Level: Middle Learning Theory: Social Cognitive Theory
Motivational Factors, Self-Efficacy, and Performance in Middle School Math (Research - Quantitative)
Pajares and Graham (1999) set-out to assess the effects of a variety of motivational factors in predicting mathematics performance among (N=273) middle school students. The authors also sought to assess whether these effects change during students’ first year in middle school. In a review of self-efficacy research, the authors say, “Across ability levels, students whose self-efficacy is higher are more accurate in their mathematics computation and show greater persistence on difficult items than do students whose self-efficacy is low.” (p. 125) In terms of gender differences, Pajares and Graham describe six studies that found no differences in performance between boys and girls, but that boys held higher confidence in mathematics than girls starting in middle school and persisting through high school. Other motivational variables that predict academic performance include math anxiety, self-concept, self-efficacy for self-regulation, perceived value, and academic engagement (persistence and effort). The article contains detailed explanation of self-efficacy and calibration instrumentation, with justification for the choices of measures in the literature. The authors also highlight the implications of administering self-efficacy surveys on high stakes assessments, which is atypical for studies of self-efficacy and academic achievement. The authors found no gender differences, but did find that gifted students performed better, held higher self-efficacy ratings, and better calibrated than non-gifted students. After controlling for all other motivational variables, self-efficacy was the largest predictor of performance, and the only significant predictor on both administrations of exams.
Pajares, F., & Schunk, D. H. (2002). Self and self-belief in psychology and education: An historical perspective. In J. Aronson (Ed.), Improving academic achievement (pp. 5-25). New York: Academic Press.
Pajares & Schunk, 2002.
History of Self-Beliefs in Educational Psychology (Theory)
Historical development of the Self in educational psychology, ranging from William James to Freud, the Humanistic Revolt, and current academic motivation research on constructs like self-concept and self-efficacy.
Reyes, L. H. (1984). Affective variables and mathematics education. The Elementary School Journal, 84 (5), 558-581.
Reyes, 1984.
Affect in Math Education (Theory)
Zimmerman, B. J., & Schunk, D. H. (1989). Self-regulated learning and academic achievement: theory, research, and practice. New York: Springer-Verlag.
Zimmerman & Schunk, 1989.
Learning Theory: Social Cognitive Theory
Self-Regulation and Achievement (Theory)
Self-regulation theory, with applications to classroom learning. See Chapter 7 for connections to constructivism.
Zimmerman, B. J., Bandura, A., & Martinez-Pons, M. (1992). Self-motivation for academic attainment: The role of self-efficacy beliefs and personal goal setting. American Educational Research Journal, 29 (3), 663-676.
Zimmerman, Bandura, & Martinez-Pons, 1992.
Level: Primary Learning Theory: Social Cognitive Theory
Self-Efficacy and Goals in Academic Motivation (Research - Quantitative)
Abstract: The causal role of students’ self-efficacy beliefs and academic goals in self-motivated academic attainment was studied using path analysis procedures. Parental goal setting and students’ self-efficacy and personal goals at the beginning of the semester served as predictors of students’ final course grades in social studies. In addition, their grades in a prior course in social studies were included in the analyses. A path model of four self-motivation variables and prior grades predicted students ‘final grades in social studies, R = .56. Students’ beliefs in their efficacy for self-regulated learning affected their perceived self-efficacy for academic achievement, which in turn influenced the academic goals they set for themselves and their final academic achievement. Students’ prior grades were predictive of their parents’ grade goals for them, which in turn were linked to the grade goals students set for themselves. These findings were interpreted in terms of the social cognitive theory of academic self- motivation.
Need (5 Refs)
Alliance for Excellent Education. (2008). What keeps good teachers in the classroom? Understanding and reducing teacher turnover. Washington, DC: Author.
Alliance for Excellent Education, 2008.
Teacher Turnover (Research - Quantitative)
Ingersoll, R. M. (2003). Is there really a teacher shortage? (Document No. R-03-4). University of Washington: Center for the Study of Teaching and Policy.
Ingersoll, 2003.
Teacher shortages (Research - Quantitative)
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Retrieved June 17, 2007, from http://my.nctm.org/
National Council of Teachers of Mathematics, 2000.
Level: K-12
Best Practices in K-12 Math (Practice)
No Child Left Behind Act, 20 U.S.C. § 6301 (2001).
No Child Left Behind Act,, 20 §, 6301.
Level: K-12
Federal Oversight of K-12 Education (Practice)
Federal mandate regarding qualifications of teachers, support for students, and expectations for student performance and improvement.
U. S. Department of Education. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Retrieved July 19, 2008, from http://www.ed.gov/athPanel
Department of Education, 2008.
Level: K-12 Learning Theory: Cognitive Information Processing
Policy Change and Closing the Gap (Practice)
Participants (5 Refs)
Kersaint, G., Horton, B., Stohl, H., & Garofalo, J. (2003). Technology beliefs and practices of mathematics education faculty. Journal of Technology and Teacher Education, 11(4), 549-577.
Kersaint, Horton, Stohl, & Garofalo, 2003.
Level: College
Math Educators and Technology Use (Research - Quantitative)
Mathematics educators talk about how little they use technology in their methods, etc. classes.
Laughbaum, E. D. (1999). Hand-held technology in mathematics education at the college level. Ohio State University, Department of Mathematics. Retrieved May 26, 2007, from http://www.math.ohio-state.edu
Laughbaum, 1999.
Level: College
Calculator use Among College Faculty (Research - Quantitative)
Calculator usage survey of all universities.
Lutzer, D. J. (2002). Mathematics majors 2002. Williamsburg, VA: College of William and Mary, Department of Mathematics.
Lutzer, 2002.
Level: College
Estimates of Mathematics Majors (Research - Quantitative)
Lutzer, D. J., Maxwell, J. W., & Rodi, S. B. (2002). Statistical abstract of undergraduate programs in the mathematical sciences in the United States. American Mathematical Society. Retrieved May 26, 2007, from http://www.ams.org/
Lutzer, Maxwell, & Rodi, 2002.
Level: College
U.S. Math Departments (Research - Quantitative)
Page 127 or 137 gives percents of depts using graphing calculators, specifically for calculus.
Lutzer, D. J., Rodi, S. B., Kirkman, E. E., & Maxwell, J. W. (2007). Statistical abstract of undergraduate programs in the mathematical sciences in the United States: Fall 2005 CBMS survey. American Mathematical Society.
Lutzer, Rodi, Kirkman, & Maxwell, 2007.
Level: College
Statistical Summary of Mathematics Programs (Research - Quantitative)
Postdiction Calibration (9 Refs)
Fischbein, E. (1987). Investigations in overconfidence. In Intuition in science and mathematics (pp. 28-42). Dordrecht: D. Reidel Publishing.
Fischbein, 1987.
Learning Theory: Cognitive Information Processing
Psychological Foundations of Overconfidence (Theory)
Kahneman, D., Slovic, P., & Tversky, A. (Eds.). (1982). Judgment under uncertainty: Heuristics and biases. Cambridge: Cambridge University Press.
Kahneman, Slovic, & Tversky, 1982.
Learning Theory: Cognitive Information Processing
Cognitive Science Perspective on Calibration (Theory)
THE textbook on the cognition of people involved in making uncertain judgments.
Lichtenstein, S., & Fischhoff, B. (1980). Training for calibration. Organizational Behavior and Human Performance, 26, 149-171.
Lichtenstein & Fischhoff, 1980.
Learning Theory: Cognitive Information Processing
Calibration in Postdictions (Research - Quantitative)
Abstract: Two experiments attempted to improve the quality of people's probability assessments through intensive training. The first involved 11 sessions of 200 assessments each followed by comprehensive feedback. It produced considerable learning, almost all of which was accomplished after receipt of the first feedback. There was modest generalization to several related probability assessment tasks, but no generalization at all to two others. The second experiment reduced the training to three sessions. It revealed the same pattern of learning and limited generalization. About one-third of all subjects appeared to use probabilities quite appropriately on some tasks before training began. Further research is needed to understand why the training worked as well as it did, why that training did not always generalize, and why some individuals seemed to need no training at all. [Relates to calibration research in other arenas; specifically, on probability assessments in which people estimate the probability that a given statement is true. With training, this article says there is improvement.]
Lichtenstein, S., Fischoff, B., & Phillips, L. D. (1982). Calibration of probabilities: The state of the art to 1980. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judment under uncertainty: Heuristics and biases (pp. 306-334). Cambridge: Cambridge University Press.
Lichtenstein, Fischoff, & Phillips, 1982.
Learning Theory: Cognitive Information Processing
Calibration Curves and Other Postdiction Calibration Measures (Theory)
Techniques for measuring postdiction calibration, especially the calibration curve.
O’Connor, M. (1989). Models of human behaviour and confidence in judgment: A review. International Journal of Forecasting, 5, 159-169.
O’Connor, 1989.
Learning Theory: Cognitive Information Processing
Review of Calibration Research in 1960s and 70s (Theory)
This article reviews the large body of research in the 1960s and 70s into individuals’ calibration in assigning confidence ratings to objective statements (e.g., How confident are you that the following is true? “Israel is larger than Nepal”) . While this form of calibration is different from calibration in self-efficacy judgments, results from psychological experiments underscores factors influencing the accuracy of confidence judgments. O’Connor gleans several factors from the literature: (1) familiarity with task requirements (e.g., assigning probability values to feelings of uncertainty takes practice), (2) familiarity with the topic of interest (subject matter knowledge), and (3) adequate feedback (on the accuracy of prior judgments). For example, the widely reported tendency of people to be overconfident in assigning confidence values is much less likely when participants have deep understanding of the content domain. The author cites Sieber (1974) and Pitz (1974) as reporting very high calibration of college students in rating their confidence in attaining given final grades in a course. O’Connor situates the results in Beach and Mitchell’s contingencies model (behaviorism).
Pillai, K. G. (2005). Accuracy, confidence, and calibration of consumer knowledge: Roles of product type, product involvement, and general self-efficacy. Unpublished doctoral dissertation, Florida State University.
Pillai, 2005.
Level: Adult
Calibration in Postdiction Consumer Knowledge with General Self-Efficacy (Research - Quantitative)
Schraw, G. (1995). Measures of feeling-of-knowing accuracy: A new look at an old problem. Applied Cognitive Psychology, 9, 321-332.
Schraw, 1995.
Learning Theory: Cognitive Information Processing
Feeling-of-knowing Accuracy and Calibration of Postdictions (Theory)
First introduced the terms accuracy and bias, but used them for postdiction reading comprehension assessments, not self-efficacy judgments.
Schraw, G., Polenza, M. T., & Nebelsick-Gullet, L. (1993). Constraints on the calibration of performance. Contemporary Educational Psychology, 18, 455-463.
Schraw, Polenza, & Nebelsick-Gullet, 1993.
Learning Theory: Cognitive Information Processing
Calibration of Postdictions (Research - Quantitative)
Zhao, Q., & Linderholm, T. (2008). Adult metacomprehension: Judgment processes and accuracy constraints. Educational Psychology Review, 20 (2), 191-206.
Zhao & Linderholm, 2008.
Level: Adult
Calibration as Metacomprehension Accuracy in Reading (Theory)
Abstract: The objective of this paper is to review and synthesize two interrelated topics in the adult metacomprehension literature: the bases of metacomprehension judgment and the constraints on metacomprehension accuracy. Our review shows that adult readers base their metacomprehension judgments on different types of information, including experiences with current tasks and pre-formed expectations of performance affected by factors such as self-perception of ability. We propose a model that shows the anchoring and adjustment mechanism (Tversky and Kahneman, Science 185:1124–1130, 1974) underlies metacomprehension judgments. Specifically, due to test uncertainty, people may judge future comprehension performance by starting with an anchor such as pre-formed performance expectations and then (insufficiently) adjust away from it based on experiences with current tasks. This anchoring and adjustment model of metacomprehension judgment sheds light on what constrains metacomprehension accuracy. We conclude that two main accuracy constraints are the anchoring effect and the poor diagnostic validity of experiential cues. Based on the review, we discuss avenues for future research that will further our understanding of the mechanisms underlying metacomprehension.
Preservice Teachers (21 Refs)
Ball, D., & McDiarmid, G. (1989). The subject matter preparation of teachers (Issue Paper No. 89-4). Retrieved September 25, 2008, from Michigan State University, National Center for Research on Teacher Learning Web site: http://ncrtl.msu.edu/http/ipapers/html/pdf/ip894.pdf
Ball & McDiarmid, 1989.
Content Knowledge of Preservice Teachers (Theory)
Book, C. L., & Freeman, D. J. (1986, March/April). Differences in entry characteristics of elementary and secondary teacher candidates. Journal of Teacher Education, 47-51.
Book & Freeman, 1986.
Elementary vs. Secondary Teaching Majors (Research - Quantitative)
Book, C., Freeman, D., & Brousseau. (1985, May/June). Comparing academic backgrounds and career aspirations of education and non-education majors. Journal of Teacher Education, 27-30.
Book, Freeman, & Brousseau, 1985.
Education vs. Non-Education Majors (Research - Quantitative)
Brady, P., & Bowd, A. (2005). Mathematics anxiety, prior experience, and confidence to teach mathematics among pre-service education students. Teachers and Teaching: Theory and Practice, 11 (1), 37-46.
Brady & Bowd, 2005.
Math Anxiety, Prior Experience, Confidence in Preservice Teachers (Research - Quantitative)
Brookhart, S. M., & Freeman, D. J. (1992). Characteristics of entering teacher candidates. Review of Educational Research, 62 (1), 37-60.
Brookhart & Freeman, 1992.
Statistical Characteristics of Future Teachers (Research - Quantitative)
Conference Board of the Mathematical Sciences. (2001). The mathematical education of teachers. Providence, RI and Washington, DC: American Mathematical Society and Mathematical Association of America. Retrieved September 24, 2008, from http://www.cbmsweb.org/MET_Document/index.htm
Conference Board of the Mathematical Sciences, 2001.
Level: K-12
Involving Mathematicians in Teacher-Preparation (Practice)
The Mathematical Education of Teachers represents a vision statement compiled by the AMS and MAA on the ways in which mathematicians “should” be involved in preparing school teachers. Chapter 2, in particular, lists a number of recommendations that call for increased participation and input of mathematicians in teaching preservice teachers (in every grade band), setting standards and policies for school mathematics, collaborating with mathematics educators, and helping with professional development opportunities. The authors acknowledge some of the challenges surrounding their recommendations to increase the involvement of professional mathematicians in teacher preparation, although much of the discussion is unsubstantiated and leaves me questioning the nature of the purported challenges. In particular, is there really a distrust between mathematicians and mathematics educators? Do mathematicians and mathematics educators even know each other and what they can bring to the classroom? Also, I wonder how many mathematicians have interests in teacher-preparation.
Harding-DeKam, J. L. (2005). Construction and validation of an instrument for assessing prospective elementary teachers’ attitudes and beliefs in mathematics. Dissertation Abstracts International, 66, 1293A. (UMI No. 3171928)
Harding-DeKam, 2005.
Level: College
Mathematics Attitudes and Beliefs of Prospective Elementary Teachers (Research - Quantitative)
Abstract: This research establishes the Prospective Elementary Teachers’ Mathematics Attitudes and Beliefs Survey with the following four dimensions or subscales: (1) the Prospective Teachers’ Personal Confidence About Mathematics (2) Usefulness of Mathematics Content (3) Perception of Former Teachers’ Attitudes and Beliefs About Mathematics Ability and (4) the Prospective Teachers’ Attitudes and Beliefs on Teaching Mathematics to Elementary Students. The Prospective Elementary Teachers’ Mathematics Attitudes and Beliefs Survey is administered three times: once at the beginning of the Mathematics Teacher Education Course, once at the end of the Mathematics Teacher Education Course, and once during the fall of the prospective teachers’ first year teaching elementary students.
Hiebert, J., Morris, A. K., & Glass, B. (2003). Learning to learn to teach: An "experiment" model for teaching and teacher preparation in mathematics. Journal of Mathematics Teacher Education, 6, 201-222.
Hiebert, Morris, & Glass, 2003.
Level: K-12
Lesson Experiments as Professional Development (Practice)
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42 (2), 371-406.
Hill, Rowan, & Ball, 2005.
Level: College
Pedagogical Content Knowledge (Research - Quantitative)
Isiksal, M. (2005). Pre-service teachers’ performance in their university coursework and mathematical self-efficacy beliefs: What is the role of gender and year in program? The Mathematics Educator, 15 (2), 8-16.
Isiksal, 2005.
Level: College
Performance/elf-Efficacy for Preservice Math Teachers (Research - Quantitative)
Within a cross-sectional design of pre-service middle school mathematics teachers in Turkey, Isiksal (2005) used explored students’ mathematics self-efficacy and performance in relation to gender and year-in-program effects. Isiksal found women consistently modestly outperformed men in the program, but that men and women held similar self-efficacy views. The author also found that self-efficacy ratings increased with year in the program, which he interpreted as evidence supporting Bandura’s four sources of self-efficacy. In other words, Isiksal interpreted the apparent increase in mathematics confidence to the cumulative effect of mastery experiences in college mathematics (and education) courses.
Johnson, C. S., & Byars, J. A. (1977). Trends in content programs for preservice secondary mathematics teachers. The American Mathematical Monthly, 84 (7), 561-566.
Johnson & Byars, 1977.
Level: College
Content Preparation of Preservice Math Teachers (Research - Quantitative)
Kahan, J. A., Cooper, D. A., & Bethea, K. A. (2003). The role of mathematics teachers’ content knowledge in their teaching: A framework for research applied to a study of student teachers. Journal of Mathematics Teacher Education, 6, 223-252.
Kahan, Cooper, & Bethea, 2003.
Content Knowledge of Preservice Math Teachers (Theory - Qualitative)
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
Ma, 1999.
Level: Primary Learning Theory: Radical Constructivism Methodology: Comparative Case Study
U.S. and Chinese Elementary Teachers' Pedagogical Content Knowledge (Research - Qualitative)
Ma reports on the results of her dissertation investigation into "above average" U.S. elementary mathematics teachers' and a variety of Chinese elementary teachers' understanding of the mathematics needed to teach elementary school. Ma found that U.S. teachers focused largely on procedural aspects of mathematical tasks and held fragmented views of arithmetic operations. Chinese teachers, in contrast, focused on the need to know both the how and the why of algorithms and relayed a multiple ways of representing arithmetic operations and varied models for calculating with numbers. Ma's tasks included (1) subtraction with regrouping, (2) multiplication of three digit numbers, (3) division of fractions, and (4) relating perimeter and area of a rectangle. U.S. teachers were competent at performing calculations, but lacked "profound understanding of fundamental mathematics".
Milbourne, L. A. (2002). Finding mathematics teachers. Columbus, OH: ERIC Clearinghouse for Science Mathematics and Environmental Education. (ERIC Document Reproduction Service No. ED478713)
Milbourne, 2002.
Level: College
Statistics of Mathematics Teachers (Research - Quantitative)
Monk, D. H. (1994). Subject area preparation of secondary mathematics and science teachers and student achievement. Economics of Education Review, 13 (2), 125-145.
Monk, 1994.
Level: College
Content Preparation of Preservice Math Teachers (Research - Quantitative)
Morton, B. A., Peltola, P., Hurwitz, M. D., Orlofsky, G. F., Strizek, G. A., & Gruber, K. J. (2008). Education and certification qualifications of departmentalized public high school-level teachers of core subjects: Evidence from the 2003-04 Schools and Staffing Survey (NCES No. 2008-338). Washington, D.C.: National Center for Education Statistics.
Morton, Peltola, Hurwitz, Orlofsky, Strizek, & Gruber, 2008.
Level: College
Preparation/ualifications of Math Teachers (Research - Quantitative)
Philippou, G. N., & Christou, C. (1998). The effects of a preparatory mathematics program in changing prospective teachers' attitudes towards mathematics Educational Studies in Mathematics, 35(2), 189-206.
Philippou & Christou, 1998.
Level: College Learning Theory: Social Cognitive Theory
Teacher Prep and Attitudes toward Mathematics (Research - Quantitative)
Teacher prep can improve teachers attitudes toward mathematics, including self-efficacy
Ruthven, K., Hennessy, S., & Brindley, S. (2004). Teacher representations of the successful use of computer-based tools and resources in secondary-school english, mathematics and science. Teaching & Teacher Education: An International Journal of Research and Studies, 20(3), 259-275. Retrieved November 9, 2006, from http://sciencedirect.com
Ruthven, Hennessy, & Brindley, 2004.
Level: K-12 Methodology: Basic
Teachers' Views of Technology (Research - Qualitative)
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15 (2), 4-14.
Shulman, 1986.
Pedagogical Knowledge (Theory)
Shulman, L. S., & Shulman, J. H. (2004). How and what teachers learn: a shifting perspective. Journal of Curriculum Studies, 36 (2), 257-271.
Shulman & Shulman, 2004.
Learning Theory: Situated Cognition
Situated Perspective of Pedagogical Knowledge (Theory)
Watson, J. M. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: The case of chance and data. Journal of Mathematics Teacher Education, 4, 305-337.
Watson, 2001.
Teacher Self-Efficacy (Practice - Mixed Methods)
Research Design (15 Refs)
Creswell, J. W. (2003). Research design: Qualitative, quantitative, and mixed methods approaches. (2nd ed.). Thousand Oaks, CA: Sage.
Creswell, 2003.
Research Designs (Theory)
Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks, CA: Sage.
Creswell, 2007.
Research Design (Theory)
Crotty, M. (1998). The foundations of social research: Meaning and perspective in the research process. Thousand Oaks, CA: Sage.
Crotty, 1998.
Educational Paradigms (Theory)
Davis, B., & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137-157.
Davis & Simmt, 2003.
Learning Theory: Complexity Science
Complexity Science (Theory)
Complexity science takes the perspective that learning occurs through "ongoing, recursively elaborative adaptations through which systems maintain their coherences within their dynamic circumstances" (p. 138). The article describes a conceptual shift made by complexity science theorists about learning systems. Instead of deterministic process-product views of learning, the authors suggest that learning should be viewed as a probabilistic (dynamical) system that exists simultaneously on many levels. Events have the tendency to emerge under certain conditions and four conceptual characteristics promote effective learning systems: (1) internal diversity, (2) redundancy, (3) decentralized control, and (4) organized (constrained) randomness. An example of the spontaneous emergence of a learning system among teachers in professional development classes is examined from the complexity science perspective.
Ercikan, K., & Roth, W. (2006). What good is polarizing research into qualitative and quantitative? Educational Researcher, 35(5), 14-23.
Ercikan & Roth, 2006.
The Qualitative-Quantitative Debate (Theory)
Ercikan and Roth aim to debunk the qualitative-quantitative dichotomy by pointing out that all contexts in education have both quantifications and interpretive qualities. They also point to the goals of most qualitative research (provide thick description and develop theories) as one reason for the difference between qualitative and quantitative approaches to generalizability. On the other hand, the authors note that most quantitative educational research does not employ random sampling and rarely meets criteria for generalizing beyond samples, so making inferences can be difficult in both arenas. Though "Research activities are polarized into qualitative and quantitative classifications based on how phenomena are represented." (p.16), it is important to use both qualitative and quantitative representations of data during analysis. The authors also point to the fact that nearly all educational research requires researches to use subjective, defensible judgments instead of objectivity. They conclude with a framework for discussing inference along 8 continuums:
Gall, M. D., Gall, J. P., & Borg, W. R. (2003). Questions for evaluating quantitative research reports. In Educational research: An introduction (pp. 606-608). Allyn & Bacon.
Gall, Gall, & Borg, 2003.
Criteria for Evaluating Research (Theory)
Glesne, C. (2006). Becoming qualitative researchers: An introduction (3rd ed.). Boston: Pearson Education.
Glesne, 2006.
Qualitative Methods (Theory)
Guba, E., & Lincoln, L. (1998). Do inquiry paradigms imply inquiry methodologies? In D. M. Fetterman (Ed.), Qualitative approaches to evaluation in education. New York: Praeger.
Guba & Lincoln, 1998.
Educational Paradigms (Theory)
Merriam, S. B. (1998). Qualitative research and case study applications in education (2nd ed.). San Francisco: Jossey-Bass.
Merriam, 1998.
Qualitative Research Design and Case Study (Theory)
Mertens, D. M. (2005). Research and evaluation in educational psychology: Integrating diversity with quantitative, qualitative, and mixed methods (2nd ed.). Thousand Oaks, CA: Sage.
Mertens, 2005.
Research Design and Methods (Theory)
This "how to" manual for educational research includes very good discussions of validity and reliability, as well as sampling techniques and various forms of research. The discussion of methods to enhance reliability and validity (in both quantitative and qualitative designs) is especially good in the "single-case" research designs.
Patton, M. Q. (2002). Qualitative research & evaluation methods (3rd ed.). Thousand Oaks, CA: Sage Publications.
Patton, 2002.
Overview of Qualitative Research Design (Theory)
Salomon, G. (1991). Transcending the qualitative-quantitative debate: The analytic and systemic approaches to educational research. Educational Researcher, 20(6), 11-17.
Salomon, 1991.
The Qualitative-Quantitative Debate (Theory)
Salomon (1991) describes the increasing acceptance of the view that quantitative and qualitative paradigms are complementary and can be used pragmatically by researchers looking for the best methods to address their questions. Salomon also points to three shared concerns in the paradigms, including issues of validity:"While answered differently by the two paradigms, is still common to both: How do you know? Why should one accept your findings, observations, conclusions, and interpretations?" (p.10) Second, all paradigms need some standards of quality. They third common challenge that "all paradigms face is the need for some means of facilitating generalizability, answering, for example, the questions of 'What is this a case of?' (Shulman, 1988) and 'What can I learn from your description?'" (p.11)Salomon ultimately argues for a distinction between analytic (focusing on functional effects of specific variables) and systemicresearch (considering classrooms as nested conglomerates of interdependent variables functioning as a whole).
Schoenfeld, A. H. (2000). Purposes and methods of research in mathematics education. Notices of the American Mathematical Society, 24(6), 641-649.
Schoenfeld, 2000.
Criteria for Mathematics Education Research (Theory)
Schoenfeld describes Mathematics Education to mathematicians by focusing on some similarities and differences between math ed’s social science status and math’s standards for theories and proof. He goes on to give some very useful criteria for evaluating mathematics education research:
- Descriptive power (many details, nothing “important” is missing)
- Explanatory power (how and the why)
- Scope
- Predictive power
- Rigor and specificity (How well defined are the terms? Would you know one if you saw one? In real life? In the model? How well defined are the relationships among them? And how well do the objects and relations in the modelcorrespond to the things they are supposed to represent?)
- Falsifiability (making claims whose accuracy can be tested empirically)
- Replicability (Will the same thing happen if the circumstances are repeated? Will others, once appropriately trained, see the same things in the data?
- Multiple sources of evidence (“triangulation”) (seek as many sources of information as possible about the phenomenon in question and to see whether they portray a consistent message)
Sirin, S. R. (2005). Socioeconomic status and academic achievement: A meta-analytic review of research. Review of Educational Research, 75(3), 417-453.
Sirin, 2005.
Level: K-12
SES and Achievement (Research - Quantitative)
Zinn, L. M. (1999). Philosophy of adult education inventory (Rev. ed.). Boulder, CO: Lifelong Learning Options.
Zinn, 1999.
Educational Philosohy (Theory - Quantitative)
Self-Efficacy (22 Refs)
Bandura, A. (1997). Self-efficacy: the exercise of control. New York: W. H. Freeman.
Bandura, 1997.
Learning Theory: Social Cognitive Theory
Defining Social Cognitive Theory (Theory)
Bong, M. (1997). Generality of academic self-efficacy judgments: Evidence of hierarchical relations. Journal of Educational Psychology, 89 (4), 696-709.
Bong, 1997.
Level: Secondary Learning Theory: Social Cognitive Theory
Is Self-Efficacy More General than Previously Thought? (Research - Quantitative)
Abstract: The generality of academic self-efficacy judgments was examined among 588 high school students. Students rated their confidence for solving 42 problems in English, Spanish, U.S. history, algebra, geometry, and chemistry. Confirmatory factor analyses showed that students’ efficacy perceptions prevailed beyond the boundaries of specific problems. The 1st-order model with a separate self-efficacy factor for each school subject displayed the best fit. Verbal and Quantitative Academic Self-Efficacy illustrated the relations among the 1st-order factors better than General Academic Self-Efficacy. The generality of academic self-efficacy partly depended on the degree of perceived similarity among tasks. When asked to rate their efficacy toward 8 pairs of isomorphic algebra and physics problems, students reported more comparable strengths of self-efficacy as they perceived greater similarity between the problems.
Branden, N. (1994). The six pillars of self-esteem. New York: Bantam.
Branden, 1994.
Self-Esteem (Theory)
Finney, S. J., & Schraw, G. (2003). Self-efficacy beliefs in college statistics courses. Contemporary Educational Psychology, 28, 161-186.
Finney & Schraw, 2003.
Level: College Learning Theory: Social Cognitive Theory
Statistics Self-Efficacy-- Current and To Learn (Research - Quantitative)
Abstract: We developed measures of current statistics self-efficacy (CSSE) and self-efficacy to learn statistics (SELS) to address whether statistics self-efficacy is related to statistics performance, and whether self-efficacy for statistics increases during an introductory statistics course. Both instruments yielded reliable, one-factor solutions that were related positively to each other and to two measures of statistics performance (i.e., specific statistics problems and overall course performance). The CSSE and SELS also were related positively to math self-efficacy and attitudes towards statistics, but related negatively to anxiety. Changes between two different testing occasions using the CSSE indicated that statistics self-efficacy increased almost two standard deviations over a 12-week instructional period
Hoffman, B., & Spatariu, A. (2008). The influence of self-efficacy and metacognitive prompting on math problem-solving efficiency. Contemporary Educational Psychology, 33, 875-893.
Hoffman & Spatariu, 2008.
Level: College Learning Theory: Social Cognitive Theory
Testing the Motivational Efficiency Hypothesis (Research - Quantitative)
Abstract: A regression design was used to test the unique and interactive effects of self-efficacy beliefs and metacognitive prompting on solving mental multiplication problems while controlling for mathematical background knowledge and problem complexity. Problem-solving accuracy, response time, and efficiency (i.e. the ratio of problems solved correctly to time) were measured. Students completed a mathematical background inventory and then assessed their self-efficacy for mental multiplication accuracy. Before solving a series of multiplication problems, participants were randomly assigned to either a prompting or control group. We tested the motivational efficiency hypothesis, which predicted that motivational beliefs, such as self-efficacy and attributions to metacognitive strategy use are related to more efficient problem solving. Findings suggested that self-efficacy and metacognitive prompting increased problem-solving performance and efficiency separately through activation of reflection and strategy knowledge. Educational implications and future research are suggested.
James, W. (1890). The principles of psychology. In Classics in the History of Psychology. Retrieved January 2, 2009, from http://psychclassics.yorku.ca/James/Principles/index.htm
James, 1890.
Classic in Personal Psychology (Theory)
First mention of self-esteem as the quotient of successes and pretensions
Klassen, R. M. (2006). Too much confidence? The self-efficacy of adolescents with learning disabilities. In F. Pajares & T. Urdan (Eds.), Self-efficacy beliefs of adolescents (pp. 181-200). Greenwhich, CT: Information Age Publishing.
Klassen, 2006.
Level: K-12 Learning Theory: Social Cognitive Theory
Overconfidence of Students with Learning Disabilities (Research - Qualitative)
Lapan, R. T., Shaughnessy, P., & Boggs, K. (1996). Efficacy expectations and vocational interests as mediators between sex and choice of math/science college majors: A longitudinal study. Journal of Vocational Behavior, 49, 277-291.
Lapan, Shaughnessy, & Boggs, 1996.
Level: College Learning Theory: Social Cognitive Theory
Efficacy and Career Interests in Math Performance (Research - Quantitative)
Lapan et al cite research that suggest high school mathematics preparation (ACT scores, mathematics courses taken) and mathematics self-efficacy ratings explain significant and independent portions in observed sex differences in men and women’s choice of mathematics-related careers (math, science, engineering). Good quote: “Results from the present study strongly support the key role of math self-efficacy (Betz & Hackett, 1983; Hackett, 1985) as a critical filter (Sells, 1980) in the developmental process through which women either embrace or reject math/cience college majors. In this study, choice of a math/cience major was largely a function of adapting to self-efficacy (Bandura, 1977) and vocational interest patterns (Hansen & Campbell, 1985) that predated student entry into college.” (p. 289)
Lent, R. W., Brown, S. D., & Hackett, B. (1994). Toward a unifying social cognitive theory of career and academic interest, choice, and performance. Journal of Vocational Behavior, 45, 79-122.
Lent, Brown, & Hackett, 1994.
Learning Theory: Social Cognitive Theory
Modeling Self-efficacy, Outcome Expectations, and Choices (Theory)
great visual model
Lent, R. W., Lopez, F. G., Brown, S. D., & Gore, P. A. (1996). Latent structure of the sources of mathematics self-efficacy. Journal of Vocational Behavior, 49, 292-308.
Lent, Lopez, Brown, & Gore, 1996.
Learning Theory: Social Cognitive Theory
Sources of Self-Efficacy (Research - Quantitative)
Lightsey, R. (1999). Albert Bandura and the exercise of self-efficacy [Review of the book Self-efficacy: The exercise of control]. Journal of Cognitive Psychotherapy, 13 (2), 158-166.
Lightsey, 1999.
Review of Bandura's (1997) Self-Efficacy (Theory)
This article reviews Bandura’s (1997) important text on self-efficacy. Lightsey loves the book and does a very good job of placing self-efficacy theory in the context of the large body of research on the construct and its correspondence to achievement. The article reports the existence of over 1800 studies (2500 articles) related to self-efficacy and its function in a wide range of human activities and experiences.
Madewell, J., & Shaughnessy, M. F. (2003). An interview with Frank Pajares. Educational Psychology Review, 15 (4), 375-397.
Madewell & Shaughnessy, 2003.
Learning Theory: Social Cognitive Theory
Interview of Frank Pajares (Theory)
Pajares (Madewell & Shaughnessy, 2003) summarizes his views on self-efficacy and self-beliefs in educational psychology. He describes self-efficacy as “the confidence we have in our abilities” (p. 381) and states, “What we know, the skills we possess, or what we have previously accomplished are not always good predictors of subsequent attainments because the beliefs we hold about our capabilities powerfully influence the wayswe behave. Consequently, how we behave is mediated by our beliefs about our capabilities and is often better predicted by these beliefs than by the results of our previous performances.” (p. 381) Another good quote: “What seems clear, however, is that we should not tinker with overconfidence. Tailhard de Chardin wrote that “it is our duty as human beings to proceed as though the limits of our capabilities do not exist.” Who can ever assess a student’s full potential with complete accuracy? Students surprise us all the time, just as we surprise ourselves. We should be careful about attempting to “calibrate” a student’s self-efficacy beliefs. Improving students’ calibration—the accuracy of their self-efficacy beliefs—is an enterprise fraught with potential dangers. Remember that the stronger the self-efficacy, the more likely are persons to select challenging tasks, persist at them, and perform them successfully. Efforts to lower students’ efficacy beliefs should be discouraged. Improving students’ calibration should emphasize helping them to better understand what they know and do not know so that they may more effectively deploy appropriate cognitive strategies as they perform a task. We should keep carefully in mind that the issue of “accuracy” cannot easily be divorced from issues of well-being, optimism, resilience, and optimal functioning. Research findings support the notion that, as people evaluate their lives, they are more likely to regret the challenge not confronted, the contest not entered, the risk unrisked, and the road not taken as a result of underconfidence and self-doubt rather than the action taken as a result of overconfidence and optimism.” (p. 397)
Moncur, M. (2007). Henry Ford (1863-1947). In Quotations by author. Retrieved January 2, 2009, from http://www.quotationspage.com/?quotes/?Henry_Ford/
Moncur, 2007.
Learning Theory: Social Cognitive Theory
Henry Ford Quote on Self-Efficacy (Theory)
"whether you think you can or that you can't, you're probably right"
O’Brien, V., Kopala, M., & Martinez-Pons, M. (1999). Mathematics self-efficacy, ethnic identity, gender, and career interests related to mathematics and science. Journal of Educational Research, 92 (4), 231-235.
O’Brien, Kopala, & Martinez-Pons, 1999.
Level: College Learning Theory: Social Cognitive Theory
Self-Efficacy, Gender, and Career Interests (Research - Quantitative)
O’Brien, Kopola, and Martinez-Pons (1999) describe an investigation into a literature-based model of 400 secondary students’ interest in mathematics-related careers. The authors tested a model that incorporated a general mathematics self-efficacy construct (Hackett & Betz, 1985), gender, ethnic identity, and SES. Self-efficacy was the strongest correlate of career interest, prior mathematics score (PSAT), and ethnic identity, although there was no correlation between gender and self-efficacy. In fact, the only variable that correlated to gender was interest in mathematics-related careers (males were more interested than females).
Pajares, F., & Miller, M. D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology, 86 (2), 195-203.
Pajares & Miller, 1994.
Level: Middle Learning Theory: Social Cognitive Theory
Path Analysis of Self-Efficacy and Self-Concept on Achievement (Research - Quantitative)
Pajares, F., & Schunk, D. H. (2001). Self-beliefs and school success: Self-efficacy, self-concept, and school achievement. In R. Riding & S. Rayner (Eds.), Perception (pp. 239-266). London: Ablex Publishing.
Pajares & Schunk, 2001.
Level: K-12 Learning Theory: Social Cognitive Theory
Overview of Self-Beliefs and Self-Efficacy (Theory)
Pajares, F., & Urdan, T. (Eds.) (2006). Self-efficacy beliefs of adolescents. Greenwhich, CT: Information Age Publishing.
Pajares & Urdan, 2006.
Level: Secondary Learning Theory: Social Cognitive Theory
Self-Efficacy in Adolescents (Theory)
Awesome book, with a chapter from Bandura himself (on how to measure self-efficacy), and a wide range of applications of self-efficacy research for adolescent learning.
Simon, S. D. (1999). From neo-behaviorism to social constructivism? The paridigmatic non-evolution of Albert Bandura. Unpublished master's thesis, Emory University. Retrieved March 28, 2007, from http://www.des.emory.edu/
Simon, 1999.
Learning Theory: Social Cognitive Theory
Albert Bandura and Epistemology (Theory)
Urdan, T. (2004). Predictors of academic self-handicapping and achievement: Examining achievement goals, classroom goal structures, and culture. Journal of Educational Psychology, 96(2), 251-264.
Urdan, 2004.
Level: College
Goal Structures and Self-Handicapping (Research - Quantitative)
Urdan, T., Pajares, F., & Lapin, A. Z. (1997). Achievement goals, motivation, and performance: A closer look. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago. (ERIC Document Reproduction Service No. ED412268)
Urdan, Pajares, & Lapin, 1997.
Level: K-12
Goals, Motivation, and Performance (Theory)
Task goals* ability goals interaction.. results on page 3 and 4. Task goals and GPA are largest predictors of self-efficacy in 8th graders.
Zeldin, A. L. (2000). Sources and effects of the self-efficacy beliefs of men with careers in mathematics, science, and technology. Unpublished doctoral dissertation, Emory University, Atlanta, GA.
Zeldin, 2000.
Level: Adult Learning Theory: Social Cognitive Theory Methodology: Comparative Case Study
Self-Efficacy of STEM Men (Research - Qualitative)
Zeldin's (2000) dissertation on career self-efficacy of men with careers in Mathematics, Science and Technology (MST) extends and refines joint research she conducted with her adviser (Zeldin & Pajares, 2000) on the sources of career self-efficacy among 15 women with careers in (MST). Zeldin's report precedes a discussion of semi-structured interviews with 10 Caucasian males by including a thorough review of career self-efficacy constructs and related literature. The qualitative comparative case study-with men and women in MST careers viewed as separate, bounded cases in the sense defined by Merriam (1998)-relies heavily on Bandura's (1997) theoretical framework of four sources of self-efficacy. Though men and women described experiences associated with all four sources (authentic mastery experiences, vicarious experiences, verbal persuasions, and physiological indexes), Zeldin concludes that the women in her study built MST career self-efficacy primarily through verbal persuasions and verbal persuasions while men built career self-efficacy primarily through positive mastery experiences.
Zeldin, A. L., & Pajares, F. (2000). Against the odds: Self-efficacy beliefs of women in mathematical, scientific, and technological careers. American Educational Research Journal, 37(1), 215-246.
Zeldin & Pajares, 2000.
Level: Adult Learning Theory: Social Cognitive Theory Methodology: Comparative Case Study
Self-Efficacy of STEM Women (Research - Qualitative)
Self-Efficacy Calibration (14 Refs)
Bouffard-Bouchard, T. (2001). Influence on self-efficacy on performance in a cognitive task. The Journal of Social Psychology, 130 (3), 353-363.
Bouffard-Bouchard, 2001.
Level: College Learning Theory: Social Cognitive Theory
Problem-Solving Calibration of Canadian College Students (Research - Quantitative)
Looked at 64 Canadian college students’ self-efficacy judgments on cognitive performance, problem-solving strategies, and the accuracy of self-evaluation of responses. Author concludes “self-efficacy is a viable construct for comprehending performance, particularly on academic tasks required sustained self-monitoring” (p. 353).
Chen, P. P. (2002). Mathematics self-efficacy calibration of seventh graders. Dissertation Abstracts International, 63(3), 858A. (AAT No. 3047203)
Chen, 2002.
Level: Middle Learning Theory: Social Cognitive Theory
Self-Efficacy Calibration (Research - Quantitative)
Abstract: This study investigated seventh graders' math self-efficacy calibration and its effect on students' math performance, individual differences, such as gender, as well as academic variables, such as previous math achievement, post-performance effort judgment, and post-performance self-evaluation. According to Bandura (1986), students' self-efficacy beliefs about their capability to perform affects how they make choices of activities, courses of action, amount of effort to exert, and length of time engaged on a task. To date, the issue of the accuracy judgment of self-efficacy beliefs, termed calibration , has received little investigation. In the present study, it was measured in two ways: accuracy, which measures the magnitude of judgment errors; and bias, which measures the direction of judgment errors. In addition, the design of the study enabled the researcher to assess the relationship between students' personal processes (e.g., self-efficacy judgments of math capability, calibration, effort judgment, and performance evaluation) and variations in context (e.g., specific math problems and their difficulty level).
The results revealed that students' calibration accuracy significantly increased the predictiveness of their self-efficacy beliefs. Path analysis showed that calibration accuracy had both direct and indirect effects on math performance, with the indirect effects mediated through the students' self-efficacy beliefs. Self-efficacy played a direct role in predicting students' math performance, post-performance self-evaluation, and post-performance judgments of effort. The effects of prior math achievement on math performance were mediated largely through the students' self-efficacy beliefs. Unexpectedly, the effect of self-efficacy on post-performance judgments of effort was negative, indicating that high efficacy students needed to spend less effort in solving the math problems than low efficacy students. As for the individual differences in gender, the study found no statistical differences on any of the dependent measures, although boys had numerically higher self-efficacy, post-performance self-evaluation, and lower effort judgment than girls. In conclusion, the results revealed that students' self-efficacy beliefs play an important role in their acquisition of mathematical competence. Such information can be vital in assisting educators to tailor interventions that will enhance students' beliefs in their capability to learn math and as well as their actual success
Chen, P. P. (2003). Exploring the accuracy and predictability of the self-efficacy beliefs of seventh-grade mathematics students. Learning and individual differences, 14, 79-92.
Chen, 2003.
Level: Middle Learning Theory: Social Cognitive Theory
Self-Efficacy Calibration (Research - Quantitative)
This is the closest article to my proposed dissertation design. It really should be memorized word-for-word. Using path analysis techniques, Chen found significant and independent effects of calibration, self-efficacy, and prior math achievement (as measured by the ITBS) on a mathematics test based on TIMMS items. Chen found different results when students rated their confidence on the same task versus different tasks. The generalizability and power of the study is limited by a relatively small sample size and sample of seventh graders at a catholic school in Tennessee. Chen’s findings of the significance of variables in her model are particularly helpful for my design, including her finding that gender was not a significant predictor of any other variable in the model. Chen also incorporated task difficulty in the model as a “level” variable. Good quote: “As a group, seventh-grade students overestimated their math capabilities, but their inaccuracies did not relate to the strength of their self-efficacy beliefs. Both high and low self-efficacy students were overly optimistic about their performance.” (p. 91)
Chen, P., & Zimmerman, B. (2007). A cross-national comparison study of self-efficacy beliefs of middle-school mathematics students. Journal of Experimental Education, 75(3), 221-244.
Chen & Zimmerman, 2007.
Level: Middle Learning Theory: Social Cognitive Theory
International Calibration Comparison (Research - Quantitative)
This article builds on Chen’s dissertation by applying the same protocol for assessing Taiwanese students’ self-efficacy, performance, and calibration. In the review of literature, the authors point to the work of Bol and Hacker (2001), Ewers and Wood (1993), and Pajares and Graham (1999) in suggesting that “accurate estimations of capability may be important to the academic success of gifted or highly achieving students” (p. 223). This may have implications for my study, because many mathematics majors would qualify as “gifted or highly achieving.” A major focus of this study is on the role of task-difficulty in self-efficacy judgments. Because Taiwanese content is more difficult than American, the authors compared seventh-grade U.S. students to sixth-grade Taiwanese students. The researchers found “more similarities than differences” in the self-efficacy ratings and calibration scores for students in the two countries, although there were differences favoring Taiwanese students in performance and effort.
Ewers, C. A., & Wood, N. L. (1993). Sex and ability differences in children’s math self-efficacy and prediction accuracy. Learning and Individual Differences, 5 (3), 259-267.
Ewers & Wood, 1993.
Level: Primary Learning Theory: Social Cognitive Theory
Mathematics Self-Efficacy by Gifted and Sex Variables (Research - Quantitative)
Gifted and average-ability fifth graders show no differences in math self-efficacy by gender. Gifted students have higher self-efficacy than average students. Also addressed Prediction Calibration. Small study.
Hacker, D. J., Dunlosky, J., & Graesser, A. C. (1998). Metacognition in educational theory and practice. Mahwah, NJ: Lawrence Erlbaum Associates.
Hacker, Dunlosky, & Graesser, 1998.
Learning Theory: Social Cognitive Theory
Metacognition and prediction calibration for reading. (Theory)
See Chapter 4 for metacognition in constructivist mathematics. Also, Chapter 6 has information on test-predictions for students in reading.
Hackett, G., & Betz, N. E. (1989). An exploration of the mathematics self-efficacy/performance correspondence. Journal for Research in Mathematics Education, 20(3), 261-273.
Hackett & Betz, 1989.
Level: College Learning Theory: Social Cognitive Theory
Effects of Major and Gender on Calibration in Mathematics (Research - Quantitative)
This important first study on calibration includes path analysis and regression approaches to assessing self-efficacy and performance in college men and women. In arguing for self-efficacy as a predictor of career decision making, Hackett and Betz cite Bandura’s contention that mathematics anxiety is a consequence of low self-efficacy, and thus self-efficacy is a more important predictive variable. One finding includes “Hackett (1985) reported the results of a path analysis indicating that mathematics self-efficacy contributed more significantly than sex, years of high school mathematics, ACT mathematics score, or mathematics anxiety to predicting the choice of a mathematics-related college major.” The authors found no gender differences in calibration or performance. Contrary to subsequent studies, self-efficacy outweighed prior performance in influencing achievement on the mathematics performance measure.
Lin, L., & Zabrucky, K. M. (1998). Calibration of comprehension: Research and implications for education and instruction. Contemporary Educational Psychology, 23, 345-391.
Lin & Zabrucky, 1998.
Level: K-12 Learning Theory: Social Cognitive Theory
Reading Calibration (Research - Mixed Methods)
Reviews literature surrounding “calibration of comprehension” for students engaging in reading tasks. The authors place calibration in the context of metacognition (specifically evaluating knowledge instead of regulating cognition) and stress the importance of multiple measures of calibration (not just a single task) “Comprehension is a continuous variable and should be measured by multiple questions.” (p. 367) The review looks at 34 studies of young adults (college students) . Results include (1) students tend to use both self-beliefs of ability and information from tasks when rating their confidence of comprehension, (2) there is little research relating pretest and posttest calibration, (3) interest in a domain may be used to assess confidence on tasks, (4) there is an “illusion of knowing” effect related to overconfidence expressed by students on moderate and difficult tasks, (5) students tend to rate their likelihood of correctly answering an item at around 70 to 75%, (6) there is little research into the effect of item difficulty on pretest ratings. Good quote: “There is a tendency for adult students to generate unrealistic feelings of knowing when it comes to evaluating outcomes of learning. As can be seen in the present review, overconfidence is a common phenomenon among young adult students that may result in inadequate learning due to premature termination of cognitive processing.” (p. 384)
Maki, R. H., Shields, M., Wheeler, A. E., & Zacchilli, T. L. (2005). Individual differences in absolute and relative metacomprehension accuracy. Journal of Educational Psychology, 97 (4), 723-731.
Maki, Shields, Wheeler, & Zacchilli, 2005.
Level: College
Metacomprehension accuracy = Calibration (Research - Quantitative)
Abstract: The authors investigated absolute and relative metacomprehension accuracy as a function of verbal ability in college students. Students read hard texts, revised texts, or a mixed set of texts. They then predicted their performance, took a multiple-choice test on the texts, and made posttest judgments about their performance. With hard texts, students with lower verbal abilities were overconfident in predictions of future performance, and students with higher verbal abilities were underconfident in judging past performance. Revised texts produced overconfidence for predictions. Thus, absolute accuracy of predictions and confidence judgments depended on students’ abilities and text difficulty. In contrast, relative metacomprehension accuracy as measured by gamma correlations did not depend on verbal ability or on text difficulty. Absolute metacomprehension accuracy was much more dependent on types of materials and verbal skills than was relative accuracy, suggesting that they may tap different aspects of metacomprehension.
Mura, R. (1987). Sex-related differences in expectations of success in undergraduate mathematics. Journal for Research in Mathematics Education, 18(1), 15-24.
Mura, 1987.
Level: College
Sex-differences in Expectations for Success in Math (Research - Quantitative)
most overconfident, men more so than women
Pajares, F., & Kranzler, J. (1995, April). Role of self-efficacy and general math ability in mathematical problem-solving: A path analysis. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA. (ERIC Document Reproduction Service No. ED387342)
Pajares & Kranzler, 1995.
Level: Secondary Learning Theory: Social Cognitive Theory
Path Analysis of Self-Efficacy (Research - Quantitative)
This is a powerful path analysis attempt at describing the role of self-efficacy in mathematical achievement in problem solving tasks. Using a test of general mental ability (psychometric g), opportunities for students to predict their performance, and problem solving performance tasks, the authors were able to implement aspects of Bandura's theory of self-efficacy to construct a structural equations model for performance that included math anxiety, gender, race, general ability, prior math achievement, self-efficacy, and performance. Students were found to have low calibration (they overestimated their performance ability). "Students' self-efficacy about their math capability had strong direct effects on math anxiety and on mathematical problem-solving performance even when general mental ability was controlled" (p. 17) Race differences in confidence were also found.
Pajares, F., & Miller, M. D. (1997). Mathematics self-efficacy and mathematical problem solving: Implications of using different forms of assessment. Journal of Experimental Education, 65(3), 213-229.
Pajares & Miller, 1997.
Level: Secondary Learning Theory: Social Cognitive Theory
Measuring Self-Efficacy and Performance (Research - Quantitative)
Tested three methods of measuring calibration when students were asked to rate their confidence in doing tasks and then completed open-ended and multiple choice tests. Calibration was lower for the open-ended test format, but did not differ significantly based on method of measurement or pre-alg vs. algebra students. The authors found no gender differences on any of the self-efficacy, calibration, or performance measures. The authors caution that "using identical self-efficacy and performance indexes in an effort to closely match belief and criterion may lead to positively biased estimates of effects from self-efficacy to performance outcomes. Thus, researchers are encouraged to use similar rather than identical items or tasks to assess self-efficacy beliefs and performance criteria" (p. 220).
Stone, N. J. (2000). Exploring the relationship between calibration and self-regulated learning. Educational Psychology Review, 12 (4), 437-475.
Stone, 2000.
Learning Theory: Social Cognitive Theory
Potential Relationships between Calibration and Self-Regulation (Theory)
Thiede, K. W., & Anderson, M. C. M. (2003). Summarizing can improve metacomprehension accuracy. Contemporary Educational Psychology, 28, 129-160.
Thiede & Anderson, 2003.
Level: College
Possible to Improve Calibration (Research - Quantitative)
Abstract: In two experiments, it was examined whether the accuracy of comprehension monitoring (metacomprehension accuracy) was improved by summarizing texts. College students read texts and then some wrote a summary of each text (either immediately after reading or after a delay—the delay between reading and summarizing was filled by the reading of the remaining texts), whereas others did not (the control group). All the students then rated their comprehension of each text. Finally, they completed a test of the material covered in each text. In both experiments, metacomprehension accuracy, operationalized as the correlation between ratings of comprehension and subsequent test performance, was dramatically greater for the group of students that wrote summaries after a delay than for the control group or the group of students that wrote summaries immediately after reading a text. These findings are described in the context of a discrepancy-reduction model of self-regulated study.
Sources of Self-Efficacy (6 Refs)
Campbell, J. R., & Beaudry, J. S. (1998). Gender gap linked to differential socialization for high-achieving senior mathematics students. The Journal of Educational Research, 91 (3), 140-147.
Campbell & Beaudry, 1998.
Level: Secondary
Gender Gap and Socialization (Research - Quantitative)
interesting theoretical view of the gender gap... pertains to high-achieving students (like math majors)
Campbell, N. K., & Hackett, G. (1986). The effects of mathematics task performance on math self-efficacy and task interest. Journal of Vocational Behavior, 28, 149-162.
Campbell & Hackett, 1986.
Level: College Learning Theory: Social Cognitive Theory
Manipulating Mastery Experiences and Self-Efficacy (Research - Quantitative)
How does performance influence self-efficacy, task interest and self-evaluations of performance?
Hackett, G., Betz, N. E., O’Halloran, M. S., & Romac, D. S. (1990). Effects of verbal and mathematics task performance on task and career self-efficacy and interest. Journal of Counseling Psychology, 37 (2), 169-177.
Hackett, Betz, O’Halloran, & Romac, 1990.
Level: College Learning Theory: Social Cognitive Theory
Manipulating Mastery Experiences and Self-Efficacy (Research - Quantitative)
experimental manipulation of self-efficacy by passing or failing math problems
Lent, R. W., Lopez, F. G., & Bieschke, K. J. (1991). Mathematics self-efficacy: Sources and relation to science-based career choice. Journal of Counseling Psychology, 38 (4), 424-430.
Lent, Lopez, & Bieschke, 1991.
Level: College Learning Theory: Social Cognitive Theory
Sources of Self-efficacy and the relationship to Career Choices (Research - Quantitative)
sources of self-efficacy helped explain gender differences in math self-efficacy
Lopez, F., & Lent, R. (1992). Sources of mathematics self-efficacy in high school students. Career Development Quarterly, 41(1), 3-11.
Lopez & Lent, 1992.
Level: Secondary Learning Theory: Social Cognitive Theory
Sources of self-efficacy in High School (Research - Quantitative)
Usher, E. L., & Pajares, F. (2008). Sources of self-efficacy in school: Critical review of the literature and future research. Review of Educational Research (78)(4), 751-796.
Usher & Pajares, 2008.
Learning Theory: Social Cognitive Theory
Meta-analysis of Sources of Self Efficacy Research (Research - Mixed Methods)
Complete synthesis of the literature on sources of self-efficacy in education. Includes a nice summary of the very limited qualitative research into the sources, along with a recommendation for more of it. Thorough discussion of the quantitative and construct validity issues surrounding measurement of the sources.
