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]

Level: Primary  

Hawaiian School Children Learning Mathematics (Research - Mixed Methods)

Brenner (1998) reports on a long-term program of ethnographic research into culturally relevant mathematics instruction for Native Hawaiian children. Within a constructivist theoretical framework emphasizing social, cultural, and cognitive dimensions of mathematical learning, Brenner first conducted an ethnographic field study of Hawaiian school children's everyday use of mathematics outside of the classroom. She observed everyday practices of the children, interviewed and administered surveys to Native Hawaiian families, and ultimately concluded rural and urban Native Hawaiian students entered kindergarten with mathematical understandings largely derived from shopping and participation in family activities. Rural students, in particular, expressed quantified properties in Hawaiian Creole English, a language they never used in school. Brenner triangulated these ethnographic results with standardized student achievement and cognitive test data. She compares her findings and subsequent experience designing and implementing culturally relevant instruction with kindergarten and second grade instructors at the Kamehameha Early Education Program (KEEP) to other reform efforts aimed at culturally relevant instruction.

Level: Middle   Learning Theory: Situated Cognition  

Street Mathematics (Research - Mixed Methods)

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.

Level: Secondary  

Calculators and Assessments (Research - Mixed Methods)

Good discussion on the use of calculators in high school by students and teachers and how assessment doesn't neccesarily align with NCTM standards for technology use.

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.

Level: College  

Clickers in Large Classes (Research - Mixed Methods)

Reviews 33 years research of electronic response systems in college lecture halls.

Level: Secondary  

Review of Graphing Calculator Research (Research - Mixed Methods)

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)

Level: Secondary  

Street Mathematics (Research - Mixed Methods)

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.

Level: Secondary  

TI-Navigator and Professional Development (Research - Mixed Methods)

CCS = TI Navigator... effects on learning environment... 34 teachers trained.

Level: Secondary  

Review of Graphing Calculator Research (Research - Mixed Methods)

Level: Secondary  

TI-Navigator Research (Research - Mixed Methods)

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.

Level: College   Methodology: Spreadsheets in College Algebra  

The researchers' discussion highlighted the likelihood that some mathematical knowledge developed in college can be transferred to the workplace easily. Spreadsheets were identified as being particularly important to this transfer by virtue of their ease of use. Students also appeared to respond positively to the fact that the police inspector used mathematics only in response to a clear need. However, when the role of the spreadsheet was not apparent in necessary calculations, students had difficulty applying their mathematical knowledge to the situation. (Research - Mixed Methods)

This short proceedings article reports on a case study of college mathematics students who are introduced to individuals who use spreadhsheets in the workplace. Participating students with limited college mathematics background met with (1) a police inspector who analyzed job performance of officers in a large city, and (2) a finance specialist at a medium-sized company. Qualitative analysis focused on the role of mathematics in the police inspectors' work as well as the interaction between students and the Inspector as the participants attempted to make sense of the mathematics used in the spreadsheet application.

Level: Secondary   Methodology: Basic  

Clickers (Research - Qualitative)

Clickers.

Level: College   Methodology: Basic  

White Future Teachers and Racism (Research - Qualitative)

Case and Hemmings (2005) chronicled the communication strategies of preservice white teachers enrolled in a course focused on the effects of White racism in education and society. The authors' qualitative analysis of interview data and in-class conversations suggested the preservice teachers used a number of distancing strategies to avoid talking about racism, including silence in the classroom and among friends and family, dissociation from racist labels, claiming to be color-blind, and blaming reverse racism. They concluded, however, "metadialogic" strategies can be used to engage preservice teachers in reflecting upon the "white talk" of others and thus depersonalizing a topic many preservice teachers associate with feelings of guilt.

Level: College   Methodology: Comparative Case Study  

The TI-Navigator and Feedback (Research - Qualitative)

Level: Secondary   Methodology: Basic  

TI-Navigator (Research - Qualitative)

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.

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.

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.

Level: K-12   Methodology: Ethnography  

CRT and the Standards (Research - Qualitative)

Gutstein, Lipman, Hernandez, and de los Reyes (1997) report on their collaborative reform curriculum project and accompanying research at Diego Rivera Elementary and Middle School in a low-income Mexican American neighborhood in Chicago. The reform initiative included teachers' using the standards-based (NCTM, 1989) program Mathematics in Context (MiC) while engaging in research and professional development efforts aimed at developing a critical orientation to teaching and learning. The authors' present a grounded theory model of intersections between their understandings of culturally relevant pedagogy and the 1989 NCTM standards. The model is particularly grounded in the research teams' observations, interviews, and analysis of Ms. Herrera, Ms. Andula, Mr. Chamarro, and Mr. Simkin. Vignettes describing these teacher's pedagogical orientations, classroom practices, and dispositions toward and involvement with students and parents constitute much of the authors' support for their model. Major aspects of the instructional model include teachers' understanding of critical mathematical thinking, children's informal and cultural knowledge, and orientations to culture.

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.

Level: College   Methodology: Phenomenology  

White Teachers and Racism (Research - Qualitative)

Level: Adult   Methodology: Ethnography  

Ethnography of Blue Collar Families in Washington, D.C. (Research - Qualitative)

Level: K-12   Learning Theory: Social Cognitive Theory  

Overconfidence of Students with Learning Disabilities (Research - Qualitative)

Level: K-12   Methodology: Basic  

Examples of "Good" CRT (Research - Qualitative)

Level: Primary   Learning Theory: Social Constructivism   Methodology: Case Study  

Mathematical Discourse in Teaching Exponents (Research - Qualitative)

Level: College   Methodology: Comparative Case Study  

Actor-Oriented Transfer and Understanding Slope (Research - Qualitative)

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".

Level: Secondary   Methodology: Ethnography  

Learning Theory in Street Mathematics (Research - Qualitative)

Nasir (2002) summarizes her research into ways African American men (of all ages) learn mathematics while participating in dominoes and basketball play. Pointing to low mathematical achievement among the urban African American students that participated in her research, Nasir contends that better understanding of how these students come to learn mathematics in their out of school practice can inform efforts to improve the students' in-school performance. The author sets much of her narrative in the vocabulary of Wegner's communities of practice learning theory and argues for a theoretical model of learning that focuses on goals, identities, and learning in practice. A unique aspect of Nasir's approach is her choice to use goals and identities instead of, for example, communities or individuals as units for analysis when analyzing young men's participation in dominoes and basketball. Specifically, Nasir describes the mathematical identities and mathematical goals of the dominoes and basketball players using concepts such as imagination and development, suggesting that "development occurs at both an individual level and at the level of the practice itself" (p. 237) as players age and improve. The article concludes with implications for teaching and learning, including an argument for using Nasir's description of goals, identities, and learning in practice as a conceptual framework in mathematics education research.

Level: Primary   Learning Theory: Radical Constructivism   Methodology: Case Study  

Informal Probability Understanding (Research - Qualitative)

Nicolson (2005) reports on a series of three videotaped interviews with a fifth grader named Paul. The task-based interviews introduced Paul to common probability activities surrounding flipping a single coin (once and then ten times), drawing from candy bags with different distributions of raspberry and blueberry candies, rolling a single die, and spinning a spinner with colored regions. Though well-articulated, Paul's subjectively based interpretations of chance-- level 1 according to Jones' (1997) framework-- were based largely on prior experiences and incorrect generalizations from small trials. Paul believed that occurrences involving chance were entirely unpredictable unless a physical (deterministic) explanation could be found, and thus did not fully understand representativeness. For example, Paul reported that when he flips coins they usually come up heads, but when he flipped a coin ten times it came up tails six times. Paul reasoned that the result was different because the "tail" of a penny was lighter than the head and that since he usually flipped a coin by reversing the coin onto the back of his hand at the end the results actually supported his theory that the heavier side lands face up. Paul used similar logic to describe dice and spinner outcomes. Nicolson found Paul's "misconceptions" remained after six hands-on classroom lessons on probability, suggesting that Paul's beliefs were not changed by classroom experience. Nicolson concludes that probability understanding may not improve from empirical activities (e.g., with coins or spinners) because variations in distributions of results may be explained by "luck", "loaded dice", "extra effort", etc., and thus may not give students persuasive reasons to abandon subjectively based probability beliefs. Nicolson instead advocates for more "real-world" experiences that are not based on repeated trials; for example, What is the probability of me picking a student's name out of a hat with a summer birthday?

Level: K-12   Methodology: Basic  

Teachers' Views of Technology (Research - Qualitative)

Level: K-12   Methodology: Comparative Case Study  

Teacher Change (Research - Qualitative)

Level: Middle   Methodology: Basic  

Trial Size and Empirical Probability (Research - Qualitative)

Level: Middle   Methodology: Basic  

Probability Simulation (Research - Qualitative)

Stohl and Tarr's qualitative case study of students' learning of statistical inference through probability simulations summarizes a twelve-session instructional intervention using a technology-based learning environment. The researchers developed a series of activities using the software program Probability Explorer, which were then implemented in a sixth grade classroom of average ability students. The activities were designed to engage students in thinking about common conceptual difficulties regarding probability, including connections between theoretical probability and expected distributions at differing sample sizes. The researchers videotaped three pairs of students during all class sessions and analyzed the recordings using Powells analytic method. The final report focuses on two students, Manuel and Brandon, and their developing understanding through three critical instruction sessions referred to as Mystery Marble Bag, the Spinner Simulation task, and Schoolopoly. Transcripts of conversations between and among the students and the teacher-researcher support claims of developing understanding. The authors conclude that carefully designed problem solving tasks can foster sound understanding of probability and statistical inference in a technology-enhanced learning environment.

Level: College   Methodology: Basic  

Concept Image and Definition (Research - Qualitative)

Level: Middle   Methodology: Comparative Case Study  

Teachers' Views of Mathematics (Research - Qualitative)

Level: College   Methodology: Grounded Theory  

Learning Disability through Grounded Theory (Research - Qualitative)

Using many aspects of grounded theory methodology, Troiano (2003) interviewed 9 college students with learning disabilities with the aim of building a conceptual theory of how students come to understand and manage a learning disability. Troiano's narrative is particularly useful as an example of enacted grounded theory strategies and includes a thorough and accessible explanation of the process Troiano went through during his inquiry. While the text explains the broad principles and components of grounded theory well, the authors (usually passive) voice in the article and his implementation of grounded theory methodology limits the value of the author's findings. Troiano also addresses "criteria of soundness" by aligning choices in his research with Lincoln and Guba's (1985) criteria: credibility, transferability, dependability, and confirmability. One limitation in the article can be attributed to the author's apparent lack of attention to the later stages of grounded theory methods, including procedures related to falsifiability and achieving theoretical saturation.

Level: Secondary   Methodology: Case Study  

A Computer-Probability Paradox (Research - Qualitative)

Wilensky is a mathematician associated with the Connected Mathematics project who conduction 17 in-depth interviews with participants ranging from 14 to 64 years old (averaging 7 hours each). The interview questions related to statistical and probability concepts, and the case study he presents is of Ellie, a computer programmer, who is asked to give a solution to Bertrand's Paradox: "From a given circle, choose a random chord. What's the probability that the chord is longer than a radius?" Since "choose a random chord" is not a well-defined term, there are multiple "right" answers to the question, and Ellie used a solid argument to show the result is 2. Wilensky, seeking to challenge Ellie's reasoning, gave a logical argument for the probability equaling 3. Ellie struggled with the concept, wrote a computer program to simulate her reasoning, and was not able to resolve the cognitive conflict until she considered her code in the context of real life (i.e., "we could drop pins on a circle, and see which way they pointed too", "it depends on what you mean by random"). Wilensky believes the interaction with the problem, together with Ellie's attempts to simulate her reasoning on a computer (using thousands of "turtles" in StarLogo), helped her to better understand the epistemological foundations of "randomness" and reflect on the possibility of multiple correct interpretations of the problem. Wilensky also warns of "black box simulations" that do not allow students access to the underlying code of a simulation. He argues for giving students access to controlled programming environments based on the perceived conceptual thinking of Ellie, but since the "student" in his interview was a professional computer programmer, his claims may not transfer to typical secondary student populations.

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.

Level: Adult   Learning Theory: Social Cognitive Theory   Methodology: Comparative Case Study  

Self-Efficacy of STEM Women (Research - Qualitative)

Level: Secondary  

SES and School Size (Replicates O'Callaghan, 1998) (Research - Quantitative)

Teacher Turnover (Research - Quantitative)

Level: Middle  

Closing the Gap through Reform (Research - Quantitative)

Balfanz and Byrnes (2006) measure "closing the gap" for students in high-poverty middle schools using growth in grade-level performance of students on standardized tests over a period of three or four years. They also investigated the effects of whole-school reform initiatives in four such schools. Balfanz and Byrnes found a bimodal pattern in the students' performance-- suggesting that some students close the gap and flourish during middle school while others fall even further behind national norms. The authors' logistic regression models for "closing the gap" accounted for a number of classroom and student-level variables, including SES, ethnicity, homeroom performance, attendance, and effort. They suggest patterns in performance along these factors, though the analysis lacks evidence of validity in places.

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.

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.

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.

Elementary vs. Secondary Teaching Majors (Research - Quantitative)

Education vs. Non-Education Majors (Research - Quantitative)

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).

Math Anxiety, Prior Experience, Confidence in Preservice Teachers (Research - Quantitative)

Level: College  

Progressivism vs. Transmission and its Effect on Student Perceptions (Research - Quantitative)

Statistical Characteristics of Future Teachers (Research - Quantitative)

Level: Secondary  

Gender Gap and Socialization (Research - Quantitative)

interesting theoretical view of the gender gap... pertains to high-achieving students (like math majors)

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?

Level: Middle   Learning Theory: Radical Constructivism  

Cognitively Guided Instruction (Research - Quantitative)

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

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)

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.

Level: College  

Small-Group instruction (Research - Quantitative)

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.

Level: College   Learning Theory: Social Cognitive Theory  

Guided Exploration and Learning to Search (Research - Quantitative)

Level: College  

Cooperative Learning in Remedial Math (Research - Quantitative)

Level: College  

Mathematics Confidence Scale (Research - Quantitative)

Dissertation addresses the reliability and validity of a mathematics confidence scale for college women.

Level: K-12  

Graphing Calculator Research (Research - Quantitative)

Level: Secondary  

Calculators in Secondary Math (Research - Quantitative)

Level: College  

Effects of a Quantitative Literacy Course (Research - Quantitative)

Ellington reports on an assessment of the impact of introductory mathematics courses at Virginia Commonwealth University on students' quantitative reasoning skills. Through workshop meetings and collaboration among faculty, the mathematics department developed 16 multiple choice items to test quantitative reasoning skills relative to topics in unit analysis, interpretation of charts and graphs, proportional reasoning, counting, percentages, percent increase or decrease, use of mathematical formulas, average, and exponential growth. Every student taking Contemporary Mathematics, College Algebra, Precalculus, or Calculus I in one of the three semesters between Fall 2002 and Fall 2003 completed a random subset of 4 of the 16 items as part of a required placement test (before taking a math class) and again as part of the final examination in the course. Performance on the placement test items may have been negatively biased by instructions that described a quarter-point penalty for incorrectly answering questions on the placement test. The items listed on final exams were described as bonus items. The summary statistics suggested that a similar number of items were answered in both settings, with a marked increase in the mean percentage of correct responses between the pre- and post-test items. All classes combined, students answered 13 of the 16 items significantly more often after taking one of the introductory mathematics courses. However, students taking the only course that specifically addressed quantitative reasoning (Contemporary Mathematics) both (1) initially scored lower than the combined mean on all of the items and (2) showed less improvement than the combined sample. The final exam mean score was significantly higher than the placement means on only 9 of the 16 items in the Contemporary Mathematics group. The results in the Contemporary Mathematics group might be due to lower initial quantitative reasoning skills, ineffective instruction, or limitations in the validity of the instrument.

Level: College  

Interdisciplinary Algebra (Research - Quantitative)

This article describes the effects of a course developed at Southeastern Oklahoma State University entitled 'Algebra for the Sciences'. The course introduced college algebra topics by first introducing science topics through guest lectures from professors in Biology, Physics, and Chemistry. The research team compared student performance in four sections of the Algebra for the Sciences class to corresponding performance of four sections of College Algebra over the course of a year. Problem-solving skills were assessed by comparing mean scores on common final exam items, critical thinking skills were assessed using the Watson-Glaser Critical Thinking Appraisal, and student attitudes at the end of the course were measured using Likert-type responses to five statements such as "math is important in my life" and "I found this class to be interesting." Students in the two groups performed equally well on the all of the individual common problem-solving items. In terms of critical thinking, the Algebra for the Sciences students outperformed the College Algebra students on only one subscale: "Inference". However, the students taking the interdisciplinary algebra course expressed much more favorable views toward the course than those taking the traditional algebra course (Elliot et al., 2001, Table 3). The results are strikingly more positive in the experimental group, especially on the items "I found this class to be interesting" (84% agreed compared to 42%) and "The materials in this course are related to practical situations" (90% agreed compared to 53%).

Level: Primary  

DIF: Testing Items (Research - Quantitative)

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.

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

Level: K-12  

Informal Probability Understanding (Research - Quantitative)

Fischbein and Schnarch (1997) administered a probability questionnaire to 20 students in each of grades 5, 7, 9, 11 as well as 18 preservice teachers in college. The instrument (p. 98-100) asks questions directly related to seven intuitive (as opposed to logical) misconceptions identified in probability research. While the authors claim their instrument was designed to study the evolution of students' misconceptions over time, they did not collect time series data, choosing instead to conduct independent random samples. Their results suggest students at all ages frequently hold the misconception that a 5-6 and a 6-6 dice throw are equally likely. Five of the main misconceptions consistently increased with age, except college students held fewer misconceptions regarding the effect of sample size on probabilistic events. The only misconception that appeared to reduce with age was the "conjunction fallacy", defined as the mistaken belief that the probability of an event appears to be higher than the probability of the intersection of the event with another event (e.g., If Dan wants to be a doctor and enrolls in school, it might seem more likely Dan is enrolled in medical school than in school). The seven misconceptions, in order of the their frequency in the populations, were 1) Compound and Simple Events, 2) Effect of Sample Size, 3) Heuristic of Availability, 4) The Conjunction Fallacy, 5) Representativeness, 6) Negative Recency, and 7) The Time Axis Effect. Each effect, along with its roots in literature, is described on p. 100. Many fifth graders did not respond to some of the items, suggesting their understanding of probability was too low for intuitive misconceptions to have formed.

Level: College  

Change in College Students' Preferences (Research - Quantitative)

Level: College  

Effects of Graphing Calculator Use (Research - Quantitative)

Lists 4 phases of calculator implementation for both texts and instruction, tested whether calc II scores were different for the treatment group (calculators in precalc).

Level: Primary  

Evaluating a Reform Initiative (Research - Quantitative)

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.

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

Level: College  

Reform in College Physics (Research - Quantitative)

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.

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.

Level: Secondary  

Reformed Curriculum and Achievement (Research - Quantitative)

Level: Secondary  

Calculators and Achievement (Research - Quantitative)

Level: College  

Pedagogical Content Knowledge (Research - Quantitative)

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.

Level: College  

Graphing Calculators and Understanding (Research - Quantitative)

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.

Teacher shortages (Research - Quantitative)

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.

Level: College  

Quantitative Study of Psychological Burnout (Research - Quantitative)

Jacobs and Dodd (2003) conducted a correlational study of burnout among college upperclassmen at a small, selective, private university. The authors defined burnout as a constellation of three subjective experiences: emotional exhaustion, depersonalization (cynical attitudes that may lead to a callous view of others), and reduced sense of personal accomplishment. Using participants' scores on the Maslach Burnout Inventory as the dependent variable, Jacobs and Dodd collected data that purported to measure the participants' personality, perceived social support, actual workload, and perceived workload. The authors report descriptive statistics and reliability coefficients for the measures, correlations amongst the independent variables, and results of a stepwise linear regression analysis they used to model burnout as a function of the independent variables. The analysis results indicated negative temperament (personality) and perceived workload were positively correlated to burnout, while social support related to lower burnout values. The authors caution against generalizing their findings to general college populations and emphasize their design does not allow for claims of causality. The study could be strengthened by adding qualitative data, such as illuminative case studies, in order to further explore the experience of college students with burnout in more holistic ways.

Level: College  

Content Preparation of Preservice Math Teachers (Research - Quantitative)

Level: Secondary  

Types of Classroom Cooperative Learning Structures (Research - Quantitative)

Meta analysis of goal structures research.

Level: Primary  

Strategies for Measurement (Research - Quantitative)

LISREL (Research - Quantitative)

Common Structural Equation Modeling Software

Level: Secondary  

International Calculus Comparison (Research - Quantitative)

Level: College   Learning Theory: Cognitive Information Processing  

General vs. Concrete in Transfer Experiments (Research - Quantitative)

Level: College  

Math Educators and Technology Use (Research - Quantitative)

Mathematics educators talk about how little they use technology in their methods, etc. classes.

Level: K-12  

Informal Probability Understanding (Research - Quantitative)

This article tests a theoretical model for students' informal understanding of probability called the outcome approach. The outcome approach posits that students view probabilistic statements, e.g., "their is a 70% chance it will rain", as aids in predicting single outcomes rather than frequency based statements (i.e., it's probably going to rain vs. it will rain 7 out of 10 times). Students with an outcome orientation tend to think of probabilistic events as causal relationships with weighted influences (the object will land face up because it is heavier on the bottom and has a small side on the top), which may lead to misconceptions. To test his model, Konold conducted and analyzed task-based interviews of 16 undergraduates for instances of incorrect informal reasoning. These initial problems (the Weather Problem, the Misfortune Problem, and the Bone Problem) were chosen to vary along dimensions relating to the sample space, chance factors, and cultural tendency to view the problem statistically. The students responses were coded according to the outcome approach model in order to predict students' performance during follow-up task-based interviews. The predictive strength of the model was strong, suggesting that students who used outcome approaches in the initial tasks used them again in the follow-up tasks. Konold connects an outcome orientation to a "personalist interpretation" of probability, whereby students use prior experience and "feelings of certainty" to assist their probability judgments. These strong prior conceptions, based on experience, may be viable in everyday probability settings but might also interfere with the learning of formal probability. The article also includes appendices of problems that tend to illicit outcome approaches from students.

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)

Level: College  

Calculator use Among College Faculty (Research - Quantitative)

Calculator usage survey of all universities.

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

Learning Theory: Social Cognitive Theory  

Sources of Self-Efficacy (Research - Quantitative)

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.]

Level: Secondary   Learning Theory: Social Cognitive Theory  

Sources of self-efficacy in High School (Research - Quantitative)

Level: College  

Estimates of Mathematics Majors (Research - Quantitative)

Level: College  

U.S. Math Departments (Research - Quantitative)

Page 127 or 137 gives percents of depts using graphing calculators, specifically for calculus.

Level: College  

Statistical Summary of Mathematics Programs (Research - Quantitative)

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.

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.

Level: College  

Statistics of Mathematics Teachers (Research - Quantitative)

Level: College  

Content Preparation of Preservice Math Teachers (Research - Quantitative)

Level: College  

Preparation/ualifications of Math Teachers (Research - Quantitative)

Level: College  

Sex-differences in Expectations for Success in Math (Research - Quantitative)

most overconfident, men more so than women

Level: Secondary  

Algebraic Reasoning (Research - Quantitative)

Suggesting that "teachers' beliefs about students' ability and learning greatly influence their instructional practices" (p. 168), Nathan and Koedinger (2000) set out to investigate the degree of correspondence between students' performance on algebraic problem solving tasks and rankings made by (n=67) secondary teachers and (n=35) mathematics education researchers regarding the relative difficulty of the algebra problems. Informed by a review of literature, the authors distinguish between start-unknown (SU) and result-unknown (RU) tasks in Algebra I. Nathan and Koedinger further categorized the tasks into story problems (prose and context), word equation problems (prose but no context), and symbolic equations (of the "solve for x" type). Combining the two categorizations, the authors designed and administered an algebra exam that contained each of the six types of elementary algebra problems to (n=245) students who completed Algebra I in middle school or high school (Koedinger & Nathan, 1998). In descending order of percentage-correct, students were most likely to successfully complete RU Story, RU Word, SU Story, RU Equation, SU Word, and SU Equation. The most successful student solution strategies were guess-and-check and "unwinding" (working backwards). Though the sample of teachers and researchers was a convenience sample, the beliefs implicit in the rankings of the teachers did not accurately match the students' performance. When asked to rank-order the six types of algebra problems from "easiest" to "hardest" for students in Algebra I, the mean teacher and researcher list was RU Equation, RU Word, RU Story, SU Equation, SU Story, and SU Word. Thus, the teachers and researchers appeared to stress the result-unknown/tart-unknown order above the roles played by word, story, and equation problems. Based on the results of the surveys, the authors propose an alternative developmental model for understanding algebra that they call the Verbal Precedence Model (VPM). The VPM more successfully categorized students' solution patterns than the Symbol Precedence Model implicit in the teacher and researcher rankings and most Algebra I textbooks.

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).

Assumptions of Multiple Linear Regressions (Research - Quantitative)

Lists assumptions and gives preactical reasons for testing for them.

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.

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.

Level: Middle   Learning Theory: Social Cognitive Theory  

Path Analysis of Self-Efficacy and Self-Concept on Achievement (Research - Quantitative)

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).

Level: College  

Clickers and Formative Assessment (Research - Quantitative)

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

Level: Adult  

Calibration in Postdiction Consumer Knowledge with General Self-Efficacy (Research - Quantitative)

Level: Middle  

Middle-school Effects of Reform Curricula (Research - Quantitative)

Post et al. (2008) describe a follow-up study to Harwell et al. (2007) by reporting results of students' patterns of performance on standardized tests (the traditional SAT-9 and the less-traditional NSREM). Post et al used the same analysis techniques and report similar findings to Harwell et al (with fewer districts and only two standards-based curricula). The Post article focuses more on effects due to SES, special education status, and ethnicity, while repeating the conclusion that the districts implementing standards-based curricula performed above the national average on (traditional) measures of mathematics skills. However, the standards-based students performed below the 50th percentile on procedural tasks. The authors appear to recognize that reduced procedural skills might come with reformed curriculum due to time-on-task concerns. The observed effects in their modeling follow traditional findings: lower SES, non-white, and special education students each performed lower on the standardized tests than higher SES, white, and non-special education students. The authors also point to a significant portion of lower achievement in the urban school district that was not explained by the variables in the model.

Level: Middle  

Performance vs. Number Sense (Research - Quantitative)

Level: K-12  

Probability and Coins (Research - Quantitative)

As part of her dissertation, Rubel's (2007) investigation of student's reasoning with probability related to coin tasks is thorough and remarkably well-set in related literature. The article is a great example of integrating clinical or "teaching interviews" into a well-designed quantitative study of students' reasoning. The diagnostic task asked grade 6-12 students at a private New York high school to complete tasks (adapted from existing instruments) related to coin-toss scenarios and common misconceptions regarding sample space, randomness, compound events, and independence. Using Chi-squared analysis and interviews of 33 students, Rubel found much of the errors in students' responses could be explained using a theoretical framework combining representativeness heuristics, the negative recency effect (p. 533), core beliefs about coins (p. 534), and Jones' classification of student reasoning (subjective, transitional, informal quantitative, numerical). A unique strength of Rubel's Probability Inventory was that it asked for justification of all solutions, meaning that students' reasoning could be classified into general categories. The clinical interviews added great validity to Rubel's claims, with transcripts of students' explanations providing some of the most compelling evidence for how students think about independence and distributions of outcomes (see especially "Bob" on p. 545).

Learning Theory: Cognitive Information Processing  

Calibration of Postdictions (Research - Quantitative)

Level: College  

Change in College Students' Preferences (Research - Quantitative)

Level: K-12  

SES and Achievement (Research - Quantitative)

Path Analysis Guidelines (Research - Quantitative)

contains criteria for path analysis and reporting... VERY GOOD

Level: Secondary  

TI-Navigator (Research - Quantitative)

Level: College  

Students' Perceptions of Evaluations (Research - Quantitative)

Path Analysis Step-by-Step (Research - Quantitative)

Some procedural steps for path analysis.

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.

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.

Level: Primary   Learning Theory: Behaviorism  

Behaviorism in Arithmetic (Research - Quantitative)

Bonds, or associations, or connections, are reinforced patterns of interacting with the environment. In this early paper on the psychology of learning, Thorndike describes his intuitive theory of how an individual forms and maintains bonds for arithmetic. As the frequency of correct responses to a predetermined type of task increase, we see evidence for strengthened bonds. Thorndike believes that if conditions are set properly, students can develop strong bonds in mathematics through the rewards of successfully and reliably completing basic tasks. Later, students are able to generalize certain abstract properties of numbers from the many examples they complete during practice. The article also argues for inductive approaches to arithmetic instruction, where students naturally discover deeper principles of numbers only after they become comfortable with procedures.

Level: K-12  

Assessing Best Practices (Research - Quantitative)

Level: College  

Goal Structures and Self-Handicapping (Research - Quantitative)

Level: K-12  

Fairness and Probability (Research - Quantitative)

The authors suggest students and teachers should consider the fairness of dice (and other probability tools) as an important and questionable property. They report on a longitudinal study of 78 grade 3, 5, 6, 7, and 9 students in Australia and Tasmania. Initial survey data of students' conceptions of fairness in dice was followed by clinical interviews of a subsample of 44 students 4 years later. The students responses to the survey and subsequent interviews supported previously reported observations that students may hold a variety of conceptions about the fairness of dice, from idiosyncratic beliefs that dice are unfair (based on experience), inconsistent beliefs that dice are fair but extremes (1 and 6) are less likely, unistructural beliefs that dice are fair for theoretical reasons (their shape, number of sides, etc.), multistructural beliefs that dice are fair subject to how they are manufactured and rolled, and relational beliefs that short term outcomes may vary but long term behavior of dice represents fairness. Students' strategies for determining whether a particular set of dice is fair ranged from Ikonic (intuition and luck-based), Untestable (they are always fair), Observational (unsystematic trials or inspection of physical dimensions), and Empirical (large or small sampling based on recording trials). The results of the study indicate that many students progressed from an idiosyncratic or inconsistent belief of dice fairness to a unistructural belief system. Most students' strategies for evaluating dice did not change over time; students consistently used the Observational approach. The authors did not employ an educational intervention to improve students' strategies for assessing dice fairness, so suggest the students' normal education over the four years did not help them to develop empirical strategies or begin to see dice as fair only under certain conditions. They suggest experimenting with loaded dice or unfair coins could help students learn about theoretical and empirical distributions as well as variation and inference.

Level: Secondary  

Formative Assessment and Achievement (Research - Quantitative)

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.