Learning Theory &
Cognition Readings

  APOS (1 Refs)

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/ annotationSearch Title on Google

Dubinsky, 2001. annotationSearch Title on Google

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.

  Behaviorism (3 Refs)

Erlwanger, S. H. (1973). Benny's conception of rules and answers in IPI mathematics. Journal of Children's Mathematical Behavior, 1(2), 7-25. annotationSearch Title on Google

Erlwanger, 1973. annotationSearch Title on Google

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.

Schunk, D. H. (2004). Behavioral theories. In Learning theories: an educational perspective (pp. 29-81). Upper Saddle River, NJ: Pearson Education. annotationSearch Title on Google

Schunk, 2004. annotationSearch Title on Google

Learning Theory: Behaviorism  

Overview of Behaviorism (Theory)

Thorndike, E. L. (1924). The psychology of arithmetic. In The '1923 Report' and connectionism (pp. 102-121). New York: Macmillan. annotationSearch Title on Google

Thorndike, 1924. annotationSearch Title on Google

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.

  Cognitive Information Processing (12 Refs)

Driscoll, M. P. (2004). Cognitive Information Processing. In Psychology of learning for instruction (3rd ed., pp. 71-110). Boston, MA: Allyn & Bacon. annotationSearch Title on Google

Driscoll, 2004. annotationSearch Title on Google

Learning Theory: Cognitive Information Processing  

Cognitive Information Processing (Theory)

This chapter includes a thorough summary of the basic principles of cognitive information processing (CIP). CIP began with a three stage model for memory-- short term, working, and long term memory are seen as the basic mediums for cognitive processes. Subprocesses include attention, executive monitoring, pattern recognition, rehearsal, chunking, encoding, and retrieval. The summary also lists many of the major scientific results in CIP. Of particular interest are the studies that helped to establish the Stroop effect, primacy and recency effects, effective elaborative encoding methods, and possible models for long term memory and forgetting processes. The chapter concludes with some implications of the theory for learning and instruction.

Fischbein, E. (1987). Investigations in overconfidence. In Intuition in science and mathematics (pp. 28-42). Dordrecht: D. Reidel Publishing. annotationSearch Title on Google

Fischbein, 1987. annotationSearch Title on Google

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. annotationSearch Title on Google

Kahneman, Slovic, & Tversky, 1982. annotationSearch Title on Google

Learning Theory: Cognitive Information Processing  

Cognitive Science Perspective on Calibration (Theory)

THE textbook on the cognition of people involved in making uncertain judgments.

Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2008). Learning theory: The advantage of abstract examples in learning math. Science, 320(5825), 454 - 455. annotationSearch Title on Google

Kaminski, Sloutsky, & Heckler, 2008. annotationSearch Title on Google

Level: College   Learning Theory: Cognitive Information Processing  

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

Lichtenstein, S., & Fischhoff, B. (1980). Training for calibration. Organizational Behavior and Human Performance, 26, 149-171. annotationSearch Title on Google

Lichtenstein & Fischhoff, 1980. annotationSearch Title on Google

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. annotationSearch Title on Google

Lichtenstein, Fischoff, & Phillips, 1982. annotationSearch Title on Google

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. annotationSearch Title on Google

O’Connor, 1989. annotationSearch Title on Google

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).

Resnick, L. B., & Ford, W. W. (1981). Information-processing analyses of understanding. In The psychology of mathematics for instruction (pp. 196-237). Hillsdale, NJ: Lawrence Erlbaum Associates. annotationSearch Title on Google

Resnick & Ford, 1981. annotationSearch Title on Google

Learning Theory: Cognitive Information Processing  

Cognitive Information Processing (Theory)

This chapter includes a description of semantic memory (long term memory) from the cognitive information processing perspective. In this view, knowledge structures are viewed as concept maps with dual qualities of structuredness and associativity, which means that concepts are understood to exist in the mind in terms of relationships that are constructed among them. Qualities characterizing well-structured mental concepts of mathematical ideas include integratedness, connectedness, and correspondence. The discussion leads rather naturally to some implications of this model for long term memory in problem solving strategies. Instructional modes that might improve the three qualities of well-structured memory are suggested and developed around examples of problem solving tasks for children.

Schraw, G. (1995). Measures of feeling-of-knowing accuracy: A new look at an old problem. Applied Cognitive Psychology, 9, 321-332. annotationSearch Title on Google

Schraw, 1995. annotationSearch Title on Google

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. annotationSearch Title on Google

Schraw, Polenza, & Nebelsick-Gullet, 1993. annotationSearch Title on Google

Learning Theory: Cognitive Information Processing  

Calibration of Postdictions (Research - Quantitative)

Schunk, D. H. (2004). Information processing. In Learning theories: An educational perspective (pp. 136-189). Upper Saddle River, NJ: Pearson Education. annotationSearch Title on Google

Schunk, 2004. annotationSearch Title on Google

Learning Theory: Cognitive Information Processing  

Cognitive Information Processing (Theory)

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 annotationSearch Title on Google

Department of Education, 2008. annotationSearch Title on Google

Level: K-12   Learning Theory: Cognitive Information Processing  

Policy Change and Closing the Gap (Practice)

  Complexity Science (5 Refs)

Caine, R. N., & Caine, G. (1998). Building a bridge between the neurosciences and education: Cautions and possibilities. NASSP Bulletin, 82(598), 1-8. annotationSearch Title on Google

Caine & Caine, 1998. annotationSearch Title on Google

Learning Theory: Complexity Science  

Neuroscience (Theory)

The authors motivate the need for a biological approach to cognitive sciences by describing some of the flaws inherent in the high threat, low challenge industrial-model of education in the western world. They describe the biological implications of fear and helplessness and list the four principles of neuroscience research: (1) the brain is innately motivated to search for meaning, (2) the search for meaning takes place by patterning, (3) emotions are critical for patterning, and (4) complex learning is enhanced by challenge and inhibited by threat. The "nuts and bolts" of brain research--with the exception of some discussion of the mechanisms of fear-- are omitted as the authors focus on educational implications of considering schooling in the context of the principles of neuroscience.

Davis, B., & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137-157. annotationSearch Title on Google

Davis & Simmt, 2003. annotationSearch Title on Google

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.

McCloskey, M. (1991). Networks and theories: The place of connectionism in cognitive science. Psychological Science, 2(6), 387-395. annotationSearch Title on Google

McCloskey, 1991. annotationSearch Title on Google

Learning Theory: Complexity Science  

Connectionism (Theory)

Shepard, L. A. (2000). The role of assessment in a learning culture. Educational Researcher, 29(7), 4-14. annotationSearch Title on Google

Shepard, 2000. annotationSearch Title on Google

Learning Theory: Complexity Science  

Assessment within Systems Theory (Theory)

Sylwester, R. (1994). What the biology of the brain tells us about learning. Educational Leadership, 51(4), 46-51. annotationSearch Title on Google

Sylwester, 1994. annotationSearch Title on Google

Learning Theory: Complexity Science  

Neuroscience (Theory)

The author of this article uses the metaphor in neurosciences that the brain is a jungle (as opposed to a linear processor of stimuli or organism). Imaging technology and evolutionary principles support a neural Darwinism model for brain functioning. Sylwester suggests that the brain acts in many of the same ways that living organisms do; it has been shaped by selection over thousands of years and is organized at birth to be able to adapt to the kinds of cognitive demands that humans face. Nature and nurture exist in a balance as the genetic predispositions to learn and reorganize knowledge are reinforced by interactions and experiences. However, as the increasing cognitive demands of society begin to outpace our mental ability to adapt, we develop a technological brain to allow for distributed knowledge and abilities to respond to huge amounts of information. Sylwester also suggests several educational implications of neuroscience, mostly related to the metaphor of the mind as jungle. Maybe learning should take place in a complex environment, he suggests.

  General Learning Theory (8 Refs)

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. annotationSearch Title on Google

Bransford, Brown, & Cocking, 2000. annotationSearch Title on Google

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."

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. annotationSearch Title on Google

Bransford, Brown, &Cocking, 1999. annotationSearch Title on Google

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".

Driscoll, M. P. (2000). Psychology of learning for instruction (2nd ed.). Needham Heights, MA: Allyn & Bacon. annotationSearch Title on Google

Driscoll, 2000. annotationSearch Title on Google

Learning Theory: General Learning Theory  

Overview of Learning Theories (Theory)

Driscoll, M. P. (2004). Psychology of learning for instruction (3rd ed.). Boston, MA: Allyn & Bacon. annotationSearch Title on Google

Driscoll, 2004. annotationSearch Title on Google

Learning Theory: General Learning Theory  

Overview of Learning Theories (Theory)

Reference to the whole book.

Huetnick, L., & Munshin, S. N. (2004). Learning theories. In Teaching mathematics for the 21st century: Methods and activities for grades 6-12 (2nd ed., pp. 38-51). Upper Saddle River, NJ: Pearson Education. annotationSearch Title on Google

Huetnick & Munshin, 2004. annotationSearch Title on Google

Learning Theory: General Learning Theory  

Overview of Learning Theories (Theory)

Schunk, D. H. (2004). Learning theories: An educational perspective (pp. 285-289, 447-451). Upper Saddle River, NJ: Pearson Education. annotationSearch Title on Google

Schunk, 2004. annotationSearch Title on Google

Learning Theory: General Learning Theory  

Overview of Learning Theories (Theory)

Schunk, D. H. (2004). Cognitive learning processes. In Learning theories: an educational perspective (pp. 190-217). Upper Saddle River, NJ: Pearson Education. annotationSearch Title on Google

Schunk, 2004. annotationSearch Title on Google

Learning Theory: General Learning Theory  

Some Learning Processes (Theory)

Schunk, D. H. (2004). Learning: Introduction, issues, historical perspectives. In Learning theories: an educational perspective (pp. 1-27). Upper Saddle River, NJ: Pearson Education. annotationSearch Title on Google

Schunk, 2004. annotationSearch Title on Google

Learning Theory: General Learning Theory  

Basics of Learning (Theory)

  Models and Modeling (3 Refs)

Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2&3), 109-129. annotationSearch Title on Google

Lesh & Lehrer, 2003. annotationSearch Title on Google

Learning Theory: Models and Modeling  

Models and Modeling and Learning (Theory)

Models and modeling is outlined by the authors in terms of theory, practice, and research. The M&M perspective on knowledge, and how it derives from modeling cycles is described in the context of constructivism, followed by a description of the "paper airplane problem" as a model-eliciting activity. Then, the theoretical assumptions of the M&M paradigm are outlined so that teachers and researchers gain insight into the mechanisms for learning proposed by the theory. In Lesh's view, learning occurs as individuals make, test, refine, and retest models, or interpretations of the world. Its worth pointing out that this mechanism restricts the theory to the learning of math and science. The article also includes a list of the six design principles for problem solving tasks that might combine to form a model-eliciting activity.

Lesh, R., Lester, F. K., Jr., & Hjalmarson, M. (2003). A models and modeling perspective on metacognitive functioning in everyday situations when problem solvers develop mathematical constructs. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism (pp. 382-403). Mahwah, NJ: Lawrence Erlbaum Associates. annotationSearch Title on Google

Lesh, Lester, Jr, & Hjalmarson, 2003. annotationSearch Title on Google

Learning Theory: Models and Modeling  

Models and Modeling and Metacognition (Theory)

Zawojewski, J. S., & Lesh, R. (2003). A models and modeling perspective on problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism (pp. 317-336). Mahwah, NJ: Lawrence Erlbaum. annotationSearch Title on Google

Zawojewski & Lesh, 2003. annotationSearch Title on Google

Learning Theory: Models and Modeling  

Models and Modeling and Problem Solving (Theory)

This chapter accepts Lester's (1983) definition that a problem is a task for which (1) the individual or group wants or needs to find a solution, (2) there is not a readily determined method of solution, and (3) the individual or group must construct a solution. The authors contrast the models and modeling approach to problem solving (which includes cyclical trial procedures to use given information to reach goals) to the information processing view of problem solving (which includes the selection of a procedure that will allow for the solution to a problem from the given information). The chapter argues that Polya and other's general strategies for problem solving are of little benefit to learners, and instead suggests that heuristics and strategies are largely tied to context. They summarize the six points of the chapter: (1) the most useful strategies and procedures are learning during the solution development process for specific problems, (2) the most important purpose of strategies is to help students refine and revise models, (3) any strategy can be productive or counterproductive (depending on the problem), (4) the productivity of a strategy depends on the purpose for using it, (5) problem solving strategies develop along a variety of dimensions, and (6) early levels of understanding often emerge in social aspects of development. The chapter also includes transcripts of students working on a model-eliciting activity.

  Radical Constructivism (11 Refs)

Carpenter, T. P., Fennema, E., Peterson, P. L., & Loef, M. (1989). Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. In T. Carpenter, J. Dossey, & J. Koehler, Classics in mathematics education research (pp. 135-151). Reston, VA: National Council of Teachers of Mathematics. annotationSearch Title on Google

Carpenter, Fennema, Peterson, & Loef, 1989. annotationSearch Title on Google

Level: Middle   Learning Theory: Radical Constructivism  

Cognitively Guided Instruction (Research - Quantitative)

Driscoll, M. P. (1994). Constructivism. In Psychology of learning for instruction (pp. 373-397). Needham Heights, MA: Allyn & Bacon. annotationSearch Title on Google

Driscoll, 1994. annotationSearch Title on Google

Learning Theory: Radical Constructivism  

Overview of Constructivism (Theory)

Driscoll, M. P. (2004). Cognitive and knowledge development. In Psychology of learning for instruction (3rd ed., pp. 185-205). Boston, MA: Allyn & Bacon. annotationSearch Title on Google

Driscoll, 2004. annotationSearch Title on Google

Learning Theory: Radical Constructivism  

Learning Development (Theory)

Driscoll summarizes the developmental theories of Piaget, including his genetic epistemology, four-stage theory of cognitive development, and the developmental processes that Piaget believed explain learning and development. A particular focus is on Piaget's research into early development and the cognitive characteristics of sensorimotor, preoperational, concrete operational, and formal operational children are explained in some detail. Piaget's mechanisms for learning and epistemological shift to radical constructivism are also described, including a description of how assimilation, accommodation, and a biological drive to reach cognitive equilibrium (equilibration) promote learning. Driscoll also gives examples of the three kinds of knowledge according to Piaget: physical knowledge, logical-mathematical knowledge, and social knowledge.

Jaworski, B., & Jaworski, J. (Producers). (1998, July). Interview with Ernst von Glasersfeld [Television broadcast]. Budapest, Hungary: BBC. annotationSearch Title on Google

Jaworski, & Jaworski, Producers, 1998. annotationSearch Title on Google

Learning Theory: Radical Constructivism  

Radical Constructivism in Layman's Terms (Theory)

This is a transcript for a portion of a short interview with Ernst von Glasersfeld at the International Congress of Mathematical Education (1988). von Glasersfeld starts the interview by describing the long-standing difficulty in philosophy with the nature of reality: "Now, the skeptics who started right at the beginning of the history of philosophy of the western world have been adamant in telling us that no true picture of the real world is possible." (p.1) Radical constructivism, in his view, offers an interpretivist epistemology that avoids these difficulties by claiming that knowledge "instead of having to be a true representation of the world, has to work". This allows for the use of terms like cognitive fit or match, where people can evaluate their perceptions by checking them against their interpretations of the world and seeing if their beliefs seem consistent with their experience. The rest of the interview includes a description of trivial and radical constructivism along with some of the changes in education that might result from a shift toward a radical constructivist view of learning.

Kamii, C. (1982). Number in preschool and kindergarten: Educational implications of piaget's theory. Washington, D.C.: National Association for the Education of Young Children. annotationSearch Title on Google

Kamii, 1982. annotationSearch Title on Google

Level: Primary   Learning Theory: Radical Constructivism  

Piaget and Number (Practice)

Kamii explores the concept of number in cognition in terms of its role as a logico-mathematical form of knowledge as opposed to physical knowledge or social (conventional) knowledge. Using Piaget's theory, the description in the chapter incorporates the processes of radical constructivist development: simple and reflective abstraction, the four stages, etc. Of particular educational value are the descriptions of Piaget and other's experiments about the learning of number: hierarchical inclusion, mental ordering, conservation tasks, connexity tasks (incrementing by 1).

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates. annotationSearch Title on Google

Ma, 1999. annotationSearch Title on Google

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".

Nicolson, C. P. (2005, September). Is chance fair: One student's thoughts on probability. Teaching Children Mathematics, 83-89. annotationSearch Title on Google

Nicolson, 2005. annotationSearch Title on Google

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?

Resnick, L. B., & Ford, W. W. (1981a). Piaget and the development of cognitive structures. In The psychology of mathematics for instruction (pp. 155-172, 189-194). Hillsdale, NJ: Lawrence Erlbaum. annotationSearch Title on Google

Resnick & Ford, 1981a. annotationSearch Title on Google

Learning Theory: Radical Constructivism  

Piaget and Development (Theory)

This chapter complements Driscoll's discussion of Piaget's theory of cognitive development in children from the perspective of mathematics. Evidence for cognitive differences in Piaget's four stages of development is presented by way of examples of Piagetian task-based experiments. The angles-of-a-triangle problem (in which students may discover that all angles of a triangle sum to 180), the dot-in-a-rectangle problem (in which students need to develop a coordinate system), the number conservation task (where matched items are separated and young children no longer believe there are the same number of both items), and the bending rod experiment (where participants must identify which qualities of a rod affect bending strength) are all outlined in the chapter. Instructional considerations arising from the Piagetian and Neo-Piagetian research programs are contrasted with some criticisms of the Piaget's stage theory. The clinical interaction method developed by Piaget for research is closely tied to the kinds of things that occur in teaching and represents a major advance in educational research.

Smith, M. K. (2002). Jerome S. Bruner and the process of education. Retrieved May 27, 2007, from http://www.infed.org/ annotationSearch Title on Google

Smith, 2002. annotationSearch Title on Google

Learning Theory: Radical Constructivism  

Biography of Bruner (Theory)

Steffe, L. P., & Kieren, T. (1994). Radical constructivism and mathematics education. Journal for Research in Mathematics Education, 25(6), 711-733. annotationSearch Title on Google

Steffe & Kieren, 1994. annotationSearch Title on Google

Learning Theory: Radical Constructivism  

History of Radical Constructivism (Theory)

This article chronicles the development of radical constructivism in mathematics education since Piaget and Bruner in the 1960s. The authors claim that the preconstructivist revolution and a shift in normal science away from the Cartesian epistemology of behavioral sciences converged to support naturalistic studies into learning during the later half of the 20th century. Competing forms of constructivism have existed from the beginning and constructivists have actively debated one another and empirical sciences on the philosophical assumptions supporting their theory. The article also suggests that constructivist approaches to research in mathematics education often lead to provocative and powerful new ways of teaching, which is an added benefit of the theoretical approach.

von Glasersfeld, E. (1996). Aspects of radical constructivism and its educational implications. In P. Nesher, L. P. Steffe, P. Cobb, G. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 307-314). Mahwah,, NJ: Lawrence Erlbaum Associates. annotationSearch Title on Google

von Glasersfeld, 1996. annotationSearch Title on Google

Learning Theory: Radical Constructivism  

Philosophy of Radical Constructivism (Theory)

This short chapter outlines the educational assumptions and implications of radical constructivism in the field of mathematics education. The point is made that Piaget's developmental theories and research methodology were widely accepted and thoroughly studied while his genetic epistemology was largely ignored until the 1980s. The interpretivist perspective of radical constructivism is outlined, including the belief that all knowledge is subjective and that mental representations of the world vary widely and do not simply exist as isomorphisms of an external reality. The article concludes by developing the radical constructivists approach to how researchers and teachers might view the making of abstraction and misconceptions (ways of thinking that are not viable in the learner's interpretations).

  Situated Cognition (14 Refs)

Anderson, J. R., Simon, H. A., & Reder, L. M. (1996). Situated learning and education. Educational Researcher, 25(4), 5-11. Retrieved April 30, 2007, from http://act-r.psy.cmu.edu/. annotationSearch Title on Google

Anderson, Simon, & Reder, 1996. annotationSearch Title on Google

Learning Theory: Situated Cognition  

Critique of Situated Cognition (Theory)

Anderson et al. consider situated learning from the perspective of how situated learning theory addresses some of the issues central to cognitive science. They suggest that research contradicts many of the fundamental claims of situated cognition. In particular, they attribute four claims to social learning theory: (1) action is grounded in the concrete situation in which it occurs, (2) knowledge does not transfer between tasks, (3) training by abstraction is of little use, and (4) instruction needs to be done in complex social environments. This article was the first of a series of responses between Anderson et al. and Greeno in Educational Researcher.

Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41-62. annotationSearch Title on Google

Boaler, 1998. annotationSearch Title on Google

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]

Boaler, J. (2000). Exploring situated insights into research and learning. Journal for Research in Mathematics Education, 31(1), 113-119. annotationSearch Title on Google

Boaler, 2000. annotationSearch Title on Google

Level: Secondary   Learning Theory: Situated Cognition  

A Situated Learning Follow-Up to Boaler (1998). (Theory - Qualitative)

In a follow-up to Boaler's (1998) 3-year case studies of Amber Hill (traditional school) and Pheonix Park (reform school), Boaler (2000) revises her discussion of the students' differential functioning in school work, traditional test items, and real-world tasks by considering the students' participations in their respective schools on macro-levels. From a communities-focused situated learning perspective, Boaler concludes that the students at Amber Hill learned the norms of doing "school mathematics" in a traditional, individualized, and closed environment. The students were successful at learning how to behave in the Amber Hill environment, and Boaler recasts her 1998 findings as simply representing the students' realization of how different school and "real-world" mathematics was for them. In other words, the communities of participation in which the Amber Hill students worked simply did not give the students reason to believe they should/ould use school mathematics in out-of-school settings. Boaler essentially argues for more situated-learning theoretical perspectives in considering both students' cognition and their participation.

Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32-42. Retrieved October 14, 2006, from http://www.exploratorium.edu/ annotationSearch Title on Google

Brown, Collins, & Duguid, 1989. annotationSearch Title on Google

Learning Theory: Situated Cognition  

Overview of Situated Cognition (Theory)

Carraher, D. W. (2008). Beyond ‘blaming the victim’ and ‘standing in awe of noble savages’: a response to “Revisiting Lave’s ‘cognition in practice’”. Educational Studies in Mathematics, 69, 23-32. annotationSearch Title on Google

Carraher, 2008. annotationSearch Title on Google

Level: Primary   Learning Theory: Situated Cognition  

Why Everyday Mathematics is Valuable (Theory)

In responding to Greiffenhagen and Sharrock (2008), Carraher (of "Math in the Streets" fame) explains the value in the Everyday Mathematics movement. Carraher believes Lave's work was valuable in the descriptive sense while not endorsing or rejecting Lave's critical project. Moreover, Carraher's intention is to integrate Everyday Mathematics into the mathematics education corpus and does not subscribe to Lave's epistemological stance that knowledge resides in contexts. The author refers to Vergnaud's framework of concepts as consisting of three components: invariants, symbols, and situations. Carraher argues that the examples of Everyday Mathematics help to emphasize the role of invariants in mathematical understandings (of street vendors for example) that need not translate into the formal symbols of school mathematics. Though some Everyday Mathematics examples show a very different understanding of numbers and arithmetic, Carraher explicitly rejects the contention that Everyday Mathematics is somehow better-- instead suggesting that students' everyday techniques be used as a "point of departure" in teaching the more powerful school techniques. He does not disagree with Greiffenhagen and Sharrock's contentions regarding the results of studying Everyday Mathematics (notably that it usually includes addition, subtraction, and multiplication of typically small and "round" numbers).

Carraher, D., & Schliemann, A. D. (2002). The transfer dilemma. The Journal of the Learning Sciences, 11(1), 1-24. annotationSearch Title on Google

Carraher & Schliemann, 2002. annotationSearch Title on Google

Learning Theory: Situated Cognition  

Transfer in Situated Cognition (Theory)

This is a wonderfully written theory piece on transfer in situated learning contexts. The authors aim to redefine transfer as situated generalization instead of the traditional definitions of application of knowledge or recognizing structural similarities between learned and novel tasks. The authors give two examples of students working in a computerized number environment as the students transfer their understandings of numbers to tasks designed to engender conflicts in the students' minds regarding common misconceptions about "multiplication makes bigger" and "division makes smaller" as well as the difficult idea of negative numbers.

Carraher, T. N., Carraher, E. W., & Schliemann, A. D. (1985). 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. 187-193). Reston, VA: National Council of Teachers of Mathematics. annotationSearch Title on Google

Carraher, Carraher, & Schliemann, 1985. annotationSearch Title on Google

Level: Middle   Learning Theory: Situated Cognition  

Street Mathematics (Research - Mixed Methods)

Driscoll, M. P. (2004). Situated cognition. In Psychology of learning for instruction (3rd ed., pp. 153-183). Boston, MA: Allyn & Bacon. annotationSearch Title on Google

Driscoll, 2004. annotationSearch Title on Google

Learning Theory: Situated Cognition  

Overview of Situated Cognition (Theory)

Driscoll summarizes situated cognition from the perspective that it represents a shift in a certain segment of the educational research community towards viewing learning from a sociological perspective. With a decreased emphasis on individual psychological factors, situated learning specialists like Lave and Wenger have proposed a model for learning that incorporates co-constructed knowledge and communities of practice. Wenger's four basic premises of situated learning-- we are social, knowledge is a matter of competence with respect to valued enterprises, knowing is the pursuit of such enterprises, and meaningful understanding of the world is the ultimate goal of learning-- are couched within the process of legitimate peripheral participation. Peripheral participation is the primary learning process in situated cognition, and is characterized by varying learning trajectories and the use of signs (semiosis). A number of instructional programs rooted in situated learning are listed toward the end of the chapter, including anchored instruction, apprenticeships, anchored instruction, and learning community approaches to instruction.

Greeno, J. G. (1997). On claims that answer the wrong questions. Educational Researcher, 26(1), 5-17. annotationSearch Title on Google

Greeno, 1997. annotationSearch Title on Google

Learning Theory: Situated Cognition  

Defense of Situated Cognition (Theory)

In this article, Greeno responds to Anderson et al.'s (1996) claims that situated learning takes stances in education that are contradicted by research in the cognitive sciences. Rather than argue that Anderson was incorrect in his claims about learning, Greeno argues that situated learning theorists simply disagree with the assumptions that support Anderson's view of situated cognition. Greeno addresses each of the four claims made by Anderson by suggesting that, while the claims are appropriate considerations for cognitive information processing theory, the claims violate assumptions of situated learning. Where Anderson argues that a learner's cognitive load in complex environments can become so overwhelming that the ability to learn may suffer, Greeno simply states that from the situated learning perspective all learning is viewed as occurring in complex environments. Thus, there is no way to remove the complexity from environments and reduce learning to processes and factors. Knowledge is co-constructed and exists in the interactions among members of a community. When contrasted with the assumptions of CIP, the assumptions of situated learning make it possible to agree with Anderson's claims and simultaneously believe that they do not apply to situated learning.

Greiffenhagen, C., &Sharrock, W. (2008). School mathematics and its everyday other? Revisiting Lave’s ‘cognition in practice’. Educational Studies in Mathematics, 69, 1-21. annotationSearch Title on Google

Greiffenhagen &Sharrock, 2008. annotationSearch Title on Google

Level: Primary   Learning Theory: Situated Cognition  

Rejecting Lave's Belief in Everyday vs. School Mathematics (Theory)

Greiffenhagen and Sharrock are deeply critical of Lave's arguments for Everyday Mathematics as essentially different-- and better than-- School Mathematics. By summarizing and critiquing Lave's evidence of "just plain folks" doing arithmetic while shopping, tailoring, and dieting, the authors give detailed alternative interpretations that place Everyday Mathematics within mathematics while suggesting the research is mainly descriptive, yet is used as part of Lave's larger critical project against Lave's belief that school institutionalizes a "Western mathematics should replace everyday mathematics" belief in elitist rationality. The authors aim to debunk Lave's much cited claims that shoppers perform hundreds of calculations "nearly error free" (98% accuracy) by carefully showing alternative interpretations of the data that suggest shoppers rarely do any arithmetic, and even abandon almost all calculations that cannot be easily done by either comparing prices directly or subtracting. They ultimately claim that school mathematics is not aimed at replacing students' everyday understandings while leaving them feeling inadequate, but rather a kind of training in the simultaneous beliefs that (1) there are many correct (or equivalent) ways of doing mathematics, and (2) it is sometimes important to not use already known techniques while learning a new technique. Greiffenhagen and Sharrock point to the basketball coach that requires her students to dribble with their weak hand-- the coach is not telling the players that dribbling with their strong hand is bad, but instead that they will benefit from temporarily suspending their current skill in order to learn a new one.

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. annotationSearch Title on Google

Herzig, 2002. annotationSearch Title on Google

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.

Lave, J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. Cambridge: Cambridge University Press. annotationSearch Title on Google

Lave, 1988. annotationSearch Title on Google

Learning Theory: Situated Cognition  

Defining Situated Cognition (Theory)

Putnam, R. T., & Borko, H. (2000). What do new views of knowledge about thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4-15. annotationSearch Title on Google

Putnam & Borko, 2000. annotationSearch Title on Google

Learning Theory: Situated Cognition  

Situated Cognition's Impact on Research (Theory)

Shulman, L. S., & Shulman, J. H. (2004). How and what teachers learn: a shifting perspective. Journal of Curriculum Studies, 36 (2), 257-271. annotationSearch Title on Google

Shulman & Shulman, 2004. annotationSearch Title on Google

Learning Theory: Situated Cognition  

Situated Perspective of Pedagogical Knowledge (Theory)

  Social Cognitive Theory (48 Refs)

Alderman, M. K. (1999). Motivation for achievement. Mahwah, NJ: Lawrence Erlbaum Associates. annotationSearch Title on Google

Alderman, 1999. annotationSearch Title on Google

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.

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. annotationSearch Title on Google

Bandura, 1995. annotationSearch Title on Google

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. (1997). Self-efficacy: the exercise of control. New York: W. H. Freeman. annotationSearch Title on Google

Bandura, 1997. annotationSearch Title on Google

Learning Theory: Social Cognitive Theory  

Defining Social Cognitive Theory (Theory)

Bandura, A., Ross, D., & Ross, S. A. (1963). Imitation of film-mediated aggresive models. Journal of Abnormal and Social Psychology, 66 (1), 3-11. annotationSearch Title on Google

Bandura, Ross, & Ross, 1963. annotationSearch Title on Google

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.

Bong, M. (1997). Generality of academic self-efficacy judgments: Evidence of hierarchical relations. Journal of Educational Psychology, 89 (4), 696-709. annotationSearch Title on Google

Bong, 1997. annotationSearch Title on Google

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.

Bong, M., & Clark, R. E. (1999). Comparison between self-concept and self-efficacy in academic motivation research. Educational Psychologist, 34(3), 139-153. annotationSearch Title on Google

Bong & Clark, 1999. annotationSearch Title on Google

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.

Bouffard-Bouchard, T. (2001). Influence on self-efficacy on performance in a cognitive task. The Journal of Social Psychology, 130 (3), 353-363. annotationSearch Title on Google

Bouffard-Bouchard, 2001. annotationSearch Title on Google

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).

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. annotationSearch Title on Google

Campbell & Hackett, 1986. annotationSearch Title on Google

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?

Chen, P. P. (2002). Mathematics self-efficacy calibration of seventh graders. Dissertation Abstracts International, 63(3), 858A. (AAT No. 3047203) annotationSearch Title on Google

Chen, 2002. annotationSearch Title on Google

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. annotationSearch Title on Google

Chen, 2003. annotationSearch Title on Google

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. annotationSearch Title on Google

Chen & Zimmerman, 2007. annotationSearch Title on Google

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.

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. annotationSearch Title on Google

Debowski, Wood, & Bandura, 2001. annotationSearch Title on Google

Level: College   Learning Theory: Social Cognitive Theory  

Guided Exploration and Learning to Search (Research - Quantitative)

Driscoll, M. P. (2004). Self-regulation. In Psychology of learning for instruction (3rd ed., pp. 328-332). Boston, MA: Allyn & Bacon. annotationSearch Title on Google

Driscoll, 2004. annotationSearch Title on Google

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.

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. annotationSearch Title on Google

Ewers & Wood, 1993. annotationSearch Title on Google

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.

Finney, S. J., & Schraw, G. (2003). Self-efficacy beliefs in college statistics courses. Contemporary Educational Psychology, 28, 161-186. annotationSearch Title on Google

Finney & Schraw, 2003. annotationSearch Title on Google

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

Hacker, D. J., Dunlosky, J., & Graesser, A. C. (1998). Metacognition in educational theory and practice. Mahwah, NJ: Lawrence Erlbaum Associates. annotationSearch Title on Google

Hacker, Dunlosky, & Graesser, 1998. annotationSearch Title on Google

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. annotationSearch Title on Google

Hackett & Betz, 1989. annotationSearch Title on Google

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.

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. annotationSearch Title on Google

Hackett, Betz, O’Halloran, & Romac, 1990. annotationSearch Title on Google

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

Hoffman, B., & Spatariu, A. (2008). The influence of self-efficacy and metacognitive prompting on math problem-solving efficiency. Contemporary Educational Psychology, 33, 875-893. annotationSearch Title on Google

Hoffman & Spatariu, 2008. annotationSearch Title on Google

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.

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. annotationSearch Title on Google

Klassen, 2006. annotationSearch Title on Google

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. annotationSearch Title on Google

Lapan, Shaughnessy, & Boggs, 1996. annotationSearch Title on Google

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. annotationSearch Title on Google

Lent, Brown, & Hackett, 1994. annotationSearch Title on Google

Learning Theory: Social Cognitive Theory  

Modeling Self-efficacy, Outcome Expectations, and Choices (Theory)

great visual model

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. annotationSearch Title on Google

Lent, Lopez, & Bieschke, 1991. annotationSearch Title on Google

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

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. annotationSearch Title on Google

Lent, Lopez, Brown, & Gore, 1996. annotationSearch Title on Google

Learning Theory: Social Cognitive Theory  

Sources of Self-Efficacy (Research - Quantitative)

Lin, L., & Zabrucky, K. M. (1998). Calibration of comprehension: Research and implications for education and instruction. Contemporary Educational Psychology, 23, 345-391. annotationSearch Title on Google

Lin & Zabrucky, 1998. annotationSearch Title on Google

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)

Lopez, F., & Lent, R. (1992). Sources of mathematics self-efficacy in high school students. Career Development Quarterly, 41(1), 3-11. annotationSearch Title on Google

Lopez & Lent, 1992. annotationSearch Title on Google

Level: Secondary   Learning Theory: Social Cognitive Theory  

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

Madewell, J., & Shaughnessy, M. F. (2003). An interview with Frank Pajares. Educational Psychology Review, 15 (4), 375-397. annotationSearch Title on Google

Madewell & Shaughnessy, 2003. annotationSearch Title on Google

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)

Martin, J. (2004). Self-regulated learning, social cognitive theory, and agency. Educational Psychologist, 39(2), 135-145. annotationSearch Title on Google

Martin, 2004. annotationSearch Title on Google

Learning Theory: Social Cognitive Theory  

Overview of Social Cognitive Theory (Theory)

Moncur, M. (2007). Henry Ford (1863-1947). In Quotations by author. Retrieved January 2, 2009, from http://www.quotationspage.com/?quotes/?Henry_Ford/ annotationSearch Title on Google

Moncur, 2007. annotationSearch Title on Google

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. annotationSearch Title on Google

O’Brien, Kopala, & Martinez-Pons, 1999. annotationSearch Title on Google

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. (2004). Albert Bandura: Biographical sketch. Retrieved April 7, 2007, from http://www.des.emory.edu/ annotationSearch Title on Google

Pajares, 2004. annotationSearch Title on Google

Learning Theory: Social Cognitive Theory  

Albert Bandura (Theory)

Pajares, F., & Graham, L. (1999). Self-efficacy, motivation constructs, and mathematics performance of entering middle school students. Contemporary Educational Psychology, 24, 124-139. annotationSearch Title on Google

Pajares & Graham, 1999. annotationSearch Title on Google

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., & 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) annotationSearch Title on Google

Pajares & Kranzler, 1995. annotationSearch Title on Google

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. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology, 86 (2), 195-203. annotationSearch Title on Google

Pajares & Miller, 1994. annotationSearch Title on Google

Level: Middle   Learning Theory: Social Cognitive Theory  

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

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. annotationSearch Title on Google

Pajares & Miller, 1997. annotationSearch Title on Google

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).

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. annotationSearch Title on Google

Pajares & Schunk, 2001. annotationSearch Title on Google

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. annotationSearch Title on Google

Pajares & Urdan, 2006. annotationSearch Title on Google

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.

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. annotationSearch Title on Google

Philippou & Christou, 1998. annotationSearch Title on Google

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

Schraw, G. (1998). Promoting general metacognitive awareness. Instructional Science, 26, 113-125. annotationSearch Title on Google

Schraw, 1998. annotationSearch Title on Google

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). Social cognitive theory. In Learning theories: an educational perspective (pp. 83-134). Upper Saddle River, NJ: Pearson Education. annotationSearch Title on Google

Schunk, 2004. annotationSearch Title on Google

Learning Theory: Social Cognitive Theory  

Overview of Social Cognitive Theory (Theory)

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/ annotationSearch Title on Google

Simon, 1999. annotationSearch Title on Google

Learning Theory: Social Cognitive Theory  

Albert Bandura and Epistemology (Theory)

Stone, N. J. (2000). Exploring the relationship between calibration and self-regulated learning. Educational Psychology Review, 12 (4), 437-475. annotationSearch Title on Google

Stone, 2000. annotationSearch Title on Google

Learning Theory: Social Cognitive Theory  

Potential Relationships between Calibration and Self-Regulation (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. annotationSearch Title on Google

Teong, Threlfall, & Monaghan, 2000. annotationSearch Title on Google

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.

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. annotationSearch Title on Google

Usher & Pajares, 2008. annotationSearch Title on Google

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.

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. annotationSearch Title on Google

Zeldin, 2000. annotationSearch Title on Google

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. annotationSearch Title on Google

Zeldin & Pajares, 2000. annotationSearch Title on Google

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

Self-Efficacy of STEM Women (Research - Qualitative)

Zimmerman, B. J., & Schunk, D. H. (1989). Self-regulated learning and academic achievement: theory, research, and practice. New York: Springer-Verlag. annotationSearch Title on Google

Zimmerman & Schunk, 1989. annotationSearch Title on Google

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. annotationSearch Title on Google

Zimmerman, Bandura, & Martinez-Pons, 1992. annotationSearch Title on Google

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.

  Social Constructivism (6 Refs)

Doerr, H. M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41(2), 143-163. annotationSearch Title on Google

Doerr & Zangor, 2000. annotationSearch Title on Google

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.

Driscoll, M. P. (2004). Vygotsky: The social formation of mind. In Psychology of learning for instruction (3rd ed., pp. 245-263). Boston, MA: Allyn & Bacon. annotationSearch Title on Google

Driscoll, 2004. annotationSearch Title on Google

Learning Theory: Social Constructivism  

Vygotsky and Social Constructivism (Theory)

Vygotsky's theoretical framework included (1) a focus on development, (2) a claim that higher mental processes have their origin in social processes, and (3) a belief that mental processes can only be understood in terms of the tools and signs that mediate them. Driscoll's summary of Vygotsky's social constructivist approach to learning includes a description of each of these principles, including some elements of his theory that oppose the assumptions of radical constructivism. Three processes are understood to drive learning: the zone of proximal development, cultural mediation, and internalization. Driscoll suggests that, although Vygotsky was interested in education, his work was banned in Russia for some time and he tended to focus on the processes underlying learning and development. Thus, the promise of his writings for instruction did not begin to surface in education until the 1980s, where it quickly became associated with scaffolding and reciprocal teaching.

Ernest, P. (1996). Varieties of constructivism: A framework for comparison. In L. P. Steffe & P. Nesher (Eds.), Theories of mathematical learning (pp. 335-350). Mahwah, NJ: Lawrence Erlbaum Associates. annotationSearch Title on Google

Ernest, 1996. annotationSearch Title on Google

Learning Theory: Social Constructivism  

Philosophy of Radical Constructivism (Theory)

According to Ernest, the varieties of constructivism can be categorized into four distinct theoretical frameworks: information-processing constructivism, weak (i.e., trivial, exogenous) constructivism, radical constructivism, and social constructivism. Ernest delves into the epistemological and philosophical orientation of each variety of constructivism and even addresses each varieties' stance toward ontology, epistemology, methodology, and pedagogy. The theories are contrasted according to their metaphors for the mind, models of the world, and relative emphasis on the individual and social aspects of learning. Ernest describes himself as a social constructivist.

Gergen, K. J. (1995). Constructivism in education (L. P. Steffe & J. Gale, Eds.). Hillsdale, NJ: Lawrence Erlbaum. annotationSearch Title on Google

Gergen, 1995. annotationSearch Title on Google

Learning Theory: Social Constructivism  

History of Constructivism (Theory)

The exogenous (world centered) and endogenous (mind centered) views of the world, according to Gergen, are fraught with philosophical dilemmas and intellectual problems that are well understood and essentially irresolvable. Instead of arguing for one of the two approaches, Gergen and others claim that social constructivism provides a dialectical view of the world that, in essence, changes the subject when it comes to ontology and epistemology. The three principles of social constructionism are (1) Meaning is context dependent, (2) Meaning in language is achieved through social interdependence, and (3) Language primarily serves communal functions. Gergen goes on to describe several educational implications of the social constructionist stance, including the resulting diffusion of authority, the vitalization of student-teacher and student-student relationships, the generation of meaning through practice, and the breaking of content boundaries.

Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. In T. Carpenter, J. Dossey, &J. Koehler, Classics in mathematics education research (pp. 153-171). Reston, VA: National Council of Teachers of Mathematics. annotationSearch Title on Google

Lampert, 1990. annotationSearch Title on Google

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

Mathematical Discourse in Teaching Exponents (Research - Qualitative)

Schunk, D. H. (2004). Vygotsky's sociocultural theory. In Learning theories: An educational perspective (pp. 291-300). Upper Saddle River, NJ: Pearson Education. annotationSearch Title on Google

Schunk, 2004. annotationSearch Title on Google

Learning Theory: Social Constructivism  

Vygotsky and Social Constructivism (Theory)