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Cognitive Science and Mathematics Education
This volume is a result of mathematicians, cognitive scientists, mathematics educators, and classroom teachers combining their efforts to help address issues of importance to classroom instruction in mathematics. In so doing, the contributors provide a general introduction to fundamental ideas in cognitive science, plus an overview of cognitive theory and its direct implications for mathematics education. A practical, no-nonsense attempt to bring recent research within reach for practicing teachers, this book also raises many issues for cognitive researchers to consider.
310 pages, Paperback
First published May 1, 1987
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Displaying 1 - 2 of 2 reviews
March 13, 2018
Yes! It's amazing how the field of LEARNING and the field of TEACHING are so independent of each other. Within mathematics, this book attempts to bridge the two by getting inputs from all constituents, from math teachers, math educators, mathematicians, and cognitive scientists. As a math teacher, I found much of the information highly interesting, but less practical than I expected.
June 11, 2022
While I have skimmed the entire book, I deeply read chapter 8, "What's all the fuss about metacognition?", and that is the focus of my review. Schoenfeld addresses the teacher perspective, that metacognition is a buzzword that needs a clearer definition and an implementation path for the mathematics classroom. The problem, from the learner perspective, is that our learners choose a plan for problem solving and end up getting lost in the process, chasing wild geese. The author's solution is metacognition, that a good learner steps back to see if the plan is fruitful and changes course as needed.
What I found useful? Schoenfeld provides a good working definition of metacognition, good examples of problems that demand it and some techniques for teaching it in the mathematics classroom.
Where I found it ran short? It is a dated book that once read should be augmented with further reading (note: I provided some examples below.) The author's thinking process possibly contains microaggressions that I wouldn't have expected to be modeled in a book about metacognition. The techniques are not comprehensive (note: I provided further research-based techniques that I have found useful for teaching metacognition in the mathematics classroom below.) I wish there was a reference of videos that we could watch that demonstrate learners with and without metacognition.
Schoenfeld provides a good definition of metacognition for teachers. Metacognition is defined as your knowledge about your own thought processes and how well you are able to describe and self-regulate your problem solving actions. It includes the beliefs that the learners bring to the mathematics classroom that can shape and affect their abilities as mathematicians.
Schoenfeld provides useful problems that demonstrate where metacognition, or lack of, comes into play. He contrasts the route that a successful mathematician takes to the mathematician that gets lost in a poor approach with onerous calculations. This is useful to any mathematics teacher. I have tried these problems with learners, and the author is spot on with how we can see metacognition in play while watching these problems being solved by our learners.
However, the wording, as Schoenfeld steps through these problems, contains possible microaggressions, calling his learners' approaches "foibles," "half the students did as I hoped," "they were behind schedule and scrambling to finish the test," "disastrous consequences." I would have thought a book on metacognition would have demonstrated the author as a model teacher, providing readers with a more prescriptive response as the learners' challenges were surfaced.
The author provides some good techniques to teach metacognition in the mathematics classroom. A learner's metacognition can only be improved if they are convinced of its importance. Improvement is facilitated through watching and critiquing others performance, from peers to the teachers themselves acting as a role model for metacognitive behavior. Metacognition is also built up through whole class and group discussions with the teacher's guidance. Included is the concept of using videos of others solving problems (note: I surprisingly could not find any relevant youtube videos but did find videos like "The Broken Escalator" and Disney's "Piper" where learners can see the problem solving process in action.)
Where I felt the techniques to improve metacognition fell short? The word critiquing never sits well with me - I would prefer to guide the learners to deliberate, comparing and contrasting what works and what doesn't work with each others' approach. This section could have covered the importance to metacognition of teaching: 1) the Polya Method, "How to Solve It!," 2) how we teach heuristics to help our learners justify their approaches (i.e. not just mentioning heuristics), 3) how the understand stage can be used to help learners setup their monitoring processes, 4) examples of questions that help build metacognition and 5) the importance that deliberate practice and looking back at our work has on building metacognition.
Do definitely read this book - but augment it, with readings from Charlotte Mason, Liljedah's "Building a Thinking Classroom," Polya's "How to Solve It!," Ericsson's "The Role of Deliberate Practice" and Chapin's "Using Math Talk to Help Student's Learn."
Hope this is helpful!
What I found useful? Schoenfeld provides a good working definition of metacognition, good examples of problems that demand it and some techniques for teaching it in the mathematics classroom.
Where I found it ran short? It is a dated book that once read should be augmented with further reading (note: I provided some examples below.) The author's thinking process possibly contains microaggressions that I wouldn't have expected to be modeled in a book about metacognition. The techniques are not comprehensive (note: I provided further research-based techniques that I have found useful for teaching metacognition in the mathematics classroom below.) I wish there was a reference of videos that we could watch that demonstrate learners with and without metacognition.
Schoenfeld provides a good definition of metacognition for teachers. Metacognition is defined as your knowledge about your own thought processes and how well you are able to describe and self-regulate your problem solving actions. It includes the beliefs that the learners bring to the mathematics classroom that can shape and affect their abilities as mathematicians.
Schoenfeld provides useful problems that demonstrate where metacognition, or lack of, comes into play. He contrasts the route that a successful mathematician takes to the mathematician that gets lost in a poor approach with onerous calculations. This is useful to any mathematics teacher. I have tried these problems with learners, and the author is spot on with how we can see metacognition in play while watching these problems being solved by our learners.
However, the wording, as Schoenfeld steps through these problems, contains possible microaggressions, calling his learners' approaches "foibles," "half the students did as I hoped," "they were behind schedule and scrambling to finish the test," "disastrous consequences." I would have thought a book on metacognition would have demonstrated the author as a model teacher, providing readers with a more prescriptive response as the learners' challenges were surfaced.
The author provides some good techniques to teach metacognition in the mathematics classroom. A learner's metacognition can only be improved if they are convinced of its importance. Improvement is facilitated through watching and critiquing others performance, from peers to the teachers themselves acting as a role model for metacognitive behavior. Metacognition is also built up through whole class and group discussions with the teacher's guidance. Included is the concept of using videos of others solving problems (note: I surprisingly could not find any relevant youtube videos but did find videos like "The Broken Escalator" and Disney's "Piper" where learners can see the problem solving process in action.)
Where I felt the techniques to improve metacognition fell short? The word critiquing never sits well with me - I would prefer to guide the learners to deliberate, comparing and contrasting what works and what doesn't work with each others' approach. This section could have covered the importance to metacognition of teaching: 1) the Polya Method, "How to Solve It!," 2) how we teach heuristics to help our learners justify their approaches (i.e. not just mentioning heuristics), 3) how the understand stage can be used to help learners setup their monitoring processes, 4) examples of questions that help build metacognition and 5) the importance that deliberate practice and looking back at our work has on building metacognition.
Do definitely read this book - but augment it, with readings from Charlotte Mason, Liljedah's "Building a Thinking Classroom," Polya's "How to Solve It!," Ericsson's "The Role of Deliberate Practice" and Chapin's "Using Math Talk to Help Student's Learn."
Hope this is helpful!
Displaying 1 - 2 of 2 reviews