Teaching and learning proof across the grades: a K-16 by Despina A. Stylianou, Maria L. Blanton, Eric J. Knuth

By Despina A. Stylianou, Maria L. Blanton, Eric J. Knuth

A Co-Publication of Routledge for the nationwide Council of lecturers of arithmetic (NCTM) lately there was elevated curiosity within the nature and position of facts in arithmetic schooling; with many arithmetic educators advocating that evidence could be a relevant a part of the math schooling of scholars in any respect grade degrees. this crucial new assortment presents that much-needed discussion board for arithmetic educators to articulate a hooked up K-16 "story" of evidence. the sort of tale contains figuring out how the different types of facts, together with the character of argumentation and justification in addition to what counts as facts, evolve chronologically and cognitively and the way curricula and guideline can aid the improvement of scholars’ realizing of facts. jointly those essays tell educators and researchers at varied grade degrees in regards to the instructing and studying of facts at every one point and, therefore, aid develop the layout of additional empirical and theoretical paintings during this region. by way of construction and increasing on latest learn and through permitting a number of voices from the sector to be heard, educating and studying facts around the Grades not just highlights the most principles that experience lately emerged on facts study, but in addition defines an schedule for destiny examine.

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When teaching students to solve systems of linear equations, what it means to add two equations, how adding two equations is different from adding the same quantity to both sides of a single equation, and why it is legitimate mathematically to do so are all questions that do not regularly come up (for other sorts of mathematical questions of justification not typically addressed in algebra classrooms, see Chazan & Yerushalmy, 2003). And, even if a teacher did ask such a question, it is unclear what the nature of a reasonable student response might be to such a query.

Each of these chapters uses a cognitive paradigm as a means to understand the development of student proving competencies as well as the instruction that occurs at a particular level and curricula designed to foster the development of those competencies. The two dominant paradigms in the field, cognitive and social, underlie the design of several of the studies in this volume and provide lenses for interpreting their findings. Yet, in recent years, we have witnessed a growing tendency to study social interaction as complementary to the study of cognitive factors when characterizing mathematical growth.

With the perspective of situations, the presence of methods for solving algebra problems sets up important relationships between teachers and students that demarcate who is responsible for particular classroom work and how they are supposed to go about completing it. html 32 . Daniel Chazan & H. Michael Lueke supposed to teach this valuable knowledge to their students. , of solving equations). , how to solve equations). So, when they show their work, students are expected to show evidence of having used a method, whether it is symbolic or graphical in nature, as opposed to simply showing their answers, or justifying why these steps solve the problem.

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