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EDEE 230 (7)
Chapter 2

Chapter 2

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Elementary Education
EDEE 230
Dominic Manuel

Chapter 2: Exploring What It Means to Do Mathematics  What Does It Mean to Do Mathematics?  doing mathematics = generating strategies for solving problems, applying those approaches, seeing if they lead to solutions, checking to see if your answers make sense  doing mathematics in classroom should model doing mathematics in the real world  math = science of concepts & processes with a pattern of regularity & a logical order  discovering real-world relationships represented by linear graphs more scientific & valuable than creating graph from equation  doing math takes time & effort  knowing relationships & patterns helps students understand what they’re doing  increases accuracy & retention  A Classroom Environment for Doing Mathematics  higher-level thinking words: explore, justify, solve, construct, verify, develop, etc  lower-level thinking words: listen, copy, memorize, etc.  these words don’t prepare students for real act of doing mathematics  math requires effort  teachers pose problems so that students actively engage to come up with solutions  “when a teacher succeeds in setting up a classroom in which students feel obligated to listen to one another, to make their own contributions clear and comprehensible, and to provide evidence for their claims, that teacher has set in place a powerful context for student learning”  4 features of a productive classroom culture for math  ideas are the currency of the classroom  help others learn  students have autonomy with respect to methods used to solve problems  there is more than one way to come to a solution  the classroom culture exhibits an appreciation for mistakes as opportunities to learn  the authority for reasonability & correctness lies in the logic & structure of the subject, rather than in the social status of the participants  correctness depends on mathematical sense  An Invitation to Do Mathematics  using technology allows younger students who can’t do math in their heads participate & allows students to use bigger numbers  should decide if your solution is correct, and articulate why you did it that way  real problem solving  use multiple strategies  can make problem solutions visual, or mimic in real life  having an answer readily available through book or teacher says to children, “your job is to find the correct answer the teacher already has”  in the real world  no teachers or solution books  doing math includes deciding if an answer is correct & being able to justify your reasoning to others  What Does It Mean to Learn Mathematics?  experiences in classrooms should maximize learning opportunities for students  constructivism: children are the creators of their own learning  cognitive schema: integrated networks; product of constructing knowledge & tools with which additional new knowledge can be constructed; rearranged, added to or modified as learning occurs  assimilation: changing a schema when a new concept “fits” prior knowledge, so new information expands existing network  accommodation: changing a schema when a new concept doesn’t “fit” prior knowledge, so brain revamps or replaces existing schema  reflective thought: people modify existing schemas to incorporate new ideas  tools used to build understanding = existing ideas & knowledge  learning requires active thinking  you can pour knowledge into a student but if they aren’t active learners, they won’t construct knowledge to learn it  learners vary with number of & nature of connections  also vary in what ideas will make connections  sociocultural theory of learning  mental processes exist between & among people in social learning settings; from these social setting learner moves idea into own psychological realm  way the student internalizes information depend on if it’s in zone of proximal development (ZPD)
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