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Elementary Education
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EDEE 230
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Dominic Manuel
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Chapter 2

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Elementary Education

EDEE 230

Dominic Manuel

Fall

Description

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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