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Jim RahnJim RahnLL Teach, Inc.LL Teach, Inc.
Teachers need several different kinds of
mathematical knowledge— knowledge about the whole domain; deep, flexible knowledge about curriculum goals and
about the important ideas that are central to their grade level;
knowledge about the challenges students are likely to encounter in learning these ideas;
knowledge about how the ideas can be represented to teach them effectively; and
knowledge about how students' understanding can be assessed.
Mathematical Knowledge
This knowledge helps teachers make
curricular judgments, respond to students' questions, and look ahead to where concepts are leading and
plan accordingly.
Teachers need to understand the big ideas of
mathematics and be able to represent mathematics as a coherent and connected enterprise.
Their decisions and their actions in the classroom—all of which affect how well their students learn mathematics—should be based on this knowledge.
(Principles and Standards for School Mathematics. Reston, VA: NCTM, 2000, p. 17)
What is a Big Idea in mathematics?
A Big Idea is a statement of an idea that is
central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole.
DEFINITION:
is a Statement
Example of a Big Idea
Any number, measure, numerical expression, algebraic expression, or equation can be
represented in an infinite number of ways that have the same value.
A Big Idea
is an idea central to the learning of
mathematicsAny number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.
This statement is describing the big idea of equivalence.
A Big Idea
links numerous mathematics understandings
into a coherent whole.Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.
A Big Idea
Big Ideas should be the foundation for one’s
mathematics content knowledge, for one’s teaching practices, and for the mathematics curriculum.
Grounding one’s mathematics content knowledge on a relatively few Big Ideas establishes a robust understanding of mathematics.
Because Big Ideas have connections to many other ideas, understanding Big Ideas develops a deep understanding of mathematics.
Why are Big Ideas Important?
When one understands Big Ideas,
mathematics is no longer seen as a set of disconnected concepts, skills, and facts.
Rather, mathematics becomes a coherent set of ideas.
is motivating. promotes more understanding. promotes memory. influences beliefs. promotes the development of autonomous
learners. enhances transfer. reduces the amount that must be remembered.
(Lambdin, 2003).
Understanding:
As teachers understand the Big Ideas of
mathematics they are able to translate that to their teaching practices by consistently connecting new ideas to Big Ideas and by reinforcing Big Ideas throughout teaching
(Ma 1999).
Effective teachers know how Big Ideas connect
topics across grades; they know the concepts and skills developed at each grade and how those connect to previous and subsequent grades.
Big Ideas are important in building and using
curricula. The Curriculum Principle from the Principles and Standards for School Mathematics (NCTM, 2000) gives three attributes of a powerful curriculum.
1) A mathematics curriculum should be coherent. 2) A mathematics curriculum should focus on
important mathematics. 3) A mathematics curriculum should be well
articulated across the grades.
The New Jersey State Standards in
Algebra I, Geometry, and Algebra II have identified the Big ideas for each subject.
Study these Big Ideas in your subject area.
Big Ideas
Turn to Chapter 1 in Discovering Geometry
Turn to Page 27 in the Teacher’s Edition. Read the overview of the chapter.
Describe the Big Idea of chapter 1
Find the Big Idea
Turn to Chapter 1 in Discovering Advanced
Algebra
Turn to Page ?? in the Teacher’s Edition. Read the overview of the chapter.
Describe the Big Idea of chapter 1
Find the Big Idea
Divide into several groups. Study each chapter in your textbook. Describe and record the Big Idea is for each
chapter. Remember a Big Idea
Is a Statement Is an idea central to the learning of mathematics That links numerous mathematics understandings
into a coherent whole. Be Prepared to Share Your Big Idea Statement for
each chapter.
Find the Big Idea
