Strategies That Support All Learners

Strategies that Support All Learners

· Creating a Positive Learning Environment

· Avoiding Negative Experiences That Increase Anxiety

· Establishing Clear Expectations

· Treating All Students as Equally Likely to Have

Aptitude for Mathematics

· Helping Students Improve Their Ability to Retain

Mathematical Knowledge and Skills

Master 2-1: Strategies that Support all Learners

Procedural Knowledge-skillful use of mathematical rules or

algorithms

Conceptual Knowledge-understanding meaning of

mathematical concepts

Which is it?

To divide 23 candies among four friends, Steve knows

each must receive an equal amount and there may be some left.

To take 23 divided by 4, Steve knows to take 5 x 4 and

subtract the result from 23.

Sara knows when counting, 7 follows 6.

Sara knows 7 represents 7 objects.

Joe knows that to find 25% of a price he can cut

the price in half, then half again to find one-fourth.

Joe knows that to find 25% of a price he can

multiply the price by .25.

Nancy knows that to find the area of a rectangle, she

must find out how much space it covers.

Nancy knows that to find the area of a rectangle, she

must multiply the length times the width.

Master 2-2: Procedural and Conceptual Knowledge

Behaviorism and Constructivism

What Does it Look Like in a Classroom?

Behaviorism

· Behavior can be shaped by reinforcement of drill

and practice.

· Specific skills need to be learned in a fixed order.

· Clear objectives help students and teachers.

· Edward L. Thorndike, B.F. Skinner, Robert Gagne

Constructivism

· Learners actively create or invent (construct) their own

knowledge.

· Students create (construct) new mathematical

knowledge by reflecting on their physical and mental

actions.

· Learning reflects a social process in which children

engage in dialogue and discussion with themselves as

well as others as they develop intellectually.

· William Brownell, Jean Piaget, Jerome Bruner, Zoltan

Dienes

Master 2-3: Behaviorism and Constructivism

How Children Learn: Similarity

of Learning Frameworks and Recommendations for Teachers

• Several characteristics and stages of thinking exist;

Children progress through stages as they mature.

Therefore, teachers should teach to the

developmental characteristics of students.

• Learners are actively involved in the learning process.

Therefore, teachers should actively involve students.

• Learning proceeds from the concrete to abstract.

Therefore, teachers should move learning from

concrete to abstract.

• Learners need opportunities for talking and

communicating their ideas with others.

Therefore, teachers should use communication to

encourage understanding.

Master 2-4: How Children Learn

Examine these staircases:

Describe in words a relationship (formula) involving

the sum of the first 4 counting numbers suggested.

Examine these staircases:

Describe in words a relationship (formula) suggested.

How many counting numbers are involved? What is

their sum?

Examine these staircases:

The sum of the first n counting numbers is:

1 + 2 + 3 + 4 + . . . . + n = ______

Master 2-5: The Staircase Problem