"I cannot teach anybody anything, I can only make them

think."-- Socrates

Math Reform - It is an improvement!

The Good Old Days Never Were

In 1937 one-half of freshmen in Teacher’s College could not divide 175 by 0.35

In 1942 68% of freshmen at 27 US Universities could not pass the arithmetical/reasoning portion of the entrance exam for the Naval Reserve Officers' Training Corps

These were pre-calculator days when computation was very important and was the main focus of the math curriculum.

In the 1960s and 1970s, 40% of 13 year olds could NOT multiply two fractions and only 17% of them could multiply two fractions given a story problem! Conceptual understanding was even worse than procedural understanding!

Computation was still dominant in the curriculum.

Larry Sowder, San Diego State University

What Research Shows The human brain is malleable. Environmental factors are more

important than genetic factors; this means an enriched environment is necessary to maximize every learner’s potential, starting at birth. (Eric Jenson, Enriching the Brain)

A growing body of evidence in the study of cognition now shows that the vast majority of children are born with the ability to learn anything and that the brain is plastic until much later in life than scientists previously believed…. The brain can acquire new abilities that emerge suddenly and dramatically from a series of small conceptual advances. (John Mighton, The End of Ignorance)

How Children Learn Children construct their own knowledge. The tools people use to build

understanding are our existing ideas. The materials we act on to build understanding may be things we see, hear, or touch. The effort that must be supplied is active and reflective thought. (Van de Walle)

We use the ideas we already have (blue dots) to construct a new idea (red dot), developing in the process a network of connections between ideas. The more ideas used and the more connections made, the better we understand.

What does this mean for Math Class?

✏ Children need to “do” math, not just follow rules with drill and practice.

Goals for Students• Learn to value mathematics• Become confident in their ability to do mathematics• Become mathematical Problem Solvers• Learn to communicate mathematics• Learn to reason mathematically

(NCTM Principles & Standards)

Problem Solving Math Lesson

• Teacher and students solve a simpler problem

• A new problem is presented

• Students work together to solve it

• Students share their work with class

• Teacher helps to summarize and clarify

Why the Problem Solving model?• It places the focus of

the students’ attention on ideas and sense making.

• It develops “mathematical power”.

• It develops the belief in students that they are capable of doing mathematics and that mathematics makes sense.

• It is a lot of fun!

• Knowledge and Understanding

• Thinking• Communication• Application

It covers all the categories of knowledge and skills in the Ontario Curriculum Documents:

What does that look like?

What About Basic Arithmetic?

• Computation is a very important skill.• Students should be able to compute

mentally and on paper.• Estimation and mental calculations are

used daily.• Traditional algorithms are useful, they

should be learned, but only after the concept is understood.

Understanding the Algorithm

• Here are some students who understand the algorithm.

• They have had plenty of opportunities to solve problems in multiple and varied ways.

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Supporting Math at Home

• Include your child in the math you “do”, shopping, budgeting, baking and cooking.

• Avoid saying “I was never good at math”.

• Ask your child about what she or he is learning in math class.

• Use the math kits that are sent home and write in the journals with your child.

• Play math games.