It was a pleasure speaking to you about Raising Mathematical Thinkers. You CAN raise a mathematical thinker. Remember—be intentional! I pulled together resources we discussed in the workshop to equip you to raise mathematical thinkers.

## Who is Louis Benezet and why should I care what he thinks?

Louis Benezet was a superintendent of schools in New England in the 1930’s and recognized that teachers were being asked to add more subjects to the curriculum and school children were being asked to memorize facts without having any practice in reasoning and communication skills.

So, he decided to remove formal math instruction from the first six grades and instead focus on his new “3 R’s—read, reason, and recite.” Five classrooms in his district followed this new method. Teachers did not teach the students how to solve problems on paper. Instead, they focused on discussing math the students encountered during their day and reading and discussing a wide variety of subjects.

You can read Louis Benezet’s three part series about his new method of teaching and the amazing results he saw. The children raised under the new method excelled far better than their peers.

## 10 principles of raising mathematical thinkers

**1. Be excited about math!**

Overcome any fear or apprehension of math and find something interesting. Check out this list of books about math to find one that interests you.

This hexaflexagon video sparked an interest for us that encouraged my daughter to say, “Mom, I’m a hexaflexagon expert!”

**2. Limit electronic devices and workbooks**

Do not rely solely on electronic media and workbooks for math learning. Encourage your child to explore, read, and narrate.

**3. Learn from errors**

Create an atmosphere in which wrong answers are viewed as a learning opportunity and where children are encouraged to take intellectual risks. ~ Jane Healy

This parallelogram video was a good opportunity for my daughters to see their dad questioning a theory and see that it is okay to be wrong and learn something new.

**4. Find learning opportunities**

Find ways throughout your day to teach a new math concept or reinforce one already learned. There are five math skills kids use on a regular basis. Read what they are and how you can help them master these skills throughout your day.

**5. Encourage questions**

Read about why you should ask questions. Includes book suggestions to help you learn how to ask questions.

Learn how to incorporate six types of Socratic questions to help your student learn to think mathematically.

**6. Require narration**

We encourage our children to narrate all other school subjects. Math should be no exception. Read more about how to evaluate student learning through narration. You can also read about using a narration jar or narration cube.

An excellent method of narration for mathematics is to have an older student teach a younger student or you. This is also a great way to encourage family bonding and involvement.

**7. Emphasize mental work**

Read why math strategies are important and how to incorporate them into your child’s learning.

One strategy for solving problems mentally is to think in terms of fives and tens. The Six Tens card deck was designed to help children visually see sums of ten in groups of five. This video explains a little about the deck. The Six Tens card deck is sold with the Math Facts Game Set.

*Level Thinking*lays out a number of games you can play on the number balance to practice mental math skills and develop math strategies.

**8. Emphasize the process, not the answer**

Getting the correct answer for a math problem is important, but understanding the process and learning new strategies is more important to your student’s mathematical understanding and thinking than solving the problem correctly. If your student understands the process, he will be able to solve the problem correctly in the future.

Use Socratic questions to guide your student to an answer when a problem is a little beyond his ability.

**9. Focus on mastery, not completion**

If you use a curriculum, it’s okay to pause to explore a lesson in greater detail. Allow your child to spend as much time as needed on a particular concept. Math is like a tower of blocks. It will be much more stable if your child masters each block than if he is missing a block or two.

**10. Use math language**

Math is a foreign language. Remember Jane Healy says, “Math is a science of relationships using numerical symbols to describe fundamental truths about our universe.” The numerical symbols are the foreign language our children must learn. Help your children learn the language of math by requiring them to answer a math problem in a complete sentence and by including math language in your daily conversations. Here is a list of mathematical terms to include in your daily conversations.

## 7 areas of study to include in your mathematics program

**1. Spatial Skills**

Dr. Gwen Dewar defines spatial thinking as “what we do when we visualize shapes in our ‘mind’s eye.’” It is our ability to perceive where we or other objects are relative to their given space.

Read more about how to improve spatial skills through games and manipulatives.

**2. Patterns**

Jane Healy believes that patterns are the key to intelligence.

**3. Critical Thinking**

Critical thinking can be defined as a disciplined manner of thought that a person uses to assess the validity of something: a statement, news story, argument, research, etc. (quotation from Robert Ennis, and paraphrase of Barry Beyer)

Read more about why critical thinking skills are important and how to develop them.

**4. Number Theory and Operations**

You can use games to build number awareness and practice math facts. Math games can breathe fresh air into your math program.

See a list of games to build number awareness and practice math facts.

**5. Geometry**

Elementary school is a perfect time to introduce geometry concepts. During the elementary school years, students learn to visualize shapes and how they relate. “A good mathematician must be good at visualization. Almost all problems have a geometric interpretation, and being able to visualize and manipulate geometric images in your head can vastly improve your ability to solve mathematical problems.”

Here is a list of geometry games and activities for elementary school.

**6. Estimation & Measurement**

The ability to estimate and measure accurately is beneficial in many professions including sewing and decorating, carpentry-related professions, baking, purchasing, and in everyday life situations.

Here is a list of estimation and measurement activities.

**7. Math Literature**

Reading living math books lays a great foundation for hearing mathematical language. Read at least one book of math literature each week. There are so many available. When looking for books for math literature, try to find ones in which you learn math concepts or terms without being “taught.”

Here is a list of math books listed by age.

**Implementing the 7 areas of study**

You can supplement any math program with these principles by choosing one area of focus a few days a week or this could be a stand alone curriculum for grades 1-5 by choosing one area of focus each day.

**Download a one page handout summarizing how to raise mathematical thinkers. You may also be interested in purchasing the workshop to listen to again.**