# Thinking Boards - Representing Mathematical Thinking

Manipulatives can be powerful tools to support sense making, mathematical thinking and reasoning when they are used as tools to support the processes rather than as adjuncts to blindly following a taught procedure to arrive at an answer.

As is common in mathematics education, the research suggests that it is not just what we use that will make a difference to our children's learning but how we use it...

Here are 3 SUGGESTIONS FOR DEVELOPING YOUR USE OF MANIPULATIVES SO THAT CHILDREN SEE THEM AS **TOOLS AND NOT CRUTCHES**:

The best way to use TOOLS is alongside a Frayer Model THINKING BOARD. Rather than experiencing mathematics as the acquisition of isolated facts and procedures and MANY CHILDREN DO (I’ve seen the worksheets and Pinterest ready ideas that are just really glorified sums on lollypop sticks!) a **THINKING BOARD ** will help children to construct mathematical **MEANING**.

This is **EQUITABLE** practice that acknowledges the involvement of ALL children in **MAKING SENSE** of their mathematical learning within classroom communities that are respectful of difference (NCTM, 2000).

This approach is built on the thesis that children come to school with a great deal of intuitive and informal mathematical knowledge which serves as the basis for developing more formal understanding (Carpenter et al., 1999). It is NOT a prescriptive pedagogy or an acquirable teaching technique. It is a principled approach to teaching mathematics which recognises mathematics learning as a **sense - making** activity.

Through attending to the structure of the problems in this way, children engage with important mathematical ideas and develop basic concepts of addition, subtraction, multiplication and division. They can then build on intuitive mathematical knowledge and construct concepts of place value and multi-digit computational procedures.

Part of The Thinking Board is giving children opportunities to use their own Mathematical Graphics (Carruthers & Worthington, 2006) and mathematics notation. For me, it was a **huge cultural shift** giving children the freedom to work out and communicate their emerging mathematical findings for themselves. "From this perspective, children use tools such as pens and paper because they need these to help them think through the process of their problem, rather than to simply record what they have calculated mentally. I now always have both large and small pieces of blank paper out for children to explore numbers in their own ways graphically, with any signs, tallies, drawings or numerals using oversized pens, biros and pencils."

Rather than mathematics belonging exclusively to the policy makers, curriculum writers and adults, **CHILDREN **should have some ownership of **THEIR MATHEMATICS** so that they develop agency and confidence, and enjoy and understand mathematics at a deep level.

**I’d love to hear your thoughts. Do you use THINKING BOARDS? How do you use them? Which ideas resonate with you? What do you disagree with? All views are welcome - post in the comments. Maths IS Visual. Let’s teach it that way.**

**Thank you for all you do to support your children's number journey. Thank you for watching and listening.**

**Love, Janey x**

**Here are some additional links/ reading that might inform your thinking further:**

Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction

Thank you so much for this site and this post. I’m learning more and more about number sense routines. I’ve been using them with my kindergarteners over the past five years, and it’s made the most significant difference in their mathematical growth. I didn’t know the research behind the “thinking boards,” so thank you again. I’m going to implement this tool immediately. I can’t wait to see where this takes our learning.