Our Math Inquiry

To begin, we would like to acknowledge that in our FDK classes there is a wide range of abilities due to prior experiences, family background and age of the children – a child who is soon to be 4 can be developmentally very different from the child who is soon to be 6. It is important to keep this varied spectrum of ability in mind when planning math experiences for this age group.

Using Picture Books in Math

During the winter and spring of 2011, our Primary Division participated in a Math Inquiry. We were wondering if using Picture Books in Math would increase Math language in our students. We were supported by our Math Consultant and as a division, were given $2000 to purchase picture books that were rich in opportunity to relate to Math concepts.

We loved the idea of picture books because they fascinate all ages, and can create a starting point from which each child is able to move forward based on their individual, developmental needs.

During the course of our Inquiry, we discovered that the picture books focused and guided the learning. The children were engaged during the reading of the books and eager to explore Math problems and strategies that we drew from the text.

Re-thinking a 3-Part Math Lesson

When we first started our Inquiry, we had intended to use the books to engage the students while still trying to put the parts of a 3-Part Math lesson into place.
However, it didn’t seem to fit. The wide-range of abilities and developmental needs of our students made it difficult to stay true to the 3-Part Math lesson. Our students hadn’t yet developed much of a knowledge base or attack skills for problem-solving. Although highly motivated and quick to learn, many needed a lot of encouragement and scaffolding in order to begin to solve a problem. Shorter attention spans and an ego-centric stage of development made group work and remaining on task difficult for many. So, we started to massage the structure of the 3-Part lesson… and then it was no longer a 3-part lesson.

An Inquiry Format

As we learned from our experience, we began to use valuable pieces from the 3-part math lesson in an inquiry format. We started with good literature related to our play-lead, and then posed a math problem. We used modeling and guided practice when needed. We worked briefly as a whole group at times, but usually in small groups or sometimes with individual students. We always conclude our play period with a Sharing Time where we celebrate our learning, so we used that time to highlight our Math learning for the day. Sometimes, we shared what we noticed and wanted to consolidate, other times we drew on students to talk to their learning and processes. One Math problem usually lasts over several days.

We found that having explicit instruction combined with an inquiry/exploratory component was developmentally appropriate. The children were beginning to learn strategies to solve problems, and choose the tools that satisfied their needs and individual learning styles. Three to five year olds are enthusiastic learners and natural problem solvers and it was exciting to see them tackle problems.

Using Books to Find Out ‘How Many?’

One of the first books we read became our all time favourite for introducing problem solving “How Many Feet In the Bed?” …. We worked together through the book, calculating how many feet were in the bed at one time. Modeling and soliciting from the children, different strategies and tools we could use to answer the question – How many feet are in the bed now?

On another day, we revisited the book briefly and then took a blanket and covered the legs and feet of 3 students. We posed the question, “How many feet are under the blanket?”
How can we find out?
We reviewed some of the strategies we used as we read the book and tried them out. We took particular note of those students who needed to physically lift the blanket and touch the feet of each student as they counted, as well as those students who could quickly calculate the number of feet under a blanket in their heads.
In small groups, we played games with appendages hiding under a blanket giving support to those who needed it and challenging others. Those that could quickly figure out the number of feet were asked to find out how many fingers or toes were hidden from view.

We continued to pose similar, “How many..” questions using books to engage the students in the problems. Here are some photos of different tools the children are using to answer the question, “ How many buttons will you need to gather, if you are building 3 snowmen and each snowman has 3 buttons?” We had read the book Sadie’s Snowman.

These boys made the Snowmen using play dough for an even more concrete representation.

Counting three rows of three buttons on the abacus

This child loves to build so it is appropriate that he chose blocks to represent the snowmen’s buttons. He is just beginning to add so is thinking about 3 plus 3 more.

This girl and her group loved the writing centre so paper and pencil representations came naturally to them. She put the 3 at the top of her paper to remind herself how many snowmen were needed. You can see she corrected the orientation of the numeral which shows her stage of development.

At the beginning, we help the children to find materials that support their learning styles. Some children are very comfortable exploring through paper and pencil, others are more drawn to blocks and manipulatives, and others to play dough. As they gain knowledge, we gradually release more and more of the responsibility to them to choose the right tool for the job. We ask them to consider – Is that the best tool for the job?

By the time we read, “The Mitten”, the children were becoming pros at selecting materials to help themselves solve problems of quantity. We counted how many animals were in the mitten and discussed what we knew that could help us answer the question – This many animals, each with 4 feet… how many feet are in the mitten? The students went off in pairs, small groups, or individually to select their preferred materials for solving the problem. We were surprised when a four year old announced during his calculation that we had all made a mistake. The owl only had 2 feet! We were calculating for 4 feet!

Our Learning!

What has stuck with us through this experience is the positives of using high quality children’s literature to engage the students in mathematical learning. We found then and continue to use rich children’s literature to launch new learning. Texts that capture the student’s interest and imaginations get them excited about the learning and we find that they are more motivated to learn and are more persistent- they keep trying even when things are difficult. We begin the first lesson by reading our chosen text in it’s entirety but then in subsequent lessons only read pertinent parts of the text or make referrals to what has happened.

For some high quality children’s books recommended by Marilyn Burns click on link “Texts for Math” below:
Texts for Math