Number lines as a thinking tool?

Do young children intuitively use number lines as a thinking tool? And I don’t mean rote counting…

I have been working with two teams of teachers who are investigating the use of number lines to help young children (ages 4-7) think about proportional reasoning, magnitude, and number relationships. One group of teachers is at a school in Toronto and one team spans two schools in Peterborough. Although the communities are quite different, some astounding similarities have emerged.

To begin, the teams conducted task-based interviews where the teachers asked students to try a math task and sat with the student to observe, and ask follow-up questions. Our goal was to uncover students’ early understandings of number but also to see if they could intuitively use the number line as a thinking tool. Here’s an example of a task in the interview set that comes from Saxe (2010):

Here is a number line. Where would you put the number 7? How do you know?

Interesting question! Intervals are missing, numbers are missing, there’s no beginning or end intervals…. Not a simple question! Six students from each class were interviewed by the teacher with the support of our researcher team; the interviews were videotaped and analyzed as a group. Amazingly VERY young children were thinking about spacing (partitions that would help find the location of 7), they were thinking about the relative location of 7 compared to 4 and 6, and they were using their counting numbers. There’s a lot going on here and we were amazed at how four year olds and slightly older students found the tasks engaging, but also worked with the number lines very very quickly, even though they had only been exposed to fixed number lines posted on the walls in the classroom to support counting. Our observations and findings led us to want to explore the number line further. And we have!

Recently, the two teacher teams held a public research lesson, where they invited guests in to observe students engaging with number lines as thinking tools to explore intervals and conceptions of “half way” (or middle). We have learned a ton from this work, and the observations of colleagues.

Here’s a summary of some of some of what we have learned about working with number lines. This was recorded by the research team but generated by teachers in the study.

These are just SOME of the things we are learning about number lines.
What an exciting process for digging into math learning with young children.

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