Mathematicians

Students entering third grade are never in exactly the same place in their math learning journey. Their knowledge, understanding, skills and attitudes can differ significantly. The diversity of ideas and background knowledge makes math lessons interesting. No matter where the students are with their development they can still do what mathematicians do, how they think and approach problems.

We followed these big ideas:

Mathematicians work together.
They explain their ideas and thinking.
They listen to the thinking of other mathematicians.
Mathematicians learn from watching, listening to and working with other mathematicians.


This week we explored numbers and patterns to grow our number sense. "Number sense" is a broad term for the way a learner understands and feels numbers. It includes understanding of what number means, more-less and part-whole relationship of numbers, using some numbers (e.g. 5, 10, 100) as anchors, having an idea of the size of numbers in real life situations, and much more. Number sense develops gradually when children explore numbers in variety of ways, with variety of models and tools in many different situations. Having a strong number sense helps to estimate, compute, reason and problem solve in all areas of math.

In our first lesson we shared some different ways to easily to count a set of objects. When the students worked in groups I noted that they used counting by 1-s, 2-s, 3-s, 5-s, 8-s and 10-s. When we later sat together and the students explained their various strategies, we discussed that in the end mathematicians look for the most efficient strategy to find solutions. We agreed that counting by fives and tens was more efficient than counting by eights or threes.

During the following lessons we looked at some dot patterns on dice and dominoes and the mathematicians practiced explaining how they knew how many dots there were without counting.

Pildiallkirja lisamine

Sharing the thinking is certainly easier than listening. We talked that we know someone is listening when they look at the speaker, when they are able to ask for clarification and when they can recognize whether their strategy was similar or different from the speaker's strategy.

These fascinating math exchanges surprised me. The children came up with some combinations I had not noticed. Here is an quick image exercise for you. When you look at the following set quickly (about three seconds) tell how many there are and what subsets helped you to know it?

When I gave this exercise to kids, we ended up with eight different explanations.