Manipulatives as Thinking Tools

As the school year winds down, at the AIMS Center we too are wrapping up our work with students.  The tasks we asked second and third graders to engage in this year had students working with various manipulatives (cubes, blocks, bags, strips, etc). This made me think about Math Practice 5: Use appropriate tools strategically.  When I was teaching second grade I would drag out the tub of tens and ones blocks, and model the concept of double-digit addition and subtraction with my students. I remember trying to get my students to copy exactly what I was doing with my tens and ones blocks – build a number, build another number, and finally put them together grouping all the ones into sticks of tens. Alongside what we were doing I tried to show how the algorithm represented what we were doing with the blocks. We would use the manipulative a few times, put them away, and then go straight to the practice page in the textbook that had twenty problems for students to practice the algorithm. How did I feel after those lessons? Frustrated! I was doing all the work, I had a few students that would be able to complete the lesson but most of them would just follow along blindly without any understanding.  I didn’t know what else to do.

The tasks we have had students engage in this year have had them use manipulatives in a purposeful way that allows students to do the heavy lifting… . . i.e. “productive struggle”.  

In the towers tasks, we had students build a certain number of towers and with “n” number of cubes in each and then bring them back to their partner who hides them and asks how many blocks they brought back.

In the subtraction task, we had students count out a number of blocks, cover them with a cloth, and then reach under, take out a certain amount, put them in a cup and think about how many blocks are left underneath.

In the fraction task, students pretend a strip of paper is a candy bar and are asked to share it among 3 friends, 5 friends, etc. At first, they work to cut the strip into the requested number of pieces, then they are asked to cut what one person’s share would look like, and then test it to see if it is the right size.  

In all these tasks students are given material to work with, then they are asked to think about the material without it being in front of them. This requires students to reflect on previous experiences and operate on material mentally. This is a crucial step in having a concept become abstract to students. Were the students engaged in these tasks? Yes! Were they doing the heavy lifting? Definitely!

With our work this year we have seen Math Practice 5 in action and I truly understand what it means for students to use appropriate tools strategically.  How have your students used manipulatives strategically? I would love to hear your thoughts!

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