Rekenrek - Mental Images

Today we had another lesson using the rekenrek. We talked about making mental images of things we see. For example if you close your eyes and think of an elephant a large gray animal with big ears comes to mind. You can see that image in your mind because you have seen one before. Well in math we want students to also create mental images of numbers. If we say the number 4 to students, they should have a mental image of what that would look like. We use the rekenrek to help with that image.

Today each student had a blank paper divided into four squares. I had 9 rows of our rekenrek covered, so only the top row could be seen and used. I held a paper in front of the rekenrek and pushed 4 beads over to the other side. With all eyes on the rekenrek, I flashed them the beads. They only saw it for 2 seconds before I covered it again. The students next wrote what they saw. It should have been 4 balls. They could have also written the number four. The students next had another chance to see the beads before we check their thinking.
With the beads still hidden, I asked "What did you see?" Bryce raised his hand and said he saw 4 beads. I asked him, "How did you see them?". He said, "I saw two red beads, then two more red beads. I know that two and two more is four."

Next I asked, "Did someone else see something different?". Courtney said she just saw four red beads because she counted them.

Finally I asked Lainey, "What did you see?" Lainey explained that she noticed that not all of the red beads were used. She saw one left on the other side, so she knew that there were only four beads. Each student was correct. They all had the right answer but saw the beads in different ways.

We continued to follow the same routine with the numbers 5, 7,10, 11 and 15. The conversations continued to sound the same, with students seeing the same number but having different mental images of those numbers. With the numbers 11 and 15 we used two rows of beads. Even though you would think the higher numbers would be more difficult the students said it was easy because you don't have to count the first row if you see that all the beads have been moved over, you only have to count how many beads are on the second line. Because you just add the second row with 10 from the first row. Already the students in our class have a clear understanding of numbers and how the rekenrek works. When we finally get around to introducing addition the concept will have deeper meaning since the students will have a deeper understanding of numbers.