# What Did I Learn?

Now that the school year has ended, our research team has been gathering our data from time spent working with students and analyzing it to answer the question: “what have you learned this year?” More importantly, I wanted to figure out what I have learned that will actually enable us to help kids. After completing a rough draft of our findings, I wish I could tell every teacher about what I experienced, but since I can’t, I’m going to share it here.

First and foremost, children will learn to skip count meaningfully even if they are taught, and they may also learn how if they aren’t. What do I mean by this? Instead of learning, for example, 3, 6, 9 as a memorized sequence, give them items to count that are in sets of three and let them count however they want. We worked with blocks and had students build towers of 3 or 4. As they progress, we can begin to cover the sets so that they have to imagine them and create new ways of counting.

I witnessed one 2nd grade student, Max, learn to skip count by fours and we never once demonstrated the sequence 4, 8, 12. When I started working with him, he would try to count the sets of four by counting them out; first 1, 2, 3, 4, followed by 5, 6, 7, 8, and so on. The problem was that he had no idea how many sets of four he had counted. He figured out that he could use one hand to keep track of how many sets of four he had counted and the other to reuse three fingers repeatedly as he counted by one. Eventually, he would skip count and use his fingers to track how many sets of 3 or 4 he had counted.

Another 2nd grade student I worked with, Naomi, began just as Max did, without being able to track how many sets of 3 she had counted as she counted by one. After six 20 minute sessions with her in a group setting, she had developed her method of counting the number of blocks in towers of three. After mastering counting imaginary rows of three, she eventually decided to hold up a finger for each tower and tap each finger three times as she counted by ones. If we had longer to work with her, I believe she was a short time away from noticing the skip count just like Max.

The reason I am saying that this method is so much more powerful than teaching to skip count, is that the students know when to use it, and if the problem forces them to count further than their memorized skip count, they know to continue to count by ones. I worked with many students that could skip count, but would be stuck where their memorized sequence ended because the memorization had no meaning behind it. If I leave you with one takeaway from this post, it would be don’t teach skip counting, let them learn it on their own.