A friend asked me if I wanted to learn to crochet with her. I felt pretty confident about it because I used to crochet when I was a kid. As I was thinking about learning something new, I was brought back to Dan Meyer and Bethany Lockhart Johnson on the Math Teacher Lounge podcast. They asked their guests, “What is something, outside of math, where you are developing fluency?” in their last season focused on fluency. I loved listening to what people were doing in their non-professional lives.
My friend and I signed up for an art club that offers lots of different types of kits from which to choose. We picked an afghan with 30 squares of different stitches. Each month the company sends you the materials to make 3 squares and a video with instructions to learn the stitches. We started to learn the first square together, listening to the video, learning how to hold the hook and the yarn. The first stitch is a single crochet which is the only stitch I have ever known so I thought I was golden. Although I found it easier than my friend, as I continued to complete the square I found that my rows were gradually getting shorter. Each row wasn’t quite the same length. I finished it up and moved on to the second square, carefully listening to the directions for the double crochet stitch. This block was not a square either. I easily learned the stitch but couldn’t figure out why mine weren’t coming out square. My friend was having the same trouble. Together, we learned the third pattern which was a combination of the first two stitches. We loved learning this pattern but still came out with an oddly shaped rectangle. We decided to take a trip to focus on our crocheting. I know, there was no end to the teasing about our crocheting retreat.
We spent 2 days focusing on watching the videos, rewatching and slowing them down, and counting the stitches. We realized that we needed to pay closer to the details of the whole block rather than just learning the stitches and then plugging along. As we got more cognizant of the bigger picture, we got more confident in the details. We learned that we needed to have 25 stitches on each side of each block so that we can eventually crochet them together. This helped us to stop concentrating on the stitches and to look at the overall size where we started to count our stitches after every row. After finishing my fifth block, I decided to go back and do block 1 and 2 again. I was able to pay attention to the row counts instead of the stitch and the block was the right size. Neither of those two blocks are perfect but each block is getting better and better.
All of this to say that I started to think about learning something new and how this learning curve gave me a fresher perspective on student learning. Students need to focus on so many things when they are learning something entirely new. I needed practice with the stitches to be able to make the sizes uniform. Like learning multi-step processes, students need to be fluent with the operations to be able to see the big picture. Does the answer make sense? Is the process the same every time? We need to give students time to develop fluency. As I got better at the stitches I could see the big picture. I wanted to go back and figure out what I was doing wrong. I was motivated by my own discoveries as I developed fluency with more experience. Students can also be motivated by their own misunderstandings if they are given time to grapple with new information. We often rush through teaching topics, giving students direct instruction, so we can cover all of our standards. We have a whole year to teach our standards and sometimes students need more time than others to develop their understanding of concepts.
Consider a student in September compared to their future selves in June. I would hope this student would have a greater understanding of many concepts taught in prior years and early in the year that would allow them to develop a deeper understanding of grade level content. Giving students a chance to demonstrate their learning, over the course of the year, on concepts that aren’t fully developed in their minds, is giving students the best chance at building their afghan so that it fits together in the end.