Okay, so I’m almost done reading Math Recess by Sunil Singh and Dr. Christopher Brownell. Sunil is one of my recent friends on Twitter, and I’m intrigued by some of his posts. I also read this blog with a slightly different viewpoint about mathematics education. I see both viewpoints, and I remember sharing my doubts with Sunil about whether re-inventing math education was possible. After all, we as educators often teach the way we were taught.
Reading this book has been both eye-opening and a bit depressing because it clearly emphasized how much I don’t remember about the math I learned way back, over 50 years ago when I was in high school. I got up to Algebra 5/Trigonometry but decided not to take Pre-Calculus in my senior year. I figured I didn’t really need higher math when I got to college since I planned to major in early childhood education. As I grappled with the puzzles and the concepts in Math Recess, I realized that even if I received pretty good grades in my high school math classes, I certainly didn’t remember much. It was staircase math, and I was good at remembering and applying formulas to solve problems so I could move on to the next level of math. But once I didn’t use those skills, I forgot them. I believe that’s the problem with math education today. Someone (math experts?) decides what needs to be taught in what grade or what class, and students are then assessed to see if they mastered the concept or not. Then they move on to the next chapter in the curriculum.
As an early childhood teacher, however, I believe that ‘play’ is children’s work. Through hands-on exploration, play, and discussions with their peers, children discover much more than they would if we ‘taught’ it. When I taught first and second graders, I had already spent 15 years teaching preschoolers. Those early years were influential in how I viewed learning especially for math. I’d like to share some examples of how my students taught me about math exploration and discovery, about playing with math.
One of the greatest strategies I learned was from a kindergarten teacher called “Number of the Day.” If it was the 15th day of school, students came up with number sentences that equaled 15 such as 15+0=15 or 14+1=15 or 10+5. When someone suggested that 5+5+5=15, I wrote that number sentence on the board, drew a picture, and then introduced the students to multiplication: 3 groups of 5 or 3×5=15. The students were so excited to realize that they could do multiplication, and from then on, they looked for opportunities to show the number of the day using multiplication: (3×5) +2 =17 or (5×4) -1 = 19, etc. On the 25th day, a student shared that 5×5=25, and that was an opportunity to show the class how to write that with an exponent – five squared = 25. And when students were playing with the magnetic tiles, they suddenly had an “aha” moment: “Mrs. Iwase, now I know why they call it a square number! Because it makes a square!” They then made more squares and wrote those equations in their math journals. It was exciting for these students to share with their classmates. Sometimes, I had kids do “Number of the Day” as an assessment task. They loved it, and I was proud of how much their math confidence and competence grew from this activity.
I loved using literature with math, and I remember reading a book titled, One Cow Moo Moo! It is a cumulative counting story. The boy saw one cow pass by, then two horses, three donkeys, etc. up to ten animals. At the end, we wondered how many animals the boy saw in all and the students got to work in their math journal. Some started drawing the animals, but that took too long, so they started drawing little circles. Others drew tally marks, but they found out that they lost track and had to start over. After most students came up with an answer, they got into groups to compare their responses as well as to share their strategy. One student (R) shared a strategy that was different from anyone else. When we got back to the whole group, we had a discussion about strategies. It was evident that drawing circles or tally marks was not efficient because students found out they had different answers. Finally, I asked R to share. He went up to the board and wrote down the numbers 1-10 in a vertical column. R had discovered that he could make sums of 10: 1+9=10; 2+8=10, etc. Then he just added all the tens and added the leftover 5 to come up with his answer: 55. The other students were so excited and clapped for him after he was done. From then on, ‘making tens’ was a strategy these students used when it made sense to do so. It was more meaningful coming from their classmate than if I had taught it to them.
In our classroom, the students had access to many math manipulatives, and one of our first graders’ favorite time was Math Centers where they could explore any of the different activities and share their learning in their math journal. Because some of our students needed more help with patterning and fine motor coordination, I had a bin of small beads, laces, and pattern cards. Two of our more capable learners (S and J) chose that bin and went to sit on the carpet. I called them over. “I think you need to find something a little more challenging,” I suggested. “But we want to do beads,” they said. As we looked at each other, neither saying a word, J came up with a suggestion: “I know; what if we make it challenging?” I agreed, but I kept my eye on them as I worked with small groups. I saw them stringing their own beads in a pattern, then when they were done, they started to write in their math journal. When they each went over to get a calculator. I was intrigued. Finally, they came to show me what they had done. They each had made their own repeating pattern of 7 beads then counted out how many times the pattern repeated. They had started to add up how many beads they used in all by doing repeated addition but realized they could use the calculator to do a multiplication problem instead. They checked their answer then counted the beads to make sure their answer was correct. As I reviewed their entry in their math journal, I was contemplating what to say to them, but J beat me to it. “Well, Mrs. Iwase. Do you think this was challenging enough?” he asked me. I looked at the two beaming students and said, “Definitely!” and gave them each a high five. I had them share their activity with the whole group, and needless to say, that became a favorite activity with their classmates.
I share these stories because even after all these years, I remember the excitement of my students for these kinds of math activities. I learned that math discussions and playing with math really helped my students to learn concepts and make connections they would not have made if we had just stuck to the math curriculum and the grade level standards.
On page 208 of Math Recess, the authors share what is possible in math education: “We see mathematics as fun, and we could have a whole K-12 curriculum in which it is fun. As we have said explicitly and implicitly many times in this book, play and fun can and should be rigorous! The best word that elevates learning and play to that rigorous level is explore. Kids need to explore mathematics, and we, the math educators, have to explore what they get to explore. This is a tremendous but rewarding responsibility.”
Educators, are you up to the challenge to get our students to explore math?