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Emphasize the process over the product
For as long as I can remember, math was about finding the right answer. Some people even say that they like math because there is a right answer and a wrong answer. That is changing. With standards that emphasize understanding over rote memorization of procedures and increasing calls for balancing content with process, math instruction is beginning to look different. Students need opportunities to see that while, yes, there might be only one right answer, there are many approaches to solving the problem. Even if the problem is as simple as finding the sum of 6 + 7.
- I know that 6 + 6 equals 12, so 6 + 7 is just one more, or 13.
- I decomposed the 6 into 3 and 3. I used one of the 3s with the 7 to make 10, and then added the other 3 for 13.
- Seven and seven is 14 and one less is 13.
- I put 7 in my head and counted on 6 more using my fingers.
I recently taught a lesson in a 1st grade classroom, and I knew some kiddos would know the solution as soon as we finished reading the problem. So before I began I made them promise to keep their solutions in their heads because the really “fun” part of the lesson was discussing all the different ways we could solve the problem and how we could communicate our mathematical thinking. Just look at all the wonderful thinking we captured from our discussions!
Give students think time
Face it, we don’t all process at the same speed. It’s time to think about the routines in our classrooms and reflect on what we are rewarding, speed or depth. Often, we ask students questions, hands fly up, and we call on the same five hands every time. Build think time into your routines. I’m a big fan of Sherry’s Parrish’s number talks. When I began using them in my classroom, I adopted the thumb-to-chest signal from the videos in the book for children to indicate they were ready with their answer. No hands shooting up in the air and waving around, because how distracting is that if you’re trying to think? I soon realized that I liked the signal so much that I began using it all the time in place of raised hands. It is a subtle shift that makes a big difference to students who need a little more time. It is also an expectation that I’m going to wait until I see “thumbs” from most all students before I call on anyone, and that I’m more interested in how you got your answer than the actual answer itself.
Quit timing students
There is just so much research to indicate that timed tests are the beginning of math anxiety for large numbers of students and that the effects are long-term. This is a harmful practice that needs to be stopped. We would never put a reading passage in front of students, time them for a minute, and put big red x’s on any words they didn’t have time to read, so why in the world do we still do it in math? Do we want students to have automaticity with their basic facts? Of course we do! The difference is how we achieve automaticity, and it’s not from rote memorization and timed tests. Students learn their facts through reasoning strategies and they develop automaticity through practice with games. Be mindful of games like Around the World that not only emphasize speed, but do it in a very public way. Be sure to check out the links in this post, because several of them contain freebies that you can download and use in your classroom. But here’s one more little idea that requires nothing more than a deck of playing cards. Remove the Jacks, Queens, and Kings and use the Aces as 1s. Students turn over two cards, add the numbers, tell the sum, and explain their solutions. The player with the greater sum takes the cards. If both sums are the same, the cards remain on the table and are taken by the winner of the next hand. This game works for multiplication as well, of course.