In David Sousa’s book “How The Brain Learns Mathematics,” he cites researchers who have found that number sense is not intrinsic but can be shaped though both formal and informal activities. Sousa lists a number of effective strategies for developing number sense. Here are a few of them:
Meaningful estimates. Helping students practice meaningful estimates goes far beyond, “Guess how many goldfish crackers are in the jar.” In my experience, those kinds of estimates require more than number sense; they tap visual spatial understandings, as well. Estimation jars are often used in lower grades where many kids are unlikely to have sufficient practice with this skill. Early number estimates should involve items and quantities which can easily be counted (certainly less than a hundred) so that kids can improve their ability to estimate. Kids should also be exposed to multiple opportunities for making reasonable estimates. Teachers can create realistic and necessary opportunities for estimation. For instance, kids might estimate how many books are in a reading bin and how many pencils are in a caddy. It’s important for kids to learn early on that estimation is not just another tedious step on worksheets, that estimation is not a hurdle to make math more burdensome. One student recently blew off the estimation portion of his classroom assignment, saying, “It doesn’t matter what I get. Anything is right.” Clearly, estimation was taught in isolation and as a meaningless activity.
Solve problems and consider the reasonableness of the solutions. This strategy sounds reasonable, but for kids with math difficulties, an unreasonable answer can be hard to recognize. The kind of problem where I typically see younger kids struggling is comparing values or quantities. A classic question is: If Kevin is 8 and his sister is 5, how much older is Kevin? The majority of K-2 special needs kids I teach will add those two numbers and feel their answer is reasonable. They have learned to subtract when items are missing, eaten, or given away, but using subtraction to compare is another beast altogether. Some kids learn faster when they start solving this type of problem with pieces of cereal or other food. Using cubes that interlock or stacking blocks is another way to visualize the number comparison problem, helping them “see” how much more one quantity is than another. It can take a LOT of experience for kids with math difficulties to master this process. Simply asking students if their answer is reasonable is ineffective if not preceded by plenty of experience with manipulatives and real-life math problems.
Model the enjoyment of numbers and number patterns. Research studies conclude that the teacher’s attitude “is the most critical factor in establishing a climate for curiosity and enjoyment of mathematics.” For me personally, this statement means that I must watch myself for subtle (and not-so-subtle) signs that math has not been my favorite subject. As I set a goal of making math enjoyable for my students, I am also enjoying it more. I ask myself: If I am short on time, what subject is going to be curtailed? Do I look for opportunities to create and solve math problems? Do I encourage kids to talk to each other during math instruction? Is my math instruction engaging and meaningful? Integrating math into other content areas is a terrific way to make problem solving meaningful. Free Math is another classroom strategy to provide time and resources for those “random” math questions that arise during the course of the day. Dedicate a space where teacher and kids can jot/dictate questions on sticky notes, to be addressed during Free Math time.
Do you have favorite strategies for developing number sense?