I've noticed that each year, the incoming freshman class has little or no number sense. They do the math and whatever the answer is, it is right in their minds. I am not bemoaning the job their previous teachers did because of the books they had. They've gotten a whole new program which will work on that but it will be a few years before results start showing but in the mean time I need to work on that now.
Number sense is defined as being fluid and flexible with numbers. It is a skill needed by all students to do well in math because with a strong foundation in number sense, students do better. The ones who struggle with it, have never really developed it.
With an undeveloped number sense, students are unable to develop a strong foundation even in mathematics let alone higher maths. These are the students who struggle when they get to high school, potentially choosing to drop out.
Why be concerned with it? It is something needed in real life to ensure success at what ever job is chosen. With out it, it leaves adults unqualified for many of today's jobs. So what are ways that we can use in our classrooms to help develop number sense.
1. Model different ways to do the computation - This exposes students to ways to solve problems they may not have thought of. One of the methods just might be right one which allows the student to "get it".
2. Encourage mental math because it helps students develop the understanding of numbers and their relationships. At the same time, have the students discuss how they found the answer in their head. Take time to talk about the numerical relationships used.
3. Lead classroom discussions on strategies for solving equations because it helps crystallize their own thinking and consider classmate's approaches. Be sure to write ideas on the board so students see the connection between mathematical thinking and symbolic representation.
4. Encourage more estimation in school because it is used all the time in real life. Note that estimation is not always about rounding. Encourage them to estimate an answer for calculations before completing the math. My students love doing the math before rounding to create their estimate. I'm working on turning that around.
5. Ask students to share their reasoning both for mistakes and for correct results because math needs to make sense to them.
6. Pose questions that have more than one right answer so they can see that not every problem has a single correct answer.
It is important to encourage the development of number sense. Although it should happen in elementary, it does not always work out that way. Integrate it in your classroom to encourage those whose number sense is not as advanced to improve and to fine tune those with a decently developed number sense.
What do you think?