by NCTM President Henry (Hank) Kepner
NCTM Summing Up, December 2009

It’s that time—the time of year when many of us are preparing for major celebrations that include family and friends. As you approach the winter break, reflect with your students on the mathematical knowledge, skills, and problem solving strategies that they have acquired so far this school year.

Questions can spark fruitful discussions with your students: What have I learned in math class this fall?  What can I do now that I couldn’t do in September?  And in what areas have I recognized how math is used outside of the math classroom?

For most of us, we’ve had a little more than three months of classroom time. No two days were the same, yet too often, we marched routinely from lesson to lesson, day to day, without capturing what was happening and where we were going. Now is a good time to pause and help your students recognize and summarize in their own words the big mathematical ideas that they’ve encountered so far this year. Push them to make the connection to the math that they experienced in earlier years. See if they can explain, for example, how they extended ideas and procedures in going from whole numbers to fractions (rational numbers), or—eventually—from whole numbers to polynomials. How did they extend geometric relationships and the corresponding measurement concepts and formulas in moving from two dimensions to three dimensions?

Use this opportunity to help students make decisions about the mathematics that they should use in a wide range of applications or extensions. Have students examine problems taken from earlier in the year on different topics. One of our goals is to develop students’ competency in strategic thinking on new problems—both mathematically based and in context. Show students the importance of formulating the problem so that they can apply their knowledge—and know what knowledge to apply.

Don’t forget to challenge your students in using mathematics outside the classroom as well as within a tight math curriculum. Prepare students to make financial decisions that arise out of school—from estimating and purchasing games or treats, to interpreting sale prices, to budgeting and buying gifts, to determining the costs of purchases involving a loan or a payment plan involving interest. Are we preparing our juniors and seniors to handle the credit card offers that they are already receiving? Financial decision making is a major challenge, and not just at this time of the year. Students can’t start learning early enough!

Are your students learning to interpret data from content areas and the daily media? The current focus on flu vaccinations and the frequency of cancer screening is built on medical data and the likelihood of prevention. This data should be a part of every family’s decision-making process. In the medical field, a major challenge is a doctor’s ability to communicate the research data in a way that the patient is able to use that data in making a significant personal decision.

In addition to finishing a chapter and giving a test, make sure your students are thinking of mathematics in a broader sense. As the holiday break begins, remind them of the importance of mathematics, and give them a piece of valuable advice: Math—don’t leave school without it!