Critical thinking, which has long been relegated to the back of the classroom in favor of standardized-testing-friendly rote learning, should be the priority in teaching math. This is the new finding from the National Council of Teachers of Mathematics, which released a report that forcefully advocates an instructional emphasis on reasoning and sense making -- comprehending based on prior knowledge or experience -- in high school.
Focus in High School Mathematics: Reasoning and Sense Making, available in print or electronic form, will have broad implications for the way math is taught. (Go to the NCTM Web site to download PDFs of guides for teachers, administrators, policy makers, and parents.) But how does a classroom teacher apply the NCTM's guidelines? Do the math: Just as with any other academic subject -- think of literary analysis, for example -- mathematics is best taught from the baseline of analytical thinking. But here are some basic tips for laying the groundwork:
- Point out reasoning and sense making as crucial life skills.
- Share examples in which math is integral to making real-world decisions.
- Provide examples of the wide array of mathematically focused careers -- not just the usual suspects but also criminal justice, sports journalism, and graphic design, for example.
How can you help champion this new formula for teaching math? If you teach high school mathematics, consider the influence you have as a highly trained specialist when serving in your school, in your school district, and perhaps beyond as an evangelist for a math curriculum based on critical thinking. In the meantime, within the framework of your current teaching methods, find ways to cultivate higher-order thinking skills in your students:
- Foster a classroom and school atmosphere that supports critical thinking.
- Choose problems, activities, and projects that encourage students to exercise their reasoning and sense-making aptitudes.
- Maintain a focus on helping students develop critical-thinking skills as you plan your instruction.
- Frame lessons, discussions, and tests to encourage students to articulate their reasoning.
- Integrate evaluation of reasoning and sense making into your formative and summative assessments -- and into self-appraisal of your teaching methods.
School and district administrators can apply these suggestions to their own goals, including reminding parents and the community at large that the world is more technologically complex than it was when they studied math in high school and that the typical career is much more likely to require not only competency in statistics and analytics but also problem-solving skills.
As the global marketplace makes economic competition and concern about career prospects far more acute, the NCTM's call for a greater concentration on critical thinking is a timely one. Just run the numbers -- but talk about them, too.