How does math encourage higher-level thinking?

Math can be a challenge for some students. Struggling high school and middle school math students especially might grumble about how they’ll never use certain math concepts in the real world. However, math encourages higher-level thinking, which can include attention to detail, identifying patterns and making connections—all key to critical thinking and creativity.
As students learn math, they practice these skills that enhance their emotional learning and that they can apply to real life.
Promoting logic and application
Higher levels of thinking involve using analysis to support logical reasoning. Here, our brains evaluate and compare solutions, then eventually form new ideas based on the ideas and concepts we’ve already mastered.
Thinking skills such as creating, analyzing and evaluating are referred to in the upper levels of Bloom’s Taxonomy. Named after researcher Benjamin Bloom, whose team developed this in the 1950s, this model describes six levels of thinking, often depicted as a pyramid.
Skills such as remembering, understanding and applying are the foundation of the pyramid, making them highly significant. These skills involve remembering information, understanding its meaning, then applying this existing knowledge in a new way.
Many basic math activities naturally comprise these foundational levels. When we teach students how to memorize multiplication tables, for example, we lay the foundation for more advanced math lessons that involve multiplying fractions. Later, students apply this knowledge to new topics, such as algebra and geometry.
Encouraging reflection
When we reach higher levels of thinking, all essential to critical thinking skills. These involve analysis, where we identify categories of information and relationships among them; evaluation, where we make judgments based on our analysis; and creation or using all the information we’ve absorbed so far to generate, develop or design something new.
This moves beyond finding the correct answer to a problem on a worksheet. The evaluation, analysis and creation in high school equivalent math classes actually help students develop and practice problem-solving skills and can inspire creative thinking, where students build on their previous knowledge and experiences to experiment with new ideas.
When we encourage students to analyze how they’ll solve the problem or evaluate how they arrived at the right or wrong answer, we’re fostering skills they can use in social studies, science and throughout their lives. This can help students collectively make sense of mathematics.
Student engagement can be heightened by encouraging conjecture and participation. Although you should help students when they get stuck, you first should try to guide students to apply the knowledge they can remember and apply it accurately. Then they can use critical thinking skills, such as analysis, to study the worksheets.
Lastly, emphasize a belief in students’ potential. Look for pioneers in other disciplines and examples from other subject areas, such as art or architecture, noting people who mastered individual concepts before moving on to the next. All of this can highlight how mathematical thinking and problem solving aren’t limited to math class.