Think and Do Lessons
According to Nicolaus Copernicus, “Mathematics is written for mathematicians.” If this claim is true, we need to look no further than the format of our lessons in the classroom to see if they encourage thinking mathematically or focus on memorization of facts. Math lessons should empower students to communicate their knowledge, understanding and critical thinking. Students should encounter unfamiliar problems where they need to think like a mathematician and make logical claims, instead of merely following rigid step-by-step procedures. In order to meet this standard, any lesson should have at least one, if not more, of the following observable pieces.
Create an environment that promotes thinking, doing, and communicating
Looking back on my own math learning experiences, I was a student who could take information directly shown to me and then use it (“plug and chug”) with little understanding of why or how it worked. Usually my classes involved taking notes, doing homework, and daily quizzes, which did not effectively help me think critically or independently. When this lesson format is used enough to be the “normal” expectation of students, it encourages students to mimic and “plug and chug.” It does not allow any room for misunderstandings to surface and be discussed. Instead lessons should engage students and help them discover how to think mathematically through both success and failure. This goal can be achieved by presenting students with provocative questions that challenge their thinking.
Don’t rush to get to the “end” of a lesson
Discussions and dialogues are critical pieces that help enrich and deepen the learning for each student in the class. These conversations present a logistical challenge, especially when the learning is locked into a pacing calendar. With the right design changes, every math lesson can have more time built in for discussion so that students develop true understanding. A student doesn’t have to be the one talking in order to have an epiphany. Sometimes when one of their peers explains her rationale, it helps another student have the proverbial light bulb learning moment. These discussions will be a challenge at first but if it is a daily expectation they will become second nature for both teachers and students.
Embrace failure as a necessary and regular occurrence
Learning from failures is a critical part of not only math, but also life. A popular sentiment these days is that FAIL stands for “First Attempt In Learning.” An enemy and hindrance to any growth and thinking is a never ending stream of success. A simple and effective way to make failure comfortable is to avoid penalizing it in grades or in a classroom reward system. Every student should feel a well-balanced level of failure and success with-in a lesson. Mathematicians are keenly interested in the pathway to a final result, as it reveals insights about mathematics, strategies and potential strategies to solving the problems. Therefore when a class values the pathway more than they fear being wrong, their ability to think critically increases tremendously.
So the next time you plan a lesson, challenge yourself to allocate more time for students to think independently, to question, to learn from mistakes, and to discuss their thinking. Build more time for discussions and be patient because it takes time and sustained effort to build a strong collaborative community. Finally, build an expectation of failure (yes, failure!) which in turn will build and expectation of growth. By requiring students to think like a mathematician they will be equipped to understand and embrace any mathematical challenges they encounter.