One day, in my third year as a math specialist, I gave my sixth graders a multi-step word problem in which they had to discover the area of an irregular geometric figure. Ross Bent, confident and gregarious, especially for a twelve-year-old, took to the board with enthusiasm. His handwriting was barely legible, but his thinking was organized and his work methodical. Those who could decipher his writing could see that each of his steps was accurate and efficient.
I noticed, however, as he closed in on a final value for X (representing the area of the shape), his pace begin to drop off dramatically. Is he lost? I wondered. He’s on the right track; why is he slowing down?
Now at the final step of the problem, Ross wrote “X = ,” very deliberately. Then, he paused, and, with a quick glance over his shoulder at me, and a mischievous twinkle in his eye, he wrote, “doesn’t matter.”
The significance of Ross’s intuition in that moment has become ever more apparent as I’ve engaged in dialogues with other teachers about the values they hope to foster in developing mathematicians. Little did Ross know, when he made his cheeky joke and drew smiles from even the most cynical of his peers, he had already demonstrated mastery, not only of the content knowledge he needed to solve the problem, but of several more important skills:
- He could apply prior knowledge to make sense of a new problem.
- He could use numbers fluently.
- He could communicate his thinking clearly and with precision.
- He could attack an unfamiliar problem fearlessly, with a calm certainty that he would, ultimately, reach the solution, if he just worked at it a little bit.
In a world where students are often still assessed based on their right and wrong answers, I wonder: how are teachers meeting the challenge of communicating other critically important academic values to developing thinkers?
Here are some ideas that other teachers have shared with me:
Make Your Values Visible
A second grade teacher walks silently between desks during independent work time, leaving a trail of paper awards with students as she passes them. The color-coded awards, which the students sign proudly and hang on a bulletin board at the end of class, make reference to attributes like perseverance, collaboration, use of tools, and precise communication.
Spoiler Alert! Give the Answer First
A fourth grade teacher starts each class period by presenting a problem… along with its precise numerical solution. Students are expected to work silently on uncovering how to solve the problem or why the answer makes sense. The answer itself is shrugged off.
Rewrite the Rules
In a fifth grade classroom, students work in teams on a problem-solving relay race. The team to finish first receives a point — but so do the teams that demonstrate strong collaboration, clear explanation of their solution strategy, and flexible numeracy.
Celebrate Mistakes and Wrong Answers
Every mistake reveals a misconception or a misunderstanding to a perceptive teacher, so it warrants as much praise and attention as a correct answer! One first grade teacher asked her class cheerfully, as a student named Martha discovered and corrected a mistake: “Wow — whose math muscles just got stronger?” On cue, several students answered, green with envy, “Martha!”
What are some methods you have used, to give your students insight into your values as their teacher?
This piece was originally submitted to our community forums by a reader. Due to audience interest, we’ve preserved it. The opinions expressed here are the writer’s own.