What do you remember about your math classes in high school? Middle school?
If you remember sitting in rows, working through problem sets, and moving from one section of a textbook to the next, then you learned math in a traditional way. Often teachers just checked to see if you completed your homework rather than setting up varied ways for you to apply the skills you had learned.
Middle School Years are Crucial for Math Learning
The middle school years are especially important for learning how to feel good about math and see it as an area where you can succeed. It’s a great time to find out how math applies to the real world.
Middle school is a time period when students’ brains are beginning to grasp abstract concepts. And, it’s a key time to develop collaboration skills.
On the other hand, 8th grade is often the time when students give up on being good at math, setting them up for struggles in the years to come.
Developing a Passion for Math
The high school years are important for reinforcing a strong math foundation and helping students find areas of interest and even passion, making it possible to have more college and career options upon graduation.
Combatting Consistent Mediocrity in the U.S.
The vast majority of math classrooms rely on standard ways of teaching math that involve rote learning. As a result, students are often able to complete recognizable problems, but when asked to go deeper or to explain their reasoning, they are unable to do so.
The Inquiry Method in Action
Bosque School faculty use an inquiry model to guide their planning, whether at the middle or high school levels. While staying true to developmentally appropriate content, teachers figure out how to prompt, encourage, and challenge students to stretch their thinking and their skills.
For example, faculty use truly randomized grouping when creating student teams. Students are given a “stretch problem” at the board and use critical thinking and questioning to collaborate their way through a problem that they haven’t seen before.
The math faculty at Bosque School purposefully hold back from giving easy answers when students are stuck. It is much easier to rescue students when they are struggling; however, the aim is to develop resilient math learners who know how math works, rather than expert regurgitators.
A Conversation with Math Department Chair TJ Middleton
Math Department Chair TJ Middleton says:
“As a department, we decided we were going to implement this. For some of us, it was that little extra tweak we needed, and for others, it was life-altering: ‘this is what I have been trying to have happen in my class but couldn’t get it.’”
Randomized grouping breaks down hierarchy that can happen in groups or being the one who always does the work. It mixes up the skill and experience levels.
Why is this important? Students learn to speak up when they have ideas, even if they don’t have the skills yet to solve the problem on their own. By getting away from labels (“He’s good at math,” “I’m bad at math”), students see math as a continuum with room for themselves to grow.
Middleton says that this is also the best, most authentic way for us to integrate equity into the math classroom.
The Importance of Everyone’s Voices in the Math Classroom
“In Calculus Two, I knew the next skill we wanted to work on, and I put a problem up there that uses that skill. It’s like ok, GO,” he says, “And they would start working on it and talking about it, and different people would go up to the board to write their idea.
“‘Well no, I think this’...and they were discussing it and getting really, really stumped on it. And it was just this magical aha that needed to happen. It wasn’t anything super clever.
“So, I heard [a quieter student] say, ‘Well, would this be something where we’d want to complete the square?’ Nobody else heard her. But I heard her. And then she was like, ‘oh, no, no, no, no, because we don’t have an equation.’
“Meanwhile, [a more outgoing student] said, ‘Oh, we should try such and such!’”
Holding Back While Students Explore the Problem
“I knew that wasn’t going to work, but I didn’t know in what way it wasn’t going to work. But it was a clever idea.
“So. . .for 15 minutes they were going with [that second student’s] approach, and then I see the roadblock that they are about to hit. And I say, ‘Ok, here’s why this didn’t work. Did anybody notice what [the quieter student] said about 15 minutes ago?’
“And the student says, ‘I was just thinking about how you could complete the square but . . .’
“Right then, another student said, ‘Oh, yeah! We could. . . .’”
The Aha Moment Arrives
“See? When you dismiss ideas, that doesn’t work. We need everybody’s ideas in here,” Middleton says to his students. “Maybe you can’t think of how to implement that idea, but another person didn’t even have the idea in the first place who does have the skill to implement it.
“We need everybody joining this conversation and not dismissing yourself simply because you can’t figure out where or how it’s going to help.”
It’s really important to spend time at the beginning of the school year with non-curricular, really engaging problems and to keep changing those year after year to keep them fresh
Middleton calls these “low floor, high ceiling, open middle problems.” He says, “You can at least start on the problems, and then if you have a lot of skill, you can go really far with the problem.”
The Opening Day Problem: All School Problem Solving
“Last year and this year, we found one of those low enough floor, high enough ceiling problems that we were able to use for 6th through 12th grade. On convocation day, we only had a short amount of time, and we did this method with that one common problem for all classes in 6th through 12th.
“After the first day, we break out into our different courses and decide which problems are good for which class for which year. The first 4-5 days, it has to be super cool interesting stories. You can’t do that the whole period, though.
“Once they are used to the method and starting to get used to the teaching, we start to bring in curricular work.”
Changing How We Teach: More Depth in Student Learning
As Middleton says, in an inquiry-based classroom, you are not supposed to answer student questions too quickly. You acknowledge that they asked the question, and you guide them in ways to answer their questions. That’s hard for a lot of teachers to do. Teachers are used to asking a question, and because they want students to understand, they answer for them when students seem stuck.
When to Start? Start Now!
It’s not too early, but it might be too late if you wait. Middle school students need a safe enough environment to know it’s ok to try and fail. They benefit from experiences of small successes and encouragement from peers and teachers. Once students get to the high school level, it is very difficult to change the ingrained patterns of thinking that they are failures when it comes to math.
However, opening up a vibrant and fun path forward with math sets up students for opportunities they haven’t even considered yet. Regardless of whether they go into a STEM field after college, their lives are much richer for learning the language of math and practicing the logic and reasoning needed to understand math at a deeper level.
In addition, real-world problems or tasks that come up in their career and in life will make sense, and the solutions will come more easily for those who built a strong foundation in math.