Math Has Feelings, Too
Why we should care less about math tracks and more about "math affect"
A few weeks ago I wrote about some of the shortcomings of math instruction in the United States – mainly that our schools divide math up into discrete content areas (rather than different kinds of math applications) and then define the “good” math students as the ones who can move through those curricular structures quickly. As parents, we often feel anxious about nudging our kids into those accelerated forms of instruction.
But getting into an advanced math track doesn’t guarantee that students will learn to apply and use mathematical concepts. Unfortunately, traditional forms of math instruction can drift into prompting students to mimic and reproduce the examples they’ve been given – the dreaded “plug and chug” approach to learning. Too often, this approach fails to create math learners who can be nimble, curious, and self-directed.
As parents, we have very little control over this system, and so we often try to exert control where we (think we) have it: where our own kids get placed in the math curriculum. A scarcity mindset – the fear that there won’t be enough good jobs for our kids, or that only students who are technologically oriented will be able to earn a good living – leads parents to anxiously advocate for their kids to get a spot in the more advanced math classes, whether or not they’re likely to benefit from that pace of instruction.
This system has a number of problems, and one of them is that parents and students buy into what tracking says about them, and that once they’ve landed in a “track” it will be difficult to get on or off that track that was determined at a young age. We also have a relatively fixed mindset about math, as if it’s a natural orientation that can’t be changed or tweaked in a classroom setting: there are students who “just get it” or someone is or is not “a math person.”
Carol Dweck’s growth mindset work – a perspective that emphasizes learning through challenges and the ability of students to improve and grow – is one powerful antidote. Another comes from Stanford Professor of Education Jo Boaler, who has long been one of the most prominent activists for a different approach to teaching math.
For instance, Boaler and her coauthor Sarah Kate Selling differentiate between the active and passive forms of engagement that can influence kids’ ability to learn despite encountering the inevitable challenges:
“Active engagement in mathematics, we propose, takes place when students are engaged in problem solving, the discussion of ideas, and the application of methods. Passive engagement, we propose, takes place when students are mainly required to listen to a teacher explain methods and solve problems and then reproduce the teacher’s methods.”
I spoke with my friend and colleague Dr. Evelyn Hanna about this research, as Hanna has a doctoral degree in math education and has spent decades thinking about how educators, both at the high school and college level, could approach math education differently. In talking about the difference between passive and active forms of math engagement, she introduced me to a concept called “math affect” – a term coined by Dr. Gerald Goldin at Rutgers.
Math affect refers to students’ attitude, interest, motivation, and self-efficacy in math learning, different components of the individual orientation that students bring to math class. Ideally, we want students to be motivated by intrinsic factors, like their own desire to learn. But the scarcity mindset that we often bring to math – the idea that you’re going to be left behind by the top math track – tends to encourage a more transactional, passive model of learning.
I talked with Dr. Hanna about this research, starting with the most obvious question: Why should we care about how kids feel about math?
“Let me first approach this as a parent,” she said. “Even my own children have come home stating that they ‘hate math’ and when we unpack this statement, it often translates to ‘I don’t feel good about math.’ The feelings are real and as we have experienced with so many other aspects of our life, when we don’t feel good about something, our desire to engage in that ‘thing’ is often minimal… may I dare say, we avoid it.”
She went on to explain how she first encountered these concepts as a researcher. “An effort to study “feelings” toward math was the motivating factor for one of my graduate school mentors, Dr. Gerald Goldin. I’ll never forget sitting around a conference room table during my first year in graduate school and listening to Dr. Goldin explain math affect to my cohort. He shared that the different constructs (or components of affect) can be described along a continuum: that attitude ranges from positive to negative, interest ranges from intrinsic to extrinsic, motivation ranges from genuine curiosity to external pressures, and self-efficacy ranges from confidence to despair.”
She went on to offer some examples from Goldin’s research, which highlight the ways in which academic performance in math can mask how students actually feel about their learning. A student could have generally positive attitudes about math because they’re motivated to pursue a STEM field by parental pressure, but feel good about those plans so long as they do well on tests. And another student could be truly interested in math but get frustrated when they don’t figure things out the first time because they perceive themselves to be destined to get bad grades. In both examples, the academic performance masks the student’s feelings and motivations.
This perspective offers a different way of understanding the factors that we can control when it comes to our kids’ learning – and it’s not what math track they get placed into. “Wearing both my math educator and parent hats, I believe that when we nurture our kids’ natural curiosity for patterns, problem-solving, and abstract reasoning, we help foster motivation and deepen their interest in math,” Hanna said. “When we help them identify the steps needed to accomplish a task or solve a problem (not solve it for them), we help them enhance their self-efficacy.” In her view, that’s the place to intervene – not pushing them into more advanced and challenging courses out of fear that they’ll fall behind.
Instead, Hanna advises parents to look for kids’ math affect by listening for some of the key phrases. Do kids say they hate math or that math is one of their favorite subjects? Do they complain that they’ll never use math skills in real life, or do they find that time flies when they’re doing math homework? Do they feel confident that they know the steps to solve a problem, or do they struggle to know how to get started?
And perhaps most importantly, we can ask them how they’re feeling about those advanced classes. Do they say “I have to take Calculus as a junior in high school so that I can get into a good college”? Or could they imagine saying something different, like “It makes me feel really good when I understand what’s going on in math and how things are connected.”
I also asked Hanna to give us some concrete suggestions about what we could do to try to create more positive attitudes toward math among our students – especially those of us with a kid who may already believe they’re “not a math person.”
She thinks that referencing Dweck’s techniques for cultivating a growth mindset are always wise, and added that “instead of enrolling students in a remedial or ‘plug and chug” programs’” – we all know about those math centers that push more and faster math – we could “seek a tutor who could supplement instruction, provide differentiated instruction, cultivate a growth mindset, or provide interesting challenges to keep your child’s interests peaked.” And rather than using summers as a time to seek more advanced or accelerated math programs, she recommends instead the kind of math enrichment programs that many independent schools and universities offer during the summer. These often situate math in interesting, applied contexts, like computer programming, engineering, or creative arts, adding that creativity and math are closely linked.
I’d love to hear what parts of this perspective resonate with readers’ experiences, either as parents, teachers, or as former students. How do you (or your kids or students) feel about math?