This week’s article summary is Debates Over Math Teaching Are Heating Up.
In literacy, the debate is between Whole Language and the Science of Reading.
In math, it's about explicit instruction versus student inquiry.
As referenced in a previous article summary about top educational research studies from 2025, student inquiry in isolation does not advance student learning; similarly, explicit teacher instruction too often leads to disengaged students.
Like most debates in education, the best option in math is a balance of explicit teacher instruction and student inquiry/discovery/problem-solving--what is called Guided Inquiry.
As a teacher, I have always felt the need to have a multitude of teaching strategies in my quiver. If I found myself using too much of teacher-centered pedagogy (an easy trap for any teacher to fall into), I’d shift to more student-centered methods. While kids need structure, routine, and consistency in the classroom, they also need variety and novelty.
Visiting classrooms as a Head of School, I particularly enjoy math time: our students are learning the skills/concepts/procedures of numeracy, while also being given ample time to offer their observations when being introduced to new topics, to problem-solve with classmates, and to find multiple ways to solve and demonstrate their understanding.
Just like a recent Summary on SEL, Trinity continues to find the balance of best practices to the benefit of our students!
Joe
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Last December, several members of a national organization for math education leaders came together to issue a warning. A growing movement in the field was calling on schools to adopt an “impoverished” approach to math teaching that would strip students of their autonomy and relegate them to “mimicking their teacher.” This movement misapplying educational research, they said.
Debate over best practices in math education is far from new; it's been debated for over 100 years.
The stakes are particularly high now, as national math scores have continued to decline.
One side of the debate comes from the Science of Math website, which promotes explicit instruction, a method in which teachers explain and model new concepts and procedures step-by-step and then ask students to practice them. It’s a myth, they say, that inquiry-based approaches boost outcomes for all kids. Explicit instruction lays a crucial foundation, especially for students who struggle, and can equip students with the skills they need to tackle more complex problem-solving.
The other side contends that while explicit instruction has some value in math teaching, it should be minimized. Instead, the predominant approach should be “guided inquiry, in which teachers provide structure and support in well-designed inquiry-oriented activities.” This side believes that explicit instruction is a “pedagogy of poverty,” arguing that it is more commonly used in schools in low-income areas, systematically denying these children opportunities for discussion and collaborative problem-solving.
Which side is right?
As usual, let’s find the middle ground through 'guided inquiry’ which should include moments of explicit instruction. Good explicit instruction should then incorporate time for meaning-making and student reflection.
But debates continue over how to prioritize and sequence these two types of teaching, and over the conceptual underpinnings of each approach: Are there foundational processes, like adding multi-digit numbers, teachers must explain directly before students can move on to more complex problem-solving? Or does doing so inherently short-circuit the development of problem-solving skills?
There’s a lot of evidence to suggest that good math instruction includes some explicit instruction and some more student-led problem-solving.
“There needs to be a balance of both,” Ashley Davis, a 4th grade math teacher, said of explicit instruction and inquiry. “I don’t think one is right and one is wrong. When both are used properly, they’re both super effective—regardless of the students.”
Over the past 30 years, leading organizations in the field have promoted a more inquiry-forward approach to math. Popular curricula tend to emphasize problem-solving and discussion of mathematical ideas. Davis thinks these are good goals. She wants her students to be able to use math flexibly in their everyday lives.
There are times when she introduces a new concept through discovery, Davis said, like when she started a lesson about equivalent fractions. She gave students pieces of paper and asked them to fold them in half, and then in half again and again, and asked them what they noticed. Her students figured out that 1/2 was equivalent to 2/4, which was equivalent to 4/8.
“There are other instances where I can think of, where you have to explicitly teach something, so they can then use inquiry later on,” she said—how to use an area model for multiplication of multi-digit whole numbers, for instance.
Still, there’s often little guidance about how to negotiate and sequence these two priorities to lead to the best outcomes.
Some work has tried to fill that gap. Last year, for example, a group of researchers in cognitive psychology and special education published research-based recommendations to get students fluent with math facts, integrating both explicit instruction and what they describe as “cognitive reflection.”
Getting this balance right is hard, and there’s not always a roadmap, said Star, the Harvard professor: “We as a field could be better at guiding teachers toward what that mix looks like.”
