Teaching math as if there is only one correct way to solve a problem makes us think we are solving problems, but in reality we are “getting answers.” I have seen it over and over again, but nothing bothers me more than seeing elementary and middle school students solving word problems this way.

Consider this typical middle school prompt: *A store sells 6 bags of marbles for $18. What is the unit price of a bag of marbles? *When I read this problem, I imagine a child looking at me and asking, “Does ‘of’ mean multiplication?” This has happened to me many times when I visit math classes.

There is no secret code. *Of* This might mean “multiply,” but it might not. These are very counterproductive questions that children ask when they are presented with “only one way” to solve word problems, such as searching for keywords.

In this example, students can immediately multiply 6 × 18. If you then ask them why the unit price of a single bag of marbles would cost $108—and would be much higher than the price of 6 bags of marbles—they will look at you with uncertainty. This is the end result of getting answers.

Problem solving is a special cognitive experience. Instead, we ask ourselves what is going on in the problem. It is not a matter of mindlessly following a single set of prescriptive steps. The way to solve this problem, like all problems, is to understand what is going on. But that means there will be many paths to the answer. How I understand the problem may be very different from how you understand it.

## The right way is the wrong way

When we are taught to rely on a single, step-by-step process to solve a math problem, we turn off our problem-solving brains. These skills require ongoing work to keep them sharp, and constant reliance on someone else’s “exact” method dulls them. Over the years, we may even lose at least some of our problem-solving insight by not using it.

This dependence also discourages courage: we must take risks to solve problems, and the insistence on following a singular method prevents us from risking wrong answers through experimentation.

We can solve problems in many different ways. In fact, trying different approaches is both fun and educational, and it’s necessary when problem solving becomes difficult—which is often when the problems are most worth solving. Engineers who write software code or build bridges consciously try to solve problems in multiple ways, even when a solution is readily available to them.

Why not fix this problem and move on?

First, if you dig deeper to find more than one solution, you can decide which one is the cheapest, the most sustainable, or the most elegant—whichever outcome matters most to you. Second, and perhaps more importantly, when solving a problem gets really hard and the path forward is unclear, you have to be willing to try everything. And the first step in the “try everything” approach is to step back and look at a problem from all angles, or at least from more angles than you initially see.

In the real world, of course, we often resort to novel approaches to problems out of desperation. “Try everything,” is the motto. As part of a household with two working parents and twins in elementary school during the COVID-19 pandemic, we’ve often been forced to try everything to solve problems related to work, social distancing protocols, intermittent remote school, and limited child care.

To dispel the myth of the one correct method, we must understand the consequences of answer-seeking versus problem-solving. Because we have been brainwashed to believe that answer-seeking is a good thing, and because most of us have spent years in math programs focused on answer-seeking, we do not realize the negative effects it has on us.

Here are some typical ways we react in an answer-seeking environment:

**The mind becomes empty.**For a while, nothing comes to mind because we are not allowed to use our minds creatively.

**Heart racing.**We react anxiously, trying to remember how the teacher did the calculations on the board. What was her first step again?

**Negative self-talk.**For a moment we have the germ of an idea, an instinct for how to begin solving a difficult math problem, but because we have been conditioned to look for the answer in only one way, we chastise ourselves for thinking we know better than we have been taught, and we revert to standard operating procedure.

**Reluctance to discuss issues and concerns.**We are ashamed to address these issues with others, assuming that they are followers of the “right path.” This reluctance to involve others is an obstacle to a creative and collaborative process.

The overall effect of a system that seeks answers is a feeling of helplessness. We feel defeated before we even try to solve a problem.

Here are some recent conversations I’ve had with children and adults about what it feels like to do this kind of math:

*“I want to use decimals. The teacher wants me to use fractions for no reason. I just have to do what he says. I don’t have the freedom to do math the way I want, even if my way is easier for me. Nobody listens to me.”*

*“I remember being criticized on a math test in high school when I had the right answer but had solved the problem my way. As a teenager, that made me furious. Now, looking back on it as an adult, I think it’s like playing tennis. If you’re training me to learn or improve a new skill, like backhand volleys, then I can understand the reasoning behind forcing me to take a specific approach. But if you have no reason to force me to do it your way, it still makes me cringe.”*

A problem-solving approach elicits very mixed reactions, reflecting a sense of autonomy and courage. Ideally, schools should teach mathematics with problem solving as their guiding principle rather than the myth of a single right way. To achieve this ideal, however, we need to understand what problem solving is.

## How to counter the myth

We make mathematics a performative activity rather than a learning experience. When the teacher asks the class, “What is the answer to 63 plus 37?” he turns mathematics into an individual sport.

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Add to that the myth of speed, and every student is racing to find the answer first and win the game. The answer becomes the only thing that matters, and understanding and collaboration take a back seat.

Some of you are probably wondering if I have lost my mind in mathematics. After all, we need to find the right answers in order to buy the right amount of carpet to cover the floor of a room or to ensure that our rocket reaches the moon.

Again, this is a question of integrative complexity. Of course, we need to know what 63 + 37 is. But if that’s all we know, we’re missing out on a lot of what mathematics has to offer.

Fortunately, we can learn in ways that give us precision and other advantages. Consider 63 + 37 again. What if the teacher phrased the question this way: “Don’t tell me the answer. It’s 100. How would you begin to calculate 63 plus 37 in your head? What’s your first step?” Mathematics is a process.

I have had the opportunity to listen to the brains of second graders working on this exact moment many times. It is a joy every time. One might say, “I broke this down as 60 plus 30 plus 3 plus 7. And the next thing I saw in my head was 93 plus 7. And then I knew it was 100.” Another second grader might offer another option: “I looked at this for a moment, and I saw that 3 and 7 equal 10. So I knew I had 60 plus 30 plus 10. And I know it is 100.”

This is the mathematics that people need in their lives. This is what they need to build bridges. This is also how you develop a deep sense of mathematics.

Math should be taught as a collaborative process, like other subjects. We often think of math as separate from other subjects in K-8, as something that should be taught as an individual sport where everyone has to figure out the right answer first. Other subjects are taught as team sports, where the process matters, where students don’t rely on tricks, where students are encouraged to work together, and where a variety of ways to answer can be acceptable. But when it comes to math, collaboration and process work are subordinated or eliminated.