Key points:

Learning math takes effort and can even feel uncomfortable, but moments of struggle and mistakes are part of the process.

Research shows that productive struggle in math leads to better learning. But there’s a fine line between productive and unproductive struggle. When tasks are too difficult, frustration takes over. Without appropriate support, students may disengage, lose confidence, and eventually decide they’re “just not a math person.”

The right hints at the right time can help.

Think about the delicate balance that video games maintain. Good games aren’t designed to be easy. If they’re too easy, players get bored. But if they’re too hard, players quit. A well-designed game makes players think they can win, even when they lose. That’s what’s motivating. “I almost did it! I want to try again!”

That’s the experience we want to create in math classrooms. Well-designed hints can help maintain that balance where students feel they are making progress and want to put in the effort to get to the next level. Hints help students persevere so they stay engaged and challenged but not overwhelmed.

Consider Carter Buhler, a North Carolina student who called math “one of his least favorite subjects.” In the eighth grade, he started working on a math program that uses AI to provide just-in-time feedback and contextual hints. With the hint button at his fingertips, Carter said, “I never felt like I was overwhelmed or didn’t have the right amount of help needed to understand any of my lessons.” Over time, he said he felt “smarter and more confident” and no longer worried about math.

Not all hints, however, are created equal.

Providing too much help can sometimes interfere with learning. This is called the “assistance dilemma.”

Another challenge is that many hints in textbooks and software programs are one-size-fits-all. Suppose a student struggles to add fractions. In that case, a hint might tell them to determine the least common denominator, convert the fractions so they all have the common denominator, and then add the numerators. That general advice might work for some learners, but for others, it’s meaningless jargon. Hints that are more concrete and that use numbers from the specific problem–saying, for example, “Find the common denominator between ½ and ⅔”–can help students connect abstract terms directly to the problem at hand.

A fundamental principle of cognitive science is that knowledge builds on prior knowledge. Every student has a unique background, and their prior knowledge and experiences in math can vary widely.

Scores from the 2024 National Assessment of Educational Progress illustrate some of these differences in alarming detail. Math scores, which are still below pre-pandemic levels, show growing achievement gaps between higher- and lower-performing students. Among students who scored below the national average, the majority–68 percent in grade four and 75 percent in grade eight–are economically disadvantaged.

These data points merely scratch the surface. Teachers work incredibly hard to help students meet grade-level expectations and excel. Still, teachers need support to meet learners where they are in their math journeys. AI can assist with that.

AI can build on what a student knows and present information in a way that makes sense to that individual. It can follow a student’s solution strategies and provide hints relevant to their approach. If one student works through a problem one way, she’ll see one set of hints. If another student works it differently, he’ll see different hints. Those hints will adapt to each student’s thinking and adjust to every action they take.

Useful hints are context-sensitive. They’re based on the specific problem the student is working through and the student’s specific mistake. This makes the content relevant and meaningful.

Having multiple levels of hints is essential, too. Hints start with a gentle nudge and progressively provide more information.

It is important to note that after accessing a hint, students need the opportunity to reflect or engage in self-explanation. Even a hint that shares the answer can be educational if it helps the student think. “Hmm, the answer is 26. Why is that?” When the student is given another chance to demonstrate mastery, they can apply what they learned to the new problem.

Hints can also help students who have a fear of math. Math anxiety can stem from a variety of factors, such as fear of failure, gaps in prior knowledge, negative feedback, or societal stereotypes. Social pressures, too, can interfere with learning and make students reluctant to ask for help because they don’t want to look “dumb” in front of their peers or teachers. With on-demand access to hints, students can move at their own pace and seek help without fear of judgment or ridicule. They can stretch their math skills and plug away at a problem because they know help is just a click away if they get stuck.

Looking ahead, there is much more to explore regarding what AI can do for math education. Right now, AI-generated hints are primarily text-based. Future developments could include personalized videos that address students by name or instant visual representations like interactive graphs.

AI, however, will never replace the teacher. Teachers understand students in a way that AI may never duplicate, and human interaction can be uniquely motivating. AI simply assists the teacher by acting as a one-to-one coach for students who need different types of help at different times. This personalized support can bridge the gap between productive and unproductive struggle. Instead of getting stuck, students get help as they progress toward deeper mathematical understanding.

Over time, this also helps students become more adept at evaluating their understanding. They better recognize when to persist and push through on their own, and when to seek help. This metacognitive awareness is an advantageous skill in and out of school.

By combining cognitive and learning science, research, practical instruction, and the power of AI, we can motivate and show students that every math learner is a mathematician. We can help them embrace and appreciate the struggle. “I know I can solve this! I want to try again!”