Maths Solver“I just can’t do algebra.” I have heard some version of this sentence from a hundred different students, in pretty much the same defeated tone, across eight years of teaching. And in nearly every case where I sat down with the student and worked through what was actually going wrong, the problem was not algebra.
The problem was almost always something two topics earlier — a shaky grip on negative numbers, or fractions, or what an equals sign actually means — that had quietly stayed unfixed while the syllabus moved on. Algebra felt impossible because algebra requires you to manipulate the thing that is broken. The student was not bad at algebra. They were bad at the prerequisite, and algebra was where the gap finally became visible.
This is the single most useful idea I can give you about maths feeling hard: when you hit a wall, the wall is rarely where you think it is. The rest of this post is about why that’s the case, what to do about it, and what to stop doing about it.
Maths is the most cumulative subject you will ever study
Most school subjects are forgiving. If you missed two weeks of history, you can still understand the next chapter; you just don’t know what was in those two weeks. If you missed two weeks of biology, the next topic might still make sense even if you have to look up some vocabulary.
Maths is not like that. Almost every topic in school maths is built directly on top of an earlier one. Quadratics depend on factoring, which depends on multiplying out brackets, which depends on the distributive property, which depends on negative numbers and basic arithmetic. If any single layer in that stack is shaky, every layer above it will feel wobbly, even if the wobble is happening somewhere you cannot see.
What this means in practice is that when a topic feels impossible, the useful question is not “why can’t I do this topic?” The useful question is: “which earlier topic, that this one depends on, am I actually shaky on?”
The wall is almost never where it looks
Here are the diagnoses I make most often when a student tells me they cannot do X. These are not guesses; they are the patterns I have seen play out year after year.
- “I can’t solve quadratics” almost always means the student is dropping a sign somewhere when they expand brackets. The quadratic technique is fine. The earlier algebra step is not.
- “I can’t do simultaneous equations” almost always means the student is uncomfortable with substitution because they don’t fully trust that $x$ “is” some specific number you can use as a name. That’s a problem with what variables are, not with the technique.
- “I can’t do trigonometry” about half the time means the student doesn’t have a confident grip on similar triangles, which is the geometric idea trig is built on.
- “I can’t do calculus” almost always means the student is shaky on function notation — what $f(x)$ is, what $f(x + h)$ means, why $f$ and $g$ are different objects.
- “I can’t do fractions” sometimes really is fractions, but more often is a problem with what division means in the first place. (When you divide $20$ by $4$, what are you doing? If the student can’t answer that without thinking, fractions are going to feel arbitrary.)
The implication is uncomfortable but useful: when you are stuck on a topic, doing more practice problems on that topic might not help. It might be exactly the wrong move — you are reinforcing the wrong diagnosis. Sometimes the right thing to do is go back two topics and make sure those are actually solid first.
The other reason: maths is a language you have to think in
Most subjects you learn by reading about them. Maths you have to learn by doing, because the symbols mean nothing until you have used them yourself. Reading about how to factor a quadratic and factoring one are not the same activity, and neither produces the same understanding.
A specific consequence: it is impossible to learn maths from passive reading. If you sit on the sofa with a textbook and read the chapter on the chain rule, you will follow the worked examples, nod, and feel like you understood. Then you will close the book, sit down to do a problem, and discover you have no idea where to start. This isn’t a character flaw; it is just how maths works. You have to do the manipulation yourself for it to stick.
This is also why maths feels much harder than other subjects relative to how much time you spent on it. An hour of reading history is an hour of learning history. An hour of reading maths is maybe twenty minutes of learning maths and forty minutes of generating the feeling of having learned. The fix is to make sure that when you sit down with a maths book, there is a pen and paper next to it from the start.
The diagnostic backtrack
The technique I would teach myself, if I could go back to school: when you hit a topic where two practice problems in a row feel impossible, stop. Do not push through with another problem. Instead, write down the question “what is the smallest, simplest version of this problem I can imagine?” and try to solve that.
If “solve $3x + 5 = 17$” feels hard, try “solve $x + 5 = 17$.” If that’s easy, you’re fine on the basic technique; the issue must be the multiplication in the original. If that’s also hard, go further down: solve $x = 12$. (Trivial, but it tells you that you understand what “solving” means.) Then walk back up the staircase, adding one piece at a time, until you hit the step that breaks. That step is the actual gap.
This is the single most useful diagnostic technique I know, and it applies to almost every topic in maths. It works because it locates the wall. Once you know where the wall is, knocking it down is usually a matter of half an hour with the relevant section of an earlier chapter.
What does not help
Two things, in particular, do not help when maths feels hard, even though they feel like they should.
First, more of the same problem. If you have done six problems on factoring quadratics and the seventh is still impossible, the eighth will almost certainly be too. The pattern is not going to install itself by repetition; you need to work out which step you are missing first, then try the seventh problem with that step in place.
Second, watching more videos. Maths YouTube is excellent, but it is the same passive-reading trap with better animation. You will watch a brilliant explanation, follow it perfectly, and then sit down to a problem and stall. Watch one video, then close the laptop and try a problem from scratch. If you stall, watch another. Don’t binge.
What does help, in roughly the order I would try things
- Diagnose the actual gap, using the backtrack technique above.
- Re-read the relevant earlier section with a pen in your hand. Re-do the worked examples on paper, looking only at the problem, not the solution.
- Now try one harder problem from the topic that was bothering you. If it works, you have found and fixed the gap. If it doesn’t, you have not fully fixed it, and you should backtrack further.
- Get a different explanation. Different textbooks, different teachers, different videos all explain the same topic in slightly different ways, and one of them is going to click for you in a way the others didn’t. This is not a moral failure of any of the explanations; it is just how learning works.
- Talk to a person. There is something that happens when you have to say out loud, “I get this part, but I don’t understand why we’re allowed to do this next step,” that surfaces the gap faster than any amount of solo work. Get a teacher, a tutor, a smart friend, your parent — anyone willing to listen patiently while you talk through it.
The thing that almost no one says out loud
Maths being hard is not, in itself, a sign that you are bad at maths. It is a sign that maths is hard. Almost every mathematician I have ever met has stories of topics that took them two or three serious attempts before clicking. The difference between the people who get through and the people who give up is not raw ability; it is the willingness to backtrack, find the actual gap, and patch it instead of just feeling bad.
If maths feels hard right now, that is information, not a verdict. The information is: somewhere in the last few topics, there is a piece that doesn’t quite click. Find it. Fix it. The next thing will be a lot easier than you think.