Building Educational Tools That Actually Teach

What if educational tools actually taught students how to think, instead of just giving them answers?

That's the question that led me to build the Equation Solver — a tool designed to show students the process, not just the result.

Not Just Another Calculator

This tool was built for a specific purpose — to help students understand how to solve equations (linear and quadratic for now), but unlike regular equation solvers that just give you the final answer or show the steps in static text, this tool animates each step, showing how the equation transforms over time.

It's designed mainly for students who aren't looking for shortcuts, but who actually want to understand how to solve linear and quadratic equations.

The Real Problem Students Face

I notice that many students don't struggle with the final answer — they struggle with how we get there. Especially when solving equations, one missed step or confusing transformation can throw them off completely.

Think about it:

• You're solving $2x + 3 = 7$
• You subtract 3 from both sides
• But wait, did you remember to subtract from both sides?
• And what about that negative sign?

One small mistake, and the whole process falls apart.

Here's what I want students to actually see happen — not just the answer, but the transformation:

$$2x + 3 = 7$$

$$2x = 7 - 3$$

$$2x = 4$$

$$x = 2$$

Once you watch a tool actually move that 3 across, the abstract idea becomes concrete. And once linear equations click, you can build up to harder ones — like quadratics of the form $ax^2 + bx + c = 0$, which are solved by the formula:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

That formula intimidates a lot of students. But it stops being scary the moment you can see the algebra that builds it.

What If We Made the Process Visible?

So what if I make the steps visible, one by one, with smooth transitions that show how each part of the equation changes?

That's exactly what this tool does.

Why "Showing the Process" Is Actually What Teaching Is

I want to spend a second on this, because I think it's the part most ed-tech tools get wrong.

When a student watches me solve an equation on the board, they're not just seeing the steps. They're seeing my hand pause before I commit to a move. They're seeing me ask out loud, "OK, what's blocking the x right now?" They're seeing me cross something out, redo it, look back at the line above. That hesitation, that internal monologue — that's the lesson. The final answer is almost beside the point.

This is something educators have been writing about for decades. Cognitive scientists call it the worked-example effect: students learn faster from watching a problem solved step-by-step than from solving it themselves cold, especially when they're new to the topic. Why? Because the working memory of a beginner is fragile. If they're trying to discover the rules while also applying them, neither sticks. But if they watch the process unfold first, they can soak in the structure, and then they're ready to do it themselves.

A static "show me the steps" page kind of does this. But it dumps the whole solution on the page at once. The eye doesn't know where to land. The animated version is different — the equation changes in front of you, one transformation at a time, at a pace your brain can actually track. It's the closest thing to watching a teacher work through it on a whiteboard, except this whiteboard is patient and never gets tired.

A Small Story From My Classroom

I had a student last year — sharp kid, but algebra had broken him in 8th grade and he'd carried the "I'm just bad at math" story ever since. We worked on −3(x − 2) = 9 together. Standard problem. He stared at it for a minute, then said, "I never know whether to distribute first or divide first."

That sentence told me something important. He didn't have a strategy gap. He had a visualization gap. He couldn't see what each step was doing to the equation.

I opened the equation solver, typed it in, and he watched the animation. The −3 floated outside, multiplied through, the parentheses dissolved, and the equation rearranged itself line by line. He said "oh." Just that. "Oh."

The next problem he did alone, in 30 seconds, on paper. Not because he memorized a recipe — because he'd seen what the recipe was for. That's the whole goal of this kind of tool.

This Is Part of Something Bigger

This is part of a bigger direction I'm working on:

Building educational tools that focus on clarity, interactivity, and simplicity.

I'm not trying to compete with large platforms — just experimenting with ways to make learning more understandable.

What Makes This Different?

Most equation solvers out there either:

• Give you the final answer instantly (which doesn't help you learn)
• Show static steps that you have to read through (which can be confusing)
• Assume you already understand the process (which many students don't)

This tool is different because it:

• Animates each step — you can see the equation actually changing
• Shows the process — not just the result
• Makes it visual — you can see what's happening to each part
• Goes at your pace — you control when to move to the next step

More Tools Are Coming

This is just the beginning. More tools are coming soon, and I'll keep sharing them here.

Each tool will follow the same principle: focus on understanding, not just getting answers.

Some of the things I'm working on or sketching:

• An animated factoring trainer — for the moment students hit quadratics and feel like the floor opened up. Visual, with the structure of (x + a)(x + b) shown as the boxes that it actually is.
• A fraction-operations visualizer — pizzas are the cliché for a reason, but most tools bail out at addition. Multiplying and dividing fractions visually is where the real confusion lives.
• A word-problem decoder — not a solver. A tool that shows students how to translate a sentence into an equation, line by line, with the original wording staying visible. Word problems aren't a math problem; they're a reading problem with a math problem inside.

None of these will do the work for the student. They'll just make the work visible long enough for the student to copy the thinking, then do it themselves. That's the whole pedagogy in one sentence.

For Fellow Teachers

If you've found yourself saying "they should already know this from last year" — same. We all do. The gap between "covered the topic" and "actually internalized the topic" is huge, and it gets wider every year. These kinds of tools aren't replacements for what you do; they're warm-ups. Five minutes on the projector at the start of class, a quick reminder of how the structure works, and now the lesson can start at the height it's supposed to start at — instead of you re-teaching last year's material for the third time this week.

I'd Love Your Feedback

If you try the equation solver, I'd love to hear your feedback to improve or build new educational tools.

What subjects do you think would benefit from this kind of animated, step-by-step approach?

What tools do you wish existed when you were learning?