Teaching one step at a time

TL;DR:

• Going too fast is the most common way an explanation fails.

• We want DuckyHelper to give one step, say why, and check you are with it before it moves on.

• This describes how we want it to behave, not a promise about results.

Most explanations that fail do not fail because they are wrong. They fail because they are too fast. This post is about how we want DuckyHelper to pace what it teaches, and we say it as a goal for how it should behave, not as a claim about outcomes.

Too fast is the most common problem

Think of the worst explanation of a math problem you have heard. It was probably correct. The person simply moved through four steps in the time you needed for one, and by the second step you were behind, nodding to be polite. After that, none of the rest registered.

An assistant is especially prone to this. It can produce a whole worked solution in an instant, and it is tempting to hand over all of it at once. But a complete solution you cannot follow is not much more help than no solution.

One step and why

Our aim is simple to say. DuckyHelper should give one step at a time, and with each step say why it is there. Not just "subtract 3 from both sides", but also what that does: it keeps the two sides equal while getting the unknown by itself.

The reason matters as much as the move. A step with no reason has to be memorized. A step with a reason can be rebuilt next time you need it, including in a problem that looks different.

This works best on the blackboard, where each step appears as it is spoken and the earlier ones stay visible. You can look back at line two while hearing about line four.

Checking before moving on

A teacher at your shoulder watches your face. If you look lost, they stop. DuckyHelper cannot read your face, but it can ask. After a step that tends to trip people up, it should pause and check that you are with it, then go on when you say you are.

You can also take the lead. Say "slower", "go back" or "why did you do that?" and it should respond to exactly that. The pace is yours to set.

Maths at hand

Math is where pacing shows most, because each line depends on the one before. Missing one step means the next makes no sense. For that reason we want math handled slowly and carefully: write the line, say what was done, say why, and only then continue.

What we are and are not saying: This is a description of how we want DuckyHelper to teach. We do not claim it guarantees that you will understand, and nothing in this post is a measured result. If a step goes too fast, tell it.

Why we say it as a principle

A principle can be checked by you, one conversation at a time. You will know within a minute whether it gave you a step and a reason or dumped a whole solution. That is a fairer test than any statistic we could quote.

It also keeps the product honest. If it runs ahead of you, that is a fault in our design, and we would like to hear about it at support@duckyhelper.com.

A worked picture

Take the equation 2x + 3 = 11. The paced version goes like this. First: "We want x by itself, so we undo the plus 3 first." Write 2x = 8 and check that both sides were changed the same way: 11 − 3 = 8. Pause: does that make sense so far? Then: "Now x is multiplied by 2, so we divide both sides by 2." Write x = 4.

Then comes the check, which is also a step: put 4 back in. 2 × 4 + 3 = 11, so it holds. Five short moves, each with its reason, and a stop in the middle. Nothing here is hard, which is the point: a hard topic is a chain of easy moves when they are given at a pace you can follow.

What this means for you

Ask for what you want. If you want a quicker pass, say so, and it should speed up. If you want to understand, ask it to go one step at a time. For more on the choice to do what you ask, read doing what you asked, then a short why.