A low mark does not diagnose the problem. A high mark does not prove understanding.

When parents show me their child’s test, they usually point to the number first.

A mark of 58% tells me the student struggled. It cannot tell me why. Was today’s lesson unclear? Is an earlier idea missing? Did unfamiliar wording or pressure get in the way? The mark alerts me to a problem, but it does not locate it.

A mark of 92% feels reassuring. But did the student understand why the method worked, or did the test closely match the procedures they practised? Both can produce a high mark. Only deeper understanding is likely to hold up when the problem looks different.

Marks matter, but they are only one signal. Fluency matters too: knowing facts and procedures helps students work accurately and confidently. Yet a student can be ready for familiar questions and still struggle when the same idea appears in a new form. Deeper understanding comes from connecting the ideas behind the methods.

This matters even more now that ready-made solutions are everywhere. Students need the judgment to ask: Does this method fit? Does this result make sense?

MathGraph helps me see whether those connections are forming.

A mark records the outcome. MathGraph helps explain what sits beneath the mark. PrepBox connects each student’s complete written solutions to an educator-built map of small math ideas and the links between them. Over time, I can see which foundations appear strong, where I need to see more work, and how today’s result fits into the larger picture.

In a one-to-one lesson, I can follow a student’s thinking by asking them to explain a step, changing the example, or trying a different representation. Even then, there may be several reasons they are stuck. Finding the real cause often starts with an informed hunch, followed by careful checking.

The hard part is tracking that investigation across many students and sessions: what I noticed, what I tried, and what still needs checking. MathGraph keeps that history in one place. Even after more than 20 years of teaching, it helps me follow up consistently, choose the right next lesson, and explain to parents why that lesson comes next.

I have often seen a student earn marks in the 80s, then drop into the 60s the following year. Parents feel blindsided, but the foundations may have been incomplete long before the mark changed. Looking at the mark and MathGraph together can reveal those gaps earlier and show whether a child is ready for what comes next.

Parents are usually shown the result: a mark, a report card, or a completed page. They rarely get to see how the ideas underneath are connecting.

You can now see your child’s MathGraph. It gives us a shared view of which foundations appear solid, which are still developing, and where we need to look more closely. The graph is not a verdict. It gives us a place to begin. When a gap becomes visible, we can check it, address it, and strengthen the connected foundation your child needs to reason through unfamiliar mathematics.

If your child currently studies with me, open MathPulse. If you do not have it yet, you can download MathPulse from the App Store or get MathPulse on Google Play. Go to Units, then Explore MathGraph. Look at how complete the graph is and how much is green. Bring me anything that surprises you, and together we can decide what deserves attention next.

Too often, a gap becomes visible only after the mark falls. MathGraph gives us a chance to see it and act on it earlier.