The Matrix That Adds Instead of Turns
A tutor reviews six figural matrices with Priya, age 7. Each 2x2 matrix has a shape in three cells and a missing fourth. In three matrices, the rule is additive: the bottom-right cell contains the features that appear in both the top-right and bottom-left cells. In three, the rule is rotational: the shape rotates 90 degrees clockwise from left to right in each row. Priya is correct on all three additive matrices and wrong on all three rotational ones. On the rotational items, she chooses the answer that combines the two shapes, often adding a line that should have rotated away. She says, 'The last box always has the most parts.' She is quick and confident. The next unit mixes additive and rotational rules on the same page. The tutor can use a whiteboard, colored markers, and three practice matrices but has only 18 minutes before Priya's break.
1. What is the likely reason she applies 'most parts' even when it fails?
Read the worked answer
Priya has extracted a default rule-'the last box has the most parts'-from the first three items and is not testing it against the other three cells. The additive items reward that rule, so it is reinforced. On rotational items, the number of parts stays the same; the shape only turns. Her choice, which combines shapes and adds a line, fits her default but not the visible row. This is a rule-selection error rather than a spatial-processing failure: she can compare features, but she is not asking whether her rule explains all three given cells. The confidence and speed make sense; a default rule feels efficient. The instructional target is to make rule choice explicit before answer choice.
2. Design a contrast pair to make the difference visible.
Read the worked answer
Use two matrices side by side with the same shapes and colors. In matrix A, the bottom-right cell is the sum of features from the top-right and bottom-left cells. In matrix B, the shape rotates 90 degrees clockwise across each row. Ask Priya to cover the missing cell and describe two relationships: left-to-right and top-to-bottom. Then uncover. For matrix A, ask which choice keeps both relationships true; for B, ask the same. The contrast is minimal, so the only variable is the rule. Follow with a sorting task: 'Which matrix adds? Which turns?' Have her point to the cell that proves it. This makes the rule visible rather than relying on a verbal definition.
3. What prompt would you give during practice that does not give away the answer?
Read the worked answer
A neutral prompt is: 'Before you choose, say what happens from the left box to the right box, and from the top box to the bottom box. Then find the choice that keeps both true.' This forces a rule check without naming the rule. Another version: 'Which rule explains all three boxes you can see?' Avoid prompts like 'Look for rotation' or 'Count the parts,' because they replace reasoning with a cue and will not transfer when the rules are mixed. If she still chooses by 'most parts,' ask her to test her favorite choice against each visible pair and say where it fails. The goal is for her to reject a rule because it does not fit, not because the tutor says so.