MM9: Three levels of understanding a game rule

MM9 learning exercise: naming a term, judging a condition and explaining a complete example require different skills. Try the three-level mini test.

You recognise every word in a game guide, yet struggle to explain why an example is incomplete. That does not mean you learnt nothing. It means naming the terms and applying the conditions are different achievements. In MM9 learning discussions, we use three levels: recognise the vocabulary, judge a specific case, and explain the whole decision. A short test at each level shows where the next useful explanation should begin.

Our invented board exercise has nine squares arranged in three rows. A valid finish requires every square in one horizontal row to be marked. A diagonal does not qualify in this exercise. Call the rows top, middle and bottom. There is no timer or other condition. This small rule is enough for a useful learning test because the objective, permitted pattern and excluded alternative are all stated clearly before the questions begin.

## Level one: recognise

Level one asks for recognition. What does “horizontal row” mean here: three squares across, three down or three diagonally? The answer is three across. Someone who chooses down may need a visual distinction between a row and a column. They do not yet need a longer explanation of the entire exercise. Naming the term correctly supplies a foundation, but it does not demonstrate that they can evaluate a complicated arrangement using that term.

## Level two: judge

Level two asks for a judgment. Suppose the top-left, top-middle and top-right squares are marked. Is the finish valid? Yes, because all three squares in the top horizontal row are marked. Now change only the top-right square to the centre square. The marked positions no longer complete the top row. The answer changes because a required position is missing, not because three marks are generally insufficient or because the centre square is always forbidden.

A third level-two case has marks at top-left, centre and bottom-right. It is a complete diagonal, but it does not qualify under our stated rule. This is a revealing error test. Someone might correctly identify the word diagonal and still accept it because they remember another game using that pattern. Understanding this exercise means applying the rule in front of them, rather than transferring a familiar completion condition from somewhere else without checking.

## Level three: explain

Level three asks for a complete explanation of a mixed board. Mark all three middle-row squares plus top-left and bottom-right. The answer should identify the completed middle horizontal row, state that this satisfies the finish condition and explain why the extra marks do not undo it under the given rule. A simple “yes” could be a guess. The explanation reveals whether the learner can connect the relevant evidence with the full condition.

For MM9 practice, compare two explanations. “It works because there are five marks” relies on a count the rule never required. “It works because the entire middle row is marked; the rule does not require all other squares to be empty” follows the stated condition. Both explanations reach the same yes answer on this board, but only the second can be reliably carried to a different arrangement. Correct conclusions can hide incorrect reasoning unless somebody explains them.

Use the test results to choose the next task. If recognition fails, show the terms with one small diagram. If recognition succeeds but judgments fail, change one position at a time and ask what difference that makes. If judgments succeed but explanation is weak, ask the learner to point to the exact condition and its supporting squares. Repeating the complete guide at the same speed does not respond to these different needs.

Finally change the exercise's rule: now only a complete diagonal qualifies. Ask the learner to reconsider the earlier diagonal and top-row cases. The diagonal now passes and the top row alone does not. This is a transfer question, showing whether they can use a changed condition rather than memorise the old answers. Declare the rule change before the test. Otherwise you would be testing whether they can guess an undisclosed change, rather than whether they understand the game.

The MM9 mini lesson ends with a teachback prompt: “Explain why three diagonal marks failed in the first exercise.” A complete answer is: “The marks were a diagonal, but the first rule required a horizontal row.” That one sentence joins vocabulary, evidence and condition. When a learner can produce it in their own words, they have moved beyond recognising the page's terms toward explaining an actual decision, and the next practice task can begin from that stronger position.