Mathematics · Number System Pedagogy

During an activity on real numbers, the teacher presents different decimal forms: 1.25, 0.333…, 1.732 (with dots indicating non-repetition). Students are asked to categorize each number into rational or irrational through group discussion. Many students initially think all decimals are rational because they 'look like fractions.' Instead of correcting them immediately, the teacher encourages them to search for a pattern that separates these numbers. They test converting decimals into fractions and observe which succeed and which don't, discovering that non-terminating and non-repeating decimals behave differently. Which teaching approach does this reflect?