Editor's Synopsis
Craig Barton, a veteran maths teacher and resource creator, shares his evolving framework for using AI as a thought partner rather than as a passive content generator or mere formatting tool. He identifies two traps educators commonly fall into: cognitive outsourcing (letting AI do all the thinking) and ego-driven underuse (doing all the thinking yourself and only using AI for layout). His five-step framework includes ending prompts with "Before you build, ask me some clarifying questions," explicitly inviting the AI to challenge your ideas with reasons, scrutinizing outputs like a colleague's draft, iterating through multiple versions, and asking the AI to reflect on what it learned for future sessions.
The bulk of the post consists of five detailed exchanges from Barton's recent work with Claude on building teaching sequences for categorical concepts — resources that use carefully sequenced positive and negative examples to help students induce mathematical rules. In one exchange, Claude pushed back on Barton's five-example sequence for "What is an integer?", arguing that a sixth example with a negative decimal was needed because students wouldn't generalize across fractions and decimals. In another, Claude rejected a visually elegant animation idea because it risked planting the misconception that -1/3 equals -1.3. Barton also pushed back on Claude when animations failed to hold invariant features in fixed positions on screen.
The exchanges illustrate a genuinely collaborative dynamic where both human expertise and AI reasoning improve the final output. Barton emphasizes that the value lies not in the AI producing correct resources on the first try, but in the pedagogical reasoning surfaced through back-and-forth dialogue — reasoning he might have missed when bogged down in formatting and typing. He also advocates using voice dictation (via Wispr Flow) to free up working memory for deeper thinking, and shares links to the resulting interactive resources on topics like integers, standard form, and angles on a straight line.
