Instructional Design and Planning in Mathematics
What this domain asks you to know
Planning questions probe whether you can build coherent units backward from enduring understandings and standards, sequence tasks so that concepts emerge before procedures are formalized, and anticipate student thinking before the lesson begins.
Concepts to master
- Backward design: enduring understandings → essential questions → evidence of learning → learning activities.
- Task selection: the cognitive demand of a task, low-floor/high-ceiling problems, and the difference between tasks as written and tasks as enacted.
- Lesson architecture: launch (activate prior knowledge, establish the problem) → explore (productive struggle) → synthesize (formalize the mathematics) → practice.
- Anticipating responses: listing likely strategies and errors in advance so you can select and sequence student work for the whole-class discussion.
- Alignment: every objective should be observable and matched to a task that actually requires that thinking.
Traps to watch for
Distractors favor activities that are engaging but misaligned with the stated objective, or that reduce cognitive demand through over-scaffolding. Another frequent trap: choosing a plan that tells the procedure first instead of letting students construct it. Watch for objectives that use vague verbs ("understand") with no observable evidence.
Rule of thumb
If the assessment item could be answered by following a memorized procedure, the task does not build the intended understanding-revise the task, not the objective.
Worked example
Objective: students explain why the slope is constant on a line. A weak plan has students compute slopes from a table. A stronger plan has students compare multiple representations and justify constancy with similar triangles, then generalize-aligning task, evidence, and understanding.