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Meeting Students Where They Are

Two more KTCP workshops sit naturally together: what students already know when they walk in, and what they need from you once they start doing the work. Both come down to the same underlying idea — you can't design good instruction, or give good feedback, without a fairly precise model of where a specific student currently stands.

Prior knowledge is bigger than content

The instinct is to treat "prior knowledge" as a checklist of prerequisite facts — did they take the intro course, do they remember the formula. Ambrose & Lovett (2014) argue it's really four things at once:

Type of prior knowledge What it means Example failure mode
Content knowledge Facts, procedures, terminology A genuine gap in a prerequisite
Intellectual skills Domain-general abilities — evaluating evidence, writing an argument Strong content knowledge, but can't structure an argument with it
Epistemological beliefs What a student thinks knowledge even is — fixed vs. malleable intelligence, memorizing vs. building models Believes struggle proves they're "not a math person"
Metacognition Whether a student can accurately judge their own understanding Confidently wrong — doesn't know what they don't know

Each of those can help or hurt independently. Prior knowledge helps when it's accurate, sufficient, active, and appropriately applied. It hurts in three distinct ways: it can be flatly inaccurate (a misconception a student will defend against evidence), insufficient (a genuine gap), or simply inert — technically present, but never cued, so the student never connects it to the new material because nobody prompted the connection. That last failure mode is the one I find easiest to overlook: the knowledge is there, it's just asleep.

Scaffolding is the tool for building on it deliberately: support scaled inversely to what a student already has, explicitly designed to fade as they gain independence. It works because it manages cognitive load — working memory holds roughly five to seven items, and unguided trial-and-error on a new skill blows through that budget fast.

flowchart LR
    subgraph S1["Stage 1: New skill"]
        direction TB
        A1["Worked examples"]
        A2["Guiding questions"]
        A3["Small, simple task"]
    end
    subgraph S2["Stage 2: Building competence"]
        direction TB
        B1["Partial examples"]
        B2["Occasional prompts"]
        B3["Moderate task"]
    end
    subgraph S3["Stage 3: Independence"]
        direction TB
        C1["No worked examples"]
        C2["Self-directed"]
        C3["Full-complexity task"]
    end
    S1 -->|"support fades"| S2 --> S3

Worked example: a leveled model sequence

In my own course design, this showed up as a leveled sequence of climate models — a single-layer atmosphere, then a two-layer version, then a generalized N-layer model — where each stage is a scaffold for the next, and the support (worked derivations, guided questions) is heaviest at the start and deliberately withdrawn as students build competence.

Feedback has to be targeted, not just present

The natural next question is what happens once a student is actually practicing. The workshop leaned on a chapter from How Learning Works (Ambrose et al., 2010) that opens with a blunt warning: effort plus feedback is not automatically learning, if the feedback isn't structured right. Good feedback works like a GPS — it tells you specifically where you are relative to a target and what to do about it — not like a map that just shows the whole terrain and leaves you to figure out your position.

Two properties matter most: content (feedback needs to name specific criteria, not just deliver a score) and timing (earlier and more frequent generally helps, but not always — delaying feedback slightly, so a student attempts self-correction first, can produce better learning than immediate correction).

Feedback design checklist — the practical prescriptions, in triage order:

  • [ ] Feedback names specific criteria, not just a score
  • [ ] It's prioritized (a few key fixes, not every possible error at once)
  • [ ] It's not so dense that a student can only fix the easy items and ignore the rest
  • [ ] Timing matches intent — immediate if the student can't self-correct, delayed if they can
  • [ ] Recurring errors are addressed at the group/class level, not repeated 20 times individually
  • [ ] Students are asked to state how they used the last round of feedback in their next submission

Dwyer's (2010) work on praise adds a wording-level detail worth calling out on its own:

Praise type Example phrasing Effect
Process praise "You tried three different approaches before this one worked" Builds resilience, growth mindset, persistence after failure
Person praise "You're just good at this" Reinforces fixed mindset — struggle later reads as proof of a limit, not a normal step

The effect is reportedly larger for women and underrepresented students, who are more prone to reading struggle as confirmation they don't belong — which loops straight back to the belonging discussion from the last post.

For my own microteaching lesson, this meant designing feedback into the structure rather than adding it afterward: an in-class activity with a partially-filled table so students get an immediate self-check, and — because I knew from experience which mistakes students tend to make with this material — three pre-written fallback explanations ready for the misconceptions I expected to see, rather than improvising a response in the moment.

Next in this series: feedback only means something if the grading system underneath it doesn't undercut it — which is where the program's most contrarian workshop comes in.