Pedagogical Content Knowledge Developer Agent Skill

Develop pedagogical content knowledge for a topic by surfacing common misconceptions and effective representations.

Context cost
10.7k tokensestimated from the bundle, loaded when it triggers
Bundle
1 file · 42.9 kBtext throughout, nothing executable
Licence
not declarednone named by its author
Last change
—v1.0
Servers it uses
Noneruns standalone

What it does

Develop pedagogical content knowledge for a topic by surfacing common misconceptions and effective representations. Use when preparing to teach unfamiliar content or improving teaching of hard topics.

What this skill changes about the agent has not been set out here as a list. Its SKILL.md, shown below, says it in the author’s own words.

content-knowledgeknowledge-contingentmisconceptionspckpedagogical-content-knowledgeprofessional-learningshulmanteacher-development

The skill itself

A skill is instructions the model reads, so you can see what you are getting: below is the start of its SKILL.md. The front matter loads with every session, the body loads when the skill triggers, and the whole file comes with the install.

SKILL.md42.9 kB · preview
--- # AGENT SKILLS STANDARD FIELDS (v2) name: pedagogical-content-knowledge-developer disable-model-invocation: false user-invocable: true effort: medium # EXISTING FIELDS skill_id: "professional-learning/pedagogical-content-knowledge-developer" skill_name: "Pedagogical Content Knowledge Developer" domain: "professional-learning" version: "1.0" evidence_strength: "strong" evidence_sources: - "Shulman (1986) — Those who understand: Knowledge growth in teaching — original PCK framework" - "Shulman (1987) — Knowledge and teaching: Foundations of the new reform" - "Ball, Thames & Phelps (2008) — Content knowledge for teaching: What makes it special?" - "Magnusson, Krajcik & Borko (1999) — Nature, sources and development of PCK for science teaching" - "Cochran, DeRuiter & King (1993) — Pedagogical content knowing: An integrative model" - "Hattie (2009) — Visible Learning: teacher content knowledge and PCK as distinct predictors" - "Depaepe, Verschaffel & Kelchtermans (2013) — Pedagogical content knowledge: A systematic review" - "Bernstein (1999) — Vertical and horizontal discourse: knowledge structures and recontextualisation" - "Willingham (2009) — Why Don't Students Like School: content knowledge as prerequisite for teaching" - "Timperley et al. (2007) — Teacher Professional Learning and Development: content-specific PD effectiveness" input_schema: required: - field: "teaching_context" type: "string" - field: "learner_stage" type: "string" - field: "teacher_background" type: "string" optional: - field: "known_student_misconceptions" type: "string" - field: "curriculum_framework" type: "string" - field: "knowledge_architecture_output" type: "string" output_schema: type: "object" fields: - field: "pck_diagnosis" type: "object" - field: "content_knowledge_foundations" type: "object" - field: "common_student_misconceptions" type: "object" - field: "pedagogical_representations" type: "object" - field: "disciplinary_thinking_standards" type: "object" - field: "developmental_action_plan" type: "object" chains_well_with: - "curriculum-knowledge-architecture-designer" - "critical-thinking-task-designer" - "lesson-observation-protocol-designer" - "reflective-practice-prompt-generator" - "technological-pedagogical-content-knowledge-developer" teacher_time: "10 minutes" tags: ["PCK", "pedagogical-content-knowledge", "teacher-development", "content-knowledge", "misconceptions", "Shulman", "professional-learning", "knowledge-contingent"] ---
79# Pedagogical Content Knowledge Developer
80
81## What This Skill Does
82
83Takes a description of what a teacher is about to teach and their background, diagnoses their likely pedagogical content knowledge gaps for that specific topic, and produces a development plan to close those gaps before teaching begins. Shulman's (1986) foundational insight is that knowing a subject and knowing how to teach it are genuinely different capabilities — a mathematician who has never taught fractions to nine-year-olds does not automatically know which representations work, which misconceptions will form, or what conceptual threshold students need to cross before the next idea makes sense. This skill makes those gaps visible and actionable. It covers all three knowledge dimensions: the hierarchical content knowledge the teacher must have secure, the horizontal thinking frameworks that define expert reasoning in the domain, and the dispositional orientation toward noticing and responding to student understanding in real time. The output is both a diagnosis and a development plan — not just identifying what is missing but sequencing what the teacher should do about it. This is particularly valuable when teachers are working outside their primary subject expertise, teaching ambitious new programmes (regenerative project-based learning, interdisciplinary units, wellbeing science), or moving to a new age group where their existing PCK needs recalibration. AI is specifically valuable here because mapping PCK gaps requires simultaneously knowing the content domain, the research on student misconceptions, the evidence on pedagogical representations, and the developmental appropriateness of different approaches — a combination that takes years to develop through experience and that most pre-service training delivers only partially.
84
85## Evidence Foundation
86
87Shulman (1986, 1987) distinguished PCK from general content knowledge and general pedagogical knowledge as a third, distinct category: the blend of content and pedagogy that is uniquely the province of teachers. A chemist and a chemistry teacher may have identical content knowledge, but the teacher also knows which analogies work for ionic bonding at age 14, which misconceptions about atoms are nearly universal, and which representations mislead more than they illuminate. This is PCK — the knowledge that makes content teachable. Shulman identified it as "the most useful forms of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstrations — in a word, the ways of representing and formulating the subject that make it comprehensible to others."
88
89Ball, Thames & Phelps (2008) refined Shulman's framework into six sub-domains of mathematical knowledge for teaching, finding that this form of PCK predicted student achievement gains independently of general content knowledge. Their key finding: a teacher's ability to identify why a student's incorrect answer makes sense given the student's likely reasoning was a stronger predictor of student learning than the teacher's own ability to solve mathematical problems. The implication: content knowledge is necessary but not sufficient. What matters is the transformation of content knowledge into teachable form — which requires knowing how students think about this content, not just knowing the content itself.
90
91Magnusson, Krajcik & Borko (1999) mapped the components of PCK for science teaching: knowledge of science curricula, knowledge of students' understanding of specific science topics, knowledge of instructional strategies and representations for teaching specific science topics, and knowledge of assessment of specific science topics. Each component is topic-specific — a teacher's PCK for photosynthesis does not transfer to their PCK for Newtonian mechanics. This topic-specificity is what makes PCK development so demanding and why a diagnostic tool is needed.
92
93Depaepe, Verschaffel & Kelchtermans (2013) conducted a systematic review confirming PCK as a distinct, teachable, and measurable construct across subjects, while noting that it develops primarily through subject-specific teaching experience and targeted reflection — not through generic professional development. Cochran, DeRuiter & King (1993) proposed the concept of "pedagogical content knowing" — emphasising that PCK is dynamic and continually developing, not a fixed body of knowledge to be acquired.
94
95Hattie (2009) found that teacher subject matter knowledge has a moderate effect on student achievement (d = 0.09 for content knowledge alone), but that PCK — the ability to represent content in ways students can access — has a substantially larger effect. Willingham (2009) reinforced this from a cognitive science perspective: teachers cannot make good in-the-moment decisions about explanations, examples, and representations if they do not have deep, flexible content knowledge to draw from. Content knowledge is the raw material from which PCK is constructed.
96
97Timperley et al. (2007) found in their Best Evidence Synthesis that the most effective professional development is content-specific and directly connected to teaching practice: teachers who study student misconceptions in their subject and refine their pedagogical representations improve student outcomes more than teachers who study general teaching strategies. The implication for this skill: PCK development must be targeted at the specific topic the teacher is about to teach, not at general pedagogical principles.
This is a preview of SKILL.md. Download or install the skill to get the whole thing.
In the file
SKILL.md5,948 words
Files1
Licencenot declared
Why you can read it

Nothing in a skill executes. The client loads the text and the model follows it, so a skill can be audited the way a runbook is — by reading it.

What it costs in context

Skills are not billed by the call. They are paid for in context: every token the instructions occupy is a token your code, your diff and your conversation cannot use. Here is what this one takes and when it takes it.

≈1,110
always loaded
The name and description, so the model knows the skill exists and when to reach for it.
9,615
on trigger
The instruction body, read only when the skill fires.
5.4%
of a 200k window
Ten skills this size would take about 54% of the window before you open a file.
050k100k150k200k context window

10.7k tokens, estimated from the bundle at four bytes to the token, held for the rest of the session once it triggers. Heavy. Teams tend to install this one per project rather than globally, and load it only when the job comes up.

Servers bill, skills cost

A server charges by the month. A skill charges once per session, in context, and then keeps charging it for as long as the session lives.

Before and after

The same question, put to the same model twice: once as it comes, and once with these instructions loaded.

No worked example has been published for this skill yet.

The procedure it runs

The procedure has not been set out here step by step. It is in the body of its SKILL.md: the start of it is shown above, and the whole file comes with the install.

Prose, not code

These steps are written for a model to follow, not executed by a runtime. It can still be told to skip one, and it will say so when it does.

Servers it uses

None. This skill calls no MCP servers at all.

Everything it needs is in the instructions, so it works in a project with nothing connected — the model reads the file and changes how it works with what it can already reach.

Its SKILL.md does not declare which tools it asks the agent for, so what it touches is whatever the instructions themselves ask for — read them before you install it.

What it asks for
Writes filesnot declared
Network accessnot declared

This SKILL.md carries no allowed-tools line, so neither is declared. A skill grants no permissions of its own — it can only ask for tools your client already has.

What it will not do

Every skill is narrow, and the useful ones say where they stop. These are the jobs this one is the wrong tool for.

What this skill is not for has not been published here. Nothing is implied by that: it is a section the author has not filled in.

What is in the bundle

1 file, 42.9 kB on disk. A bundle is text throughout: the instructions the model reads, plus the templates it fills in.

  • SKILL.md42.9 kB
What is not in it

No dependencies and nothing executable: a skill is text the agent reads, so the bundle is 1 file you can review in full before installing.

Install

Installing copies the bundle into your project. Nothing runs at install time — the files sit on disk until the model reads them.

# Pedagogical Content Knowledge Developer · 10.7k tokens when loaded · macOS, Linux mkdir -p .claude/skills && t=$(mktemp -d) && curl -fsSL -o "$t/bundle.tar.gz" https://mcprush.com/api/skills/pedagogical-content-knowledge-developer/bundle.tar.gz && tar -xzf "$t/bundle.tar.gz" -C "$t" && [ -d "$t/pedagogical-content-knowledge-developer" ] && { [ ! -e .claude/skills/pedagogical-content-knowledge-developer ] || { mv .claude/skills/pedagogical-content-knowledge-developer "$t/.previous" && echo "Previous copy moved to $t/.previous"; }; } && mv "$t/pedagogical-content-knowledge-developer" .claude/skills/ && echo "Installed .claude/skills/pedagogical-content-knowledge-developer"
On Windows, or any OS with Node 20+
npx mcprush@latest skill add garethmanning/pedagogical-content-knowledge-developer

Windows PowerShell says 'running scripts is disabled on this system'? Run Set-ExecutionPolicy -Scope CurrentUser RemoteSigned once, or type npx.cmd instead of npx (codex.cmd, gemini.cmd, grok.cmd likewise). PowerShell 7 needs neither. Writes to .claude/skills/pedagogical-content-knowledge-developer/ in the current project. For every project instead, run mkdir -p ~/.claude/skills && t=$(mktemp -d) && curl -fsSL -o "$t/bundle.tar.gz" https://mcprush.com/api/skills/pedagogical-content-knowledge-developer/bundle.tar.gz && tar -xzf "$t/bundle.tar.gz" -C "$t" && [ -d "$t/pedagogical-content-knowledge-developer" ] && { [ ! -e ~/.claude/skills/pedagogical-content-knowledge-developer ] || { mv ~/.claude/skills/pedagogical-content-knowledge-developer "$t/.previous" && echo "Previous copy moved to $t/.previous"; }; } && mv "$t/pedagogical-content-knowledge-developer" ~/.claude/skills/ && echo "Installed ~/.claude/skills/pedagogical-content-knowledge-developer" (macOS, Linux) — or add --global to the npx line. The curl line replaces .claude/skills/pedagogical-content-knowledge-developer/ only after the download succeeds, so files left there by another skill of the same name, or by an older release, do not mix in. A copy already there is moved aside, not deleted, and the line prints where.

Which clients pick it up on their own

A skill is a folder of text. Most of these read a skills folder and pick it up without being told; the rest take the same folder another way — an upload in the app, a parameter on an API call — and then choose it by its description just the same.

Claude Code.claude/skills/
Claude DesktopCustomize › Skills
ChatGPTSkills › Create › Upload
Cursor.cursor/skills/
VS Code.github/skills/
Codex CLI.agents/skills/
Gemini CLI.gemini/skills/
Grok Build.grok/skills/
Microsoft CopilotSkills › Upload a skill
PerplexityComputer › Skills › Upload a skill
DeepSeek Harness.dsh/skills/
Zed.agents/skills/
Devin Desktop.devin/skills/
Windsurf (legacy).windsurf/skills/
OpenAI Agents SDKInstructions or sandbox Skills
HTTP / APIa request parameter
This release
Version1.0
Publishedno release date on file
PriceFree
Referencegarethmanning/pedagogical-content-knowledge-developer

Versions

v1.0 is what is on the shelf; no release here carries a date. Instructions change more often than APIs do — a skill can be rewritten entirely without anything it depends on moving.

v1.0
  • No earlier releases have been published to the marketplace.
Pinning

The install command always fetches the release that is current the day you run it — v1.0 today — and cannot ask for an earlier one. The copy on your disk does not change until you run it again.

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