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Use this file to discover all available pages before exploring further.

Learning pathways help your application suggest related mathematical topics to students after they solve a problem. Rather than leaving learners at a dead end after receiving a result, you can surface a curated list of connected concepts — the next topics to explore, prerequisites to revisit, or complementary techniques to try. This turns a single API call into the starting point for a guided learning journey.

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What learning pathways are

When you set learning_pathways: true in a request, the API includes a learning_pathways array in the response. Each entry links to a related mathematical concept or Stemfard endpoint that naturally extends the topic the student just worked on. For example, after solving a matrix multiplication problem, pathways might point toward determinants, matrix inverses, or eigenvalues. The related field works differently: setting related: true returns an array of other Stemfard API endpoints that are closely related to the one you called. This is useful for building navigation within your application — showing students what other operations are available that relate to what they just did.
FieldTypeWhat it returns
learning_pathwaysbooleanConceptual learning topics to explore next
relatedbooleanOther Stemfard API endpoints in the same mathematical neighborhood

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Enabling learning pathways

Add learning_pathways: true (and optionally related: true) to any request body: 
{
  "a": [[1, 2], [3, 4]],
  "b": [[5, 6], [7, 8]],
  "api_level": "standard",
  "learning_pathways": true,
  "related": true
}

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Complete example

The following request multiplies two matrices and asks for both learning pathways and related endpoints: 
curl --request POST \
  --url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/matmul \
  --header 'Authorization: Bearer <your-api-key>' \
  --header 'Content-Type: application/json' \
  --data '{
    "a": [[1, 2], [3, 4]],
    "b": [[5, 6], [7, 8]],
    "api_level": "standard",
    "result_name": "product",
    "learning_pathways": true,
    "related": true
  }'
Sample response 
{
  "result_name": "product",
  "result": [[19, 22], [43, 50]],
  "steps": { "html": "..." },
  "learning_pathways": [
    {
      "title": "Matrix determinants",
      "description": "Compute the scalar value that summarizes a square matrix's properties.",
      "href": "/api/v1/mathematics/linear-algebra/matrix-determinant"
    },
    {
      "title": "Matrix inverse",
      "description": "Find the matrix that undoes a transformation.",
      "href": "/api/v1/mathematics/linear-algebra/matrix-inverse"
    },
    {
      "title": "Eigenvalues and eigenvectors",
      "description": "Discover the fundamental directions that a matrix scales without rotating.",
      "href": "/api/v1/mathematics/linear-algebra/eigenvalues"
    }
  ],
  "related": [
    {
      "title": "Matrix addition",
      "href": "/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/add"
    },
    {
      "title": "Matrix subtraction",
      "href": "/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/subtract"
    },
    {
      "title": "Matrix statistics",
      "href": "/api/v1/mathematics/linear-algebra/matrix-operations/matrix-statistics"
    }
  ]
}

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Using pathways in an educational app

Once you have the learning_pathways array, you can render it as a “what to explore next” section. Below is a pattern that works well after displaying a result. 
async function solveAndRenderPathways(matrixA, matrixB) {
  const response = await fetch(
    'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/matmul',
    {
      method: 'POST',
      headers: {
        'Authorization': 'Bearer <your-api-key>',
        'Content-Type': 'application/json',
      },
      body: JSON.stringify({
        a: matrixA,
        b: matrixB,
        api_level: 'standard',
        learning_pathways: true,
        related: true,
      }),
    }
  );

  const data = await response.json();

  // Display the result
  displayResult(data.result);

  // Render pathway cards
  const pathwayList = document.getElementById('next-topics');
  pathwayList.innerHTML = '';

  for (const pathway of data.learning_pathways) {
    const card = document.createElement('a');
    card.href = `/topics${pathway.href}`;
    card.className = 'pathway-card';
    card.innerHTML = `
      <h4>${pathway.title}</h4>
      <p>${pathway.description}</p>
    `;
    pathwayList.appendChild(card);
  }
}

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Pathway use cases

Use learning pathways to drive a structured curriculum. After a student completes a problem at one level, fetch the pathways and present only those that match the student’s current progress tier. Store completed topics in your own database and filter the pathway list to surface the most relevant next step.
const nextTopics = data.learning_pathways.filter(
  (p) => !student.completedTopics.includes(p.href)
);
If a student’s solution contains errors, use pathways to suggest prerequisite topics for review rather than pointing forward. You can combine pathway data with your own difficulty scoring to decide whether to route a student forward or backward through the curriculum.
Present the full learning_pathways array in a visual map so students can freely explore connected concepts. Pair this with the related endpoints array to show which API operations are available for each topic, letting curious learners dive deeper on their own terms.
Both fields help students navigate, but they serve different purposes:
  • learning_pathways points to mathematical concepts — the next things to learn. These are topic-level suggestions designed to guide curriculum progression.
  • related points to other Stemfard API endpoints in the same operational family. These are practical suggestions for exploring what else the API can compute in the same domain.
Use learning_pathways to drive curriculum flow and student growth. Use related to build discoverable API navigation within your interface.