How to Design Academic Learning for Kids (Based on Science)

A call with Caleb homeschooling two daughters

Recently I was on the phone with a good friend named Caleb Guilliams. He and his wife April are looking at homeschooling their daughters, and given my dive into the education space he was asking my perspective on curriculum and instructional design for their daughters.

While I’ve learned about learning, motivation science, and generally the education space, curriculum design and instructional design are phrases that don’t come with any clear understanding in my head. So in the interest of giving an educated answer to Caleb, while educating myself, I’ll start with defining those terms.

Curriculum design is WHAT gets taught and WHEN it gets taught, or in other words the scope and sequence. For example learning multiplication tables in the third grade. Instructional design is HOW it gets taught. Pieces like how information is presented and practiced, and how the students are given feedback.

The terms seven of them

Some other important terms to know for this essay are prerequisite structure, formative vs summative assessments, knowledge space, mastery, spacing, and transfer.

Prerequisite structure is a map of what skills are required before moving on to compound skills.¹

Formative Assessment happens during the learning, and is used to adjust the teaching while there is still time to act on it. Summative Assessment happens at the end, and is used to judge what was learned.²³

A knowledge space is a concept like math, english language, bowling theory, or physics.⁴

Mastery is defined scientifically as command over a certain subject over a period of time. Typically above 90% correct answers over three different tests.⁵

Spacing is the setting of distance between practice based on studies showing that the harder it is to recall (a.k.a. retrieve) a thing the more that action of recalling it improves the neuropathway to that information (the more it improves the learning of that info).⁶

There are two parts of Transfer. Near transfer is applying knowledge in the same structure and shape that you learned it, and far transfer is applying it to situations or structures outside of where you learned it.⁷ I.e. Learning multiplication in the context of baseball, but then applying the same math to farming.

Designing the curriculum start from the result

There are some best practices when designing curriculum that are as follows. The first, as detailed by Wiggins and McTighe is Backwards design, starting from the desired result.⁸ This means defining in observable, measurable terms what it means to have learned the lesson.

The second is mapping the prerequisite structures. Once you know what the desired lesson of the unit is, also known as the scope, you can work backwards by breaking each fact or skill the student needs to learn, into an order that completes the lesson. Let’s take for example addition: The student must know their numbers (A set of 5 skills)⁹, and they must know the operation of addition.

Those 5 skills are:

• One-to-one — each object gets exactly one number word, no skips, no doubles.
• Stable order — the words come in the same sequence every time.
• Cardinal — the last word you said is how many there are.
• Abstraction — this works on anything, including things you can’t touch.
• Order irrelevance — count them in any order, same total.

Spiral or mastery a mile wide, an inch deep

From there come some concepts that have been studied, but still have some debate. One is sequencing. In 1960 Bruner proposed a spiral curriculum that revisits topics once a year and moves kids forward through the units of a grade level by time.¹⁰ On the other hand, learning science studies from Bloom and others have shown that learning progression gated by mastery is more effective for learning.^11121314 The debate is around whether or not moving students forward only on mastery is possible in a public school system. If you’re designing curriculum for a more flexible system like homeschooling or private schools I find it undeniable that mastery sequencing is more effective in teaching students, and honestly weak minded to consider something else even for public schools.

In a TIMSS study Schmidt said that the American math and science system is a mile wide and an inch deep for this reason, which was a quotable phrase that traveled far since that analysis.¹⁵ Said differently, topics were touched, but only reappeared years later without the reps to accumulate into neural pathways.

Another concept like this is that content is not the enemy of thinking. Hirsch and Willingham argue that critical thinking comes once domain knowledge is established and therefore kids learning to think is less useful than them learning a space.¹⁶¹⁷ Also there is evidence to support that the current school learning model is not helping to improve critical thinking anyway.

Designing the instruction EDGE, working memory, 80–85%

After it is defined and mapped out what will be taught and when, then one can move onto designing how the teaching will be delivered.

For best practices in instructional design the best proven one is explicit instruction.¹⁸¹⁹ Which I like to explain with the EDGE method.

Explain the skill first, then Do the skill in front of them, then Guide them through an example problem, and as they learn it give them less guidance, and less scaffolding until they are Enabled to do it independently.²⁰

The biggest binding constraint for instructional design is working memory. While adult brains can hold ~5 chunks of information in their working memory, young students hold less.²¹²² This means that if there is lots of information in a question, multiple parts to the problem, or other such structural defects the students are not set up to learn well.²³ To combat this a worked example is typically the best way to move them from not knowing how to do the problem to doing it independently (similar to the EDGE method).

Another best practice in instructional design is keeping kids in the Zone of Proximal Development. Which Vygotsky²⁴ defined as ‘too hard to do alone, but possible with guidance’ essentially. To give it a number, In a separate study Rosenshine¹⁸ defined a similar concept as 80% correct answers that kept up engagement while maintaining learning quality and retention from watching students and Wilson defined it as 85% correct answers is the mathematically fastest percentage for learning based on training AI models.²⁵ So upon looking at the data of both engagement and learning we’ll say this Goldilocks zone is between 80 and 85% correct answers.

Another practice supported by science is practice done by retrieving rather than reviewing. Low stakes quizzing and testing is a significantly more effective way of improving the pathways to the information in their brain than simply re-consuming something they’ve already done.²⁶

One of the instructors most critical tasks is giving feedback. In fact, Kluger and DeNisi’s meta analysis shows that over ⅓ of feedback given in schools reduces performance.²⁷ So effective instructional design looks at the motivation science and considers practices like focusing feedback on the task rather than the person.

The steps eight of them

Now, while this explains what these concepts are, it does not explain the steps to build a curriculum and design the instruction around it. So while the above concepts and more are important to doing the following steps well, here are the steps:

1. Decide ‘placement’ if creating a school.

I suggest doing this by knowledge space and checking mastery. Also check laws in your area of what is required in terms of what knowledge spaces need to be taught.

You can do this testing by testing downward from where you would guess the child is. Most programs also offer placement tests if you’d like to use them.

In terms of checking laws I’d look to your state department of education site. Also HSLDA keeps a 50-state summary of homeschool requirements, those are faster to read than the statutes.

2. Define what you want the kid to learn.

I.e. What knowledge spaces, math, english language, physics, entrepreneurship, painting, art history, bowling, whatever it is you would like. Just make a list with whatever you want.

3. Find the legal standards for that knowledge space.

Where you live has laws governing what kids must learn by certain times. Finding these, regardless of how out-dated, is necessary legally, but keep in mind they will rarely be actionable, or based on science. (see common core)²⁸²⁹

4. Translate each standard, however they are written, into observable actions that you can measure.

I.e. Has learned multiplication of numbers → can complete multiplication tables from 0-13 in under 3 minutes from memory. This is for the law, not the design.

5. Build the knowledge graph of the knowledge space up from first principles and their definitions (“standards” are a weak proxy for this) or take/buy one from a company that has already put one together.

DEFINITION: Knowledge graph is a map of each concept, what observable action demonstrates mastery, and the prerequisites between concepts. Arranged as nodes (the concept, an actionable way to measure it, and the content to teach it).

Where to look if you do not want to build one yourself:

• Achieve the Core’s Coherence Map. K-8 Common Core math as a dependency graph with prerequisite arrows. Free, public domain.
• Math Academy. Proprietary and far finer, thousands of nodes. Justin Skycak’s The Math Academy Way is free online and explains the pedagogy — graph construction, mastery gating, spaced review — in more detail than anyone else has published.
• ALEKS. Proprietary, built on knowledge space theory, now McGraw-Hill.
• Clements & Sarama’s learning trajectories. Early math only, free at learningtrajectories.org, built from observing children and tested in a randomized trial.

Nothing public exists for reading, writing, science or history.

If you don’t have the time to build this yourself, you can proxy this with standards offered in different curriculums you can find online or through community groups.

6. Find engaging, interesting activities used to anchor concepts and guide your units of learning.

I.e. Competing with other kids on races to fill out multiplication tables of 3 x 1-13

Write these down in a list as you’re going through your analysis and translation of standards

By the end of your work on the knowledge graph you should have a clear list of What you are going to teach, and a fun list of activities to potentially teach most, if not all, of the concepts

If you are looking for lesson ideas many of the published curriculum products and programs offer content to teach it.

7. Organize

There are patterns, order, and relationships in everything you’ve written out. Group related topics together. Enough related topics and you have a unit.

Typically the hierarchy is Course > Units > Nodes > Observable Actions > Lessons > Content

I.e. addition and subtraction are similar, so we learn those together.

8. Fill in the lessons with content

• Lecture notes, lecture stories, lecture videos — I.e. How to download information into the students brain
• Instructional resource — visuals, puzzles, formative assessments
• Resources for practicing

Again if you are looking for lesson ideas many of the published curriculum products and programs offer content to teach it.

Structuring a lesson worked examples, faded guidance

Once you are done with the curriculum design then comes the instructional design.

How it’s presented, How they practice it, How it’s measured

Once you have written the lesson/activity/content (Steps 6-8 in the above curriculum design method) that teaches for each node’s near transfer in varied environments and contexts you can now structure it as the following science based structure.

Using a worked example with faded guidance (i.e. EDGE method)

Great Lesson Examples:

• Review previous lesson — spaced retrieval⁶²⁶
• Check for their understanding — mastery
• IF hit mastery then proceed to next lesson
• IF do not hit mastery go back and practice/re-learn earlier concepts

NEXT LESSON

• Motivating problem — A problem they cannot solve, or is better solved by the new skill
• Explicit Instruction — State explicitly what the concept is and how to do it
• Knowledge transfer with content in small steps — Do this in small chunks and check for comprehension
• Worked Examples with releasing guidance — Do an example in front of them (that they wouldn’t be able to do because they haven’t built the skill. Then slowly loop them in to doing more and more of the work as you go through more examples)
• Motivation science + Many checks for comprehension and engagement through questions

One other note here is the science of feedback, especially Butler’s work on grades suggests that just giving feedback on the process a student took to complete a task and how close their work was to demonstrating mastery achieves better performance than giving a student a grade.³⁰

So I suggest no old school grades, and instead a % of the correct process to get to the answer.