Consiliae
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Built on how memory works.

Each part of Consiliae rests on research into how people learn and remember. For each part, this page explains the idea in plain words and tells you what the researchers found. It shows what Consiliae does with it, and says where the evidence stops.

You don’t need to follow the links to understand any of it. They are there if you want to read the studies yourself.

Jump to a section

Find out what you know. Learn what is next. Keep it.

Consiliae finds out what you already know and teaches the next thing you are ready for, in short lessons. You prove it by answering questions. Then it comes back at growing gaps until it sticks. Each answer updates an estimate of how well you know each concept, and that estimate decides when each one comes back. The 11 sections below explain why each part is there.

Every concept on your route
  1. PlaceA short scan finds what you already know, so your route skips it.
  2. LearnThe next concept you are ready for, in one short lesson.
  3. ProveA 10-question quiz. Score 75% or more to pass.
  4. ReviewIt comes back after 2 days, then at longer and longer gaps.
  5. KeepIt counts as mastered once you still know it after a gap of 60 days or more.

Start where you are.

Maths builds on itself. Find where you are in it, and you won’t repeat what you know or miss what you need.

In plain words

Almost every idea in maths sits on top of others. You can’t work with fractions until you can multiply, and percentages need fractions. Something you need first is called a prerequisite.

Those links make testing faster. If you can add two fractions, you can almost certainly multiply whole numbers. So one well-chosen question tells you about several concepts at once, and a short test can place you across a whole subject.

It works a bit like the game Twenty Questions. Each good question rules out a large group of answers, so you get to the right one in far fewer steps than asking about everything.

One answer, several concepts
You get fractions rightA right answer on fractions raises the odds you know adding and multiplyingAddingMultiplyingFractionsRatiosPercentages
The question you answered: FractionsMore likely known: Adding, MultiplyingNo change: Ratios, Percentages
You get fractions wrongA wrong answer on fractions lowers the odds you know ratios and percentagesAddingMultiplyingFractionsRatiosPercentages
The question you answered: FractionsMore likely still to learn: Ratios, PercentagesNo change: Adding, Multiplying
Illustrative: a small slice of the map.

What the researchers did

Evidence: established method

In 1985 two mathematicians, Jean-Paul Doignon and Jean-Claude Falmagne, set out a way to describe what a person knows in a subject. It treats knowledge as the set of problems you can solve, and uses the links between problems to rule out combinations that can’t happen.

In a later paper the same group showed how much this narrows things down. For 24 algebra problems there are about 16.8 million possible combinations of known and unknown. Using an expert’s judgement of which problems depend on which, and then testing, they cut that to 312.

This theory is the basis of ALEKS, a maths system that adapts to each student. Its creators say millions of students have used it. ALEKS’s own researchers report that its placement test asks at most 16 questions to estimate what a student knows across up to 501 topics.

What Consiliae does

Our maths map has 1,424 concepts in 9 chapters, from basic arithmetic to linear algebra. 2,812 links between them record which concept you need first.

The Knowledge Scan asks up to 25 questions before you sign up. Once you have an account, the full scan asks up to 40. It asks at least 10 unless it runs out of things to ask, and after that it stops early once more questions would barely change the picture.

After each answer it updates the chance that you know each concept. A right answer raises the chance for the concepts underneath. A wrong answer, or tapping “I don’t know”, lowers it for the concepts built on top. The next question goes to a concept it hasn’t asked about and is still unsure of, chosen to split what is left to find out.

A concept you were asked about counts as known only if you got it right, the chance you know it reaches 95%, and a second piece of evidence agrees, such as a right answer on a concept built on it. The concepts underneath one you clearly know are counted as known too, so the scan doesn’t need to ask about each of them. Anything it is unsure of stays on your route as a normal lesson.

What this does not prove

Knowledge Space Theory is a piece of mathematics for describing knowledge. It was never tested in one single experiment. The evidence that short adaptive tests place students well comes mostly from ALEKS’s own staff.

Real maths is messier than any map. Sometimes you can learn a skill from more than one set of earlier skills. How accurately our scan places people on our map is something we still have to measure.

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Master each step before moving on.

Gaps in maths grow. Moving on only once you have shown you can do something stops them forming.

In plain words

In most classes, everyone moves to the next topic when the timetable says so, whether or not they have understood this one. In maths that is risky, because the next topic is built on this one. A small gap now turns into a big one later.

Mastery learning changes what decides when you move on. You move on when you have shown you understand, usually by passing a short test. If you don’t pass, you go back over it and try again.

Think of building a wall. You check each row is solid before you lay the next one on top.

The lesson quiz
Under 75%. The concept is not passed yet. You can take the quiz again.75% or more. The concept is passed, and the ones that build on it can open.

What the researchers did

Evidence: many studies agree

In 1990 Chen-Lin Kulik, James Kulik and Robert Bangert-Drowns combined the results of 108 studies that compared mastery classes with ordinary ones. They ran in colleges, high schools and the upper years of primary school.

Students in mastery programmes did better on exams than students taught the usual way. The gains were larger for students who had been struggling.

What Consiliae does

A concept opens on your map once every concept it builds on is passed.

Passing means 75% or more on the lesson’s 10-question quiz. If you score less, the concept isn’t passed yet and you can take the quiz again.

Once a concept is passed it stays passed. A later review can lower your level on it, but it never undoes the pass.

What this does not prove

Results varied with how the programme was run and what was tested. The review also found that mastery programmes can take more time, and that self-paced college courses lost more students before the end.

You may have heard Benjamin Bloom’s claim that tutored students beat 98% of an ordinary class, known as the “2 sigma” result. It paired mastery learning with one-to-one tutoring, rested on two small studies, and later reviews found much smaller effects. We don’t claim it.

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Small steps and worked examples.

You can only hold a few new things in mind at once. New ideas land better in small pieces, with an example worked through before you try one.

In plain words

Working memory is the part of your mind that holds what you are thinking about right now. It is small. Most adults can keep about four new pieces in mind at once.

When you are new to a topic and try a problem cold, those slots fill up with searching. What is the question asking? What have I got? What could I try? There is little room left to notice how the method works.

A worked example shows every step and why it is there. It takes the searching away, so your attention goes on the idea itself. It is like watching someone cook a dish once before you cook it yourself.

About four slots of working memory
Trying a new kind of problem cold
What is it asking?What do I know?What could I try?Did that work?
Studying a worked example
This stepWhy it worksfreefree
Illustrative.
The shape of a lesson
  1. Explain
  2. Quick check
  3. Explain, with a worked example
  4. Quick check
  5. Explain
  6. Quick check
  7. 10-question quiz
A typical lesson. Worked examples sit inside the explanations. The number of pages varies by concept.

What the researchers did

Evidence: many studies agree

In 1985 John Sweller and Graham Cooper ran experiments on learning algebra. One group studied worked examples paired with practice problems. The other group solved the same kind of problems on their own. The worked-example group did better on similar problems afterwards.

Three years later Sweller explained why, in what became known as cognitive load theory. Solving a problem by searching for a way through uses up so much working memory that little is left for learning from it.

The psychologist Nelson Cowan later reviewed the evidence on how much we can hold in mind at once. His 2001 review put the limit at about four pieces.

What Consiliae does

Each concept is one lesson: a run of short explanation pages, most of them followed by a quick question, ending with the 10-question quiz.

Almost every lesson includes at least one worked example, inside its explanations.

A quick check is a question on what you have just read. It doesn’t count toward your score, and you answer it before you move on.

What this does not prove

Worked examples help beginners most. Once you know a topic well, studying examples helps less and can even get in the way, so practice should take over. Researchers call this the expertise reversal effect.

We haven’t measured how long our lessons take, so we don’t quote a time.

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Learn by recalling, not rereading.

Pulling an answer out of your memory strengthens it more than reading it again.

In plain words

When you reread your notes, the words look familiar, and familiar feels like knowing. But spotting something on a page is easier than bringing it back with the page closed. Bringing it back is what a test asks of you.

Each time you recall something, it gets easier to recall the next time. Researchers call this the testing effect, or retrieval practice. Think of a path across a field. Walking it is what wears it in.

Share of the passage remembered
Tested 5 minutes later
Read it 4 times
83%
Read once, recalled 3 times
71%
Tested a week later
Read it 4 times
40%
Read once, recalled 3 times
61%
Roediger & Karpicke 2006, Experiment 2. Results from the study, not from Consiliae.

What the researchers did

Evidence: many studies agree

In 2006 Henry Roediger and Jeffrey Karpicke gave 180 university students a short passage to learn. One group read it four times. Another read it once, then wrote down everything they could remember, three times over, with no feedback.

Tested five minutes later, the readers did better. Tested a week later, it had flipped. The recall group remembered 61% of the passage, and the readers 40%.

The readers had gone through the text about 14 times on average, against about 3 for the recall group. They also felt more sure they would remember it.

A 2017 review by Olusola Adesope and colleagues combined 272 results from 188 experiments. On average, practice tests beat restudying by a clear margin.

What Consiliae does

Lessons have quick questions between the explanations and end with a 10-question quiz.

Reviews are all questions, with nothing to reread.

Quizzes, reviews and the scan have an “I don’t know” button, so you never have to guess. It counts as a miss, which keeps our picture of what you know honest.

What this does not prove

The 2006 study used university students learning short passages in a lab, about 30 to a group. The numbers belong to that study. They don’t mean Consiliae makes you remember 50% more.

In that study, recalling only won after a delay. Straight after studying, rereading can look just as good or better, which is why it is so easy to trust.

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Feedback right away.

Finding out straight away whether you were right, and what right looks like, stops a mistake from setting in.

In plain words

If you practise a method the wrong way and nobody tells you, you get better at the wrong method. Quick, clear feedback catches that early, before it turns into a habit.

Feedback helps most when it tells you something you can use, like what the right answer was or where your working went off. A plain “well done” helps far less.

When you miss a question
  1. You answerA quiz or review question.
  2. You see the resultRight or wrong, and the correct answer where it can be shown.
  3. Another tryIf you miss, you get a fresh question on the same idea.
  4. Up to 3 triesThey count toward your estimate. Your score stays the same.

What the researchers did

Evidence: moderate

In 2020 Benedikt Wisniewski, Klaus Zierer and John Hattie combined 435 studies of feedback in education, with more than 61,000 people taking part.

On average, feedback helped learning by a medium amount. The effect varied a great deal. Feedback that gave rich information about the task did best, about twice the average. Rewards and punishments did much less, about half the average.

What Consiliae does

After every question in a lesson quiz or a review you see whether you were right and, where it can be shown, the correct answer. The Knowledge Scan shows less, because it is measuring what you know rather than teaching.

Miss a question in a lesson quiz or a review and an “another try” round gives you a fresh question on the same idea, up to 3 tries. These tries don’t change your score, but they count a little toward our estimate of what you know.

A written explanation of why an answer is right or wrong exists for only some questions so far. Adding more is ongoing work.

What this does not prove

The studies varied so much that the authors warn feedback can’t be treated as one thing. Its effect depends on what kind it is.

Written explanations for every question aren’t built yet.

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Spaced reviews at growing gaps.

Memory fades unless you refresh it. Spreading reviews out builds memory that lasts, and the gaps can grow as you keep getting it right.

In plain words

Much of what you learn today will fade within days unless you come back to it. The psychologist Hermann Ebbinghaus measured this on himself in the 1880s, and a 2015 repeat of his experiment found the same pattern. We forget fast at first, then more slowly.

Each time you come back to something and still get it right, the memory gets stronger and fades more slowly. So the next gap can be longer than the last. Spreading study out like this beats doing the same amount in one sitting.

It is a bit like watering a plant. A little every few days keeps it alive far better than a whole bucket once a month.

Why the gaps can grow
Illustration: memory fades after a lesson, and more slowly after each review at days 2, 6, 14, 30, 62100%50%261430620Days after the lessonWith no reviewsA review you passHow much you would recallIllustrative. Real forgetting varies by person and topic.

What the researchers did

Evidence: many studies agree

In 2006 Nicholas Cepeda and colleagues gathered 317 experiments on spacing from 184 published articles. In 259 of 271 direct comparisons, spreading study out beat doing it in one block. On average, people recalled 47% after spaced study and 37% after studying it all in one go.

In 2008 the same group tested more than 1,350 people over up to a year. The best gap depended on how long the memory had to last. For a test a week away, the best gap was about one and a half to three days. For a test a year away, it was about three to five weeks.

Jaap Murre and Joeri Dros repeated Ebbinghaus’s experiment in 2015, again with a single person learning, and found the same forgetting curve.

What Consiliae does

Your first review of a concept comes 2 days after you pass its lesson.

After each review, the next gap depends on how well we now estimate you know it. At 85% or more the gap doubles. From 70% it grows by half. From 50% it stays the same, and below 50% it halves. The longest gap is 180 days, and a failed review never makes the gap longer.

If you keep remembering, the gaps run 2, 4, 8, 16, 32 and 64 days. The review after the 64-day gap can make the concept Mastered, which ends its reviews. Until then the gaps keep growing, up to 180 days. Your reviews hold only the concepts that are due.

A review asks at least 3 questions on each concept, one on each part of its lesson. A standard review session stops adding concepts at 16 questions, not counting another tries.

What this does not prove

Most spacing research used word lists and facts, usually with young adults, and few studies tested memory more than a month later. It doesn’t settle whether growing gaps beat equal ones.

Our schedule is a starting point we expect to adjust. It spaces reviews by an estimate of what you know. It doesn’t predict the moment you would forget.

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Mixed reviews.

Mixing different kinds of problem makes you work out which method each one needs. A real test asks you to make that choice.

In plain words

Textbook exercises usually come in blocks: twenty questions on one method, then twenty on the next. You know which method to use before you read each question, so you never practise choosing it.

In a test the questions come mixed, and picking the method is a big part of the work. Mixed practice, which researchers call interleaving, trains that choice. It feels harder while you do it, and the extra effort is part of why it works.

Two ways to practise
One topic at a time
Topics mixed
Surprise test about a month later
One topic at a time
38%
Topics mixed
61%
Rohrer et al. 2020. Results from the study, not from Consiliae. Each letter is one kind of problem.

What the researchers did

Evidence: moderate

In the 2017 to 2018 school year, Doug Rohrer and colleagues ran a trial in 54 maths classes of 12-year-olds (US seventh grade) in Florida. 787 students were in the final count.

Each of the 15 teachers taught some classes with mixed practice sheets and others with sheets that kept one kind of problem together. About a month after the last practice sheet, students sat a test they weren’t told about in advance.

The mixed classes scored 61% on average and the others 38%. Mixed practice came out ahead for every one of the 15 teachers.

What Consiliae does

A review takes your due concepts, most overdue first, and mixes their questions together. It avoids asking two questions on the same concept back to back.

Those concepts come from everything you have passed, so one review can move from fractions to slope to percentages.

Lesson quizzes stay on one concept, because a lesson is where you meet it for the first time.

What this does not prove

Mixed practice took longer: all 15 teachers said the mixed sheets took more time. The benefit may be smaller on a test soon after practice, and students probably need some practice on one kind of problem first.

It was one grade, one subject and one school district. In 2013, a large review of study methods rated mixed practice as moderately useful, mainly because the evidence was still limited then.

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Varied questions.

If every question looks the same, you learn the look of it. Asking about a concept in different ways helps you understand the idea underneath.

In plain words

Suppose every slope question you ever saw gave you two points and asked for the slope. You could get quick at the steps without knowing what slope means. Then a graph, or a word problem, would catch you out.

Seeing the same idea in different forms helps. The core stays the same, so you notice which part of it is the idea itself.

One concept, asked four ways
Work it outFind the slope of the line through (1, 2) and (4, 8).
Read a graphRead the slope of the line shown on this graph.
Find the errorSam says the slope from (0, 5) to (2, 1) is 2. What went wrong?
Explain whyWhy does a flat, horizontal line have a slope of 0?
Example questions, written for this page.

What the researchers did

Evidence: weaker direct evidence

Ference Marton and Shirley Booth set out variation theory in 1997. It holds that we notice what is essential about an idea by seeing it vary against what stays the same.

Direct experiments are fewer than for the other ideas on this page. In one, by Bethany Rittle-Johnson and Jon Star in 2007, 12-year-olds compared two ways of solving the same equation side by side. They got better at choosing between methods than students who saw one method at a time. In another, by David Braithwaite and Robert Goldstone in 2015, varied examples helped students who already knew a little about the concept. They didn’t help complete beginners.

What Consiliae does

Questions come from templates that make fresh numbers each time they are served, so remembering last time’s answer won’t help.

We are adding more ways to ask about each concept. They include working it out, spotting the structure, building an example, judging a claim, choosing a strategy, arguing a case and using it in context. So far only a small share of concepts have them.

A quiz puts questions you haven’t seen yet first. In a review, each concept starts with the questions you last got wrong, then ones you haven’t seen.

What this does not prove

The evidence here is thinner than for spacing or recall, so we use it as a guide for designing questions.

Only a small share of our concepts have the new kinds of question so far.

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A model of what you know.

Every answer is evidence. Consiliae keeps a running estimate of how well you know each concept, and uses it to decide when each one comes back.

In plain words

One answer on its own doesn’t tell you much. You might guess right, or slip on something you know well. So instead of trusting single answers, the system keeps a running chance. It says how likely it is that you know this concept, given everything you have answered so far.

A right answer pushes the chance up and a wrong one pulls it down. Because guesses and slips are allowed for, no single answer decides it. Between sessions it drifts down slowly, the way memory fades.

The estimate for one concept
Illustration: the estimate for one concept rises with right answers, dips a little on a slip and fades slowly between sessionsMastered needs 95%Strong needs 85%50%a slipLessonReviewReviewfades with timeIllustrative. The dashed lines are the bars for the Strong and Mastered levels.

What the researchers did

Evidence: established method

In 1995 Albert Corbett and John Anderson described knowledge tracing. It is a way for tutoring software to judge from a student’s answers whether they have learned a skill.

It uses four numbers. The first is how likely the student knew the skill at the start, and the second how likely they learn it with each practice. The other two are how likely they guess right without knowing it, and how likely they slip when they do know it. It was used in the Cognitive Tutor maths software.

What Consiliae does

Each answer updates the chance that you know the concept, allowing for guesses and slips. There is a cap on how far one answer can move it.

The chance fades with time since you last practised.

We set the model’s numbers by replaying real answers from Consiliae learners.

The estimate sets your review gaps, and with your review results it sets your level on each concept. XP doesn’t come from it: you get a set amount for passing each lesson, 10 for each review you pass, and 20 extra for a perfect quiz. Reaching Mastered pays the lesson’s amount again.

What this does not prove

It is a statistical model, not a tutor that understands you. Its numbers are tuned on our learners so far, and they will change as we collect more answers.

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Mastered means it lasts.

Getting it right today shows it is fresh. Getting it right months later shows you have learned it. We only call the second one mastered.

In plain words

Straight after a lesson, everything is easy to recall, so a high quiz score can flatter you. It shows how fresh the memory is. It can’t show how firmly it is stored. The only way to tell the two apart is to wait and check again.

The psychologists Robert and Elizabeth Bjork call these retrieval strength and storage strength. Retrieval strength is how easy it is to recall right now. Storage strength is how deeply it is learned. Things that make practice feel harder, like spacing and mixing, can lower your score in the moment while building the deeper kind. They call these desirable difficulties.

Three levels for every concept
  1. CompetentRight after the lessonYou passed the lesson’s 10-question quiz with 75% or more.
  2. StrongFrom the first reviewYou passed a review after a gap, and our estimate is at least 85%.
  3. MasteredAfter a 60-day gapThree reviews passed in a row, the last after a gap of 60 days or more, with our estimate at least 95%.

What the researchers did

Evidence: many studies agree

The Bjorks set out the difference between retrieval strength and storage strength in 1992. Robert Bjork described desirable difficulties in 1994. In 2011 the pair added one condition. A difficulty only helps if you have the background to meet it, otherwise it just gets in the way.

In 2022 Katherine Rawson and John Dunlosky reviewed successive relearning. That means practising until you get something right, then coming back in later sessions and getting it right again. In university courses it raised exam scores by about 10% and helped students remember more over the long term.

The 2006 recall study in the section on recalling shows this too. The students who reread felt most confident and remembered least a week later.

What Consiliae does

With strong recall, the earliest a concept can reach Mastered is the review after the 64-day gap, about four months after the lesson.

A failed review drops a concept back to Competent until you pass again. It never goes back to unlearned. Mastered concepts leave your reviews.

Concepts you mark with “I already know this” are marked Mastered straight away, and so are the ones the full Knowledge Scan, taken with an account, is confident you already know.

What this does not prove

Concepts marked Mastered by the scan, or by you, skip the review ladder. They rest on the scan’s evidence or your word. They haven’t been through months of reviews.

The level rules are ours. The research says lasting learning should be judged after a delay. It doesn’t say 60 days is the right number.

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Habit and motivation.

Spaced reviews only work if you come back. Small game features, like a streak, can make coming back easier to keep up.

In plain words

Every idea on this page needs you to return, often for months. Most people find that hard. Small, visible rewards for showing up, like a streak count, can help a habit take hold.

These features help you come back. The learning itself comes from the methods above.

What the researchers did

Evidence: modest

In 2020 Michael Sailer and Lisa Homner combined studies of game features in education, such as points, badges and leaderboards. They found small benefits for learning, and smaller ones for motivation and behaviour.

The benefit for learning held up in the most careful studies. The benefits for motivation and behaviour varied more from study to study.

What Consiliae does

You earn XP (points) for the lessons and reviews you pass, with a bonus for a perfect quiz.

Your daily streak has one Recovery Day each week, which you can spend to cover a missed day so it doesn’t wipe the streak out.

One daily quest and one weekly challenge are active at a time. Weekly leagues have 10 tiers, and a Big Day marks a day when you learn far more than usual.

Rewards follow the same rules for every learner, whatever their plan.

What this does not prove

The evidence for game features is small and mixed.

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The research explains the method. It has not measured Consiliae.

The research on this page tested methods in classrooms and labs, or set out the theory behind them. None of it measured Consiliae, and we haven’t run a controlled study of our own yet. So we don’t promise results in numbers. These are the questions we still have to answer with our own learners:

  • How often is the scan right about what a learner already knows?
  • How much do learners still remember two days, and two months, after a lesson?
  • How many lessons that are started get finished?
  • How long does a lesson take?

Every study on this page.

Most figures from the research were checked against the original papers. A few come from reviews that cite them. Figures about Consiliae are read from the product itself, so they change when it does.

  1. Adesope, O. O., Trevisan, D. A., & Sundararajan, N. (2017). Rethinking the use of tests: A meta-analysis of practice testing. Review of Educational Research, 87(3), 659-701.
  2. Bjork, E. L., & Bjork, R. A. (2011). Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning. In Psychology and the real world (pp. 56-64). Worth.
  3. Bjork, R. A. (1994). Memory and metamemory considerations in the training of human beings. In J. Metcalfe & A. Shimamura (Eds.), Metacognition: Knowing about knowing (pp. 185-205). MIT Press.
  4. Bjork, R. A., & Bjork, E. L. (1992). A new theory of disuse and an old theory of stimulus fluctuation. In A. Healy, S. Kosslyn, & R. Shiffrin (Eds.), From learning processes to cognitive processes (Vol. 2, pp. 35-67). Erlbaum.
  5. Bloom, B. S. (1984). The 2 sigma problem: The search for methods of group instruction as effective as one-to-one tutoring. Educational Researcher, 13(6), 4-16.
  6. Braithwaite, D. W., & Goldstone, R. L. (2015). Effects of variation and prior knowledge on abstract concept learning. Cognition and Instruction, 33(3), 226-256.
  7. Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132(3), 354-380.
  8. Cepeda, N. J., Vul, E., Rohrer, D., Wixted, J. T., & Pashler, H. (2008). Spacing effects in learning: A temporal ridgeline of optimal retention. Psychological Science, 19(11), 1095-1102.
  9. Corbett, A. T., & Anderson, J. R. (1995). Knowledge tracing: Modeling the acquisition of procedural knowledge. User Modeling and User-Adapted Interaction, 4(4), 253-278.
  10. Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87-114.
  11. Doignon, J.-P., & Falmagne, J.-C. (1985). Spaces for the assessment of knowledge. International Journal of Man-Machine Studies, 23(2), 175-196.
  12. Doignon, J.-P., & Falmagne, J.-C. (2015). Knowledge spaces and learning spaces. arXiv:1511.06757.
  13. Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students’ learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4-58.
  14. Ebbinghaus, H. (1885). Über das Gedächtnis. Translated as Memory: A contribution to experimental psychology (1913).
  15. Falmagne, J.-C., Koppen, M., Villano, M., Doignon, J.-P., & Johannesen, L. (1990). Introduction to knowledge spaces: How to build, test, and search them. Psychological Review, 97(2), 201-224.
  16. Kalyuga, S., Ayres, P., Chandler, P., & Sweller, J. (2003). The expertise reversal effect. Educational Psychologist, 38(1), 23-31.
  17. Kulik, C.-L. C., Kulik, J. A., & Bangert-Drowns, R. L. (1990). Effectiveness of mastery learning programs: A meta-analysis. Review of Educational Research, 60(2), 265-299.
  18. Marton, F., & Booth, S. (1997). Learning and awareness. Lawrence Erlbaum.
  19. Matayoshi, J., Cosyn, E., Lechuga, C., & Uzun, H. (2024). An evaluation of a placement assessment for an adaptive learning system. Proceedings of the 17th International Conference on Educational Data Mining. (The authors work for McGraw Hill ALEKS.)
  20. Murre, J. M. J., & Dros, J. (2015). Replication and analysis of Ebbinghaus’ forgetting curve. PLOS ONE, 10(7), e0120644.
  21. Rawson, K. A., & Dunlosky, J. (2022). Successive relearning: An underexplored but potent technique for obtaining and maintaining knowledge. Current Directions in Psychological Science, 31(4), 362-368.
  22. Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? Journal of Educational Psychology, 99(3), 561-574.
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