Learning Styles: What role should they play?

Many students misunderstand the  concept of “learning style” and its role in learning mathematics.  There are no “fixed styles you are born with”.  Learning style preferences are not fixed and can be changed.  They should be used selectively to support meeting your learning goals in many different contexts.

There are seven “learning style preferences”.

Visual (spatial): You prefer using pictures, images, and spatial understanding.

Aural (auditory-musical):  You prefer using sound and music.

Verbal (linguistic):  You prefer using words, both in speech and writing.

Physical (kinesthetic):  You prefer using your body, hands and sense of touch.

Logical (mathematical):  You prefer using logic, reasoning and systems.

Social (inter-personal):  You prefer to learn in groups or with other people.

Solitary (intra-personal): You prefer to work alone and use self-study.

You can find out what your current preferences are by taking a simple inventory, as here.

Get beyond the notion that your learning depends solely on not satisfying your “preferred learning style”.

Your preferences are not fixed – they can be changed.  Your success in learning

You can use the different preference styles in many ways to learn the mathematics you need. Ultimately you will need to work alone and responsible for your selfstudy program.

Be the one in charge of your own learning.

Mastery is a quest , especially of complex ideas, skills, and processes, .

Get beyond”learning style preferences” and embrace the notion of successful intelligence.

Describe what you want to know, do, or accomplish. Then list the competencies required, what you need to learn, and where you can find the knowledge or skill. Then go get it.

Consider your expertise to be in a state of continuing development.

Practice self- testing as a learning strategy to discover your strengths and weaknesses.

Build on your strengths. Then focus becoming more competent on improving yourself in the weakness areas.

Adopt active learning strategies like retrieval practice , spacing, and interleaving. Be aggressive.

Don’t rely on what feels best:  use quizzing, peer review, and  other tools such as journals

Maintain your enthusiasm for learning.  Remember that the difficulties you can overcome with more cognitive effort will more than repay you in the strength of your learning.


Analyze your learning objectives and the needed knowledge structure.

Define your learning objectives explicitly.

Understand the context of your learning objectives.

Break down each one into their component parts.

Carefully build the knowledge structure that addresses them.

Then summarize and represent that structure

If you’re an example learner, study examples two at a time or more, rather than one by one, asking yourself in what ways they are alike and different. Are the differences such that they require different solutions, or are the similarities such that they respond to a common solution?

If you think you are a low structure-builder or an example learner trying to learn new material, pause periodically and ask what the central ideas are, what the rules are.

Describe each idea and recall the related points. Which are the big ideas, and which are supporting concepts or nuances? If you were to test yourself on the main ideas, how would you describe them?

What kind of scaffold or framework can you imagine that holds these central ideas together?

As in concept formation by abstracting the underlying rules and piecing them into a structure, you go then use it both to increase knowledge – but also for more than knowledge – your know-how skills.

And that kind of mastery will put you ahead.


Brown, Peter C. (2014-04-14). Make It Stick (p. 161). Harvard University Press. Kindle Edition.



Learn for Mastery

By learning for mastery we mean acquiring knowledge and skills and having them] readily available from memory so you can make sense of future problems and opportunities.

There are some immutable aspects of learning that we can probably all agree on:

First, to be useful, learning requires memory , so what we’ve learned is still there later when we need it.

Second, we need to keep learning and remembering all our lives.

We can’t advance through middle school without some mastery of language arts, math, science, and social studies.

Getting ahead at work takes mastery of job skills and difficult colleagues.

In retirement, we pick up new interests.

In our “dotage”, we move into simpler housing while we’re still able to adapt. If you’re good at learning, you have an advantage in life.

Third, learning is an acquired skill, and the most effective strategies are often counter-intuitive.

For true mastery or durability some study strategies like simple repeated re-reading are largely a waste of time.

Retrieval practice—recalling facts or concepts or events from memory— is a more effective learning strategy than review by rereading. Flashcards are a simple example

Retrieval strengthens the memory and interrupts forgetting.

A single, simple quiz after reading a text or hearing a lecture produces better learning and remembering than rereading the text or reviewing lecture notes.

In virtually all areas of learning, you build better mastery when you use testing as a tool to identify and bring up your areas of weakness.

All new learning requires a foundation of prior knowledge.

People who learn to extract the key ideas from new material and organize them into a mental model and connect that model to prior knowledge show an advantage in learning complex mastery.

Rereading has three strikes against it. It is time consuming. It doesn’t result in durable memory. And it often involves a kind of unwitting self-deception, as growing familiarity with the text comes to feel like mastery of the content.

A flight simulator provides retrieval practice, and the practice is spaced, interleaved, and varied and involves as far as possible the same mental processes Matt will invoke when he’s at altitude. In a simulator, the abstract is made concrete and personal. A simulator is also a series of tests, in that it helps Matt and his instructors calibrate their judgments.

Mastery in any field, from cooking to chess to brain surgery, is a gradual accretion of knowledge, conceptual understanding, judgment, and skill. These are the fruits of variety in the practice of new skills, and of striving, reflection , and mental rehearsal.

Memorizing facts is like stocking a construction site with the supplies to put up a house. Building the house requires not only knowledge of countless different fittings and materials but conceptual understanding, too,

Mastery requires both the possession of ready knowledge and the conceptual understanding of how to use it.

you hardly ever have an emergency, so if you don’t practice what to do, there’s no way to keep it fresh. Both of these cases— the research in the classroom and the experience of Matt Brown in updating his knowledge— point to the critical role of retrieval practice in keeping our knowledge accessible to us when we need it.

is how to do better at building knowledge and creativity, for without knowledge you don’t have the foundation for the higher-level skills of analysis, synthesis, and creative

students who don’t quiz themselves (and most do not) tend to overestimate how well they have mastered class material. Why? When they hear a lecture or read a text that is a paragon of clarity, the ease with which they follow the argument gives them the feeling that they already know it and don’t need to study it. In other words, they tend not to know what they don’t know; when put to the test , they find they cannot recall the critical ideas or apply them in a new context.

hardly ever have an emergency, so if you don’t practice what to do, there’s no way to keep it fresh.

the critical role of retrieval practice in keeping our knowledge accessible to us when we need it.

mastery, longer retention, and more versatility. But these benefits come at a price: when practice is spaced, interleaved, and varied, it requires more effort. You feel the increased effort, but not the benefits the effort produces. Learning feels slower from this kind of practice, and you don’t get the rapid improvements and affirmations you’re accustomed to seeing from massed practice .

research shows unequivocally that mastery and long-term retention are much better if you interleave practice than if you mass it.

Brown, Peter C. (2014-04-14). Make It Stick (p. 50). Harvard University Press. Kindle Edition.

A simulator is also a series of tests, in that it helps Matt and his instructors calibrate their judgment of where he needs to focus to bring up his mastery.

Mastering the lecture or the text is not the same as mastering the ideas behind them.

failure to know the areas where their learning is weak—that is, where they need to do more work to bring up their knowledge— and a preference for study methods that create a false sense of mastery.

for kids to be able to evaluate, synthesize, and apply a concept in different settings, they’re going to be much more efficient at getting there when they have the base of knowledge and the retention, so they’re not wasting time trying to go back and figure out what that word might mean or what that concept was about. It allows them to go to a higher level.”

Students who take practice tests have a better grasp of their progress than those who simply reread the material .

Repeated retrieval not only makes memories more durable but produces knowledge that can be retrieved more readily, in more varied settings, and applied to a wider variety of problems. While cramming can produce better scores on an immediate exam, the advantage quickly fades because there is much greater forgetting after rereading than after retrieval practice.

Practice at retrieving new knowledge or skill from memory is a potent tool for learning and durable retention.

Effortful retrieval makes for stronger learning and retention.

While any kind of retrieval practice generally benefits learning, the implication seems to be that where more cognitive effort is required for retrieval, greater retention results.

Are some kinds of retrieval practice more effective for long-term learning than others? Tests that require the learner to supply the answer, like an essay or short -answer test, or simply practice with flashcards, appear to be more effective than simple recognition tests like multiple choice or true/ false tests.

How does giving feedback on wrong answers to test questions affect learning? Studies show that giving feedback strengthens retention more than testing alone does , and, interestingly, some evidence shows that delaying the feedback briefly produces better long-term learning than immediate feedback.

classes continue today to follow a schedule of quizzes before lessons, quizzes after lessons, and then a review quiz prior to the chapter test. Jon Wehrenberg, an eighth grade history teacher who was not part of the research, has knitted retrieval practice into his classroom in many different forms, including quizzing, and he provides additional online tools at his website, like flashcards and games.

The results were compelling: The kids scored a full grade level higher on the material that had been quizzed than on the material that had not been

One quiz was given at the start of class, on material from assigned reading that hadn’t yet been discussed. A second was given at the end of class after the teacher had covered the material for the day’s lesson. And a review quiz was given twenty-four hours before each unit exam.

One argument suggested that the greater effort required by the delayed recall solidified the memory better. Researchers began to ask whether the schedule of testing mattered. The answer is yes. When retrieval practice is spaced, allowing some forgetting to occur between tests, it leads to stronger long-term retention than when it is massed.

In another study, researchers showed that simply asking a subject to fill in a word’s missing letters resulted in better memory of the word.

Brown, Peter C. (2014-04-14). Make It Stick (p. 32). Harvard University Press. Kindle Edition.

Testing doesn’t need to be initiated by the instructor. Students can practice retrieval anywhere; no quizzes in the classroom are necessary. Think flashcards— the way second graders learn the multiplication tables can work just as well for learners at any age to quiz themselves on anatomy, mathematics, or law. Self-testing may be unappealing because it takes more effort than rereading, but as noted already, the greater the effort at retrieval, the

Brown, Peter C. (2014-04-14). Make It Stick (p. 44). Harvard University Press. Kindle Edition.

Giving students corrective feedback after tests keeps them from incorrectly retaining material they have misunderstood and produces better learning of the correct answers.

Brown, Peter C. (2014-04-14). Make It Stick (p. 44). Harvard University Press. Kindle Edition.


Brown, Peter C. (2014-04-14). Make It Stick (p. 45). Harvard University Press. Kindle Edition.

Brown, Peter C. (2014-04-14). Make It Stick (p. 10). Harvard University Press. Kindle Edition.

ess. Kindle Edition.

Brown, Peter C. (2014-04-14). Make It Stick (p. 2). Harvard University Press. Kindle Edition.

Practice Retrieval for Progressive Mastery?

Learning for mastery is an iterative process that requires  you to ____ what you have learned earlier.


That means you need to continually ____ your learning and ____ it with new knowledge.

update       connect

Learning skills requires that we practice ____ review as we repeatedly  ____  through the topics several times along the way.

on-going         spiral

What are some simple and practical strategies to learn better and remember longer?

Various forms of retrieval practice

Name five forms of retrieval practice?
  1. On-going low-stakes quizzing and self-testing
  2. Spacing out practice through re-teaching worked examples
  3. Interleaving practice of different but related topics or skills
  4. Trying to solve problems before being taught their solution
  5. Using your own words to name and summarize the underlying principles or rules that differentiate types of problems
Reference for this summary post:

Brown, Peter C. (2014-04-14). Make It Stick (pp. 21-22). Harvard University Press. Kindle Edition.