Make the math stick

This is a living document. While I wrote this from the perspective of mathematics instruction, I’ve found that the strategies transfer quite well into other domains. Feel free to reach out if you have any ideas or questions.

Build relationships with learners

This decides everything that follows. If I am a deliverer, i.e., I get to work with a learner directly:

• Get to know them as a person. Begin working sessions by asking them how their week was. Chat about their interests and hobbies. Spark a little fun debate from time to time.
• Invest in, and show that you’re invested in, the learner’s holistic success. Be a trusted strategic partner without imparting authority.
• Acknowledge mistakes with an analytical yet positive attitude. Provide a safe space to fail.

If I am a designer behind the scenes I can still implicitly do this. It boils down to understanding the audience as a group.

• What common goals are they driven by?
• What does it look like when they apply what they learn in the real world?

Retrieval practice

These days, learners are constantly overwhelmed by noisy information and rapid context-switching. Take warm-up seriously—start the session with simple active recall questions that get the learner to dig into their own knowledge pool.

• Retrieval strengthens their memory muscles and leads them to discover learning gaps.
  • Learners often run into illusions of competence, where they assume they have acquired a skill just from listening to a presenter or rereading their notes. They then find themselves “blanking out” when they’re assessed.
• As a rule of thumb, do not start by passively summarizing past learning for the learner.

Spaced practice

Spread out learning and practice sessions over time rather than cramming them into a short period. Our brains retain information better this way. This is why, for complex subjects, people benefit from structured learning, such as a course with periodic take-home work, more than if they just swam through an ocean of information and self-learned in a week. We benefit from curation, structure, modularity, downtime, and revisits.

• As an example, I always recommend that learners start preparing for a big culminating exam at least a month in advance. Every weekend, they dedicate a few hours to revisiting (assessing themselves, not just rescanning information) a topic or a unit. Rinse and repeat.

Positive affect

Who can learn well while crushed by overflowing anxiety, discomfort, or distractions? Our emotions decide how we process and interpret the world. Feeling safe and positive has been proven to expand working memory, speed up problem-solving, and enhance retention.

• Delivering learning that fosters positive affect is straightforward—this goes back to the first point of building positive relationships.
• Designing learning that fosters positive affect is more abstract. A couple of ways this can look in action:
  • Thoughtful scaffolding of tasks that takes into account cognitive load, complexity, and demand for spontaneity.
  • Tasks that are engaging and feel directly relevant to the learner.
• Note: a major benefit of spaced practice is that it leverages positive affect. We learn better when we have a healthy but only minor dose of time pressure.

Make it visual, make it interactive

Math instruction doesn’t have to utilize bleeding-edge AR/VR tech or put up a screencast of Subway Surfers to grab learners’ attention and get them to learn. Engaging learners can be as simple as sketching a quick graph, chalk-on-blackboard, to illustrate a point. It can mean getting the learner up to the board. It can be a “see it for yourself” on Desmos. It can be a Kahoot game. It can be a “put your heads together” time with your peer. For an abstract and technical subject, infusing moments of tangibility is key.

Let them teach it back

A.K.A. the Feynman Method, the Rubber Duck Debugging Method, or Flipped Classrooms. Have learners explain a concept they learned or walk through their problem-solving process in gruesome detail to their peers, their instructors, or themselves.

• Point is, just like the retrieval practice, create an opportunity where learners can consolidate their learning, discover their potential learning gaps, and overcome the illusion of competence.
• Added benefit: build long-term confidence.
  • When working with learners who start out struggling in math, I noticed a trend: They are hesitant to articulate the why behind their work or show work at all. This could come from years of feeling like they don’t have a voice in math classrooms or that they “don’t know what they don’t know.” Consistent teach-it-backs builds the muscle for communicating math and accurately assessing their own skills.

Embrace complexity

Sometimes, skills are difficult to learn because they are difficult. From what I’ve seen, the thought that “I’m supposed to get this quickly” is a common culprit that drives up anxiety in learners. The role of the instructor or instructional designer is not to dilute and dumb down content but to pave a road for the learner to navigate its complex topography. We achieve this by acknowledging the challenge of learning something new, facilitating diverse modalities of practice, surfacing hidden structures, and laying down new structures into arenas where they do not yet exist.