Learners Need to Focus on Errors

Dec 9, 2016 by

Let’s move on to the excellent article It’s Not How Much; It’s How: Characteristics of Practice Behavior and Retention of Performance Skills, by Duke et al. (2009), which is another dive into analyzing what leads to good retention of learning in music education.  Just to be different, I’ll start with the conclusion, and then circle around to the study construction.

“The results showed that the strategies employed during practice were more determinative of performance quality at retention than was how much or how long the pianists practiced”

17 students (advanced piano performance students) were given a 3-measure passage from a difficult Concerto to learn. The students each followed the following protocol for practice:

  • 2-min warmup of their choice
  • As much time as they need with the passage, a metronome, a pencil, and a piano, to lean the passage well and play it confidently at the target tempo.
  • A 24-hour break away from the music, with a promise not to practice it at all

The next day, the students had the same 2-minute warmup period (asking that they do not warm up with the practiced passage). Then they were asked to play straight through the 3 measures at the target tempo 15 times without stopping (these are the retention trials).

After recording numerical data about the practice sessions and retention trials, the researchers watched the recorded practice sessions to make detailed observations about the techniques each participant used to practice. Then they ranked the retention trials of the 17 participants, examining tone, character, and expressiveness of musical performance.

Here are the practice variables that were NOT related significantly to the retention trial rankings:

  • total time practiced
  • total number of times through the passage during practice
  • total number of correct and near-correct times through the passage

Here are the practice variables that were significantly related to the retention trial rankings:

  • number of complete incorrect performance trials (positive correlation)
  • percentage of all complete trials that were correct (negative correlation)
  • percentage of complete trials that were correct and near-correct (negative correlation)

Three of the participants were ranked as clearly superior to the other 14 students. Examining the practice sessions from these three students yielded a set of 8 strategies (see p. 317 of the article for the full list), a few of which are summarized here :

  • early in practicing, the playing was hands-together
  • when errors appeared, they were addressed immediately
  • the precise location and source of each error was identified accurately, rehearsed, and corrected
  • the tempo was varied
  • target passages were repeated until stabilized (no more errors)

While the other 14 players would employ some of the 8 strategies, it was only the top 3 that used all of them. In other words, the top-performing practicers had very good metacognition skills. They could accurately identify their mistakes, sometimes anticipating them in advance, and knew what kinds of actions to take to work in the direction of correcting the mistakes and avoiding them in the future.

One of my key takeaways from this article was a quote from the literature review, which I think is much more widely applicable to many subjects (not just music):

“making practice assignments in terms of time practiced instead of goals accomplished remains one of the most curious and stubbornly persistent traditions in music pedagogy”

In mathematics, we assign lists of problems, and students are to do all the problems regardless of their mastery over time. I’m wondering if we shouldn’t give the students a suggested list to practice from, with goals about what they should learn, and tell them to practice until they are reasonably sure they have accomplished the goals. I might go so far as to ask them to do the assignment in pen, crossing out and correcting mistakes as they go, so they can see the progress towards mastery of the topic.

I’m afraid that our relentless focus on time or quantity practiced might be handicapping students’ metacognitive abilities. Do our students actually know when they have mastered a topic? Do they transparently remember the mistakes they make after erasing them and overwriting them? I’m reminded of the Trevor Ragan video about Blocked and Random Practice that says that practice is going to be ugly. I think practice that produces learning IS going to be ugly, and somehow we need to help students be okay with this.

Challenge: Think about how to structure student out-of-class practice so that the focus is not on time or quantity, but on the error analysis and thoughtful correction. Try to make the whole purpose of the assignment around accurately identifying mistakes and working towards mastery of the material rather than “checking off” the to-do items on a list.

Note: A weekly bite of learning and challenge goes out every week. If you’d like to have it delivered to your inbox, sign up at Weekly Teaching Challenge.


Duke, R. A., Simmons, A. L., & Cash, C. D. (2009). It’s not how much; it’s how characteristics of practice behavior and retention of performance skills. Journal of Research in Music Education, 56(4), 310-321.

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Learning Math is Not a Spectator Sport

Dec 4, 2016 by

In November, I gave the keynote at the American Mathematical Association of Two-Year Colleges (AMATYC) Conference in Denver.

I have given versions of this talk that are not specific for mathematics, but I don’t have recordings of those. I promise that the math in this talk is not inaccessible and is used more for examples than a framework for the talk. In other words, don’t let the word “math” scare you away. The alternate version of the talk is “Learning is Not a Spectator Sport.”

Three triangles surrounding a central triangle with the letters C, I, and D
The first half of the video is the awards ceremony, so I’ve directed the embed link below to begin when the keynote actually begins at 45:48 (direct link to video on YouTube beginning at the keynote is here).

The talk emphasizes the importance of interaction, and as such, this talk has a lot of audience interaction in it near the beginning, so you may want to jump through some of that interaction as you watch (between 51:30 and 1:02:00).

At the end of the keynote, audience members are invited to participate in a Weekly Teaching Challenge to continue exploring the ideas and research in the talk. You’re invited too. Just sign up!


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Why high contextual interference?

Dec 2, 2016 by

This week I followed a hunch and, with the help of a friend who is a music educator, dug into some additional research around this idea of blocked and random practice. In music there are a few goals to achieve with any passage of music:
  • can you play a passage accurately by itself?
  • can you play the passage in the larger context of the piece?
  • can you play the passage to tempo?
  • can you play the passage with the right expression?

Think about these goals in your own subject area and see if you can find a similar set of goals. For example, here are some potential goals for solving a math problem:

  • can you find the correct solution?
  • can you solve the problem in an elegant way?
  • can you prove your solution is correct?
  • can someone else understand your solution?

The first research paper I looked at was When Repetition Isn’t the Best Practice Strategy (2001), by Laura A. Stambaugh. A short summary is available here, though the original paper is a bit harder to get ahold of. I’ll elaborate a bit on the summary with the relevant points to our study of learning design.

Students were asked to practice three passages (denoted below in three colors) in either blocked- or random-formatpractice sessions. The three practice sessions were covered on three different days (denoted 1, 2, and 3 in the diagram below). The performance during the last three trials of each practice session were used as the baseline measure of comparison for the retention measures.

In this experiment, practicing “randomly” meant practicing the same three passages in either At the end of the three sessions, there were no performance differences between the two groups. However, when tested for retention, the blocked-practice students’ performance began to slow to the level of early practice in the trials. While the accuracy of the two groups of students was still the same, the random-practice students could now play the passages faster than the blocked-practice students. Stambaugh also tested transferability of skills, but did not find any statistically significant differences from this experiment. One other variable that Stambaugh thought to test was attitude towards practice depending on the research treatment (maybe students will really dislike random practice or blocked practice?). Here too, there were no statistically significant differences in attitude towards practice between the two student groups.

One of the reasons I find this article interesting is that it discusses the idea of contextual interference, the amount of cognitive disruption the learner experiences during practice with multiple tasks. When the learner has to redirect attention as the tasks change, this results in a high degree of contextual interference. When the tasks don’t change much (blocked practice), the brain can go into a sort of “autopilot” and stop paying attention. At this point, there may not be much point to practicing more on that day. Practicing the same things on a different day would have positive effect (that’s spaced repetition).


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Algebra is Weightlifting for the Brain

Mar 29, 2010 by

This was my presentation on Friday in Austin, Texas at the Developmental Education TeamUp Conference.

The process of learning algebra should ideally teach students good logic skills, the ability to compare and contrast circumstances, and to recognize patterns and make predictions. In a world with free CAS at our fingertips, the focus on these underlying skills is even more important than it used to be. Learn how to focus on thinking skills and incorporate more active learning in algebra classes, without losing ground on topic coverage.


I’ve loaded the uncut, unedited video that I took of the presentation to YouTube.  I’m not going to claim the video recording is great (recorded with a Flip Video Camera sitting on a table), but you’ll get to hear the audio and more of the details.  View “Algebra is Weightlifting for the Brain” here.

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Speed Rounds: Test Review Game

Nov 5, 2008 by

Here’s a game we play on Test Review days that engages all the students at once and gives every team a chance at points in every round (unlike Jeopardy).

I count the students off into groups of 3-4 students. Each group gets an answer sheet for the game (a piece of colored paper with a letter, A, B, C, D, …) at the top. I make a “scoreboard” on the board to tally the results of the rounds (12 in this case). Here’s what that looks like:

Then we begin the game. Here’s a sample

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