Timed Math Practice

I finally finished a meta-analysis I worked on non-stop over the summer. The project focused on evaluating intervention studies that used timed math practice, the preprint can be found here: (https://doi.org/10.35542/osf.io/9bjtg). I have shared the data, data dictionary, statistical code, PDFs of included articles, and some other jawn (cough….cough…Arthur Glenn Dowdy IV) used to complete the project: see the OSF page here: https://osf.io/np6hk/). If readers want to access the specific PDFs of articles included, click on the folder entitled “Included Articles.” I’ll take any and all feedback readers may have - I plan to solicit input, work on revising, and submit to a journal within a month.

In this post, I do not want to summarize the findings - that would be boring and people can just read the paper. Instead, I’d like to talk about some things that stood out to me when reading the papers and hopefully spur on some useful conversations for teachers and researchers to engage in.

Disclaimer

This post will be focused only on information about the dosage of timing! For example,

1. Does the amount of time students spend engaged in timed practice affect results?

2. Does the frequency of practice sessions affect results (e.g., daily versus three times per week?)

3. Does distributing practice into smaller chunks of time throughout the day lead to better results than one practice session (i.e., mass practice)?

In subsequent posts I will discuss other tidbits I found interesting, such as the use of other intervention components (e.g., feedback, goal setting, reinforcement), content area targeted, how student baseline performance might influence effects, measurement approaches to fact fluency, and considering social validity from teacher and student perspectives.

How Long and Often Should Timed Practice Be?

Being fluent (speed + accuracy) with declarative facts and procedures is one essential aspect of building math proficiency – but not the entirety. Thus, when considering a typical math class (or intervention) - instructional tactics designed around fluency building should be part of normal routines but not the entirety of the instruction that occurs.

Time Spent Practicing

I put together two quick plots, which show the number of effect sizes (and studies these were estimated from) for various timing conditions (see below). Figure 1 shows results from group design studies that isolated timed practice and Figure 2 shows results from the single-case research design studies that isolated timed practice.

Figure 1. Number of effect sizes and studies using different timing procedures from the group design studies isolating timed practice.

Figure 2. Number of effect sizes and studies using different timing procedures from the single-case research design studies isolating timed practice.

Why did I make these plots? To highlight that across both types of designs, most effect sizes (and studies) tested timed math practice for 5 min per day or less. If we think back to our reference point of having a 60 min math block, 5 min would equate to only ~8% of the math class.

In the meta-analysis I attempted to evaluate how different practice times predicted effects through moderator analysis - however, this is correlational evidence. Of the included studies, several experimentally compared different dosages of practice. I briefly summarize them below.

Duhon (2022)

In this randomized control trial, the authors compared 8 different timing conditions.

• 8x per day: 4, 120sec trials in morning and 4, 120sec trials in afternoon

• 4x per day: 2, 120sec trials in morning and 2, 120sec trials in afternoon

• 2x per day: 1, 120sec trial in morning and 1, 120sec trial in afternoon

• 1x per day: 1, 120sec trial in morning

• Every other day: 1, 120sec trial every other school day

• 1x per week: 1, 120sec trial per week

• Every other week: 1, 120sec trial every other week

• Control: no timed practice

Authors identified the minimal amount of practice needed to see a statistically significant effect was 120sec of timed practice per day. However, readers can refer to Figure 2 in the manuscript to see the digits correct per minute at post-test by condition Table 4 that provides growth per instructional minute by condition. The conditions of 4x per day and 8x per day led to higher post-test scores; however the growth per instructional minute was smaller.

Duhon (2009)

In this single-case research design, the authors first provided class-wide fluency practice (120sec timed practice per day). The authors identified three students who made progress but continued to fall below the instructional benchmark goal. The authors provided 5, 120sec timed practice trials per day to see if intensifying the dosage of timed practice supported students in meeting the instructional goal. Two students met the instructional goal after 5 days of practice and one student made minimal progress but did not make the goal. For the last student, the team intensified practice to 10x per day and after three sessions the student met the goal. Interestingly though, one month after intervention revealed the last student’s performance regressed back to baseline levels - indicating performance was not maintained.

Fontenelle (2022)

In this single-case research design, the authors compared 1, 210sec daily practice trial versus control (1, 60sec daily practice trial) and a different intervention (taped problems). The intervention was implemented classwide to second-grade students. Results indicated the 210sec daily practice trial led to faster learning rates then the 60sec daily practice trial. Taped problem and explicit timing yielded similar rates of learning.

Knowles (2010)

In this group design, the authors compared three conditions (a) 1, 180sec time trial daily, (b) 1, 180sec time trial weekly, and (c) a control (no practice). The authors found statistically significant results favoring daily timed practice versus weekly timed practice and versus the control condition. Also, weekly timed practice led to statistically significant results over control.

Poncy (2010)

In this single-case research design, the authors compared two condition: (a) 1, 240sec daily timed trial and (b) 1, 60sec timed trial. The authors found the 240sec daily timed trial led to quicker fluency gains than the 60sec daily timed trial. Interestingly, the authors aimed to see if students would generalize their addition fact knowledge to the related subtraction fact (e.g., 3 + 5 = ___ —> 8 - 3 = ___ or 8 - 5 = ____). Students did not generalize to subtraction.

Wolfe (2018)

In this group design, the authors tested six different conditions by evaluating the two variables, the frequency of timed practice per week and the inclusion of goal setting and performance feedback. The conditions were:

• 120sec daily practice with goal setting and performance feedback

• 120sec daily practice in isolation

• 120sec practice, 2-3 times per week with goal setting and performance feedback

• 120sec practice, 2-3 times per week in isolation

• 120sec practice, once every 4 days with goal setting and performance feedback

• 120sec practice, once every 4 days in isolation

This study actually found effects counter to the others shared. No differences in growth rates were found when comparing (a) daily practice in isolation to (b) 2-3 times per week in isolation to (c) once every 4 days in isolation.

Hernandez-Nuhfer (2020)

In this group design, the authors tested 9 different conditions - manipulating both time spent practicing the the set size¹.

• 120sec daily practice, set size of 9

• 240sec daily practice, set size of 9

• 480sec daily practice, set size of 9

• 120sec daily practice, set size of 18

• 240sec daily practice, set size of 18

• 480sec daily practice, set size of 18

• 120sec daily practice, set size of 36

• 240sec daily practice, set size of 36

• 480sec daily practice, set size of 36

The authors were interested in the interaction between time spent practicing and the set size - basically, is more time going to be needed for larger set sizes. The authors found similar growth rates for 120sec, 240sec, and 480sec of practice for set sizes of 9. As set size increased to 18 though, 240sec and 480sec resulted in similar gains - which were larger than 120sec. For the set size of 36 items, it was shown that the 480sec of practice resulted in greater gains than 120sec. No differences were found for 120sec or 240sec.

Distributing Practice

Three studies kept the amount of practice time constant across conditions but instead tested whether distributing practice across the day led to better learning rates than one mass practice condition.

Bullard (2019)

This group design study tested three conditions (a) 4, 60sec practice trials in morning, (b) 2, 60sec practice trials in morning and 2, 60sec practice trials in afternoon, and (c) 4, 60sec practice trials in morning + performance feedback.

Students in the distributed practice condition scored higher than students in massed practice condition, albeit this was not statistically significant. The addition of performance feedback led to higher scores compared to mass practice in isolation, however this was not statistically significant.

Powell (2022)

This group design study tested three conditions (a) 2, 60sec practice trials; 3 hour break; 2, 60sec practice trials (b) 2, 60sec practice trials; 10 min break; 2, 60sec practice trials, and (c) 4, 60sec practice trials (no break).

Students in the 3 hour distributed practice condition scored higher than students in the massed practice condition or 10 min break condition. Thus, the 10 min break between practice was insufficient to reap rewards of distributing practice in this experiment.

Schutte (2015)

This group design study tested three conditions

• 4x daily: 1, 60sec trial; 2.75hr break; 1, 60sec trial; 1.25hr break; 1, 60sec trial; 1.75hr break; 1, 60sec trial

• 2x daily: 2, 60sec trials; 2.75hr break; 2, 60sec trials

• Massed practice: 4, 60sec trials

Students in both distributed practice conditions outperformed students in the massed practice condition. The 4x per day condition had greater gains than 2x per day, however it was not statistically significant.

Conclusions

Although not unanimous, there is evidence that enhancing the amount of time students engaged in timed practice led to greater gains. Educators can use their own class (or individual student’s) data to guide this decision-making process. Start small, such as 4min of devoted timed practice per day and track student growth. If growth is less than desirable, time is ONE of many variables that can be modified to enhance learning rates (I’ll dive into other variables in future posts).

Breaking practice time into smaller chunks versus one longer session may also support greater learning. Exactly how much time should separate practice sessions? This is something we do not have enough data on yet!. It appears 10min was insufficient (see Powell, 2022). Would 40 min work? I don’t know! But that would be sweet because educators could start and end their math class with some quick fluency practice and this would equate to ~40min time lapse between sessions.

1. Set size refers to the number of unique facts that were assigned to practice to that condition.