Why We Need To Use Less Block Practice And More Interleaving When Teaching Mathematics
Richard Andrew
? Creating Change Through Awareness-raising, Interactive, Hybrid Experiences ? School Collaborations: Whole-school, Implementations-based CPD ? Corporate: Empowering Coaches & Consultants ? Bus Networking Facilitator
Block Practice vs Interleaving
In this article, I'll explain why using too much 'Block Practice' in mathematics teaching can be problematic and why 'Interleaving' is a better approach.
What is Block Practice?
Block Practice, when applied to the mathematics classroom, is what most of us experienced at school - practice one type of question multiple times before moving on to the next. Each block of questions requires students to use only one procedure.
Block Practice in Action - Example #1
1. Find the mean of the following sets of scores:
a) 2, 5, 3, 7, 4
b) 4, 7, 9, 2, 2, 4
c) 2, 5, 3
d) 8, 4, 6, 2, 0, 3, 0
Block Practice in Action - Example #2
In a typical right-angle trigonometry unit, students may practice only the tangent ratio for finding the length of an unknown side, then only the sine ratio for the same purpose, and so on.
The problem With (Too Much) Block Practice
The problem with too much Block Practice is that it can lead to rote learning, where students replicate the procedures they have been shown. This requires minimal cognitive effort and sits at the lowest rung on?Bloom’s Taxonomy.
Block Practice tends to cause students to disengage and ‘does not effectively enable students to develop a deep understanding of the necessary mathematical ideas involved’ (Silver et al., 2009, p. 503) At best, we see many students compliantly going through the motions. At worst, we see students disengage, throw in the towel, and adopt as their main aim to walk out that door!?
‘Blocked practice provides students with a crutch. If students don't learn to solve problems without it, they will struggle during a test when their crutch is snatched away’ (Rohrer, Dedrick, Agarwal, 2017, p.6)
Is Block Practice Always Detrimental?
Again, from?Rohrer, Dedrick, Agarwal ? 2017, p11,?'Some blocked practice is useful, especially when students encounter a new concept or skill.'
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However, when Block Practice is overused, it becomes an ineffective pedagogy. The question is then, what is the alternative??
The alternative is Interleaving.
What is Interleaving?
Interleaved questions require students to work on several related ideas simultaneously, preventing them from relying on a single procedure to solve a block of questions. Interleaved questions are mixed so that different procedures are required for each question, but the same concepts are being explored.
Interleaving - An Example
The screenshot below was taken from?the guide referenced above.
Interleaving Explained
Interleaving aims to engage students with several connected concepts simultaneously, resulting in more reasoning and cognitive thinking. It's inherently more engaging and pushes practice higher up the?Bloom’s Taxonomy triangle.
How much interleaved practice is enough??
'The ideal amount depends on the student and the material, but studies suggest that at least a third of the practice problems should be interleaved.’?Rohrer, Dedrick, Agarwal ? 2017, p11.
However, we need to be very?careful?about the ? Interleaved recommendation because this means we will use a whopping ? of Block Practice! The way I see it, to advocate such a high portion of Block Practice implies that procedures are prioritised over understanding which can be problematic.?
If we prioritise understanding equally with procedures, e.g. by using an Understanding-first, Procedures-second approach, (where students explore and think mathematically before learning procedures), less Block Practice, perhaps 50 per cent, will be required. However, if our major focus is procedural, we may need ? Block Practice.
Interleaving infused through a unit of work
If you want to see a unit of work that strongly features Interleaving as part of a conceptually-based approach, check out the mini-course, An Understanding-1st Approach To Right-Angled Trigonometry.
Call to Action?
A short commentary on a related randomised trial?can be accessed here.
We would love to hear from you about your experience with Block Practice and Interleaving - feel free to comment below.?
Teacher of Mathematics/Department Chair at Millburn High School - Retired
1 年Richard Andrew These terms are new to me, too. However, after reading your article, I know the practice. My all time favorite Algebra II textbook was one where the problem sets were virtually completely different from problem to problem. The student could not simply rely on what they had done from the previous problem to do the next one. The examples were thought-provoking, interesting, different, challenging and fun. But, there were students who had not sufficiently mastered the skills to be comfortable with the variety in the assignment. However, the text materials also included more practice of the new skill with worksheets that ranged from easy to hard; three levels, if I recall correctly. I only assigned these worksheets as extra credit for those students who felt they needed the additional practice. Once they were comfortable with the new skill, they then tackled the assigned problem sets. Students who were more comfortable would simply do the assigned work and did not have to do the drudgery of rote practice. I let them be their own guide, but gave them the credit for the extra effort they expended. This approach worked well.
Educational Consultant Director at Raising Achievement
1 年I agree and often talk about little and often with students with learning differences. If the average student takes 7 repetitions for students with learning difficulties it can be exponential. Up to 49 times! Interleaving is one way of supporting this. What are your thoughts on how we can get in additional repetition and overlearning/understanding?
Senior Primary Teacher, Teaching development Trainer, Mentor for ECT Teachers,Private Tutor, Interpreter 5 languages
1 年With my Year 3 teacher hat on, I must say problem solving and reasoning proves to be more and more tricky for students to master . Unless you’re using clear differentiation and appropriate scaffolding and have enough adults available to help with individual needs, these skills are being developed a lot slower and this delay then creates more challenges for students when we are trying to introduce new concepts .. Definitely an interesting read ! Thanks for that Richard!!
Creating Schools Where Students and Teachers Want to Be
1 年No easy answers or magic proportions here. Block practice and interleaving should be considered as approaches serving a broader purpose. Are we problem-solving or developing procedural fluency? We need both forms of development to build strong mathematics ability in students. The block has its negatives, particularly if it is the only mathematics students come to know. The leaf is essential for deeper understanding but often enough requires sets of block-driven skills to happen. Both approaches, serving an aim of conjuring a powerful, robust and versatile mathematics capacity in our students, have their place.
AI-reckoning online maths teacher || Flipped Learning Master Practitioner
1 年(Continuing) As for the research you shared, it reminded me of the trainer mentioning “familiarity” in the training I attended a few days ago. It was Pearson’s one-day training on IGCSE and iA-Level Maths Exams, and the trainer briefly said “every question is hard until students get a familiarity of similar questions”, which makes sense. Hence if one group of students were exposed to question sets based on Interleaving, and the others didn’t, then the findings of the research is kind of inevitable, therefore not a good piece of proof for Interleaving. That said, I would like to read the full article and review the test given to students before jumping into such a bold conclusion.