Tes Maths: Pedagogy place - Interleaving

Craig Barton
16th January 2018
Tes Maths: Pedagogy place - Interleaving

In this series, we dive into the realm of educational research to help you best formulate effective classroom practice

What is interleaving, and how can we ensure that pupils reap the benefits of it from our lessons and homework activities?  Let’s find out.

What does the research say?

The interleaving effect is closely related to the concept of desirable difficulties and spacing. Directly contrasting to a blocking approach, whereby students repeatedly study the same material before moving on to a new subject area, interleaving allows students to practise a variety of topics in a less predictable order.

The positive effects of interleaving have been demonstrated in several studies, such as one conducted by Mayfield, Kristin and Chase (2012). In this investigation two groups of students were challenged with solving problems using the five algebraic rules about the laws of indices. One set of pupils learned the rules through a procedure akin to blocking. The other, through interleaving. In subsequent tests, the interleaved practice group outscored the blocked practice group by factor of at least 1.3, excelling both on skill-based and problem-solving questions.

Of course, curriculum design plays an important role in the successful implementation of interleaving within lessons. Schemes of work that allow for previous concepts to be seamlessly integrated into the practise of new topics lend themselves well to an interleaving approach. For example, when teaching linear equations, negative numbers, fractions, and decimals can easily be revisited by including them as coefficients or solutions.

However, as Rohrer, Dedrick and Stershic (2015) suggest, it is possible to gain the benefits of interleaving without radically changing our schemes of work. In a study on homework assignments, a group of 7th grade students were split into two, receiving either blocked or interleaved practice sheets. Blocked homework exercises were topic-based, whereas the interleaved exercises contained a mixture of questions across topics. Later, these same pupils received a review of all the content, followed by a surprise assignment. Students following the interleaving program performed significantly better on the tests.

Therefore, moving away from topic-based assignments to mixed-topic exercises could be of great benefit to pupils. However, it is also important to note that it takes time for the effects of interleaving to be felt. Remember to reassure students if initially lessons feel a little harder than usual. Indeed, we can hope that they learn to revel in the difficulty!

In summary

Interleaving topics and concepts in both lessons and homework assignments, as opposed to presenting them in blocks, is an effective and time-efficient way to improve learning. However, as the effects take a little time to show, it is important to reassure students that they’re on the right track when first introducing them to the concept.

How can Tes help?

Give learners the opportunity to practise a variety of key maths skills with the help of these lesson ideas and activities.  From schemes of learning to problem-solving papers, there are plenty of ways to make use of the principals of interleaving when teaching.
 

Fractions mastery and problem solving

Multiplying, dividing, adding and subtracting fractions mastery lesson including problem solving from nrich.

If there are any mistakes on the answers, let me know and I can update.

Thanks
By j2dutto

White Rose Maths Hub - Year 7 Scheme of Learning

Please note that this file was updated on 27.06.2016

One of the most frequent requests we get as a Maths Hub is for a suggested long term curriculum plan for mathematics at KS3. We have listened to what teachers need and the following mastery overviews have been developed by secondary practitioners in conjunction with the White Rose Maths Hub to provide a curriculum plan that will support ‘Teaching for Mastery’.

There is a termly plan for each year group from Year 7 to Year 9; each term is split into twelve weeks. You will see from the overviews that a significant amount of time in Year 7 Autumn and Spring term is devoted to developing key number concepts. This is to build their competency as number sense will affect their success in other areas of mathematics. Students who are successful with number are much more confident mathematicians.

Alongside these curriculum plans, our aim is also to provide an assessment for each term. There are two versions of the assessment:

Paper A: Support for lower attaining students
Paper B: For the core with appropriate challenge

You can use these assessments to determine gaps in your students’ knowledge and use them to plan support and intervention strategies.

Our assessments are designed to test students understanding. They support teaching approaches such as bar modelling, place value grids, other part whole diagrams and using concrete materials to introduce topics.

We hope you find them useful. If you have any comments about this document or have any ideas please do get in touch.

The White Rose Maths Hub Team
By WRMaths

Going for gold! - GCSE problem solving papers

These papers test skills that appear on both foundation and higher tier papers.

Each paper has three versions to choose from: Bronze, Silver and Gold. They are the same questions, but the amount of scaffolding is adjusted in each.

There are worked solutions to accompany every paper.

The Platinum paper is an extension to further challenge your students.

Full preview available at http://www.missbanks.co.uk/copy-of-going-for-gold
By Alison Banks

Brockington College Maths homework booklets

All of the homework booklets I design for my Maths department, free and in one place.

Obviously cannot post answers here, but happy for people to email me for them - a DM on twitter with your email address is the best way to get them.

Note there are a few images borrowed from different places. Apologies for any infringement and please just let me know and I am happy to credit or change as required.
By Peter Mattock

Craig Barton, Tes Maths adviser

Craig is a secondary maths teacher in the North of England.

References 

  • Barton, Craig. Mr Barton Maths Podcast - Professors Robert and Elizabeth Bjork (2017)
  • Bjork, Elizabeth L., and Robert A. Bjork. "Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning." Psychology and the real world: Essays illustrating fundamental contributions to society 2 (2011): 59-68
  • Mayfield, Kristin H., and Philip N. Chase. "The effects of cumulative practice on mathematics problem solving." Journal of applied behavior analysis 35.2 (2002): 105-123
  • Rohrer, Doug, Robert F. Dedrick, and Sandra Stershic. "Interleaved practice improves mathematics learning." Journal of Educational Psychology 107.3 (2015): 900

 

Contact us

Visit our forums

Latest education news

New to TES Resources ? Find out more about becoming an author on TES, or dive straight in and start downloading.