Tes Maths: Pedagogy place - Fluency

Craig Barton
21st March 2018
Tes Maths: Pedagogy place - Fluency

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

What is fluency in mathematics, and why is it important? Let’s find out.

What does the research say?

Perhaps the most useful way to think about mathematical fluency is procedurally, which is defined by The National Council of Teachers of Mathematics (NCTM) as “the ability to apply procedures accurately, efficiently, and flexibly”.

Closely related to the idea of fluency is automation. As proponents of the cognitive load theory (Sweller, Van Merrienboer & Paas, 1998) state, our working memories have a limited capacity. Once the limit has been reached (a state known as cognitive overload) the brain is unable to learn any further information.

So, one way we can help ease the burden on our fragile working memory is by automating key facts and procedures. This then frees up capacity, and allows our brains to concentrate on the more complex parts of a problem, such as spotting connections and plotting solutions. Therefore, students who are able to automate knowledge struggle less when faced with complex problems.

However, while the benefits of fluency and automation are widely accepted, there is no uniform answer for how best to develop them. In fact, following my discussions with Lucy Rycroft-Smith from Cambridge Mathematics, it became apparent that within the research there are actually several conflicting arguments.

One theory (Wong & Evans, 2007) suggests that without added time pressure, students are unlikely to develop the kind of automated knowledge that they need to free up capacity within their working memory. For example, students completing a simple multiplication by counting on their fingers will be at a significant disadvantage compared to peers who are able to recall answers instantly. However, Ashcraft (2002) states that such timed tests cause anxiety, therefore lowering the chances of students retaining and automating knowledge.

In summary

Fluency, and the associated process of automation, may well be the key to higher-order thinking and more complex problem solving. However, the process of automating knowledge should be approached in a fun, non-threatening way, such as through regularly conducting low-stakes quizzes.

How can Tes help?

Generators, worksheets and practice activities are just a few ways you can boost your pupils' mathematical fluency, in a stimulating way. What are you waiting for?

KS3 / GCSE Mental Maths Practice - Lite

This is the 'lite' version of the paid-for resource here.

This is an Excel file generates endless sets of key mathematical numeracy questions for regular practice to develop student’s fluency in maths.
A workbook for printing sets of questions and separate answers.
Press F9 for a new set of questions.

The paid for version of this resource also includes the following...
1. An upgraded version of the Maths Mental Tests Excel file which includes one sheet to use for printing worksheets, another sheet of the same questions and answers for projecting / displaying on screen.
2. BONUS RESOURCE – A link to a fully interactive and mobile-friendly website of all of the Key Stage 3 Mental Maths audio questions.
3. BONUS RESOURCE – 40 Arithmetic Operations
Another file for generating quick sets of addition, subtraction, multiplication, division or mixed questions for pupils to practice quick arithmetic skills. Designed to print worksheets of 40 questions for students to complete, perhaps against the clock.

Purchase upgraded files here.
By grahamcolman

Maths: Numeracy Tests Excel worksheet

Numeracy tests with an unlimted question bank. Needs Excel with macros enabled. For testing and tracking numeracy skills.
By peacocmaths

Target 100

Resource was inspired by @mrbartonmaths and @danicquinn
Skills and drills generator including:
1-step equations,
squares/triangular numbers/cubes/factors/multiple/primes/sequences,
number bonds,
fraction skills,
multiply/divide by powers of 10/remainders when dividing/divisibility,
HCF/LCM/sum-product/reciprocals/ratio division.
Aim is for students to get regular practice and improve their speed / confidence.
Target 100 generally has 5 sections of 20Q so the idea is to get 100 in the time available - for example allow 1 minute per section.
Numbers randomly generated.
Answers provided.
By pjhumph

Times tables practise sheets

These can be used weekly to practice times tables knowledge and speed of recall after children have learnt them for homework. These have now been updated to include sheets up to x12 in line with government guidelines. I have also added easier sheets of times tables in order for less able/younger children and sheets with multiplication and division facts together for more able children.
By tracey16lewis

Craig Barton, Tes Maths adviser

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

  • Ashcraft, Mark H. "Math anxiety: Personal, educational, and cognitive consequences." Current directions in psychological science 11.5 (2002): 181-185
  • Barton, Craig. “Mr Barton Maths Podcast: Lucy Rycroft-Smith” 2017
  • Gersten, Russell, et al. "Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools. NCEE 2009-4060." What Works Clearinghouse (2009)
  • NCTM. Procedural Fluency in Mathematics. http://www.nctm.org/Standards-and-Positions/Position-Statements/Procedural-Fluency-in-Mathematics/

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