Have you ever wondered why your child is convinced they’ve never learnt fractions at school, but you know they have because you remember helping them with their fractions homework…?
You are not alone!
Teachers (myself included) can really resonate – and sometimes despair! – with this situation. We often see children grasping a maths skill confidently, only to find a few weeks later they are unable to apply the same skill again in their classwork or in a mathematics test.
Hermann Ebbinghaus (over the period 1880 to 1885) developed his theory of the forgetting curve to represent the decline of memory retention over time.
At SMASH Maths we prefer to call this the learning retention curve, to show how the retention of learning deteriorates over time when acquired skills are not practised frequently and systematically to embed learning.
Often primary schools in the UK today teach on a traditional topic-by-topic basis. This is depicted by the Primary national curriculum which breaks down the curriculum for every year group into content topic domains as follows:
– Number and place value
– Addition, subtraction, multiplication and division (calculations)
– Fractions, decimals and percentages
– Ratio and proportion
– Geometry – properties of shapes
– Geometry – position and direction
In fact, around 90% of schools in the Primary sector follow the White Rose maths scheme. Shown here is a Year 4 White Rose year planner example, which shows how children are taught in long topic blocks focusing on only one area of the curriculum at a time.
Hence, after a topic is taught in school, children will typically not revisit the topic until it appears in a maths test much later. This is understandable as schools and teachers have a lot of content to cover. However, this topic-based approach does not allow topics previously taught to be systematically revisited and embedded throughout the year.
Furthermore, the majority of educational publishers follow the same pattern for their paper-based and digital products.
At SMASH Maths, our philosophy is to expose children to questions covering all topic areas of the curriculum every week, so that learning retention is improved significantly over time.
Hermann Ebbinghaus hypothesized that the speed of forgetting depends on several factors such as the difficulty of the learned material, its representation, and other physiological factors such as stress and sleep. Luckily, one of the methods Ebbinghaus hypothesised could help retain learning has since been proven to be very effective, and that is spaced repetition (or spiral practice as we at SMASH Maths call it!)
Spiral practice involves learning information on a repeated basis at regular intervals using a systematic approach.
Several different studies have proven the effectiveness of this approach, notably the 2007 study by Pashler, Rohrer, Cepeda, and Carpenter which showed that students given spiral practice scored more highly on maths tests versus a traditional topic based practice.
As a maths consultant, I too have first-hand experience on the impact this strategy can have on improving students’ maths results in schools and have used it with great success.
This is why my colleague, Trevor Dixon, and I are passionate about bringing this method of teaching to children and parents digitally. We believe this method gives every child a great opportunity to become confident and successful mathematicians.
Our SMASH Maths Spiral Practice is based on spaced repetition created to get the best results for all Primary aged students:
– We expose students to all topics at regular intervals for tricky maths topics but also ones that are considered more simple. From our teaching experience, students still need regular embedding of basic topics and maths facts!
– Our practices get more challenging on topics learnt as children progress through the year. Regular spaced intervals serve as an important foundation for pupils to apply their skills to a variety of increasingly difficult maths problems and challenges. This is important as it underpins the National Primary Maths Curriculum three key aims:
Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
Can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions [Maths Programme of Study Key Stage 1 and 2, 2013, page 3] This allows students to develop mastery of their year group expectations. Besides this, it helps pupils be successful with national maths SATs assessments, 7+ or 11+ exam style questions where pupils are often faced with maths questions that have been presented in unusual and quite tricky ways.
– We closely align all our practice to the UK maths curriculum schemes of work.
– Most importantly, at SMASH Maths we take great care and consideration in devising each practice. Two practices are sent directly to your inbox every week. Each SMASH Maths practice covers every area of the maths curriculum every week (as shown below), unlike other digital or paper products which are topic-based.
This approach ensures children gain confidence, improve maths results and not be able to give you the excuse of ‘never’ seeing a fraction (or, in fact, any other math skill taught)!