At EdAlive we strive to build the very best in online learning websites that employ sound theory to promote learning.
Automaticity is a key to learning
We know that learning a new skill requires repetition. With modern brain-scanning techniques, researchers can observe that the first few exposures to new information leads to a new neural connection being made. Further repetitions (at time intervals) lead to the new connection being strengthened (Menon 2010). For the student, the new learning becomes consolidated, and recall speed improves. With some further reinforcement, automaticity is achieved – effortless recall without needing to engage the working memory, which is then free for more advanced concepts (Cholmsky 2011).
In mathematics, this progression of learning is particularly relevant. The nature of school mathematics is that each new element of learning builds upon many earlier foundations. This works most effectively where the earlier work is not only consolidated, but automaticity is achieved. By contrast, falling short of automaticity with a learned concept makes it much more difficult to take on the next level concept because the learner must hold both the new and the old concept concurrently in their working memory. In such circumstances their working memory is quickly overwhelmed (Geary et al 2007). Sadly, this leads to a lose-lose outcome where a student is required to make a huge mental effort but is discouraged by seeing little result.
A number of academic studies have set out to determine the magic number of repeats required to master a new concept, but estimates vary widely from 17 to 30 to 400. It may be concluded that the number is affected by the type of material being learned, and also that learning methods vary in efficiency – in fact, research has shown that poor methods can result in no gains in recall (Cholmsky 2011). Definitions of mastery may differ between studies. As we often observe, there are also differences between students.
There may be no doubt, however, that repetition is of vital importance; nothing controversial in that.
The application of educational theory in the classroom
The difficulty arises from putting our knowledge of educational theory into practice in real world classrooms and homes. Many successful teachers know that devoting a small part of each mathematics lesson to fluency development will reap many rewards. In practice however, time spent on regular revision with the class as a whole is less than ideal as the needs of each student are so diverse. Students would each make more progress if revision and reinforcement to automaticity could be individualised, and constantly updated to each student’s growing capability (Cholmsky 2011). For conventional learning, this would put an unmanageable workload on teachers.
Fortunately, a well-designed online learning website can readily meet this need. At EdAlive we have spent many years developing our online learning websites to fully individualise learning and to apply the principles of sound learning theory for the best learning outcomes. For instance, EdAlive’s Maths Invaders uses automated Adaptive Learning to individualise and continually adjust material for each individual – the perfect balance of reinforcement and challenge.
Don’t just cram the night before your exam! (Here’s why)
It is well-established that learning is more efficient when a concept is learned and practised over several sessions (“spacing”) rather than being hammered in one session (“massing”). Less time is required and recall is better. It’s as simple as that. Research has demonstrated this fact many times – not just in humans, either. Other mammals, and even a simple sea slug, have been shown to follow the same pattern (Sarma 2020).
It follows that automaticity can never be an objective for regular maths lessons – it takes time, and while students will reach automaticity at different rates, no one gets there without putting in the time.
For these reasons, students benefit far more from mixed content delivery in revision, so that they need to recall different information and different types of information at each question – this super-charges learning consolidation and fluency.
Maths Invaders has been designed to avoid the trap of massing. Instead, the mix of topics is presented by the automated adaptive learning system incorporating spacing by design. This approach is in stark contrast to most other online learning systems that we have analysed where there is a narrow focus on one topic at a time with the students repeating examples over and over until a certain definition of mastery is demonstrated. They then move on to another topic never to revise the former one. The weaknesses in this approach are clear.
Active engagement promotes learning
It is also known that students learn better when their brains are actively engaged at the time. Now, it would be great if all students found that learning mathematics excited their imagination – but we know that is is rarely the case. Fortunately, the benefits of active engagement are still available if the engagement is focused on a side-issue, such as a suitable game within the learning app (Cholmsky 2011). Maths Invaders uses the Space Rescue game for this purpose – not just a simple sweetener for the learning medicine, but a crucial and central element of efficient learning. Some researchers have shown that learning through play even reduces the number of repetitions required for consolidation and automaticity.
Maths Invaders optimises learning efficiency for each student, which is great for their learning outcomes. The presentation of mathematical content is fully individualised and reinforced with repetition that leads to automaticity. Concepts being presented are spaced for greater learning efficiency and students are engaged through the embedding of the learning activities in the game context. Furthermore, when students can see that they are making real progress commensurate with their effort, they will learn that effort is worthy, and their confidence will grow, in mathematics and beyond (Cholmsky 2011). This opens to all students the love of learning that can revolutionise not only the classroom but the world beyond.
In mathematics, national and international testing repeatedly shows little or no progress across Australian school systems. Even more worrying, the numbers of students performing well below average is increasing. There is also a longer trend of fewer students enrolling in higher level maths in senior high school. All these trends can be mapped back to a break-down in the process of attaining automaticity in the basics of mathematics.
Research demonstrates that users of Maths Invaders make astounding academic progress
Our analysis of the learning outcomes for students using Maths Invaders clearly demonstrates that their knowledge expands. Research conducted by EdAlive shows that for the average user, their maths age advances by 12 months after 10 half-hour sessions or equivalent – easily completed in one school term, even in addition to scheduled maths lessons.
Substantial increases in response speed are also evident
At the same time as this advancement in knowledge, brand new research shows that recall speed also increases dramatically. Over the same course equivalent to 10 half-hour sessions, the average student’s response time for a broad sample of topics is simultaneously reduced by 1.1 seconds or 26%. That is, progressively more difficult material is nevertheless being answered more quickly. This is compelling evidence that the delivery method is effective at consolidating knowledge and allowing students to attain automaticity.
This same learning theory is applied to the full range of EdAlive’s websites
A focus on spacing rather than massing, embedding learning in fun and fully individualised instruction are also features of the core design of all the other EdAlive Online Learning websites including Typing Tournament, Words Rock, Baggin’ the Dragon Maths and Volcanic Panic Reading Success. Our research indicates that students using these websites are also making remarkable learning progress.
Cholmsky, P. (2011). From acquisition to automaticity: The Reflex solution for math fact mastery. https://harringtonmath.com/wp-content/uploads/2012/01/Reflex_White_Paper.pdf
Geary, D. C., Nugent, L., Hoard, M. K., & Byrd-Craven, J. (2007). “Strategy use, long-term memory, and working memory capacity.” In D. B. Berch & M. M. M. Mazzocco (Eds.), Why is Math So Hard for Some Children? The Nature and Origins of Mathematical Learning Difficulties and Disabilities (pp. 83-105). Baltimore, MD: Paul H. Brookes Publishing Co.
Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., et al. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved October 13, 2022, from https://ies.ed.gov/ncee/wwc/practiceguide/2
Hasselbring, T. S., Goin, L. I., & Bransford, J. D. (1987). Developing automaticity. Teaching Exceptional Children, 19(3), 30-33.
Isaacs, A., & Carroll, W. (1999). Strategies for basic fact instruction. Teaching Children Mathematics, 5(9), 508-515.
Menon, V. (2010). Developmental cognitive neuroscience of arithmetic: implications for learning and education. Zdm, 42(6), 515-525.
Miller, A. D., & Heward, W. L. (1992). “Do your students really know their math facts? Using daily time trials to build fluency.” Intervention in School and Clinic, 28(2), 98-104.
Sanjay Sarma and Luke Yoquinto. 2020. Grasp: The Science Transforming How We Learn. Doubleday/Robinson.
Storm, B. C., Bjork, R. a, & Storm, J. C. (2010). “Optimizing retrieval as a learning event: when and why expanding retrieval practice enhances long-term retention.” Memory & Cognition, 38(2), 244-53.
Woodward, J. (2006). “Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills.” Learning Disabilities Quarterly, 29(3), 269-289.