“Recognizing George Miller’s information processing research showing that short-term memory is limited in the number of elements it can contain simultaneously, Sweller builds a theory that treats schemas, or combinations of elements, as the cognitive structures that make up an individual’s knowledge base.”
– Sweller, J. 1988.
As you read through today’s article, I would like you to consider how you go about teaching multiplication and the times tables to students as that is the focus of today’s article. I am basing on my post today on my (admittedly limited) understanding of cognitive load theory (CLT) from my recollections of the educational psychology course that was part of my Initial Teacher Education (ITE), so if I err in my understanding, please let me know so that I can correct it.
One of the things that I have been doing with my class is Timetables Clocks. This is the first thing that I do with them when we commence our Mathematics block straight after our lunch break. The simplest explanation of this is that students draw a jumbled clock face, with the multiplier going in the center, as in the image below.
Students are given up to one minute to complete the twelve questions, and they write down their time. The students really enjoy this activity, and there is fierce competition to be the one with the quickest time, as they receive a bonus under our class economy program. I have only brought this program into our mathematics block recently, and on Wednesday I had them complete their four-times tables, and the results were abysmal.
My understanding of CLT is that our memory is divided into working or short-term memory and long-term memory, with only a small amount of what is in our working memory being retained and transferred into our long term memory. Our working memory can only process a certain amount of information before some of what is in our working memory must be either transferred into our long term memory or dropped from our conscious memory.
When answering a question, if part of the question can be answered by drawing upon our long-term memory than our working memory is able to bring a little bit more of itself to bear on answering the question. For example, if a student has a question such as 6×4(3-6 x24) and they can draw upon their long-term memory to know that 6×4 is 24, then their working memory is free to focus on the remainder of the question. A rather simplistic explanation and I hope it articulates clearly enough my understanding on this.
Times tables are embedded into daily life, from estimating the groceries, to budgeting, to planning a holiday, knowing and being able to easily recall times table facts is something of a basic skill, and any question or problem or problem involving multiplication is going to be significantly more difficult to solve mentally (or in writing for that matter) if you are required to utilise your working memory solving those aspects of the question than if you are able to simply recall those facts from your long-term memory.
Indeed, from the conversations that I have had with secondary mathematics teachers, and correct me if this is not your experience, it appears that students’ being unable to recall multiplication facts from their long-term memory is a source of stress and frustration for both secondary students and teachers. As an example, it seems that when algebra is introduced, or when teachers are dealing with conversions between fractions, decimals and percentages; that students are struggling to deal with the multiplication aspect of the question, and are therefore unable to process the skills and knowledge needed for the particular mathematics concept being dealt with at the time and transfer that knowledge into their long-term memory causing a flow-on effect.
So, and this is where I am looking for feedback from my PLN, my thinking is that this is one instance where rote-learning still has a place, and to my mind and understanding of CLT it seems logical. By memorising those multiplication facts, ensuring they are in students’ long-term memories, students will then be able to focus more on the remainder of any question of problem, rather than becoming stressed about multiplication issues (which is an issue for some students).
Is my understanding of CLT reasonably accurate, and more specifically, accurate for the purpose I need it to be accurate for? Additionally, what other strategies have you found successful for ensuring multiplication facts make their way into students’ long-term memory? As always, thank you for reading, and I look forward to hearing your thoughts and feedback on this topic.
- Sweller, J., (1988) Cognitive load during problem solving: Effects on learning, Cognitive Science, 12, 257-285 (1988).