Yes, children should memorise addition facts
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Memorising addition and subtraction facts is vital for making progress in maths and helps students access more complex tasks.
When I speak to teachers who are concerned about the maths proficiency of children, a common theme is that they are seeing too many students who cannot fluently recall basic addition and subtraction facts. Parents, too, are often surprised that schools are not helping their child to memorise addition and subtraction facts.
Let’s define what I mean by memorisation. I mean that when prompted with something like 8 + 4, they can respond with 12 quickly and effortlessly. What is not memorisation is applying a strategy to effortfully work out 8 + 4, say, by counting on using your fingers.
Let’s get one thing out of the way: being able to apply a strategy to derive a fact is a worthy instructional goal. My sense is that there is consensus amongst teachers that teaching students strategies is a good thing. Is there the same consensus around memorising facts? No, but there should be! So, why should children memorise addition and subtraction facts?
Students need facts in long-term memory to learn and understand new facts and concepts
Take this curriculum descriptor for Level 1 maths, taken from the Victorian Curriculum 2.0:
add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies
This means that in Grade 1, students will encounter problems like adding 12 + 7 or 6 + 7. Teachers will generally teach students a strategy to solve these problems. What becomes evident here is that, even as early as Grade 1, students who have already memorised some facts are at an advantage when learning new strategies. For example, the student who knows 2 + 7 = 9 can more easily learn the split strategy for adding 12 + 7. The student who doesn’t have that fact at hand will need to use their limited working memory to work out 2 + 7 and will have fewer cognitive resources left for thinking about the split strategy. Similarly, the student who knows 6 + 6 = 12 can more easily learn the near doubles strategy for adding 6 + 7. Students who have fluent recall of basic facts can more readily acquire new knowledge than students who do not. This is a big inequity problem! We can prevent this by giving all students access to well designed practice focused on developing fluency.
Students need to fluently recall facts to engage in more complex tasks
Not only do students need some basic facts in long-term memory to learn other basic facts; fluent retrieval of all basic addition and subtraction facts is a necessary sub-skill for higher level tasks they will encounter as they progress through school. Consider the importance of fluently recalling 6 + 7 to the following tasks:
Mentally adding 600 + 700
Using the traditional addition algorithm to add 36 + 27
Estimating 59 + 68 by rounding both addends to the nearest ten
Again, we encounter the problem of limited working memory. These tasks are accessible for a student who can fluently recall 6 + 7. If a student needs to use working memory to work out 6 + 7, they will likely get overwhelmed by the larger task. If we want students to engage in higher level tasks and feel confident, we need to ensure they have memorised basic facts.
The importance of memorising basic facts is well established now
In 2008, the Final Report of the US National Math Advisory Panel emphasised the critical importance of memorisation, describing the ‘mutually supportive’ relationship between conceptual knowledge, procedural skills and fast access to number combinations. This finding has been reinforced since then by multiple studies. The inclusion of ‘retention and recall’ in the Victorian Teaching and Learning Model 2.0 is also a big signal from the Victorian Department of Education that memorisation needs to be on the agenda for all schools if it isn’t already.
So why are some teachers wary of memorisation? The main arguments I’ve come across are:
Students don’t need to memorise facts because calculators exist.
Memorisation is just rote learning; it doesn’t build conceptual understanding.
Practice aimed at memorisation causes anxiety.
The reality, though, is that students do need to have memorised facts to engage in mathematical thinking; they can’t always rely on calculators. Memorisation isn’t an impediment to conceptual understanding; having knowledge of basic facts enables understanding. Students who are supported to develop fluent recall of facts will become more confident at maths; those who are not supported to memorise facts will have more negative experiences, especially as the demands of the curriculum increase with each grade level.
So, memorising addition and subtraction facts is vitally important. Teaching students to use concrete materials for modelling problems or teaching strategies is important too, but we have to stop pretending it’s sufficient. The question then becomes: How can we support students to memorise addition and subtraction facts? I’ll address that in my next blogpost.
Brad Nguyen is a primary teacher, learning specialist and consultant.
References
National Mathematics Advisory Panel (2008). Foundations for Success: The Final Report of the National Mathematics Advisory Panel, US Department of Education.
Michael Pershan (2022). Questions and answers about addition fact research, Pershmail.
DET Victoria (2024). Victorian Teaching and Learning Model (VTLM 2.0), Arc.
