1 Learning through memorisation

Learning through memorisation, or rote learning, is a learning technique based on repetition.

There are several arguments in favour of this learning approach: one is that having a rapid recall of certain facts in mathematics is necessary to become fluent in other mathematics topics.

Many students are encouraged to learn their ‘times tables’ by rote. This is so that when they are solving problems they do not spend too much time and effort working out relatively simple calculations such as 6 x 7 – especially when they have no access to calculators. Knowing times tables by heart also gives them a better number sense; for example, of the numbers’ magnitude, of how numbers are related or of multiples and fractions. Similar arguments could be used for learning algebraic identities through memorisation.

However, there are also many counter-arguments to using memorisation as a learning technique (De Morgan, 1865; Marton and Booth, 1997). One is about accessibility; not all students benefit from memorisation due to their poor school attendance, their lack of time or opportunity for the required practice, or just their poor recall. Students with special educational needs such as dyslexia, for example, are enormously disadvantaged.

Another argument concerns the kind of learning that memorisation affords. Memorisation does not focus on comprehension or building understanding; nor does it support any exploration of what concepts could mean, or how they are connected to other areas of mathematics. It focuses on memorising and accurate reproduction, which can become problematic when studying more complex aspects of a subject (such as formulae and algorithms) that entail many steps. Memorisation does not lead to understanding of meaning, which means that elements get missed out, details get muddled up, stress increases and exams can be failed.

The learning experience when using memorisation is often not exciting; it can even be considered boring because of its repetitive nature and lack of focus on understanding and making connections. Students mechanically ‘go through’ the exercises, engaging their brains as little as possible. This is problematic for all students, including high achievers. Boredom when learning mathematics, little demand for thinking and a lack of opportunity to work on making connections and giving meaning to mathematics makes it hard for learners to understand and enjoy the subject.

Pause for thought What are your thoughts about learning through memorisation? Do you think it works well always, sometimes or not often? How did you experience learning mathematics by memorisation? Think of one of your students who seems to be memorising well, and think of one that is struggling. What is the same and what is different about how they learn?