Doing mathematical calculations in the head or mental calculations require a great deal of working memory. Children must store the information they have heard, remember and retrieve those facts, and then process the information and apply it correctly. Because “doing math” is not a single skill, it involves a long list of cognitive abilities, in which children vary widely. Our ability to perform arithmetic operations largely depends on working memory, manipulating and keeping information in mind.
Previous research has found that, in adults, procedural strategies, particularly counting, rely more heavily on working memory than recovery strategies. During childhood, there are changes in the types of strategies employed, as well as an increase in the precision and efficiency of the execution of the strategies. Therefore, it is likely that the role of working memory in arithmetic may also change, although this has never been directly compared between children and adults. This study used the traditional dual-task methodology, with the addition of a load control condition, to investigate the extent to which the working memory requirements for different arithmetic strategies change with age.
The study included participants aged 9-11 years old, 12-14 years old, and early adulthood. The results showed that both children and adults use working memory to solve arithmetic problems, regardless of the strategy they choose. This study highlights the importance of considering working memory to understand the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition. Difficulties within a single cognitive domain that is required for mathematics will make it difficult for children to perform mathematical calculations.
Many of the numbers can be “fractionated” once students are more familiar with and master fractions, and they can also use mathematical data retrieval for many items instead of having to calculate every single one of them. There is an enormous correlation between doing mathematics in your head using the visual algorithm and considering that “you are not very good at mathematics”. I have met mathematics students who excel at some types of mathematics but are terrible at numerical calculations and do mathematics using the visual algorithm. Knowing aphantasia is important to understand why some people are good at mental mathematics.
Aphantasia is a condition where people cannot visualize images in their mind's eye. This means that they cannot use visual imagery to help them solve mathematical problems or remember facts. People with aphantasia may find it difficult to do mental calculations because they cannot visualize numbers or equations in their head. This animated article and blog explores the cognitive science of learning mathematics, explaining how different types of memory are involved, why speed is important and how practice is key to developing fluency in mathematics.
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