They have simply read ‘ten’ and ‘smaller’, and subtracted 10. The image below shows an example of a student thinking in an additive manner to solve this problem. They often think in an additive way when they hear the words ‘smaller’ and ‘larger’ and do not understand the meaning of these words in the context of the word ‘times’. Students find multiplicative comparison difficult as we rarely provide them opportunities to think in this way. It relies on the ability to think multiplicatively, something we know takes many years to develop in students. Multiplicative comparison requires a sophisticated form of understanding related to the relationship between two quantities. However, in Years 3-6 we also want to students to be able to compare multiplicatively. We want students to understand ‘more’, ‘less’, ‘larger’ and ‘smaller’. Place numbers in descending or ascending order and locate numbers on empty, partially marked or complete number lines.Ĭomparing numbers is an important concept in early maths. Compare numbers in a multiplicative manner, for example ten times larger than 54 is 540. In my research I defined this aspect in the following way: Compare numbers to determine which is larger or smaller. In this blog I am looking at the ‘compare/order’ aspect of place value. Along with each thinking mistake I also present a piece of teaching advice to help you address these issues. This series of blog posts presents six common ‘thinking mistakes’ which have repeatedly surfaced in my research into Year 3-6 students whole number place value understanding. It is during these times that real brain growth occurs. In stark contrast, ‘thinking mistakes’ are made when our brain is working hard, struggling to make thoughtful and logical conclusions. ‘Thinking mistakes’ are in direct contrast to ‘silly mistakes’- ones which I want my students to consciously avoid- these are made when our brain is not ‘switched on’. I like to label misconceptions as ‘thinking mistakes’. I encourage all students to see that through mistakes comes learning. When I work with students, I love to celebrate mistakes and promote a growth mindset (Dweck, 2016).
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