1. Misunderstanding the order of subtraction, such as thinking that 3 – 8 = 5.

2. Misreading the scale on the ruler and beginning measuring at the number 1, rather than from 0.

How and why misconception 1 can arise with students:

In his book, Issues in Mathematics Teaching, Swan (2001) makes the argument that as students make common mistakes in mathematics in their early years of education, the way in which children think or initially approach a mathematical problem does not originate in the form of wrong thinking. Rather, it is more of a “generalisation” that students make in order to make sense of problems, which come from other informed conceptual understandings that are still in the developmental

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The misconception or mistake lies in forgetting or not being aware that in subtraction, the amount you want to subtract is different from the quantity you have to subtract from. Furthermore, in subtraction, the original quantity that you have or want to subtract from is usually the larger digit (unless the equation involves positive and negative integers). A mistake like this can result in an incorrectly answered basic fact.

Specific ways to help students avoid and/or overcome misconception 1:

Students who misunderstand the order of subtraction need to learn and realise the importance of order and the rational of number quantities. They must learn to perform the right operation rather than confusing addition approaches with subtraction. This can primarily be done through breaking down the subtraction process through interactive and visual means if necessary. The first thing that students need to be reminded of is the basic idea of subtracting the smaller number from the larger number (Drake 2014). From then onwards students can interact with visual representations of problems in order to understand the concept, and also comprehend why

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A good starting point would be to teach them to line the beginning point of whatever that is being measured with the zero on the ruler, so that students are at least introduced to the correct way of approaching measurement. However, it is important to focus more on the underlying concept, and that will require students to actually be involved in creating a conceptual framework for measurement themselves (Swan, 2001). Averill and Harvey (2010) suggest introducing students to measurement through self-made scales rather than launching into using a ruler so that they can begin to grasp an understanding around the roles of units and scales. Doing simple activities such as counting the amount of steps or jumps it would take to get from one point to another, using metre rulers to measure between places or even using hands and feet as units to measure objects in the classroom. Post it notes with numbers written on them can also be used to stick alongside objects so that students can use them to count and see how many take up the length of an object. While the students interact with such activities, it would be ideal to ask student why one step, jump, hand or metre accounts for one unit so that they begin comprehending the idea of a scale, which is made up of a repetition of units (Averill &