Skip to 0 minutes and 4 seconds CHRIS: Planning for learning is important because teachers need to create opportunities where they can tap into student ideas. One of the most important findings of mathematics education research has been that all students constantly ‘invent’ rules to explain the patterns they see around them. Sometimes these explanations can be useful but some can lead to incorrect ideas and assumptions. For example, many students learn early on that a short cut to multiplying by ten is to ‘add a zero’. But what happens to this rule, and to a child’s understanding, when they are required to multiply fractions or decimals by ten?
Skip to 0 minutes and 46 seconds Malcolm Swan explained this by suggesting that a ‘misconception’ is often not wrong thinking but is a concept in embryo or a local generalisation that the [student] has made. It may in fact be a natural stage of development. (2001: 154) Knowing these likely mistakes and the nature and origin of the misconceptions that may explain them can be a useful step in deciding what to do as will some strategies for avoiding and for remedying these misconceptions .
Planning with an awareness of misconceptions
Chris discusses how misconceptions are often not wrong thinking but may be a ‘concept in embryo’ or a ‘local generalisation’ that the pupil has made. These ‘alternative ideas’ may in fact be a natural stage of development. It is therefore important for you as a teacher to take the time to ascertain these ideas and then plan with them in mind.
There are a number of different ways you can find out common misconceptions and areas of difficulty in advance of the topics you will be teaching. These include:
- Talking to colleagues;
- Reflecting on your personal experiences of teaching;
- Reading research literature;
- Students’ performance.
We will look at all of these different sources and learn with each other about common misconceptions and areas of difficulty students have in a variety of different topics. In later weeks we will explore in more detail how having planned with these alternative ideas in mind we can gather evidence to help us make inferences about students’ thinking to be better placed to respond and support their learning.
Before we provide you with a range of resources to deepen your understanding of misconceptions and areas of difficulty your students may have, we’ll consider how to create a classroom culture that can be beneficial for your students.
To start our thinking about the use of misconceptions, post in the comments below:
one benefit using misconceptions in your planning and
one drawback of using misconceptions in your planning.