Whilst planning for the next module of my course on the EEF Guidelines for KS2 and 3 mathematics I came across Simon Cox’s latest blog on Misconceptions in Maths. He uses the REACT planning framework which I had not come across before and it seems to me that this is a useful model to be used in many different subjects across the curriculum, not only in Maths.
The first two letters are about understanding the issues before beginning to plan a topic.
R – RESEARCH
Do some research into common misconceptions about the topic you are about to teach. Experienced teachers may have come across the same misunderstandings many times before. Newer teachers and non-specialists will need more support. What concepts are pre-requisites for the topic you are about to teach and how will you check that these are already embedded? Find out what misconceptions students may already have and also which may arise during your teaching. Investigate trustworthy sources of literature about misconceptions in your subject – STEM Learning has a collection of resources for Science and the Geographical Association has compiled a list of common misconceptions in Geography. Misconceptions in maths are discussed in great detail on the NCETM website.
E – EXPLORE
Explore why these misconceptions exist. This will help you to understand their basis – our ultimate goal will be to stop misconceptions arising in the first place if possible. Many misconceptions may arise due to misunderstandings about the meanings of words and understanding subject-specific vocabulary is very important. It also is vital to be precise about the way we phrase things – particularly in maths – I have lost count of the number of times I have heard students (and often adults too) saying that to multiply by ten you “add a zero”. Of course adding zero to any number will have no effect on its value, but this is not what they mean. Whilst many people manage to correctly multiply by ten despite this inconsistency, only just before Easter one of my year 7s told me that 8.06 multiplied by 10 was 8.060!
Polysemous words sound and are spelled the same but have different, but related, meanings. There are many of them in maths and in science in particular which give rise to some great teacher jokes. However the serious side is that the curse of knowledge can mean that as teachers we assume the second meaning is obvious, and overlook the fact that our students may not understand the context-specific meaning of the vocabulary that we use.
The final three letters are about planning the learning.
A – ADDRESS
Make sure that you address the misconceptions head on. Consider where in the learning it would be best to explore them with your students. You will certainly want to check for prerequisite knowledge at the start of a topic, but you will need to consider how to start introducing new information. Asking students “what do you know already?” can bring out previous misconceptions about a topic, but there is a danger that students then get hung up on these and this is what they remember. Sometimes it could be better to teach new subject matter correctly first. For example I have learned not to ask year 7 students what they already know about calculating with negative numbers as they invariably respond with “two negatives make a positive!” and then it is very difficult to dispel this unhelpful phrase once they have all been reminded of it.
A great starting point would be to discuss these at a department meeting or shared planning session. The diagnosticquestions.com website has a “Plan a lesson” feature where you can search for data on the most common wrong answers – and whilst there are now over 50 thousand maths questions on the site, there are also more than 30 thousand for other subjects. Because the questions are all written with common misconceptions in mind and contain distractors and plausible wrong answers, this is a very useful source of data.
C – CONSIDER
Consider possible issues that could arise in the future. Whilst tricks or shortcuts might help students to remember things in the short-term, they may actually give rise to further misconceptions later on. Teaching for deep understanding should mean that students can think logically about why a method works, give reasons and evaluate the feasibility of their answer, rather than relying on memory alone. There is a great book: “Nix the Tricks” which is freely available to download and covers many of these for Maths.
T – TASKS
Choose tasks to specifically draw out and address misconceptions. There is a temptation, especially with students who might be slower to grasp a topic, to give them tasks that they can “do” and so only expose them to straightforward questions which specifically practise the concept that has just been taught. These are the same students who are likely to be most confused when the topic is approached in a slightly different way. In my example earlier about multiplying by ten, I uncovered this student’s misconception through presenting the class with a set of multiple choice questions particularly designed with this in mind. If the questions had just involved standard calculations with whole numbers I would not have discovered it. True / False questions can also be a really useful and quick way of checking for understanding and that misconceptions have not arisen during your teaching. Incorrect worked examples where students are shown some work (often of a fictional student) and asked “what has this person done wrong and why?” followed up with “how would you explain to them how to answer this correctly?” also make good tasks.
Misconceptions and dealing with them really are at the heart of good teaching. For a really concise summary of the REACT model see the link to the pdf at the bottom of Simon Cox’s recent blog for the EEF:
Deb is a maths teacher at Durrington High School. She is also a Maths Research Associate for Durrington Research School and Sussex Maths Hub Secondary Co-Lead and is currently delivering our training on the EEF Guidelines for KS2 and 3 Maths.