Have you ever wondered why kids keep forgetting so much of what they have been taught?
Misconceptions stop kids learning – they either outrightly reject, or quickly forget teaching of concepts beyond the misconception. That’s a big issue and frankly a bit scary to even contemplate. It means that if we don’t deal with misconceptions now, chances are our kids will still have them years down the track, and it will affect all of their maths learning from now on. This page will give you information on what misconceptions are, how to deal with them and links for videos demonstrating questioning as well as diagnostic testing and resources for getting started.
Misconceptions describe what happens when a child’s conception or idea about something in mathematics is fundamentally opposed to what we are trying to teach them. A misconception is something that a child truly, intuitively believes, rather than an error or mistake. They are also almost always developmental, an over-generalisation that a child came up with themselves, rather than something that they were taught.
That is an important distinction. Firstly, when a child over-generalised, that means that they first generalised – showing that they are capable of generalising! Generalising is a critical part of mathematics, so the child has shown that they are capable of maths! Secondly, because the idea came from the child they are far more difficult to address than just a mistake or error. Here is an example of some misconceptions that are common to the learning of fractions.
Misconceptions are a problem with Understanding rather than Fluency. That’s why just telling a child how to do a procedure generally doesn’t fix the underlying issue – following procedures is about fluency rather than understanding. In the video below, you will see a student who has a pretty solid understanding of three, but not five.
To find misconceptions we need to ask questions in a non-routine way. Routine questions (fluency) give us back routine answers, rather than showing what a child actually thinks. Problem solving tasks, or those that require transferring and connecting concepts, work the best.
Journal problems from Back to Front Maths are designed to do this job when introducing a new concept. Misconceptions are identified in the teaching notes for each problem, as well as the main questions for addressing the students’ ideas.
If you would like whole-school or cohort testing, the following tests will help with number concepts:
When using the program across your school make sure that you moderate your marking as a staff to check that you are consistent in your approach.
To fix misconceptions, we need to get at the heart of the problem – to help a child realise the illogicallity of their idea – and change their own mind.
This is called using “cognitive conflict”, and works a bit like a science experiment. We encourage a child to make a prediction, try their own idea to solve a problem, then draw their attention to the bit that didn’t work (called the discrepancy). Often it takes a lot of discrepancy for a child to work out that their idea will not work, leading to them changing their own mind. For more great video examples of this questioning, click here.
Once a child has changed their mind, they can begin to connect the initial problem to what they have worked out, thereby moving past the misconception and growing in conceptual understanding. To read more about the four-step questioning process for fixing misconceptions, click here.
Misconceptions in key number concepts are particularly important to deal with as number underpins most of what we learn in mathematics. We need to start by using some diagnostic testing above with your class in key number concepts to determine exactly how to intervene. This post gives some of the research by Tierney, including showing students learning over two years of maths for every year of teaching as measured by PAT M. The data has been peer-reviewed, presented and published in the conference proceedings of the the Mathematics Education Research Group of Australasia conference in Auckland 2018.
Here is the academic paper if you want to read it through: Kennedy – Intervention using challenging tasks and conceptual change.
We recommend using the diagnostic testing, then implementing the Interventions in Mathematics resources for 1-2 lessons per week over 8 weeks, then retesting. Put your results into this effect size calculator to check your growth.
If your effect size is not over 0.6 after 8-10 intervention lessons, please contact us directly for a consultation.
If you are just starting out, or are coordinating mathematics at your school, we recommend that you consider subscribing to our website so that you can access recorded videos that deal specifically with fixing misconceptions. We also run webinar-discussions twice per term, so please get in contact to find out more. You might also like to click here to find upcoming training.
Check out our article on key number concepts from F-3, including watching a recorded webinar. You will probably also want to download the addition and subtraction test from the Interventions Series to use with your lower primary classes, or the place value test to use with middle and upper primary.
If you are teaching in upper primary or high school, make sure to check place value before moving on to the diagnostic testing for fractions (proportional reasoning) that is on the same page as mathematics is very developmental. If you skip place value, and particularly the concept of relative size, you will find that kids continually forget fractions. It is worth spending the time to go back and fix it before trying to move on.
Next year we are running new projects and training days designed to provide you will all the help you need to implement the approach AND train your staff. You can find all the information on upcoming courses at this link. If you would prefer a consultant to visit your school, please click this link to find out more.
If you would like to consider working with us, or with with other schools in your region or network to provide professional learning in mathematics, please contact our admin team to arrange time to speak with Tierney about your priorities. We have run multiple highly-successful projects in SA, WA, VIC and QLD, in the State and Catholic systems.
Typically our 12 month packages have included:
Download our Single School Project Quote here: Single school project for 2025
Download our Multiple School Project Quote here: Multiple school project for 2025
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