Identifying and Addressing Misconceptions in Fractions
Using posters is a great way to assess learners’ knowledge and understanding. A poster activity enables the teacher to listen to group discussions, identify what the learners know and understand and intervene if necessary.
Last week I was working with some adult learners. I asked them to draw as many different representations of 2/3 as they could. Discussions between learners regarding various representations and equivalences with decimals and percentages offer the teacher invaluable feedback on learning. Where errors or misconceptions are identified, the teacher is enabled to modify their lesson and address the errors or misconceptions as they occur.
The photo on the left shows part of one poster in addressing misconceptions in lessons.
When questioned, one of the learners explained that the circle is cut into 3 pieces and 2 pieces are shaded (two thirds!).
In seeking to address this issue, one method I used was a class discussion around a fraction wall. Each learner constructs a fraction wall using strips of paper to represent one whole. Further strips are cut into fractions of various sizes, annotated and stuck to a page.
When discussing how to represent two halves, I find the learners tend to suggest that we cut the strip into 2 pieces. I follow their instructions as shown in the photo on the left. This results in a discussion around equal sized pieces. I find this tends to address the situation of the circle cut into 3 unequal sized pieces.
Other discussions that are worth developing using a fraction wall:
- Equivalent fractions. Learners can run their fingers up the page to check that 2/4=1/2
- Two halves make one whole and three thirds make one whole etc.
- One third is greater than one quarter. This may be an opportunity to introduce the appropriate signs such as 1/3 >1/4 and 2/3<3/4
- Connections between fractions, decimals and percentages.
If you have any other suggestions for addressing this issue, or comments, they would be appreciated.
Jill Brown BEd (Hons), MA, AdvDipMP
Jill Brown, Director of LTA Solutions Ltd, is passionate about learning and teaching. Her career in education spans 30 years. She has worked across the UK and Ireland, Europe, the Middle East, USA and the Caribbean. Her innovative practices have been commended throughout her career.
LTA Solutions Ltd, provides a range of evidence-based professional development opportunities for teachers and teacher leaders. Check out the international page at http://www.ltasolutions.org.uk/