Research School Network: The wrong half Kelly Duke, Secondary Maths Evidence Specialist and Malton School Maths teacher, examines how to progress when fractions fail.

“You’ve cut it the wrong way!” come the shouts from around the breakfast table.

Yet another misconception in fractions is revealed, this time based upon the division of a piece of toast. My son, having sliced it in half as the example shown on the right of the picture above, is branded incorrect in his actions.

Whilst part of me thought about taking the simpler and swifter option of ignoring the commotion, I decided to ensure the building blocks of learning were secure, as I would in a classroom situation. Then followed a discussion around what a half is, prompted by the arising misconception.

As a secondary teacher the errors I see in fractions calculations quite frequently stem from a poor initial understanding. What Works Clearinghouse in their report ​‘Developing Effective Fractions Instruction for Kindergarten Through 8^th Grade’ (2010) state;

​“Misconceptions about fractions often interfere with understanding computational procedures”

As teachers, we need to prioritise the addressing of misconceptions in order for students to become successful with fractions. Hopefully, this will allow students to have the correct knowledge and understanding needed to move onto manipulation with fractions successfully.

Within the EEF guidance report ​‘Improving Mathematics in Key Stages 2 and 3’ (2022) recommendation 1 (using assessment to build upon pupils’ existing knowledge and understanding) addresses misconceptions.

​“It is important that misconceptions are uncovered and addressed rather than side-stepped or ignored” (EEF, 2022).

Using misconceptions can also be used as a basis for exploratory talk in the classroom (McBride et al., 2024). With the rise of oral language practices, using misconceptions can open up discussion and areas for talk.

​“Think about uncertainty and misconceptions that arise in a lesson and use them as the focus for exploratory talk in later lessons. Revisiting these points will help pupils to embed their understanding…”

(McBride et al., 2024)

The NCETM Checkpoints address many misconceptions around fractions and are tasks which are used frequently in my classroom. ​‘Where is one quarter?’ shown below, is an example of a task which not only quickly highlights misconceptions, but also allows for discussions to promote oral language practice within the classroom.

Through the NCETM Maths Hub, the Year 5 – 8 Continuity Work Group in Ryedale and East Riding are facilitating sessions across the year focusing on fractions with oracy. There is no fee to participating schools. Please follow this link to book a place.

References

What Works Clearinghouse (2010), Developing Effective Fractions Instruction for Kindergarten Through 8^th Grade’
EEF, Improving Mathematics in Key Stages 2 and 3 (updated 2022)
NCETM, ​‘Learning Fractions Shouldn’t be Difficult’
McBride et al., (2024) Talk For Maths Benchmarks, Oxford University Press
NCETM Checkpoints, (NCETM)

Further Links

NCETM Podcast Continuity in Fractions Learning Between Year 5 and Year 8