Mathematics Support Materials
Mathematics snapshot: Misconceptions about decimal place
Mathematics/Number and Algebra/Fractions and decimals
|Relevant aspects of the Achievement Standards
Recognise that the place value system can be extended beyond hundredths
Students order decimals and unit fractions and locate them on number lines.
Nature of the assessment
Individual conferencing with a small number of students previously identified as struggling with the concept of place value in the context of decimals.
Purpose of the assessment
To ascertain students’ misconceptions about the place value system to thousandths.
The teacher selected a number of tasks that would allow her to identify specific misconceptions. The questions included for example
- Which is larger? 2.75 or 2.8
- Which is larger? 2.05 or 2.5; 2.05 or 2.005
- Read out this number 0.275, 2.34, 0.105
- Which is smaller? 0.3 or 0.4; 0.03 or 0.003
- Which is smaller? 0.845 or 0.5
The conferencing allowed the teacher to ascertain the thinking behind students' responses and to identify the misconception that underpinned his or her incorrect answer. Where a student gave a correct answer he could check that the student had arrived at it because of correct thinking.
The process was time-consuming but, by allowing students time to explain how they had arrived at their answers, the teacher was able to identify fundamental misconceptions. This enabled the teacher to teach to the point of need more effectively and efficiently.
Using the information
The teacher used the results to guide targeted teaching which challenged the misconceptions identified in the conferencing.