## Mathematics Support Materials

### Mathematics snapshot: Misconceptions about decimal place

Mathematics/Number and Algebra/Fractions and decimals

Content Description Relevant aspects of the Achievement Standards

Recognise that the place value system can be extended beyond hundredths
(ACMNA104)

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.