| Goals: | To provide an opportunity for students to discuss decimal misconceptions. |
| Year level: | Year 5 to lower achieving Year 10 |
| Group size: | Works well with mixed ability groups of 3-4 followed by whole class discussion. |
| Equipment: | A "Marking Homework" sheet for each group. |
Activity Instructions:
1. Test and categorise students using the Decimal
Comparison Test.
2. Select the homework sheets for your students to correct. Students are set the task of taking on the role of teacher and are to mark and make comments on a fictitious student's homework. Each homework sheet is completed in a manner that reflects a misconception about decimal notation. See Case Studies section for explanation of misconceptions.
| Choice of homework sheets: | |
 |
Maria (Money thinking) |
|
Caitlin (Whole Number thinking) |
|
Courtney (Reciprocal thinking) |
|
Ricardo (Denominator Focussed thinking) |
|
Brad (Column Overflow thinking) |
3. Group students so that there is a task expert and students with different misconceptions in each group.
4. Introduce the activity to the students emphasising the importance of the language that they are using. For younger students, teachers might promote the use of describing the numbers instead of spelling them out i.e. promote 4 tenths instead of 0.4 (zero point four) where possible.
Comments:
The instructions on the top of Caitlin's homework are: "Caitlin
has made some mistakes with her homework. Can you find them?"
. The questions at the end of the homework are: "Can you work
out what she was thinking?" and "How would you explain decimal
numbers to Caitlin so that she could understand?" . Questions
are designed to stimulate group discussion on what decimals are
not as well as what decimals are.
Marking homework exercises provide a non-threatening opportunity
for students to hear their own misconceptions addressed through
a fictitious person's mistakes. There is no evidence that having
students think about misconceptions causes other students to develop
these misconceptions and every evidence that it is beneficial for
those with the misconceptions.
Teaching Tales:
These comments have been recorded during our research whilst we
observed students marking Courtney's homework.
Q 1b 0.32 is 32 parts
Students often express their own misconceptions very clearly as they correct Courtney's homework. We observed a column overflow thinker correcting Courtney by commenting that "Tenths start in the tenths column and so 0.32 is 32 tenths". The other students in the group began to debate this.
Q5 Think about 0.6 and 1/6 then write something in each box: How are they the same and how are they different?
"They are different. Both are one divided into 6 pieces. It is just that 1/6 has one piece coloured in and the other has zero pieces coloured in" responded a reciprocal thinker. As he said this he pointed to the 0 in the ones column. The other students got him to reconsider as they point out he has said that 0.6 is the same as nothing.
In another game a student's response was "0.6 is just like 60 and 1/6 is just like 6. The 1 is there to show you that there is a number there." For 1/6 he divided 1 into 6 pieces and coloured them all. For 0.6 he drew a block of 60 squares and coloured them all.