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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 units
place. 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.
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