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How to help Courtney
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General Principles |
| Target examples
so that Courtney realizes that she has something to learn! (eg
she incorrectly thinks that 0.4 < 0.3, but correctly thinks
that 0.12 < 0.3) |
| Teach underlying
principles with concrete models (eg LAB) |
| Incorporate decimals of various
lengths in the one situation wherever possible |
| Conduct class
or group discussions on this and other misconceptions |
| Provide opportunities for
Courtney to use her new understandings |
What does Courtney need to learn?
Courtney probably knows very little about decimals, even though she
may get quite a lot of the interview and test questions correct and
may be able to add and subtract decimals by following rules. This
is typical of student misconceptions. She realizes that decimals perform
the same function as common fractions and tries to interpret decimal
notation in these terms without considering place value. In the "Talking
about Place Value" interview, she shows that she has a tenuous
familiarity with tenths and hundredths etc, but she does not use this
in completing the Decimal Comparison Test or in the other interviews.
There, she consistently interprets the decimal part as indicating
the denominator of a fraction, with larger denominators creating smaller
fractions. For example, she thinks that 3.12 is something like 3/12
or maybe like 3 1/12 (three and one twelfth)
although she may not think it is really the same. Courtney first needs
to learn about place value, expanded notation and the "endless
base ten chain".
Lesson Ideas
| LAB |
This is our model of choice for teaching
all the fundamental principles about decimals. Carefully introduce
the largest piece first (the one) and then discuss how
to cut into 10 pieces. This partitioning process is essential
to understanding decimals! |
| Marking
Homework |
Use Courtney's homework in your class
for stimulating discussion which may demonstrate to some reciprocal
thinkers in your class what is wrong with their thinking. (More
info on this activity) |
| Skip Counting |
Any "skip counting"
activities such as Number
Trails, Decimal
Skip Counting and using number lines. |
| Number
Expander |
A visual aid way of demonstrating that
0.3 is 3 tenths and 0.4 is 4 tenths, and 0.45 is both 45 hundredths
and 4 tenths + 5 hundredths. |
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