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Understanding The Students’ Way of Thinking
An Example for The Teacher
UNDERSTANDING THE STUDENTS’ WAY OF THINKINGcompose by:Ratih Ayu Apsari [06022681318077]International Master Program on Mathematics Education (IMPoME)2013
This presentation also made to fulfill the requirement of “ICT in Mathematics “ course subject by
Prof. Dr. Zulkardi. M.I.Komp., M.Sc.
.. This material is adapted from one part of the Workshop and Interview
by Dr. Maarten Dolk (from Freudenthal Institute- Utrecht University) to
the 10 IMPoME students of Universitas Sriwijaya during selection in
teaching pedagogy aspect ..
WHY WE HAVE TO UNDERSTAND THE STUDENTS’ WAY OF THINKING
Students’ solution usually very unique
We need to make sure that the students gain the right concept
We also need to develop our method in teaching
Sandwich Problem
Consider the following story by Carol, an
elementary school teacher in New York to her
students (Fosnot & Dolk, 2002; page 2-3):
Last year I took my students on field trips related to the new project we were working on. At one point, we went to several places in New York city to gather the research. I got some parents to help me, and we scheduled four field trips in one day. Four students went to Museum of Natural History, five went to Museum of Modern Art, eight went to Ellis Island and the Statue of Liberty, and the five remaining students went to the Planetarium. The problem we ran into was that the school cafeteria staff had made seventeen submarine sandwiches for the kids for lunch. They gave three sandwiches to the four kids going to Museum of Natural History. The five kids in the second group got four subs. The eight kids going to Ellis Island got seven subs, and the left three for the five kids going to Planetarium.
PROBLEM
Sandwich Problem
Continue:
At that time, the students didn’t eat together obviously because they were all in different part of the city.
The next day after talking about the trips, several of kids complained that it hadn’t been fair, that some kids got more to eat. What do you think about this? Were they right? Because if they were, I would really like to work out a fair system to give each group when we go on field trips this year.
PROBLEM
On the next slide, we will see the Carol’s
students works based on the given problem.
Please observe it carefully. After each students’
solution, we will see my analyze about it :)
Just to make it
easier to
observe, let
separate the
answer
they divide 2
sandwich into
4 equal part
they divide the last sandwich
into 4 equal parts
Each of this
sandwich is
divided at half,
such that there is 4
equal part
First, they divide the
sandwich into 2 equal parts.
One part is given for the
fifth people in the group.
The other part are divide
again into 5 equal pieces
they divide the last
sandwich into 5 equal
parts
PROBABLYThey start from the way they divide the third sandwich into two equal parts and they divide again one of it into 5 equal parts. So that, they know that if in a half part of sandwich they can get 5 equal smaller parts, then in a full sandwich they can get 10 smaller equal parts. So that, since one people just get one part of this smaller parts, they conclude that it must be a tenth.
How they
got it?
1st group
VS 2nd
group
What they mean by this illustration?
At the last they emphasize which group
that they think get the biggest sandwich’s part
This is the group you want to
be at !!
3rd
Group
Please analyze the other 2 students’ work :)
Jennifer and
John’s Answer
Gabrielle,
Michael, and
Ashleigh’s
answer
Do you want to more clear picture, or discuss your
analyze (may be you have different idea with me)
don’t be hesitate to contact me at:
[email protected] or just give your comment on
this post :)
Reference:
Fosnot, Catherine Twomey, & Dolk, Maarten. 2002.Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents.Portsmouth: Heinemann