Understanding the students' way of thinking

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