Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Understanding the students' way of thinking


Published on

Published in: Education, Technology
  • Be the first to comment

Understanding the students' way of thinking

  1. 1. Understanding The Students’ Way of Thinking An Example for The Teacher
  2. 2. UNDERSTANDING THE STUDENTS’ WAY OF THINKING compose 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.
  3. 3. .. 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 ..
  4. 4. 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
  5. 5. 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. Sandwich Problem
  6. 6. 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. Sandwich Problem
  7. 7. 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 :)
  8. 8. Just to make it easier to observe, let separate the answer
  9. 9. they divide 2 sandwich into 4 equal part they divide the last sandwich into 4 equal parts
  10. 10. 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 How they got it? PROBABLY They 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.
  11. 11. 1st group VS 2nd group
  12. 12. What they mean by this illustration?
  13. 13. 3rd Group 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 !!
  14. 14. Please analyze the other 2 students’ work :)
  15. 15. Jennifer and John’s Answer
  16. 16. Gabrielle, Michael, and Ashleigh’s answer
  17. 17. 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: or just give your comment on this post :)
  18. 18. Reference: Fosnot, Catherine Twomey, & Dolk, Maarten. 2002. Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents. Portsmouth: Heinemann