Make your own problems
Truus Dekker
Freudenthal Institute Utrecht University
Utrecht, The Netherlands
www.fi.uu.nl
T.Dekker@fi.uu.nl
Goals of mathematics education
To become a critical and intelligent citizen (mathematical literacy) To prepare for the workplace and for future education To understand mathematics as a discipline
What is relevant in Math Ed?
The ability to carry out standard procedures? The ability to deal with new problem situations? To learn how to answer multiple choice questions? To have good results on standardized tests?
Traffic Jam
During the months September, October and November, we find no less than one quarter of all traffic jams. We are still looking for an explanation, but this might be due to the starting of the schools after the summer break, the bad weather in Fall etcetera.
(Dutch newspaper)
Realistic?
The assessment pyramid
De Lange, 1999
The assessment pyramid (2)
Level I: Reproduction, definitions, standard procedures, facts Level II: Combining, integrating, connecting Level III: Mathematizing, reasoning, generalizing, showing insight
Where do you find higher level problems?
Change an existing problem
Which of these figures has the largest area?
Use newspaper articles
Use newspaper articles
Tiles
Tiles
Tiles
Which questions do you ask?
Use an applet
For extra practice www.fi.uu.nl rekenweb Example: the jump jump game
Look in shops
Look in shops
Look in shops
Look at examples made by others
In which meadow does each cow have the most grass?
Use advertizing brochures
Which is the best buy: 100 candles for $6.99 or 75 candles for $2.99?
Use students’ own productions
Students find problems for Waku Waku to solve.
Make your own problem
Start by deciding which grade level Find a context Write down all questions you can think of Make a selection that fits the test Discuss the problem with your colleagues
Design a balanced (written) test
Start with the level III and II problems Add level I problems Use the pyramid model Write expected answers before giving the test to your students Rewrite problems if needed after the first time you use the test Change scoring guide for the next time the test will be used after you have seen student answers