foundations in math
TRANSCRIPT
Foundations in Math: Developing Mathematical
Thinking & Conceptual Understanding in
Grades KG-2
EARCOS WEEKEND WORKSHOP-MS. SARA GARRETT
November 15, 16, 2014
horizontal mathematization
Freudenthal institute (F.I.) under the auspices of Hans Freudenthal (1905-1990)
horizontal mathematization (example)
Freudenthal institute (F.I.) under the auspices of Hans Freudenthal (1905-1990)
The majority of pupils started off the problem by guessing, usually with the assumption that a t-shirt will cost more than a drink. After being asked to find another method for calculating the respective values they start to develop mathematical tools to deal with situation. This primarily involved the idea of exchange i.e.2 t-shirts + 2 drinks = $44.001 t-shirt + 3 drinks = $30.000 t-shirts + 4 drinks = $16.00
horizontal mathematization= the students come up with mathematical tools that can help to organize and solve a problem located in a real-life situation.
VERTICAL mathematization
Freudenthal institute (F.I.) under the auspices of Hans Freudenthal (1905-1990)
vertical mathematization=the process of reorganization within the mathematical system itself, like, for instance, finding shortcuts and discovering connections between concepts and strategies and then applying these discoveries.
Patti made 42 friendship bracelets to sell. She sold 17 of them on Monday.
How many friendship bracelets does Patti have now?
The rabbit jumped 17 inches further than the frog. The rabbit jumped 42 inches. How far did the frog jump?
Jane is climbing to the top of the bell tower. There are 42 steps in the tower. She has climbed 17 steps already. How many more steps does Jane need to climb to get to the top of the tower?
looking at the three different questions and the variety of answers was an eye-opening process. I was amazed at the variety in approaches to solving a problem. The richness of the mathematical discourse was thought-provoking, and helped deepen my understanding of problem-solving strategies.
Reflection
● http://bruners-stages.wikispaces.com/Bruner%27s+Stages+of+Representation
● http://www.nctm.org/profdev/content.aspx?id=23609● http://campuspaper.blogspot.com/2012/10/horizontal-and-vertical-
mathematization.html#.VJC6faSUeVI● http://www.did.stu.mmu.ac.
uk/cme/Student_Writings/RichHarrison/RichardHarrison.html
resources/reference: