Foundations in

Math

Foundations in Math: Developing Mathematical

Thinking & Conceptual Understanding in

Grades KG-2

EARCOS WEEKEND WORKSHOP-MS. SARA GARRETT

November 15, 16, 2014

What i

learned...

Building math

vocabulary

strategy: active

word wall

collaboratively,

we worked to construct meaning, & show relationships with the new

vocabulary

this...

and this...

evolved into this...

and this...

evolved into this...

evolved into this...

and evolved into this...

with a growth-mindsetwe used inquiry & discourse to construct new meaning

Let’s look a little closer

at some of the

vocabulary

THE BIG 3

enactive

enactive

enactive= action-based

Using coins...

enactive

Using blocks, chips...

enactive

Using base-ten blocks, etc.

ICONIC

ICONIC

ICONIC=image-based

ICONIC=sometimes called the pictoral stage

SYMBOLIC

SYMBOLIC

SYMBOLIC=language-based

symbolic=sometimes called the abstract stage

horizontal mathematization

Freudenthal institute (F.I.) under the auspices of Hans Freudenthal (1905-1990)

horizontal mathematization=going from the world of life to the world of symbols

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.

vertical mathematization=moving within the world of symbols

working with real examples...

In small groups we worked on 3 different problems to experience mathematical discourse

#1

Patti made 42 friendship bracelets to sell. She sold 17 of them on Monday.

How many friendship bracelets does Patti have now?

#2

The rabbit jumped 17 inches further than the frog. The rabbit jumped 42 inches. How far did the frog jump?

#3

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

PRODUCTIVE STRUGGLECREATING THIS PRESENTATION WAS A PRODUCTIVE STRUGGLE FOR MR. DARYL

Additional examples

Foundations in

Math

● 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:

http://www.youcubed.org/

TO BE CONTINUED...

MR. DARYLRUAMRUDEE INTERNATIONAL SCHOOL

facebook: https://www.facebook.com/pages/RIS-Elementary-

School/566272910150141

Twitter: @Daryl_Ilinkedin: Daryl Imanishislideshare: http://www.slideshare.net/DarylImanishi

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