Transcript Building Math in the classroom - Teaching Through Problem-Solving - Day 10 Presentation is prepared for The Park City Mathematics Institute, Secondary School.

Building Math in the classroom
- Teaching Through Problem-Solving -
Day 10
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi
Paper Pool Table
a problem
Key question(s)
Student’s
response
Student’s
response
Student’s
response
Student’s
response
Students will learn something new from the
process of problem solving and the whole
class discussion
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi
Paper Pool Table
– What is the relationship between the
dimensions of the Paper Pool Table and
the total number of hits? Be sure to count
the starting and ending points as a “hit.”
(Table 4)
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi
Visualizing the relationship between
factors and multiples
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi
Number of hits = (length + width)
÷GCF(length, width)
Finding a pattern from a table may not be sufficient…..
An anticipated student’s response from Table 8
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi
Designing a lesson for teaching
through problem solving
Curriculum &
Textbook
Teaching through
problem solving
Students
Problem
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi
The Secret of The Crystal Ball
1.
2.
3.
4.
5.
6.
Chose any two digit
number.
Add together both digits.
Subtract the total from your
original number.
When you have the final
number look it up on the
chart and find the relevant
symbol.
Concentrate on the symbol
and when you have it
clearly in your mind.
Click on the crystal ball to
see the symbol.
http://www.cbs.com/primetime/ghost_whispere
r/crystal_ball.shtml
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi
NCTM’s view of problem solving
1)
Problem solving means engaging in a task for
which the solution method is not known in advance.
Problem solving is an integral part of all
mathematics learning, and so it should not be an
isolated part of the mathematics program.
Choosing worthwhile problems and mathematical
tasks
2)
3)
–
There are many, many problems that are interesting and
fun but that may not lead to the development of the
mathematical ideas that are important for a class at a
particular time.
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi