Touchdown: Problem Solving For Little Players

1
Touchdown Problem Solving For Little Players

• By Michelle Flaming and Marv Soeken
• michellef_at_essdack.org
• msoeken_at_usd405.com

2
Agenda

• Touchdown
• Game Plan
• Run or Pass?
• Game Video
• Score Sheet

3
Touchdown Video
4
The Game PlanCognitively Guided Instruction

• Built on the belief that learning occurs as new
  knowledge is linked to existing knowledge, and
  teaching is most effective when instruction
  directly builds on what children already know.
• Focus On student thinking and how numbers and
  problems are perceived.

5
The Game Plan

• 19 children are taking a mini-bus to the zoo.
  They will have to sit either 2 or 3 to a seat.
  The bus has seven seats. How many children will
  have to sit 3 to a seat and how many will have to
  sit 2 to a seat?
• Solve in 2 different ways.

6
The Game Plan (Research)

• Based on almost 20 years of research by Thomas
  Carpenter (1988).
• Funded by the National Science Foundation.
• Focused on the development of students
  mathematical thinking.
• Research shows significant higher levels of
  achievement in problem solving.
• Works for ALL students

7
(No Transcript)
8
Kaitlins Problems Problem Type
DifficultyRate each of the following problems
from 1 (easy) to 5 (most difficult)

• 1. Using a scale - Rate each problem in
  comparison with each other. - Record under Rating
  1.

9
Run or Pass?Introduction to Strategies

• Direct Modeling
• Act out the problem.
• Follow sequence of the action in a problem.
• Represent sets with materials (unifix cubes,
  tally marks, etc.)
• Counting Strategies
• Hold one number in the head.
• Derived Facts/Facts
• Doubles 1, -1, 2, and -2
• Sums of 10 (8 3 8 2 is 10 plus 1 more 11)
• Invented Approaches

10
Video of Different Student Strategies
11
Game Video
12
Big Ideas on Childrens Solution Strategies

• At the most basic level, children use physical
  objects to directly model the action or
  relationship in each problem.
• As children mature, their strategies become more
  abstract and efficient. DM is replaced by
  counting, which in turn are replaced with derived
  fact and recall of number facts.
• Direct Modeling provides a basis for learning of
  the other strategies.
• Children in any class will be at different levels
  of understanding and will use different
  strategies to solve the same problems.
• Children naturally progress through the levels
  without direct instruction if children have the
  opportunity to explain their mathematical
  understanding.

13

• Justifying and explaining ideas improves
  students reasoning skills and their conceptual
  understanding.
• (Maher and Martino 1996)

14
Score Sheet
15
Common Components of CGI Classrooms

• Problem solving is the focus of instruction
  teachers pose a variety of problems.
• Many problem solving strategies are used to solve
  problems. Children decide how they should solve
  each problem.
• Children communicate to their teachers and peers
  how they solved the problems.
• Teachers understand childrens problem solving
  strategies and use that knowledge to plan
  instruction.

16
Remember .

• You do not have to master game to begin.
• Children can and will learn many important math
  ideas when many problems are solved and
  strategies are shared.
• This is only the tip of the iceberg.

17

• For more information contact
• Michelle Flaming at michellef_at_essdack.org
• Marv Soeken at msoeken_at_usd405.com
• Kids Who Love and Understand Math Workshop -
  April 24, 2008 at ESSDACK
• www.essdack.org/mlk2008 (handouts)