Transcript MATH IN THE MIDDLE MICHAEL A. COBELENS

MATH IN THE MIDDLE
MICHAEL A. COBELENS
2006
M
2004
2
Problem Solving
• Identify Learning Experiences
• Purpose: Methods of Teaching Problem
Solving and Computational Skills
• Addition, Subtraction, Multiplication,
Division
Problem of Practice
• Students do not use computational skills
consistently.
• Students do not transfer skills to other
situations.
• How can my teaching practices improve
student performance?
Literature Review
• Kendrick (2004): drill and practice very
•
•
•
•
important in the retention of basic math skills
Ashcroft (1981): multiple teaching methods
reinforce learning, drill and skill enhance
memory for retrieval
Pajares and Graham (1999): self-efficacy
Ball (1999): Teacher Knowledge key to student
learning
Tims Tutor (2002): basic facts need to be
learned, important component in problem
solving
Questions
• What learning experiences help math
processes become more concrete?
• What activities best help students learn
math processes and where they apply?
• How do students determine which math
process to use to solve a problem and
whether they chose the correct method?
Method
• Student views on Problem Solving Survey
• Student journals and reflections of
•
•
•
•
mathematics lessons
Daily personal journal of lessons and
observations
Student and Principal Interviews
Problem Solving Pre-test
Problem Solving Post-test
Analysis of Student Survey
Feelings on Word Problems
26%
30%
Don't Like
This stinks
I hate this
Read to find info
Neutral
22%
13%
9%
Survey Answers
Range from Strongly Agree to
Strongly Disagree
• I learn math concepts pretty easily
15/23 Agree
• There is only one way to get the right
answer to a math problem 12/23
Strongly Disagree
• Knowing basic facts helps when solving
problems 12/23 Strongly Agree
Student Strategies
Strategies for solving word problems
4%
22%
39%
9%
26%
Write down fac ts
I dentify k ey wo rds
D raw pic tures
S olve a nd c hec k
R ewrite
Knowing if you are right
How do you know you are right
17%
Check it
Strong feeling
I don't
13%
70%
What Helps?
What helps you learn math
22%
22%
P rac tic e
L is tening and
talk ing
L is tening and
pra c tic e
V is uals
17%
39%
Needed Skills
Needed skills to solve word problems
4%
17%
13%
66%
Knowing bas ic fac ts
A bility to read
L ogic
P atienc e
Further Analysis
• Homework and in class activities promote
•
learning
78% say, “Listening and talking along with
practice.”
“I see how to work problems out, step by step”
“When we work together I get to see the answer,
it’s easier than working alone.”
“Learning is easier when I know how to add,
subtract, divide, and multiply.”
Personal Daily Journal
• Retention of mathematical processes and
computation need continuous review.
• Multiple step problems are difficult with
only 11% of students completing correctly
on problem solving test.
• Most effective learning experiences
include practice, application, and talking.
Pre and Post Test
Pre-test and Post-test Results
81
80
Percentages 79
and variation
78
Pre-test
Post-test
77
76
75
Mean
Median
Interpretation
• Problem solving is difficult
• Assessment at point of instruction does
not promote retention
• Story problems are not always problem
solving
• Students need challenge and opportunity
to apply learned skills
Plan of Action
• Mastery of basic facts while challenging
students to problem solve.
• Students provide multiple solutions to
problems and explain how they solved the
problems.
• Habits of Mind type problems to promote
deeper the thinking.
Portfolio
• Teacher knowledge of Mathematics impacts
•
•
•
•
student learning
Pedagogy empowers teacher as authority
Action Research suggests problem solving is a
process
Leadership implies intellectual leader within the
learning community
Finally I plan to implement MIM strategies and
Habits of Mind problems