Transcript Using a Children`s Thinking Approach to Change Prospective

Using a Children’s Thinking
Approach to Change Prospective
Elementary Teachers’ Efficacy and
Beliefs of Mathematics
David Pratt, Ph.D.
David Feikes, Ph.D.
Sarah Hough, Ph.D.
Keith Schwingendorf, Ph.D.
AERA Paper Session
Spring 2007, Chicago
Outline
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Defining the Problem
Context of Study
Samples from Supplement
Literature Review
Results
Discussion
Future Studies and New
Possible Grants
Breaking the Traditional Beliefs about
Math
Many preservice teachers
come from traditional
mathematics classrooms
where procedural knowledge
is revered over conceptual
understanding and
investigation (Ma, 1999)
Math Teachers Need to Know
There appears to be a
disconnect between math
needed to know in
elementary school and that
which is taught in math
content courses in college.
Nathan & Koedinger (2000).
Beliefs and Knowledge about Math
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Beliefs about mathematics determine future
teaching beliefs about mathematics and are
resistant to change
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Many elementary school teachers have limited
understanding of the subject matter they are
responsible for teaching.
(Ball, 1990; Ma, 1999; Mewborn, 2000)
A Special Type of Math Content Course is
Needed
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Increasing the number of math content courses is not
effective.
The specialized knowledge of mathematics needed is
different from the mathematical content contained in most
college mathematics courses, which are principally
designed for those whose professional uses of
mathematics will be in mathematics, science, and other
technical fields.
Courses that reflect a serious examination of the nature of
the mathematics that teachers use in the practice of
teaching do have some promise of improving student
performance.
National Research Council (2001).
Mathematical Content Course Supplement for Elementary Teachers
Focus on How Children Learn Mathematics
The research for this paper was supported by the National Science Foundation, DUE
0341217. The views expressed in this paper are those of the authors and do not
necessary reflect those of NSF.
Context Supporting Change in Beliefs
- Supplement to existing textbook
- Aligned to content typically taught
The CMET supplement contains:
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problems and data from the National Assessment of
Educational Progress (NAEP)
our own data from problems given to elementary
school children
questions for discussion
Context Supporting Change in Beliefs
These descriptions are based on current research and include:
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how children come to know number
addition as a counting activity
how manipulatives may embody mathematical activity (Tall, 2004)
concept image in understanding geometry (Tall & Vinner, 1981)
Qualitative Results from Phase 1 of Study
What is the Focus of the CMET materials?
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Understanding Mathematics Conceptually
Multiple Solutions to Problems
Less Rule Oriented
Focus on Process, not final answer
Children’s Thinking Important
Problem Solving Emphasized
Discovering Patterns
Math as a Process
“The math is the same in this course
as in different courses because it is
dealing with numbers. However the
class is different because the final
answer is not he most important part
of the problem. By far the greatest
thing to learn is the understanding of
how the solution was reached.”
Children’s Thinking Important
The math isn't high school or college level
math. The math in this course requires
more thinking and attempting to
understand how children understand the
concepts.
Multiple Solutions
It is very different from the
mathematics I did in high school.
We are now learning about
multiple ways to solve a problem
and real life applications of the
math we are learning. We did
neither of those in high school.
Literature Review
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Mathematical Knowledge Necessary for
Teaching
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Children’s Thinking Approach
Self-Efficacy for Understanding and Teaching
Math
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MKNT
1) Mathematics Content Knowledge-- a textbook
understanding of mathematics.
2) Pedagogical Content Knowledge-- how to teach
mathematics.
Mathematical Knowledge Necessary for
Teaching (MKNT) includes:
- Articulating the “why’s” of procedures and concepts
- Interpreting student solutions
- Encouraging multiple solution paths to problems
(Hill & Ball, 2004)
Children’s Thinking Approach
Teachers’ greatest source of knowledge is
from the students themselves (Empson &
Junk, 2004).
Concentrating on understanding children’s
thinking may help teachers develop a broad
and deeper understanding of mathematics
(Sowder, et.al., 1998).
Efficacy
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Bandura: “people’s beliefs about their
capabilities to produce designated levels
of performance and exercise control over
events that affect their lives”
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Efficacy has been shown to lead to:
Greater levels of planning
 Increased enthusiasm
 Being more committed to the profession
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Efficacy and Instruction
Several studies have indicated a consistent
relationship between teacher efficacy and
classroom instructional strategies (Wertheim &
Leyser, 2002) as well as willingness to embrace
reform strategies (Hami, Czerniak, & Lumpe,
1996; Ross, 1992).
Efficacy and Teaching Strategies in
Mathematics Instruction
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Using manipulatives was strongly embraced by
the preservice teachers with the highest degree
of mathematics teacher efficacy
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Similarly, teachers with the lowest efficacy for
teaching expressed concern over using
manipulatives as a teaching aid.
Swars (2005)
Results from Previous Studies
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Demonstrated a possible connection
between efficacy and beliefs with pre-post
test responses.
After using the module, participants shifted
to more positive efficacy beliefs and a
more non-procedural view of math.
Pratt et. al (2006).
Results from Previous Study
Summary
A course focused on children’s thinking of
mathematics can increase preservice
teachers’ efficacy for understanding and
teaching math as well as alter other
beliefs regarding mathematics. This new
knowledge and belief may ultimately
change the way that these college
students teach in the future.
Methodology
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Large midwest university
Control and treatment groups (n=138)
Beliefs about Math Questionairre
Efficacy Beliefs Questions (Likert Scale)
IMAP survey
Correlations and ANOVA’s
Math Beliefs Instrument
A Math Beliefs Instrument, consisting of 12
forced choice items related to understanding
of Math Concepts, Children’s Thinking, and
Teaching Math was administered to
preservice teachers. The Efficacy items on
the questionnaire asked participants, on a
scale of 1 to 10, how confident they felt in
their (1) understanding of the mathematics
topics covered in the course, and (2) their
ability to teach these topics to children.
Results from Study
Beliefs of efficacy were tested
between control and CMET
groups using two one way
ANOVAs. Results indicated
that significant differences
between the two groups in
Teaching Efficacy but not in
Math Efficacy.
7.4
7.2
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6.8
Control
6.6
CMET
6.4
6.2
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5.8
MATH Efficacy
Teach Efficacy
TEACHING Math Beliefs
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Encouraging children to explore their own ways
of solving problems is as important as teaching
them to follow procedures.
Rather than teaching mathematical ideas
directly to students it is better to guide them in
figuring things out for themselves.
Mathematical skills should be taught before
concepts.
Beliefs about Math
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Mathematics is a web of interrelated concepts
and procedures.
Mathematics is mainly about learning rules
and formulas.
Frequently when doing mathematics you are
discovering patterns and making
generalizations.
In mathematics there is one correct answer.
Beliefs about Children’s Thinking
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Children should master the basic facts before
doing problem solving.
Children solve and think about mathematics in
a variety of ways and often different from
adults.
When children do not understand something in
mathematics it is because they have not had
enough practice.
Children learn mathematics better through
extensive drill and practice rather than inquiry
and exploration.
Difference in Beliefs Score
A one-way ANOVA was run on overall belief scores to
test for differences. A significant result was found
indicating a slightly higher score (about one half a
standard deviation) for the CMET group.
Multivariate Analysis of Variance (MANOVA) was run
using these three variables as dependent variables
and control versus treatment group as the
independent factor. MATH and CT contributed most
significantly to the difference between groups (MATH:
F=10.9, p<.01; CT: F=6.3, p=.01).
Correlations Between Teaching
Efficacy and Beliefs
MATH Efficacy
TEACH Efficacy
Children solve and think about
mathematics in a variety of ways
and often different from adults.
Rather than teaching
mathematical ideas directly to
students it is better to guide them
in figuring things out for
themselves.
Children learn mathematics
better through extensive drill and
practice rather than inquiry and
exploration.
Rather than teaching mathematical
ideas directly to students it is better
to guide them in figuring things out
for themselves.
Mathematical skills should be taught before concepts.
Correlations significant at p=.01
Discussion
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One way to help preservice teachers construct both
mathematical knowledge and the mathematical knowledge
necessary for teaching is by focusing on how children learn
and think about mathematics in content courses.
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Prospective teachers can use the way children think about math to
learn math themselves.
Beliefs can be changed to a more non-procedural or investigative view
towards math, when using this approach.
Efficacy for understanding AND teaching mathematics can be
positively affected by using this approach (even though the course isn’t
focused on instruction, just students’ understandings)
Using knowledge of how children learn and think about
mathematics may also improve preservice teachers’ future
teaching of mathematics to children.
Current and Future Research
 Pre-Post Test of Control and
Experimental groups
 Complete Analysis of IMAP online
surveys.
 Secure funding for continued
implementation of published materials
Future Grant Possibilities
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How Children Learn Math (HCLM):
Resource for Teachers
How Children Learn Math (HCLM):
Resource for Parents
Both grants support teachers and caregivers
with resources that help them understand
the way children think about math and how
to teach math more conceptually.
Contact Us for More Info!
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If you are interested in
using the CMET materials
in your classroom or
assisting us with potential
future grants, please
contact us!
[email protected]
[email protected]