Assessing Change in Preservice Elementary School Teachers Beliefs in an Elementary Methods Course

1
Assessing Change in Preservice Elementary School
Teachers Beliefs in an Elementary Methods Course

• Andrew T. Wilson
• Austin Peay State University
• AMTE - Tampa, January 28, 2006
• wilsona_at_apsu.edu
• http//www.apsu.edu/educ/wilson.htm

2
The Problem

• Preservice teachers enter mathematics teacher
  education programs with an enormous variety of
  beliefs and conceptions (which include
  misconceptions) about what it means to know, do
  and teach mathematics. These beliefs are formed
  by years of studying mathematics in structured
  school classrooms where students typically are
  not exposed to teaching models and classroom
  environments that reflect a constructivist view
  of learning.

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The Problem

• This classroom mathematics tradition has shaped
  preservice teachers construction of scientific
  or mathematical knowledge by constraining what
  can count as a problem, a solution, an
  explanation, and a justification (Cobb, Wood,
  Yackel, McNeal, 1992, p. 575).

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The Problem

• Beliefs and content knowledge are generally fused
  together as a result of being formed
  simultaneously. This presents a major problem for
  mathematics teacher educators as we attempt to
  have preservice teachers change their way of
  understanding mathematics, we must also introduce
  change into their belief systems. Given this
  importance of beliefs, it is critical for
  mathematics teacher educators to be able to
  assess currently held beliefs and understand if
  and how they might be changed. It is probably
  easier to introduce a new belief than to change
  an old one.

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The Questions

• What is the nature of beliefs that preservice
  teachers hold about learning and teaching
  mathematics, particularly, what are their beliefs
  about how both children and adults do and learn
  mathematics before and after exposure to modular
  media cases?
• What changes, if any, take place in preservice
  teachers beliefs after they interact with
  modular media cases in an elementary methods
  course?

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Review of the Literature

• Some research on in-service and preservice
  teachers beliefs about mathematics learning and
  teaching indicates that beliefs can be changed.
  Examples include Cobb, Wood, Yackel (1990)
  Barnett and Sather (1992) Sherin and Han (2002)
  Ball (1993, 1997) and Fennema et al. (1996).

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Review of the Literature

• Preservice teachers need opportunities to analyze
  multiple cases that exemplify theories,
  principles, and teacher decisions.
• Studies have shown the effectiveness of using
  multimedia cases in teacher education, such as
  Barron and Goldman (1990) Martin and Barron
  (1995) Risko et al. (1992) Risko (1995) Risko,
  Peter, McAllister (1996) and Lampert and Ball
  (1998).

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Method

• IMAP Web-based Belief Survey - an alternative to
  Likert-type scales.
• This survey was used as a pre and posttest to
  study preservice teachers beliefs about learning
  and teaching mathematics both before and after
  interacting with modular media cases in the
  elementary methods course.

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Method
Interviewer Six take away Jim
Two. Interviewer So six apples take away
two. Jim Four Interviewer Tell us how you
figured that out Jim Because I just thought
about it for just a minute and then I went like
four because you take away five and
six. Interviewer Ah ha, you took away five and
six, the apples called five and six. Did you see
it or did you count it? Jim I didnt count it I
just saw it in my mind.
Jims Pre-Interview
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Method
Interviewer Now what about this one, is this one
too big to figure out? Seven plus six Jim Seven
plus six. (Pause) Nine. Interviewer Tell us how
you got that. Jim Cause Interviewer I saw you
move your fingers Jim I didnt do it at my
fingers, I just thought about it cause it was
right. Interviewer You didnt sort of count or
do anything? Jim I didnt do that
Jims Pre-Interview
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Method
Interviewer Lets maybe do one more. What about
eight plus five? Jim Ooh, that is a tricky
one. Interviewer Thats a tricky one is it? Tell
us about eight plus five. Jim Eight plus five.
(Pause) They havent, they didnt teach me
that. Interviewer Ok, shall we leave that
one? Jim yea Interviewer Ok, well skip that
one.
Jims Pre-Interview
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Method
Interviewer Seven plus six. Jim (Pause)
Fifteen. Interviewer Ok, can you tell me how you
got that? Tell me how you thought about it. Jim
No three, thirteen. Interviewer Oh, ok,
Alright. Jim Thirteen cause I Interviewer Ok,
tell me how you got thirteen. Jim Because I
added the three with the seven and that makes ten
and I had three more. Interviewer Oh!
Jims Post-Interview
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Method
Interviewer Ok what if we did fifteen, do you
see a five, there is a five, fifteen and we are
going to take away seven. Jim Oh,
eight. Interviewer And how did you get
that? Jim I just, ooh, this will be good. I
knew, like seven plus seven would make, alright
fourteen, and eight plus eight, I mean eight plus
seven would make, fifteen, so I took away the
seven, it left seven, I mean eight. Interviewer
Ok, I got you, it left eight, very nice
Jims Post-Interview
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Method
Ten Frame
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Method
Doubles-Referenced Six
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Method
Five-Referenced Six
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Method
Final Challenge Topics Classroom Discourse
Classroom Norms Planning Instruction Role of
Manipulatives Spatial Reasoning Students
Thinking Worthwhile Mathematical Tasks
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Method
Final Challenge (Individual Paper - Group
Presentation) Worthwhile Mathematical Tasks
Teachers are responsible for the quality of the
mathematical tasks in which students engage.
Teachers should choose and develop tasks that
are likely to promote the development
of students' understandings of concepts and
procedures in a way that also fosters their
ability to solve problems and to reason and
communicate mathematically. Good tasks are ones
that do not separate mathematical thinking from
mathematical concepts or skills, that capture
students' curiosity, and that invite them to
speculate and to pursue their hunches. Many such
tasks can be approached in more than one
interesting and legitimate way some have more
than one reasonable solution. In this challenge,
you are to investigate the mathematical tasks
that were posed in the Patterning and
Partitioning lesson sequence and the Geometry
sequence.
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Method
Your presentation and paper should address the
following what tasks are based on sound and
significant mathematical concepts analyze
the nature of the tasks and the relation of the
tasks to each other in the development of the
lesson sequence what tasks are based on
knowledge of the range of ways that diverse
students learn mathematics how do tasks
stimulate students to make connections and
develop coherent framework for mathematical ideas.
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Method
Your presentation and paper should incorporate
the following examples from both sequences
(These could be excepts from the lessons,
interviews with the teacher or various
mathematics educators, or examples of childrens
work.) citations from outside resources that
support your main ideas. These may include
information from either of your textbooks,
from the readings packet, from the NCTM
Principles and Standards, from the following
article(s)
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Method

• Clements, D. H. (1999). Subitizing What is it?
  Why teach it?
• Teaching Children Mathematics, 5(7), 400-405
• Kline, K. (1998). Kindergarten is more than
  counting.
• Teaching Children Mathematics, 5(2), 84-87
• Hiebert, J., et al. (1997). The nature of
  classroom tasks.
• Making sense Teaching and learning mathematics
  with
• understanding (pp. 17-27). Heinemann.

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IMAP Survey Beliefs

• Beliefs about mathematics
• 1) Mathematics, including school mathematics, is
  a web of interrelated concepts and procedures.
• Beliefs about knowing or learning mathematics or
  both
• 2) One can perform standard algorithms without
  understanding the underlying concepts.
• 3) Understanding mathematical concepts is more
  powerful and more generative than remembering
  mathematical procedures.
• 4) If students learn mathematical concepts before
  they learn standard algorithms, they are more
  likely to understand the algorithms when they
  learn them. If they learn the algorithms first,
  they are less likely ever to learn the concepts.

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IMAP Survey Beliefs

• Beliefs about children (students) doing and
  learning mathematics or both
• 5) Children can solve problems in novel ways
  before being taught how to solve such problems.
  Children in primary grades generally understand
  more mathematics and have more flexible solution
  strategies than their teachers, or even their
  parents, expect.
• 6) The ways children think about mathematics are
  generally different from the ways adults would
  expect them to think about mathematics. For
  example, real-world contexts, manipulatives, and
  drawings, support childrens initial thinking
  whereas symbols often do not.
• 7) During interactions related to the learning of
  mathematics, the teacher should allow the
  children to do as much of the thinking as
  possible.

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Data Analysis Methods

• Belief 7 During interactions related
  to the learning of mathematics, the teacher
  should allow the children to do as much of the
  thinking as possible.

• Video Survey Segment 7 There are 20
  kids going on a field trip. Four children fit in
  each car. How many cars do we need to take all 20
  kids on the field trip?

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Data Analysis Methods

• 7.1 Pretest Reaction I think I would have used
  the same approach. I like the way she asked
  questions to guide him to solving the problem on
  his own.

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Data Analysis Methods

• 7.1 Posttest Reaction The teacher was very
  helpful but she guided him to the answer instead
  of letting him figure it out himself.

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Data Analysis Methods

• 7.2 Pretest Strengths When the student guessed
  the answer, the teacher never told him that his
  answer was wrong. I liked the way she guided him
  to solve the problem on his own, and I liked the
  way she built his self esteem by saying things
  like "You are a really good counter.

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Data Analysis Methods

• 7.2 Posttest Strengths She used manipulatives.

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Data Analysis Methods

• 7.3 Pretest Weaknesses If there are any
  weaknesses with her approach I have a problem
  because I used the same approach with my
  children.

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Data Analysis Methods

• 7.3 Posttest Weaknesses She didn't let the child
  think enough.

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Data Analysis Methods
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Data Analysis Methods
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Data Analysis Methods
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Data Analysis Methods
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Rubric Analysis

• Pretest Score 0
• Overall satisfaction with the guidance provided
  by the teacher. No weaknesses mentioned, in fact,
  liked the way child solved the problem on his
  own.
• Posttest Score 3
• Thought teacher was too leading in both 7.1 and
  7.3.

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Rubric Analysis

• Thirty pretest and posttest responses were coded
  for each of the 17 rubrics, for a total of 1,020.
  Seven percent (equally distributed over the 7
  beliefs) of the responses were randomly
  double-coded and we achieved, on average, 91
  reliability. The survey responses were blinded so
  that coders were not able to determine whether
  the responses were from pre or posttests.

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Analysis of Data
Table 1. Pretest and Posttest Scores for
Beliefs Percentages (Numbers) of Students (n30).
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Analysis of Data
Table 2. T-test on Pre and Posttest Scores
(n30). Four is the highest possible score for
Beliefs 2, 5, and 6, while 3 is the highest
possible score for Beliefs 1, 3, 4, and 7.
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Analysis of Data
Table 3. Accumulated Change in Belief Score for
all 7 Beliefs. The total possible accumulated
score for all seven beliefs was 24.
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Analysis of Data
Table 4. Belief Score Changes Percentages
(Numbers) of Students. No Change, -3 to 3 Small
Increase, 4 to 9 and Large Increase, 10 or
greater.
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Findings

• It is evident from Table 1 that preservice
  teachers beliefs changed over the course of
  interacting with the modular media cases and
  other course activities. There were definitely
  fewer no evidence scores and more strong evidence
  scores on the posttest in every belief, with the
  exception of the Belief 1 strong evidence scores.

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Findings

• It is important to note that Beliefs 5, 6 and 7
  all deal with how children do and learn
  mathematics. It seems fitting that preservice
  teachers at this stage of their development would
  have the most significant gains in beliefs about
  how children do and learn mathematics.
• Even though these gains were statistically
  significant, most belief levels remained low even
  at posttest.
• Testing effects and maturation (other courses)
  might have played a role in the results.

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Implications

• Beliefs related to mathematics appear to be less
  affected this late in a preservice teachers
  development, whereas beliefs about how children
  learn and do mathematics can be more affected by
  the use of modular media case implementation in
  an elementary mathematics methods course. This
  seems to imply that incorporating cases to focus
  on childrens thinking should be included in
  mathematics content courses, as well as methods
  courses.

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Implications

• It would appear that other modular media cases in
  the domains, such as fractions and place value
  concepts, might have been of some benefit to
  these preservice teachers. It is not enough for
  preservice teachers to possess overarching
  beliefs if they do not have the pedagogical
  content knowledge to implement them in meaningful
  ways in the classroom.

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Assessing Change in Preservice Elementary School
Teachers Beliefs in an Elementary Methods Course

• Thanks!
• wilsona_at_apsu.edu
• http//www.apsu.edu/educ/wilson.htm