Transcript Does a research based teacher development program affect

Does Theory Improve Practice?
Can Participation in Research
Based Workshops Improve
Teachers’ Practice?
Ronith Klein
Kibbutzim College of Education,
Tel Aviv
This work is part of a doctorial dissertation which was carried out at
Tel-Aviv University under the supervision of Prof. Dina Tirosh
•A major goal of teacher education
programs is to promote prospective
and inservice teachers' knowledge of
children's ways of thinking about the
mathematic topics they are to teach.
for example:
•The CGI programCognitively Guided Instruction:
•The CGI program explored the
impact of teachers’ knowledge of
students’ thinking on actual teaching
practices.
•Results
show
that: ways of
Knowledge
of students'
thinking can dramatically modify
teachers' instructional methodologies
Observed changes in teachers'
practices are attributed to:
(a) The participants learned the specific
research-based model that formed the
basis of the teacher development program
(b) they received ongoing support while using
this model in their classrooms
•In our study we designed a workshop
that was specifically designed for
enhancing inservice teachers' knowledge
of Students' ways of Thinking About
Rational numbers.
•This workshop focused on students’
misconceptions, possible incorrect
responses and their sources and
presented theories and research
findings concerning students’ ways
of thinking.
Questions:
1) How does participation in a workshop
that focuses on children's conceptions
and misconceptions related to specific
mathematics topics (with no support
system in classrooms) influence
inservice teachers’ knowledge of
children's thinking about this topic?
Our topic: multiplication and division
word problems with rational numbers
2) Do teachers take their knowledge of
what children know and understand into
account when designing and teaching
specific topics?
We examine the effects of such a teachers’
in-service program on lesson plans written by
the teachers as an indication to possible
changes in their teaching.
The Workshop (STAR)
Students’ Ways of Thinking About Rational
numbers
•14 meetings of 4 hours each
•Participants:
14 experienced teachers with at least five
years of teaching
experience
•All teachers, except one, taught
mathematics in the fifth and sixth
grades.
•Ten of the teachers
graduated
from teacher education
colleges;
four had university degrees.
Topics:
•Children's conceptions of
rational numbers.
•Comparing decimals.
•Incorrect algorithms- calculating
addition, subtraction, multiplication
and division expressions.
•Incorrect responses to multiplication and
division word problems
•Theories related to students’ ways of
thinking about rational numbers
•General teaching approaches for
enhancing conceptual changes
A thorough discussion on lesson plans
written by:
1) Teachers aware of students’ mistakes and
took them into account.
2) Teachers not considering students’ ways
of thinking in their planning.
The participants examined the extent to
which teachers' awareness of students' ways
of thinking was reflected in the lesson plans.
The workshop was specifically designed
for enhancing inservice teachers'
pedagogic content knowledgeKnowledge of students' ways of thinking
about rational numbers.
• We describe the effect of the workshop on
participants’ pedagogic content
knowledge –
Knowledge of students' ways of thinking
about rational numbers and on the design
of lesson plans on multiplication and
division word problems involving rational
numbers.
Data Collection and Procedure:
•A Diagnostic Questionnaire (DQ)before and after the workshop
•Lesson plans before and after
•Interviews
•worksheets
•Workshops observations
The Diagnostic Questionnaire –
Evaluated the changes in participants'
Subject Matter Knowledge (SMK) of
rational numbers and their knowledge
of children's conceptions and
misconceptions of rational numbers
(PCK).
•Comparison of and operations with
rational numbers
•Multiplication and division word
problems involving rational numbers
•Beliefs about multiplication and division
with rational numbers.
A typical item asked the teacher to:
• Solve the problem
• List common incorrect responses
• List possible sources to the
incorrect
responses .
•At the end of the course, participants
responded to a modified version of
the DQ, which was individually
tailored for each teacher. Each
teacher received the items he/she
Lesson plans- multiplication and
division word problems- rational numbers:
•Main aims of the teaching unit
•Students' prior mathematical knowledge
•Teaching methods
•Manipulatives
•Lesson plan for one lesson
• How to teach students to solve a specific,
given word problems.
The Teaching Unit
PSYCHOLOGICAL ASPECTS OF
MATHEMATICS TEACHING
Results
Before
After
• Can compute- Can
• Improvement in
not give explanations
knowledge “why”
• Aware of typical
• Awareness of
mistakes- only on
students’ typical
comparing fraction
mistakes
• Knowledge of sources • Knowledge of
of students’ mistakes
sources of students’
only on comparing
mistakes
fractions
For example:
Before the course, teachers could
not explain why in division of
fractions “we invert and multiply”.
After STAR, SMK and PCK of all
participants improved. The main
improvement was observed on
knowing “why”: Most teachers could
explain the various steps of the
standard algorithms.
Participants developed their lesson
plans in three groups: one with
four teachers and two of two
teachers each.
We shall describe, for each group,
teachers’ lesson plans before and
after STAR, emphasizing observed
changes in their consideration of
students’ ways of thinking.
Group one: from referring only to substitution
mistakes to structured dealing with possible
mistakes before they appear
Before the course
•Using mapping tables to solve word
problems
”SStudents will only have problems
placing numbers in the mapping tables"
Group one
•Behavioristic philosophy of learning
•Teaching an algorithm, “a magic rule”, will
yield no students’ mistakes
•Good teaching- teaching the “right” procedures
•Lots of drill and practice
•Good teacher and good teaching 
Students make no mistakes
it becomes technical and automatic,
and there are no problems”.
“No mistakes are expected when using mapping
tables, the student will choose the right expression
when solving the problem”.
“ This procedure always works”
After the course:
Group one- pair one
•Students’ intuitive beliefs were
considered
•You have to tell students that
“multiplication does not make bigger,
division does not make smaller”.
After the course I am trying to understand why
they answered as they did. Before, I never
thought how integers affect fraction learning. I
think I won’t emphasize that “multiplication
makes bigger”, in lower grades
Before, I never thought of students’
mistakes and why they do them.
Now it is interesting
After the course:
Group one- pair two
•Students’ intuitive beliefs were
considered
•Built structured activities in order to
make students aware that
“multiplication does not make bigger,
division does not make smaller”.
The Excel graph for the following
expressions:
1) 0.2x0.3=0.06 2) 3.2x0.3=0.96
multiplier multiplicand product
0.2
0.3
0.06
3.2
0.3
0.96
3.5
3
2.5
2
1.5
1
0.5
0
3.2
0.96
0.2
0.3
1
0.06
0.3
multiplier
multiplicand
product
2
The multiplication is
The multiplication is smaller
than each
smaller than
multiplier
multiplier 1
drill
product
2x3
6
The product is bigger than both the
multiplier and the multiplicand
¼ x8
2
The product is bigger than the
multiplier and smaller than the multiplicand
0.2x0.3
0.06
conclusion
The product is smaller than both the
multiplier and the multiplicand
•Teachers are aware of and consider
students’ possible errors
•Students make mistakes despite
good teachers and good teaching
•Try to get to the source of mistakes
•Build the same structured activities
for all students
Group two: from no reference to students’
mistakes to dealing with possible mistakes only if
and when they appear
Before the course
•Referred to different types of division
word problems in their planning :
•Partitive division - Measurement division
•“Finding a part- when given the whole”
• “Finding the whole -when given a part”.
“ We did not consider students’ mistakes”
After the course
•Differentiated between high achieving,
intermediate and low achieving students.
•Planned the lesson mostly for the
intermediate group.
High achievers learn without instruction,
No instruction can help low achievers
•Distinguished between easy and difficult
word problems
•Considered possible student responses
•Were aware of students’ misconceptions
•Built the lessons on students’ answers
•Dealt with possible mistakes as they arise
Group three: from no reference to
students’ mistakes to awareness of possible
mistakes
Before the course
•Sequenced activities from easy to
difficult ones
•“Finding a part- when given the whole”
•“Finding the whole -when given a part”
After the course
•Were acquainted with the intuitive
models of multiplication and division
•Believe in teaching for understanding
•Were aware of errors students are
likely to make, but didn’t plan the
lesson accordingly
•Were not sure how to deal with
students’ possible mistakes
•Before the course only a few written
references to possible, common
incorrect students’ responses were
made in lesson plans.
•We hypothesized that after STAR teachers
would adjust their lesson plans, taking account
of common, systematic students’ conceptions
and misconceptions when planning their
instruction.
The study showed:
•Improvement in teachers’ mathematical
and pedagocical content knowledgeEspecially “knowledge why”
•All teachers were aware of students’
common errors but the ways and the
extend to which they considered them
varied.
Group one:
•Teachers believed in subject oriented
instruction
•Teachers had university degrees in
mathematics
•In favor of teaching algorithms
•Built structured activities, taking
students’ ways of thinking into account
•Their lesson plans after STAR showed
the biggest change.
Group two:
Believed in students driven instruction
Dealt with possible mistakes as they arose
Group three:
Believed in students driven instruction
Aware of students’ mistakes
No change in lesson plans
•Participation in a course that focuses
on children's ways of thinking
emphasizes the importance of
pedagogical content knowledge and its
implementation in actual teaching, can
improve in-service teachers’
mathematical content knowledge
(“that” and “why”).
It can also convince teachers of the importance
of considering students’ ways of thinking in
teaching and can effect the lesson plans written
by the participating teachers.
•Teachers beliefs about teaching are
critical factors which determine their
teaching (Lerman, 1999).
•Research shows that change in teachers’
knowledge without change in teachers’
beliefs is not significant (Fennema,
Carpenter, Franke, Levi, Jacobs and
Empson, 1996).
•Our data show that teachers’ beliefs
are an important factor that influence
changes in teachers’ lesson plans.
•The course had an impact mainly on
teachers with substancial mathematical
knowledge.
•Mathematical knowledge is very important for
planning instruction.
Recommendation:
Mathematics in elementary school
should be taught by teachers specializing
in mathematics teaching.
Pre-service education programs for
these teachers will emphasize
mathematics and mathematics
instruction for the purpose of enhancing
the teachers’ mathematical knowledge.
In-service programs that focus on
students' ways of thinking should
be developed, implemented and
evaluated.
We suggest that:
•More research is needed for
examining the effect of mathematical
knowledge on other aspects of
teaching.
Our small sample included only three
groups of teachers. We suggest that
further studies with a larger numbers of
participants be conducted to investigate
the impact of inservice programs that
focus on students’ ways of thinking on
teachers’ lesson plans and on teachers’
actual teaching practices.
Author:
Dr. Ronith Klein
Director of Computer Applications in Education
Kibbutzim College of Education,
Tel Aviv
E-mail: [email protected]