Analysis of Preservice Teacher's Knowledge of Mathematics ...

Analysis of Preservice Teacher’s
Knowledge of Mathematics
Competencies
Dr. Marianne Reese
Dr. Violetta Lien
Jimmy Hand
Department of Curriculum and Instruction
Texas State University -- San Marcos

Who will teach the math of this
millennium?
7/8/05

Impetus for Study
• Content knowledge is a prerequisite to
teach ANY student
• If teachers are not competent in their
content area knowledge, they cannot
teach in ANY language.
• Supporting studies
7/8/05

Rationale for Implementation
• ~ 5% of Texas State University pre-service
graduates acquire mathematics and/or
science certification
• In 2004 77 % of Texas State certified math
and science teachers were EC - 4 certified.
• Only 50% of Texas graduates certified in
math actually enter math education
profession
• In San Marcos CISD only 35 of 240 math
teachers are certified in mathematics.
• 11 of these have a BS in mathematics
7/8/05

Rationale cont…
• Preservice teachers at Texas State
University often avoid math and
science courses until late in their
academic careers.
• Due to math/science anxiety
• Due to uninteresting math/science
experiences in K-12 schools
• Due to poor self efficacy on math and
science
7/8/05

Model for the Improvement of Teacher
Education in Math and Science
Goals
•All TES competent in
math and science
knowledge and increase
their self-efficacy.
•Coordinate improvement
of curricula &
instruction-K-16.
•Recruit additional Math
& Science Teachers.
•Create inquiry-based
Math & Science Ed.
communities.
met by
Model for the
Improvement of
Teacher Education
in
Math and Science
through
through
through
College of
Education
(Dept. C& I)
collaborate
College of
Science
(Mathematics
and Science
Depts.)
Austin
Community
College
develop and
revise
develop
develop
audit,
modify,
redesign
audit and
redesign
review/revise
National and
state standards
correlated to
Math and
Science
Assessments
correlated
Modules for
enhancement of
math & science
content& skills of
located in
Discovery
Learning
Lab(DLL)
Teacher
Education
courses
Core Mathematics
and Science
courses for TES
to
assess
all
correlated to
will
provide
to
include
to
K-12
Teacher Ed.
Students'(TES) math and
science content
Math, Science,
PCK,
Assessment
Domains
must be
mastered
correlated
to
for
•Math & Science academic
enrichment activities
•model inquiry instruction
•Correlated to Standards
•Inquiry-based instruction
•Integrate technology
•include research based
strategies for special needs
•Correlate with National &
State Standards
•Include research based PCK
in math, science, &
special needs
•Model inquiry and
problem-based instruction
•Incorporate technology
Prior to
student
teaching
TES
Individual
Learning
Plans
(ILP)
results
in
results
in
results
in
results
in
Outcome:
All TES will have increased
self-efficacy and mastery
of math and science
knowledge, skills, PCK,
technology, and
addressing special areas
(at risk, disabled, LEP,
culturally diverse students)
results in
Enhancement of
K-16 student
learning and
achievement in
math and
science
7/8/05

Planning and Implementing for
Mastery
General process and C&I’s Math and Science Mastery
Program
Mastery
Learning
Elements
Knowledge
and Skills to
be Learned
Unit
Objectives
Assessment
Formative &
Summative
Activities
Instruction
Enhanceme
and
Enrichmen
C & I Mastery
Program
State and
National
Standards
Domains and
Competencies
Various
Forms of
the CIMA
Modules
7/8/05

DLL Assessment flow chart
CORE
C & I
Block
Courses
ILP's
in
DLL
No
Summative
Assessment(s)
Mastery
Achieved?
prerequisite for
admittance
No
Yes
Formative
assessment
via CISA and
CIMA
Reuslts
Mastery
Achieved?
Yes
No ILP's
Student
Teaching
Consists of
Questions
reflective of
TExES
Domains
7/8/05

7/8/05
Layout of DLL

7/8/05
Technology in the DLL

7/8/05
Manipulatives and Resources

Entry level Math Prerequisites at
Texas State University
• All entering students must have at the
minimum:
• Algebra I
• Algebra II
• Geometry
• Any course that requires the above
courses as a prerequisite.
7/8/05

Curriculum and Instruction Math
Assessment (CIMA)
• CIMA was piloted in spring 2004 and
spring 2005
• Reliability indices for each domain was
greater than 0.85
• Construct validity
• Expert validation
7/8/05

CIMA Domains
• Reflective of National and State Standards
• Domain I - Number Concepts
• Domain II - Patterns and Algebra
• Domain III - Geometry and Measurement
• Domain IV - Probability and Statistics
• Domain V - Math Processes and Perspectives
• Domain VI - Math Learning , Instruction and
Assessment
7/8/05

Summary of Scores by Domains
Domain Mean STD
I 77.7 15.3
II 57.4 16.7
III 57.7 17.9
IV 59.6 15.8
V 30.2 16.4
VI 48.8 15.6
Total Score 55.2 11.0
7/8/05

Criteria for Mastery in Math
• Six domains
• Students must achieve a score of 75% in
each domain
• Twenty-three competencies
• Students must achieve a score of 50% in
each competency
7/8/05

Demographic Assessment
• Type of certification
• Content area courses taken
• Where courses were taken
• HS math/science courses taken
• Data might aid in coordinating math and science
curricula and instruction at three levels:
• Institutions of higher learning from which Texas State
students transfer
• Texas State University math and science departments
• Texas State University C & I Department
7/8/05

Certification Seekers
Demographics
EC -4 85% Generalist 4.7%
Bilingual
4 - 8 2.8%
Math
8 -12 0.5%
Math
EC -12 0.9%
Phys Ed
0.5 %
Math/Science
0.5%
Science
1.4%
Special Ed
7/8/05

Preliminary Findings from CIMA
• Logistic Regression analysis
• Domain outcomes dichotomized into pass/fail
• Model correctly classifies 94.6% of the cases
• Each Domain analyzed to determine odds
ratio for likelihood of achieving mastery
• Data will aid in aligning math courses with
domains in CISA
• Results in course alignment with national and
state standards
7/8/05

Courses with significant contribution to
mastery in Domains of interest
• Domain I - Number Concepts
• College Algebra, Informal Geometry
• Domain II - Patterns and Algebra
• College Algebra, Principles of Math I
• Domain III - Geometry and Measurement
• College Algebra, Informal Geometry, Business Math
• Domain IV - Probability and Statistics
• Elementary statistics, Business Math, Modern Geometry
• Domain V - Math Processes and Perspectives
• College Algebra, POM I, Informal and Modern Geometry,
Pre Calculus, Calculus, Elementary Statistics, History of
Math
• Domain VI - Math Learning, Instruction and
Assessment
• Business Math, Calculus, Modern Geometry, History of
Math
7/8/05

Students can access their scores
http://www.dll.txstate.edu

Individual Learning Plans
• Each pre-service teacher will have a
specific ILP designed based on their
test results---domains and
competencies mastered
• Consist of enhancement activities
completed and summative test data
noted
7/8/05

Math Modules
• Address each Domain and all Competencies
• Math and science competencies may be
integrated within one module
• Technology
• Probes and data loggers
• Computer and internet resources
• Utilize both academic and non-academic
language
• Modules designed to represent math
concepts in multiple formats
7/8/05

C&I’s Math and Science
Mastery Program
• Offers pre-service Science and Math teachers
opportunities to:
• Increase content area knowledge
• Increase pedagogic skills
• Increase self-efficacy
• Provides information to help coordinate math and
science curricula at three levels
• Provides resource for recruitment of new math and
science teachers
• Provides opportunities to increase math and
science teacher retention
• Provide a model pre-service teacher training facility
7/8/05

In Summation
• The coordinated activities presented
here will result in higher achieving K-
16 students, thus enabling each
student to share in the richness and
excitement of comprehending the
natural and technological world.
• Such students will in turn be better
prepared and more motivated to
pursue and enter careers in math,
science, and technology, and teaching
in these disciplines.
7/8/05