Transcript Mathematical Practices

Pathways to Teaching Middle
School Math: Models and Issues
Session #
• Call 37607
• Evaluation Poll
Code: 11599
Carol Fry Bohlin – California State University, Fresno
Joanne Rossi Becker – San José State University
Mark Ellis – California State University, Fullerton
Kathy Hann – California State University, East Bay
California Mathematics Council - South
Friday, 5 November 2015
Session Overview
• Introductions – Speakers, Audience
• Key issue: How should we prepare future middle school
mathematics teachers?
• National reports/guidance/research
• State (California) teacher preparation pathways
• Concerns about FLM credential authorization and teacher
preparation
– CAMTE Member Survey re FLM
– Mathematics course-taking survey among credential students
– FLM credential in light of CCSS-M, especially SMP
• Discuss possible alternatives (several examples)
• CAMTE Advocacy Committee efforts
• Brainstorming!
The Mathematical Education of Teachers II
(MET II; 2012) Recommendations
• “Prospective middle grades (5–8)
teachers of mathematics should be
required to complete at least 24
semester-hours of mathematics that
includes at least 15 semester-hours on
fundamental ideas of school
mathematics appropriate for middle
grades teachers… (p. 18)
• State education departments and
accreditation associations are urged
to require all grades 5-8 teachers of
mathematics to satisfy the 24
[semester] hour requirement
recommended by this report.” (p. 18)
Mathematical Education of Teachers II
(MET II; 2012) Recommendations
“All courses and professional
development experiences for
mathematics teachers should develop
the habits of mind of a mathematical
thinker and problem-solver, such as
reasoning and explaining, modeling,
seeing structure, and generalizing.
Courses should also use the flexible,
interactive styles of teaching that will
enable teachers to develop these habits
of mind in their students.” (p. 19)
www.cbmsweb.org/MET2
Math Courses for Future Middle Grades
Teachers: MET II Recommendations
24 Units of Mathematics Coursework (pp. 46-48)
18 Core Semester-Units
•Algebra and Number Theory (3 units)
•Geometry and Measurement (3 units)
•Number and Operations (6 units)
•Statistics and Probability (6 units)
6 Other Semester-Units (at or above pre-Calculus)
•Discrete Mathematics (3 units)
•Modeling (3 units)
•Calculus, especially applied courses (3 units)
•History of Mathematics (3 units)
NCTM/CAEP Standards for Middle Grades
• CAEP = Council for the Accreditation of Educator
Preparation
• NCTM manages the math teacher preparation
program accreditation standards and review
process for CAEP
• All colleges and universities must use
NCTM/CAEP Standards (2012)
• Standards are aligned with edTPA Mathematics
Operational Handbook rubric criteria
NCTM/CAEP Standards for Middle Grades
1.
2.
3.
4.
5.
6.
Content Knowledge
Mathematical Practices
Content Pedagogy
Mathematical Learning Environment
Impact on Student Learning
Professional Knowledge and Skills
http://tinyurl.com/NCTM-CAEP-Standards2012
www.nctm.org/Standards-and-Positions/CAEP-Standards/
NCTM/CAEP Standards for Middle Grades:
Content and Mathematics Practices
1. Content: Number, Algebra, Geometry,
Trigonometry, Statistics, Probability, and Calculus
2. Mathematical Practices: Effective middle
grades teachers solve problems, represent
mathematical ideas, prove, use math models,
attend to precision, identify elements of structure,
generalize, engage in math communication, and
make connections as essential math practices.
These practices intersect with math content.
Association of Mathematics Teacher
Educators Report on Elementary
Mathematics Specialists
Elementary Mathematics Specialists can help
meet the demands for increasing student
achievement in mathematics, especially in
grades K-8.
Standards for Elementary Mathematics
Specialists: A Reference for Teacher
Credentialing and Degree Programs,
(Association for Mathematics Teacher
Educators, 2010,
www.amte.net/resources/amte-documents)
Primary Paths for Teaching
Mathematics in the Middle School
Single Subject (SS) Credentials (SMC plus credential program):
– Full SS Mathematics Credential - Must demonstrate subject
matter competency (SMC) by (a) taking CSET: Mathematics
Subtests I, II, & III or (b) completing a 45-unit subject matter
waiver program (coursework)
– SS Credential in Foundational-Level Mathematics (FLM)
Must demonstrate subject matter competency by (a) passing
CSET: Mathematics Subtests I and II or (b) completing a 32unit subject matter waiver program. (Can teach through Alg.2)
Subject Matter Authorization in Introductory Mathematics (SMA)
– Requires 32 units of college-level mathematics; must add on to
current credential (not to be confused with Supplementary
Authorization, which is not NCLB-compliant)
Primary Paths for Teaching
Mathematics in the Middle School
Mathematics Instructional Added Authorization
(MIAA)
• Can teach math in departmentalized settings in
grades K-12
• Can either teach through pre-Algebra or Algebra I,
depending on preparation
• Teachers College of San Joaquin current has the
only CTC-approved MIAA program in the state.
• There are no approved Mathematics Instructional
Leadership Specialist (MILS) programs in the state.
The FLM Credential—Some Concerns
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•
•
•
Lack of college level coursework
Ability to teach through Algebra II, Prob./Stat.
High pass rate on the CSET Subtests I and II
Lack of experience with the Mathematical
Practices
• Difficulty in placing student teachers
• Lack of true middle school credential
Berglund Study of Collegiate Math
Preparation of CSET-Takers
• Data collected on students accepted into
mathematics credential programs at 13 CSU
campuses (Fall 2010)
• 189 undergraduate transcripts were analyzed.
– 86 (46%) took/passed CSET to establish subject matter
competence
• 48 (56%) passed all 3 CSET subtests (Full Level)
• 38 (44%) passed the first 2 (Foundational-Level)
Berglund Study of Collegiate Math
Preparation of CSET-Takers
For those who passed all three CSET Subtests:
– 24 (50%) had the equivalent of a minor or a major in
mathematics
– 18 (38%) had taken 2 semesters of calculus or more, but
less than a minor
– 6 (13%) had no mathematics course beyond first
semester calculus
Berglund Study of Collegiate Math
Preparation of CSET-Takers
For those who passed 2 CSET Subtests:
– 3 (8%) had the equivalent of a minor or a major in
mathematics
– 16 (42%) had taken 2 semesters of calculus or more, but
less than a minor
– 19 (50%) had no mathematics course beyond the first
semester of calculus
FLM Survey of CAMTE Members by Bohlin & Hsu:
Poll Respondents
Position
•Mathematics Faculty: 20
•Education Faculty: 7
•County Office of Education: 3
•Other: 2
Place of Employment
•17 CSUs
•2 UCs
•3 COEs
FLM Survey: Which Courses Should FLM
Authorize Teaching?
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•
•
•
•
•
•
Pre-Algebra: 29
General Math: 28
Consumer Math: 27
Algebra I: 27
Geometry (no trig): 14
Algebra II (no trig): 6
Prob and Stat (not AP): 8
FLM Survey: Common Comments
• Do not let FLM credential holders teach past
Algebra 1. (6 times) Our program is held up
because the department feels the scope of the
FLM goes too high. Teachers without a math
degree should not be teaching geometry, which
should involve proofs, and also should not be
teaching Algebra 2.
• Grades, Not Courses. (5 times) Should be
limited to grade level, not course level (only
grades 6-8). (“Why are you using course names
that perpetuate the American dis-integrated
focus on teaching mathematics?”)
Fresno Unified H.R. Administrator Perspective
When asked if she thought that narrowing the
authorization of the FLM to Algebra I/Math I would
be a problem for Fresno Unified, one of FUSD’s HR
administrators said, "Yes and no--It would restrict
what they could teach, and that is a GOOD thing.
That way, they couldn't hire FLMs to teach upper
level math.”
Would narrowing the authorization of the FLM
credential be viewed as a positive step in your
district or not? What are YOUR thoughts?
CTC Commissioner Perspective
• Quality of teachers is of paramount
importance
• CTC (California Commission on Teacher
Credentialing) should revisit the level of
coursework FLM holders may teach.
• Middle school credential unlikely because it
limits a district’s ability to assign teachers.
• The shortage of math teachers is a serious
concern to be addressed.
Current Efforts to Strengthen FLM
Teacher Preparation: CSU Fullerton
• Undergraduate pathways in Child/Adolescent Studies and Liberal
Studies that build-in a Mathematics Minor (21 units including one
semester of Calculus)
• Collaboration between Secondary Education and Mathematics
– Recruitment
– Discussing Mathematics minor for middle school and FLM SMPP
• Partnerships with School Districts
– Early field experiences for undergraduate Math majors/minors
– Fieldwork placements for teacher candidates
• Majority (90%) of FLM candidates in middle school
• Co-Plan, Co-Teach model for student teaching
– Attend to Staffing Needs
• middle school “experts” and high school “experts” (especially with
Common Core)
• Bilingual FLM and Mathematics teachers
CSU East Bay’s FLM Credential Program
Coursework (48 qtr. units total; SMP approved in 2011)
•College Algebra
•Trig. & Analytic Geom.
•Number Systems
•Geometry & Measurement
•Statistics, Data Analysis & Probability
•Algebra and Functions
•Advanced Study of School Math
•Mathematics for Business and Social Sciences II
•Plus 12 units of Extended Study
CSU East Bay’s FLM Credential Program
Extended Study Options (or with advisor permission)
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CHEM 1100 Introduction to College Chemistry (5)
CS 1080 Introduction to Media Computation (4)
CS 1160 Introduction to Computer Science I (4)
ENG 1011 Engineering: An Introduction (3)
MATH 1304 Calculus I (4)
MATH 1305 Calculus II (4)
MATH 2150 Discrete Structures
MATH 3000 Introduction to Proof (4)
MATH 4040 History of Mathematics (4)
MGMT 3100 Decision Science (4)
PHIL 1001 Introduction to Logic (4)
PHIL 3002 Modern Logic (4)
PHYS 1700 Elementary Physics (4)
PHYS 1800 Astronomy (4)
STAT 1000 Elements of Probability and Statistics (4)
CSU East Bay’s FLM Credential Program
Student Profile
•Only 4-5 students per year – it’s cheaper to just
take the CSETs
•Current Multiple Subject credential students
•Administrators looking to clear their credential
•Current teachers looking to clear their credential
•Prospective middle school teachers who already
have a BS in another field
Middle School Pathways at Fresno State
and San José State Universities
Presentation by Joanne Rossi Becker
Presentation by Carol Fry Bohlin
Advocacy Efforts – CAMTE
California (CAMTE) has an Advocacy
Committee that has made inroads in connecting
with the California Mathematics Council, the
State Board of Education, the California
Commission on Teacher Credentialing, and the
California State University Chancellor’s
Office to impact policy decisions related to state
textbook adoption, mathematics teacher
licensure, etc.
Early Partnership with CMC to
Influence State Policy
Early Relationship Building with CSU
CAMTE Partnerships: CMC & CSU
CAMTE/MSTI (CSU) Presentations at CMC and AMTE Conferences on Middle
School Mathematics Teacher Preparation
• www.fresnostate.edu/kremen/teachmathscience/conferences.html
• www.camte.org/conferences.html
Questioning use of Tests to Demonstrate Subject
Matter Competency – Addressing CTC
January 2009 CTC meeting: Joanne Rossi Becker raised a
concern related to the State Board's decision to have exams
(currently the CSET) satisfy the subject matter competency
requirement for Multiple Subject teachers. "This decision has
had the unintended consequence of nearly decimating
[mathematics] courses for Multiple Subject teachers" on her
campus, she said. Students are simply cramming to pass the
tests rather than taking the courses.
Commissioner David Pearson (Dean of the Graduate School
of Education at UC, Berkeley) agreed: "You should never
send a test out to do a curriculum's job.”
Resource Ideas for a Resource
Concern over FLM Credential
Conversation with CTC about the
CSET-Math for FLM Credential
Nov. 2012
CAMTE’s Influence on Statewide Math
Teacher Credentialing Matters
Successful Effort to Change Policy to
Require Subject-Specific Pedagogy
Course
January 31, 2013 – The California Association of Mathematics
Teacher Educators strongly supported proposed changes in
pedagogy course requirements for adding a credential. Joanne Rossi
Becker delivered a statement on behalf of CAMTE that stressed the
importance of prospective Single Subject mathematics teachers
taking a pedagogy course that delves into the Common Core State
Standards for Mathematics, incorporates technology specific to
learning and teaching mathematics, utilizes manipulative materials
and concrete models to exemplify mathematical concepts, and
demonstrates how to effectively teach mathematics to English
learners.
CCSS-Aligned Subject Matter Requirements for
Subject Matter Programs – CAMTE Support and
Input
Supporting Partners and Math Teacher
Educator Community via COMET
http://comet.cmpso.org/
Summary of Advocacy Strategies
• Build trust among potential partners and build strong
relationships.
• Communicate regularly (on and off the record).
• Discuss Board positions; collect data; enlist partners
(e.g., CMC); build consensus.
• Write joint letters of support and position statements.
Deliver publicly when possible.
• Encourage members to apply for and serve on
influential committees and task forces.
Current Efforts: Mathematics Teacher
Education Partnership (MTEP)
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•
National effort of 91 university partnership teams to improve secondary
mathematics teacher preparation led by Association of Public and Land-grant
Universities (APLU)
Five identified “research action clusters” (RACs)
– Active Learning in undergraduate mathematics courses
– Common Core-aligned modules for upper-division courses for future
teachers (e.g., transformational geometry)
– Recruitment, especially among underrepresented populations
– Clinical Preparation (methods coursework and fieldwork)
– Induction and Retention
Faculty-led teams work collaboratively to develop interventions, pilot them,
and revise in cycles of “plan, do, study, act” (improvement science model)
Emphasis on evidence-base for claims about improvements
Your thoughts?
Suggestions?
Concerns?
Solutions? 
CAMTE Advocacy Committee
Contacts at CMC-South 2015
•Carol Fry Bohlin (Chair) ~ California State
University, Fresno • [email protected]
•Joanne Rossi Becker ~ San José State University
[email protected]
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