Mathematics Specialist Certificate Program - Where are we now?

CMC-SS, Session 102Friday November 5, 2004 8:30-10:00 am

What is the Mathematics Specialist Certificate Program? SDSU program designed to help

elementary teachers enhance their mathematics teaching

Focus is on helping teachers acquire a deep understanding of the mathematics taught at elementary grades and the skills needed to teach mathematics effectively

Program Components Teacher Education coursework (6

units)– includes practice-based, reflective work

focused on the teaching of mathematics in the teachers’ own classrooms

Mathematics coursework (6 units)– provides a close look at the content of

topics taught at the elementary level: Number and Operations, Geometry and Measurement, Quantitative Reasoning and Algebraic Thinking

Features Designed with Teachers in Mind

Reduced tuition

Textbooks and materials provided Calendar built around K-12

schools’ calendars TE and Math components

planned collaboratively and specifically for practicing teachers

General Structure of Pedagogy Coursework

Effective Instructional Practices

Focus on student thinking

Planning and Reflecting

Student Work Learn how

children come to think about and understand math concepts

Analyze the work of their own students

Consider implications for teaching

Teaching Learn effective

instructional strategies specific to mathematics

Reflect on our teaching Analysis of student

work to guide collaborative planning

Focus on assessment Use video and written

cases to analyze effective practice

Assessing Students’ Understanding of

Multiplication What is multiplication? Write down anything you know about multiplication. You can use words, numbers and drawings.

Here is a multiplication fact: 7 x 6 Explain how you would figure out the answer.

Assessing Students’ Understanding of

Multiplication Can you write a story problem for 7 x 6?

What does the 7 mean? What does the 6 mean? What does the answer tell us?

Can you draw a picture to show how you would solve this problem?

General Structure of Math Classes

Good problemsTime to work and think,

individually and collaboratively

Instructor and class support for graded assignments

Algebraic Thinking Upper Elementary

This graph represents Jordan’s bike trip.

C B

Distance A

Time Which segment took the most time? During which segment did he go the farthest?

Number & Operations

Can you see 3/5 of something in the picture?

Can you see 2/5 of something in the picture?

Can you see 2/3 of something in the picture?

Can you see 3/2 of something in the picture?

GeometryIf this net were folded up to form a cube, which pairs of faces would be opposite each other?

1 2

4 53

6

Evolution of the Math Specialist Certificate Program 2000-2004

Considerations that have shaped our work Change in curricula

– Everyday Math– Everyday Math, revised– Harcourt with module structure

Change in Teaching models at sites– Math Specialists in Focus Schools– Team Teachers by site– Volunteers across grade levels and

districts

Year One: 2000-2001

32 teachers hired in August

Coursework began with 2-week summer intensive and shared 3 hour classes during the year, held at a Focus School

Math and TE co-planned, each class had Math and TE components

Year One: TE

Semester One– Orientation to position, to Everyday

Math– Text was Making Sense

Semester Two– “Reflective Teaching Cycle”, provided

entry into classrooms– Credit for work expected to do

• Support for parents, family math• Professional readings and reflection

Year One: Math

Instructors’ Challenge: Distilling coursework to find the essential components for practicing elementary teachers

Professional Development time at sites allowed for collaboration, and one on one support for challenging problems

Year One: Challenges

Balancing rigor with accountability

General issues of practice overshadowed by teachers’ immediate need to learn new curriculum components

Year One: Lessons learned

Less is More

Context of working with in-service

teachers– Support to be reflective– Examples of what effective practice looks like

Teacher surveys – Increased focus on ratio and fractions

Year Two

Year Two: What changed?

120 participants

Context:– Team teachers by site– More responsibilities, no designated time

Structures– 2 week summer institute + 1-week Math Solutions – 3-hour shared class to a 4 1/2 hour alternating

dinner class.– Transient classes and challenging locations– Grade level groups

Year Two: What stayed the same?

Orienting a new group to a new curriculum

Instructors continue to model inquiry based instruction

Year Two: TE

Increased focus on examining practice

Collaborative Lesson Project Additional text: So You Have to

Teach Math? By Marilyn Burns

Year Two: Math

Restructuring courses– Sequencing for grade levels– Two unit Algebraic Thinking class

broken into two one unit classes for flexibility• Motion detectors powerful for developing

graphing concepts

Year Two: Challenges

Supporting overburdened teachers Misinformation - many expected two

weeks of PD, got 12 units of coursework.

High attrition and “incomplete” rate Grading continues to be a challenge Curriculum v. Pedagogy

Year Two: Lessons learned 4 1/2 hour classes didn’t work Volunteers needed Yet another restructuring needed

– Grade level groups didn’t remain intact

– Curriculum changes planned for following year

– Scale up

Year Three

Year Three: What changed? Kickoff sessions to inform participants of program

specifics before classes began

90-100 Volunteers Settling into the “scale up” population Added one new Mathematics and one new TE

instructor January start cohorts in addition to summer start

cohorts Transition to a 2-year program One - week summer intensive Classes held in schools of attending teachers

Year Three: TE Decreased emphasis on curriculum

implementation Increased emphasis on

– Assessment and its place in a collaborative lesson cycle

– video examples of effective instruction 5 lesson algebraic reasoning sequence Text changes: Young Mathematicians

at Work, Constructing Ideas About Multiplication and Division by Fosnot

Year Three: Math

Resequencing topics– Over two years– Freed from curriculum sequencing– Result, more like a 3 unit class each

year

Year Three: Challenges

Wide range of grade levels Adding new instructors January start cohorts meant one of the

instructors taught both Math and TE sections

More than one district involved Determining appropriate level of

academic support Clarification of Policies

Year Three: Lessons learned Summer intensive important component

– Supported development of true cohort feeling

2-year program allows time to support teachers as they make changes in practice

Support is important but beyond a certain level compromises program integrity

Year Four

Year Four: What changed?

150 teachers, 6 instructors– (90 in second year of program)

All classes at one site Stipends still available, district no longer able

to reimburse tuition Creation of primary grades focus Math

Specialist Certificate program Additional text: Constructing Ideas about

Fractions, Decimals, and Percents, by Fosnot 5 class sequence on geometric reasoning in

TE

Year Four: Lessons learned

Continue to modify curriculum in response to participants’ feedback

Collaborative Lesson Cycle strengthened by:– Teachers engaging in the

mathematics prior to teaching the lesson

– Video analysis of related lesson

2004-2005

Primary and Intermediate grades programs– 4 units of coursework in common, 8 (all of the TE and 2 units of Math)

tailored to grade band Looking towards how the Professional

Development Collaborative can best serve local districts– Example: City Heights Collaborative

Observations / Questions To Date

Why attrition? What is the effect of a two-year

program? Challenge of curriculum implementation What should having an Elementary

Math Specialist Certificate mean? Completers want more

– Probability, Statistics, Foundations of Calculus, Teaching issues study groups

Implications of “No Child Left Behind”

Results So Far

One Teacher’s Comments About the MSCP’s Impact on Her

Teaching“I feel my knowledge and understanding of mathematics has been expanded to the point where I will never teach math the same again. I know too much about group/partner work, using manipulatives; reflective writing, student-directed teaching, student responsibility. In short, I feel enlightened. I feel I finally understand math.”

Changes in Teachers’ Mathematical Knowledge

MPDI Assessment Results (2002)

Our teachers’ mean gain score was 1.21 std. deviations above the mean– In other words, our teachers had an

average gain in scores that was greater than 9 out of 10 teachers in the state on this test

Changes Reported by Teachers

100% reported having a better understanding of the mathematics they teach

94% reported their mathematics teaching was better

87% said “yes”, their beliefs had changed over the course of a year, and the ones who didn’t said it reinforced existing beliefs

90% said their expectations for students had changed (those who did not report a change cited high expectations already for their students.)

> 95% were able to identify specific areas of mathematics that they would like to know more about

(Based on surveys of 71 teachers completing the program in May 2004. Results from previous years are similar.)

Other Measures

Teachers’ further study in mathematics: 23 teachers out of approximately 90 teachers from the first two years went on to take additional math coursework 7 have enrolled in a Math Ed. Master’s Degree Program on campus

Teachers in leadership roles

Student Achievement

State-wide standardized test Performance Assessment items

– CTB-MARS– Grades 4-6 take 3 items at end of

year:• Geometry• Algebraic Reasoning• Number & Operations

Nexus With Student Achievement

Changes in students’ mathematical knowledge (2003-04)– In grade six, the increase in the

percent of students scoring at Proficient or Advanced level was 6.48% ; district-wide, sixth grade increase was 4.1%.

Nexus With Student Achievement Significant decrease in students scoring at Far Below

Basic

Percentage of Students at Each Performance Level:

California Standards Test: Mathematics

Focus Schools Grades 4–6

17.75%

12.12%

38.62%

43.04%

29.97%29.97%

11.87% 12.79%

1.79% 2.07%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

2003 2004

Percent of Students

Advanced

Proficient

Basic

Below Basic

Far Below

Ongoing Analysis

Case studies of Math Specialists Journal of Mathematics Teacher

Education article by Dr. Susan Nickerson slated to appear on differences at school sites and factors influencing change

Continued measurements of student and teacher growth

Challenges in Data Analysis Focus School Attrition

– Sometimes positive, teachers move to position of influence, such as Math Resource Teacher

– After year two, not all Math Specialists at Focus Schools participated in MSCP or had completed the program

Budget cuts present challenge for timely data analysis

Measure results of teachers out of Focus Schools

Summary (What We’ve Learned) Stipends attract teachers who might

otherwise be reluctant to commit to a long-term program

Two year program allows teacher change to be nurtured and developed more completely

Integration of Math/TE topics is essential and requires on-going collaboration

Cohort model fosters a sense of learning community among teachers

Recognize that program continues to evolve

Questions?

This presentation and other information can be

found at http://pdc.sdsu.edu

Contact info.

Karen Payne Aguilar (619)594-3970 kpayne@sciences.sdsu.edu

Steve Klass (619)594-5114

sklass@projects.sdsu.edu

Gail Moriarty (858)496-8150 x 4407

moriarty@mail.sdsu.edu