Mathematics Specialist Certificate Program - Where are we now? CMC-SS, Session 102 Friday November 5, :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 problems Time 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 DistanceA 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?

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

Evolution of the Math Specialist Certificate Program

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: 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 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

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 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 ( ) –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

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

Contact info. Karen Payne Aguilar (619) Steve Klass (619) Gail Moriarty (858) x 4407