The Standards for Mathematical Practice in an Urban Context

Kyndall Brown, Executive Director, California Mathematics ProjectAndrew Thomas, Data Analyst, Public Works

Overview of Presentation

Description of Fremont HS

Description of FRAME Grant

Research on Effective PD

FRAME PD Program

Standards for Mathematical Practice and FRAME

Evaluation of FRAME

Results of FRAME

Q & A

Questions for Discussion

What kind of professional learning opportunities has your school/district provided around the Common Core Standards in Mathematics?

How effective do you feel these professional learning experiences have been?

Fremont High School 2010

Multi-Track, Year Round

4,800 students

1% Mathematics Proficiency

35% graduation rate

Had not met API target growth in 5 years

Had not met AYP in 10 years

FRemont Achievement in Mathematics for Excellence (FRAME)

Improving CAHSEE pass rate

Decreasing FBB, BB on CST

Improving Teacher Lesson Planning

Increasing Teacher Collaboration

Research on Effective Professional Development

Teacher input into professional development

Deeper understanding of student curriculum and assessment

Emphasis on active student involvement

Teachers observe each other’s instructional practices

FRAME Professional Development Program

Intensive 30 hour professional development institute Content

Algebra, Geometry, Algebra 2 Pedagogy

ELD Strategies Discourse Strategies

Technology Graphing Calculators Geometer Sketchpad

FRAME Professional Development Program

Classroom Support Administrator Coach

Leadership Team Administrators Teachers Evaluation Team UCLAMP

Year 1 Institute Schedule

Standards for Mathematical Practice

Make sense of problems and persevere in solving them

Reason abstractly and quantitatively

Construct viable arguments and critique the reasoning of others

Model with mathematics

Standards for Mathematical Practice

Use appropriate tools strategically

Attend to precision

Look for and make use of structure

Look for and express regularity in repeated reasoning

High Level Cognitively Demanding Mathematics (Stein & Smith, 1998) Require complex and non-algorithmic thinking

Require students to explore and understand the nature of mathematical concepts, processes and relationships

Demand self-monitoring or self-regulation of one’s own cognitive processes

Require students to access relevant knowledge

High Level Cognitively Demanding Mathematics (Stein & Smith, 1998) Require students to analyze the task and actively

examine task constraints that may limit possible solution strategies and solutions

Require significant cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required

Quadratic Quandry Two friends, Adam and Alyssa, are members of model rocket clubs at their

schools. Each of their schools is having a competition to see whose model rocket can stay in the air the longest. The science teachers in each school have helped the students construct equations that describe the height of the rocket from the ground when it has been launched from the roof of the school. Following are Adam’s and Alyssa’s equations:

Adam: h = -16t2 + 40t + 56 where t is measured in seconds and h is measured in feet.

Alyssa: h = -5t2 + 15t + 18 where t is measured in seconds and h is measured in meters.

1. Use a graph to determine whose rocket stays in the air the longest. Explain how you used the graph to answer the question.

2. Explain how to find the x-intercepts of any quadratic function by graphing. In general, what do the x-intercepts of a quadratic function mean? How many x-intercepts can a quadratic function have?

Discussion Question

After hearing about the FRAME grant, what questions do you have?

Evaluation Framework

Increased teacher knowledge and skills/ changes in attitudes or beliefs

Professional Development Activities: Content Focus Active Learning Coherence Duration Collective participation

Change in Instruction

Improved student learning

Enabling Context

Evaluation Design: Research Questions1. How did FRAME implementation (in terms of content focus,

active learning, coherence, duration, collective participation) and the context of implementation change over the course of the project?

2. How did teacher mathematics content knowledge and pedagogical content knowledge at Fremont High School change?

3. How did mathematics instructional practice at Fremont High School change?

4. To what extent did FRAME have an impact on student mathematics achievement (California Standards Test and California High School Exit Exam, also attendance)?

Evaluation Design: Data Collection Participation tracking

Review of Documentation

Observations

Focus Groups

Mathematical Knowledge for Teaching Measures (MKT)

Math Culture Teacher Survey (MCTS)

Archived administrative data California Standards Test (CST) for Algebra I, Geometry, and Algebra II in

addition to the California High School Exit Exam (CAHSEE) pass rates in mathematics. Also attendance.

Results: Implementation Outcomes Content Focus

Annual Institutes Math coach Full-time administrator

Active Learning Coach Retreat

Duration

Results: Implementation Outcomes Coherence

Key Instructional Strategies Active Student Engagement Inquiry-based instruction Writing across the curriculum District Framework for Instructional Change.

Collective Participation Entire math department

Enabling context Reconstitution of school; new teachers Dedicated administrator Decrease in school size Resource squeeze

Results: Increased Teacher Knowledge

MKT did not show increases

MCTS did find some sign of learning and changing attitudes

Confident and Prepared (fairly or very) to teach all content areas with the exception of computations with large and small numbers, positive integers, decimals and fractions, which started out high and decreased.

Results: Change in Mathematics Instruction from 2011 to 2013 Substantially more formal presentations of content from the teachers, which

may have been accompanied by more formalized note taking.

More peer interaction and whole class discussion.

Textbooks use decreased; replaced by a multiple-representation approach, including the use of manipulatives, graphic organizers, calculators and computers, some of this explicitly intended to benefit English language learners.

Cooperative groups and pair-share activities as well as homework features of the classroom all along, although the group activities may have improved with more teachers reporting that their students shared ideas with one another.

Neither the use of notebooks or journals for reflection and teacher feedback, nor the introduction of longer mathematics investigations or projects seem to have taken off.

Discussion

What would you expect to see in the data?

Looking at the graphs, what can you infer about what happened?

What suggestions would you make to Fremont teachers and staff based on the data?

Results: Student Achievement

2009-10

2010-11

2011-12

2012-13

2009-10

2010-11

2011-12

2012-13

2009-10

2010-11

2011-12

2012-13

Algebra I Geometry Algebra II

0%

5%

10%

15%

20%

25%

30%

35%

14% 14% 13%15%

9%

14%12% 12%

6%

13% 14%16%

7%5% 8%

13%

3%

3%4% 5%

1%

1%1%

4%

2% 1%

1%

1%

1%

APB

Results: Student Achievement

2009-10

2010-11

2011-12

2012-13

2009-10

2010-11

2011-12

2012-13

2009-10

2010-11

2011-12

2012-13

Algebra I Geometry Algebra II

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

77% 80% 78%72%

88%83% 84% 82%

92%86% 85%

78%

FBB & BB

Question for Discussion

From what you’ve heard about the planning, implementation and evaluation of FRAME… What lessons have you learned that would apply to the

PD at your school or district? What suggestions or techniques would you take back to

your school to try?

Contact Information

Kyndall BrownExecutive Director, California Mathematics Project

kyndallb@math.ucla.eduwww.cmpso.org

Andrew Thomas, PhD.Data Analyst, Public Worksathomas@ Eddetective.com