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November 2011

Spotlight on Excellence: A Series of Reports on Academic Programs at San Francisco Day School

Welcome to the first edition of Spotlight On Excellence, a new series of reports on academic programs at San Francisco Day School. Spotlight will be distributed via email and as a newsletter periodically throughout the school year. To opt out of either communication, please contact Michelle Phillips: We hope you enjoy this issue, which highlights the mathematics program at SFDS. -- Dr. David Jackson, Head of School

Mathematics Program Update at SFDS San Francisco Day School is involved in a multi-year effort to create a mathematics curriculum and teaching practices that emulate and aspire to the most rigorous international standards and assessments. The three goals of a highly effective curriculum are to achieve: 1) in-depth mastery of essential content, 2) deep conceptual understanding with keen problem solving skills and critical habits of mind, and 3) algorithmic proficiency that yields accuracy and efficiency. Our professional development program (Institute for Teaching and Learning or ITL) has afforded our teachers the resources needed to create this curriculum--comprehensive training opportunities with experienced consultants and experts. Over the past two years, our upper and lower school teachers have been devoting significant time to collaborate with their colleagues and experts to expand and refine their curriculum and teaching practices.

Lower School Update Our lower school teachers have been following a three-part procedure to further their learning and enhance the overall quality of their students’ experiences. 1) Review math curriculum scope and sequence to identify overlap, redundancies, and/or gaps. The K-4 sequence must be coherent and rigorous. Our teachers work together to ensure all critical content is taught with sufficient depth and opportunities for complex learning. 2) Engage in a series of training opportunities for teachers. Most recently, our lower school teachers have been focusing on the work of Professor Cathy Fosnot. Many teachers have participated in workshops with her as part of our professional development program. 3) Observe teachers teaching, followed by a debriefing. This process enables everyone to provide more substantive feedback and teachers can then improve their lessons or teaching techniques as needed. These types of in-depth, professional practices are necessary to implement change in teaching methods. Without this type of professional development and training it is difficult to effect meaningful change. Fortunately, we have the resources and the desire to provide the kind of intense training that is integral to the quality and rigor of our curriculum and teaching techniques. We see learning as an ongoing process not only for our students but for our teachers as well; this procedure seeks to facilitate that process and ensure our academic program is constantly improving to the benefit of each student at SFDS. -1-

Upper School Update For the past two years, our upper school teachers have been working closely with Nancy Lobell, a STEP (Stanford Teacher Education Program) Clinical Associate for Mathematics. With Nancy’s direction, our teachers re-structured the curriculum scope and sequence to identify overlaps, redundancies, and gaps to meet international standards. They engaged in a series of observations, feedback, and lesson re-design. Our teachers identified key goals around teaching students how to collaborate to solve mathematical problems and develop strong habits of mind to help their critical thinking and problem solving skills. The faculty also established specific classroom norms to encourage students to truly own and master the content.

Average SFDS Percentile Scores Private School Norms *50th Percentile Means Equal to Private School Peers

ERB Scores Last year, student achievement test scores were very high. We believe this is the result of the re-design of the curriculum and teaching practices that we’ve incorporated over the past two years. The ERB results illustrated in this chart show that in three grade levels, on two different tests, our students scored much higher than their private school peers. Wow!

Algebra Readiness Test Results For nearly two decades, seventh grade students at SFDS have been taking an Algebra Readiness Test that was originally developed by mathematics professors at the University of California, Berkeley. To be considered “prepared” for a formal high school level algebra class, students must meet the threshold of 36 correct answers out of 45. More of this year’s eighth grade students scored above the standard for algebra readiness than any other class in the history of SFDS. Knowing that we were aspiring to international math standards, we also devised an exam of complex mathematical thinking modeled after PISA (Program for International Student Assessment). Our students did exceptionally well. -2-

The Airport Problem: Introduction Although we value the information that ERB tests provide, it is important to note that they only measure basic reading, writing and math skills. ERB tests do not measure the ability to apply basic skills to solve complicated tasks or reach a sophisticated understanding of a complex problem. At SFDS, we strive for both basic skill mastery and the subtle use of thinking strategies to understand human, social, and physical realities. Consider the following task from a sixth and seventh grade end-of-year assessment, “The Airport Problem.” Ms. Dance’s grandparents live in Ukiah. Her grandpa is very sick and needs to travel to Arizona regularly for treatment. THe closest airport is SFO. They can drive their van to San Francisco airport and park at the airport. The other option is to drive to Santa Rosa, park their car in overnight parking there, and then take the shuttle to SFO. Your task is to decide which is the cheapest strategy. Your family very much wants to visit grandpa but has limited financial resources. Will one strategy always be the cheapest based on different numbers of days? Use t-tables, a graph, and words to justify your solutions, based on the following information: Driving to San Francisco • Gas: $3.60/gallon • Miles to SFO from Ukiah: 128 milles • Airport parking overnight: $14.00 • Van mileage: 26 mpg

Driving to Santa Rosa • Gas: $3.60/gallon • Miles to Santa Rosa Parking: 55 miles • Shuttle cost from Santa Rosa to SFO for two people, roundtrip: $124.00 • Van mileage: 26 mpg

The students were given several days of class time to solve the problem and prove their work. They were able to work in small groups and consult with each other, but each student was required to complete the entire product. Successful completion required: organizational skills, sustained effort, ability to sort out essential information, compilation of data in a way that reveals conclusions, and competency with written language and reasoning. Critical thinking is a multi-layered and complex process. Following is an example of a student’s finished product, the grading rubric used by the teacher to assess the work, and the final assessment. It is important to note that both ERB and critical thinking assessment tasks have value, and we appreciate your time in understanding the differences and implications of both types of tests. -3-


The Airport Problem: Student Answer






The Airport Problem: Teacher Assessment Assessment Rubric Below Standard, Must Resubmit

Approaching the Meeting the Standard Standard

Exceeding the Standard

Final Product

Work is not well Work is somewhat organized and parts organized and are missing. mostly complete.

Work is very well organized and complete.

Work has excellent organization, is neat and has a creative presentation.

Mathematical Content - Rough drafts are included - Can see how student solved problem with clear key steps - Student shows why answer is reasonable or provides a check to prove answer is correct

There are many inaccuracies and/or the work leading to the solution is not shown.

The math is mostly accurate and the work leading to the solution is included.

The work is accurate and complete. All steps leading to solutions are clearly shown.

The work is accurate and complete, and the concepts or problems were explored in deeper, more complex, or creative ways.

Communication - Problem is restated in own words - Solution is given in a complete sentence - Work is neat and/or creative

Limited or incorrect use of mathematical vocabulary, symbols, diagrams, tables, etc.

Limited use of mathematical vocabulary, symbols and/or diagrams.

Very good use of math vocabulary, symbols, and diagrams. Explanations are clear and aligned with vocabulary, symbols and diagrams.

Excellent use of vocabulary, symbols, and diagrams. Explanations are clear and complete.

Work Habits

Did not use class time wisely. Frequently needed re-direction. Didn’t have materials or missed deadlines for conrrecting or submitting drafts.

Usually stayed on task and used class time wisely. Met deadlines for correcting or submitting work.

Consistently used class time wisely. Worked well independently and with peers. Consistently met deadlines for correcting or submitting work.

A self-starter who always used class time wisely. Worked well independently and with peers. Always met deadlines and went beyond expectations.

Teacher’s Assessment of the Student Answer Final Product: Exceeding the Standard • Work is very well organized, clear and represents a carefully crafted final draft. • Problem-solving is comprehensively represented. Mathematical Content: Meeting the Standard + • Final product is formatted very well even though a final draft was not turned in. • Key steps are exhaustively shown in a well-crafted table and the solution is accurate. • Final answer demonstrates an extrapolation of different scenarios beyond what was requested. Communication: Meeting the Standard + • The problem and figures are interpreted, restated, and reformatted in your own words. • Work is straightforward, thoughtful manner and solution is well-expressed in a complete sentence. • Mathematical symbols, steps and a table clearly point to the solution and are well-chosen. Work Habits: Exceeding the Standard • You are a model student who is always on task, use your time wisely, and are an asset to the class. • You worked well independently when necessary, and were a very strong collaborator. • You met every deadline and produced a well-polished final draft within the time constraints. -5-

Visit from Cathy Fosnot Special thanks to Professor Cathy Fosnot for her recent visit to the Day School! Fosnot is the author of several books and articles on mathematics education and general teacher education. She established Mathematics in the City (MitC), a national center of professional development for K-8 mathematics education, which a number of SFDS teachers attended this past summer. MitC guides teachers to shape their classrooms into mathematics workshops where students are engaged in inquiry and worthwhile mathematical tasks, proving their thinking, and communicating it to their peers. During her visit, Fosnot met with faculty, gave lesson demonstrations, and taught with our faculty in teams. After initial debriefings, the teachers collaborated with Fosnot on lesson design, taught a lesson under her observation, and completed a session with Fosnot to discuss areas for improvement and excellence. In addition to this dedicated time with our teachers, we were also fortunate to have Fosnot lead an all-school faculty meeting and host a parent education event for lower school families, so that the entire SFDS community could benefit from her experience.

Conclusion We are very proud of our teachers’ work and their willingness to engage in this type of intensive training and curriculum review. These types of programs enable our teachers to observe a lesson, design a lesson, and teach a lesson with immediate feedback. As a result, our teachers are able to create a detailed and coherent curriculum tied to a weekly teaching schedule. This disciplined approach ensures their in-depth lesson plans are rigorous yet feasible within a school year. We will continue to keep you apprised of new developments as we continue along this path.


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SFDS Spotlight on Excellence November 2011