1. Mathematics Standards Committee High Standards for All Children

2. Our Genesis Independent Math A Panel formed to investigate large failure rates on June 2003 Math A Regents Independent Math A Panel formed to investigate large failure rates on June 2003 Math A Regents Panel had several findings, one being that the Math A standards lacked clarity and specificity Panel had several findings, one being that the Math A standards lacked clarity and specificity Panel made 41 recommendations, one being that a mathematics standards committee be established to revise the standards Panel made 41 recommendations, one being that a mathematics standards committee be established to revise the standards Our committee is that standards committee Our committee is that standards committee

3. Committee Composition 24 Members – 6 of whom served on the Math A Panel Classroom Teachers – elementary, middle, secondary and BOCES occupational education, from a very diverse group of schools Classroom Teachers – elementary, middle, secondary and BOCES occupational education, from a very diverse group of schools Math curriculum coordinators and staff developers Math curriculum coordinators and staff developers Administrators who were formerly math teachers Administrators who were formerly math teachers Representatives of higher education, both mathematics and mathematics education Representatives of higher education, both mathematics and mathematics education Practitioners (an accountant and an engineer) Practitioners (an accountant and an engineer)

4. THANK YOU! The Committee deeply appreciates the invitation to assist with this important effort. THIS IS A CONSENSUS REPORT. The recommendations are supported by all 24 Committee members. WE ARE GRATEFUL FOR ALL THE HELP. The Committee is grateful to many SED staff members.

5. Committee’s Charge Look at NYS, other states, other nations and the research Look at NYS, other states, other nations and the research Propose changes to improve clarity, specificity and functionality Propose changes to improve clarity, specificity and functionality Revised standards must be challenging, and must “consist of a clear, well-defined set of skills, the mastery of which is demonstrable” Revised standards must be challenging, and must “consist of a clear, well-defined set of skills, the mastery of which is demonstrable”

6. The Current Standards Standard 3 -- the overarching statement that guides all mathematics instruction in the state Standard 3 -- the overarching statement that guides all mathematics instruction in the state Seven ”Key Ideas” (major areas of focus) Seven ”Key Ideas” (major areas of focus) Performance Indicators – 289 statements of what children should know and be able to do, all accompanied by 876 “includes” bullets Performance Indicators – 289 statements of what children should know and be able to do, all accompanied by 876 “includes” bullets

7. The Proposed Changes Revise the wording of Standard 3 Revise the wording of Standard 3 Replace seven ”Key Ideas” with five content strands and five process strands Replace seven ”Key Ideas” with five content strands and five process strands Adopt 850 revised Performance Indicators, grade by grade, for grades Pre-K through 11 Adopt 850 revised Performance Indicators, grade by grade, for grades Pre-K through 11 To improve clarity, specificity and functionality, the Committee proposes:

8. Recommendation 1 Students will: Understand the concepts of, and become proficient with the skills of mathematics Understand the concepts of, and become proficient with the skills of mathematics Communicate and reason mathematically Communicate and reason mathematically Become problem solvers by using appropriate tools and strategies Become problem solvers by using appropriate tools and strategies Through the integrated studies of number sense and operations, algebra, geometry, measurement, and probability and statistics. Standard 3 should be revised to read as follows:

9. Recommendation 2 Replace the current seven key ideas with five content strands and five process strands: Content Strands Process Strands Number Sense and Operations Problem Solving Algebra Reasoning and Proof GeometryCommunication MeasurementConnections Statistics and Probability Representation

10. Performance Indicators This was the bulk of the work, the creation of 850 specific, grade-by-grade performance indicators in grades Pre-K through high school, to be used to guide curriculum development and assessment development.

11. Guiding Principles The committee established guiding principles for the development of the performance indicators, based on its review of mathematics programs in other states and nations.

12. Guiding Principles, continued Performance Indicators should: be presented on a grade-by-grade basis be presented on a grade-by-grade basis be appropriately sequenced from year to year be appropriately sequenced from year to year be developmentally appropriate at each grade level be developmentally appropriate at each grade level be written in language clear for all – teachers, parents, students and test developers be written in language clear for all – teachers, parents, students and test developers provide focus provide focus

13. Recommendation 3 The standards document developed by the committee and included as Attachment B should be adopted as a draft. This document includes definitions of each content strand and each process strand, the division of each content strand into bands, and 850 grade-by-grade performance indicators keyed to the strand. The standards document developed by the committee and included as Attachment B should be adopted as a draft. This document includes definitions of each content strand and each process strand, the division of each content strand into bands, and 850 grade-by-grade performance indicators keyed to the strand. Feedback from the field should be sought before finalization. Feedback from the field should be sought before finalization.

14. Recommendation 4 The field needs time to redesign curriculum and train staff on these revised standards. The committee recommends that SED seek a waiver for a one-year postponement from USDOE for the administration of the grade 3-8 tests in math. If this is not possible, we recommend the results not be considered for accountability purposes until 2006-2007.

15. Recommendation 5 Because each year’s skills and knowledge build upon the previous year, the revised high school program should be phased in over a three year period, following the implementation of the 3-8 program by one year.

16. Recommendation 6 Because Math A will be a one year course for the typical student, and because three years of math are required for an Advanced Regents diploma, Math B will become a two year course for the typical student. The Committee recommends that an additional Regents exam be created to test students at the end of the first half of Math B. Thus, the typical student will take three math Regents exams, one after each year of study.

17. Recommendation 7 From “Math A” to “Integrated Algebra” From “Math A” to “Integrated Algebra” From “Math B” to “ Integrated Geometry” for the first half and “Integrated Algebra II and Trigonometry” for the second half. From “Math B” to “ Integrated Geometry” for the first half and “Integrated Algebra II and Trigonometry” for the second half. To improve clarity, the labels for high school mathematics should be changed as follows:

18. The High School Math Program Integrated Algebra Integrated Algebra Integrated Geometry Integrated Geometry Integrated Algebra II and Trigonometry Integrated Algebra II and Trigonometry each ending in a Regents examination. If recommendations 6 and 7 are approved, the high school math program for the typical student will consist of three years of study:

19. Recommendation 8 Each local school district should establish criteria based on the course grades and Regents exam scores for students to continue to the next course in the Integrated Algebra, Integrated Geometry, Integrated Algebra II and Trigonometry sequence.

20. Recommendation 9 The amount of course credit that can be granted by local districts for Integrated Algebra should be limited to two units.

21. Recommendation 10 Encourage children to take the Advanced Regents Diploma three year sequence. Encourage children to take the Advanced Regents Diploma three year sequence. For those students who do not follow this path, locally developed programs to complete three years of required study should include a majority of the following topics: ratios and proportions, statistics, data analysis, informal geometry, number theory, financial applications (financial management, tax structures, etc.), and integration of technology. For those students who do not follow this path, locally developed programs to complete three years of required study should include a majority of the following topics: ratios and proportions, statistics, data analysis, informal geometry, number theory, financial applications (financial management, tax structures, etc.), and integration of technology.

22. Recommendation 11 Grade-by-grade curriculum guides should be developed as suggested models for mathematics instruction statewide, and there should be alignment among the standards and performance indicators, the curricula and the assessments.

23. Recommendations 12A-12B 12A In K- 4, four function calculators should continue to be an instructional tool, but not permitted on the 3-4 assessments. 12A In K- 4, four function calculators should continue to be an instructional tool, but not permitted on the 3-4 assessments. 12B In 5-8, scientific calculators should be permitted on the grades 5-8 assessments similar to the format that is currently used on the Math 8 assessment (calculator use permitted on extended response parts only) with the understanding that all students should be given access to a scientific calculator. 12B In 5-8, scientific calculators should be permitted on the grades 5-8 assessments similar to the format that is currently used on the Math 8 assessment (calculator use permitted on extended response parts only) with the understanding that all students should be given access to a scientific calculator.

24. Recommendations 12C-12D 12C In 7-8, graphing calculators should be used as an exploratory instructional tool. 12C In 7-8, graphing calculators should be used as an exploratory instructional tool. 12D In 9-12, graphing calculators should be used on a regular basis and required on the Regents exams. All students should have access to a graphing calculator. 12D In 9-12, graphing calculators should be used on a regular basis and required on the Regents exams. All students should have access to a graphing calculator.

25. Recommendation 13 9A: Strengthen K-12 and higher ed. partnerships 9A: Strengthen K-12 and higher ed. partnerships 9B: Elementary certification requirements should include 9 credits in math and 3 in math ed. 9B: Elementary certification requirements should include 9 credits in math and 3 in math ed. 9C: Courses required for certification should be specified 9C: Courses required for certification should be specified 9D: The 175 required hours of professional development should have specific math and math ed. requirements as indicated in the report. 9D: The 175 required hours of professional development should have specific math and math ed. requirements as indicated in the report. We strongly endorse Recommendations 9A, 9B, 9C and 9D of the Math A Panel: Our Committee recommends that the Panel’s Recommendations 9A and 9D be implemented immediately, and that a Professional Preparation Committee be established to make specific recommendations regarding 9B and 9C.

26. Issues/Questions Q. Comparing the proposed performance indicators with the current ones, it appears there are fewer in grades K-4, and a shift of content from higher grades into grades 5-8? A. Absolutely correct. This decision was reached after reviewing programs in other states and nations, and TIMMS and NAEP reports. In K-4, children need to spend a lot of time first developing strong numeracy skills and then proportional thinking. In 5-8, there is currently much repetition and many topics covered each year. In order to develop a strong program leading to a robust Integrated Algebra course, these middle grades need more content and more focus. (Many districts are already successfully implementing similar models.)

27. Issues/Questions, continued Q. Isn’t the proposed high school program going back to Course I, II, III? A. Absolutely not. The major change from I, II, III to Math A and B was the inclusion of process standards, which were woefully lacking in I, II, III. The Committee feels strongly that these process standards must continue, and that the curricula developed for classroom teachers will emphasize this.

28. Issue: “Power and Beauty” We believe the goal of all teachers of mathematics should be to inspire their students to appreciate the power and beauty of mathematics. This is not recommended in Standard 3 because we could not find a way to assess this, and, even if it can be assessed, we do not believe a high school diploma should be conditioned upon this. However, it is our hope that this will be listed as a goal in all curriculum documents.

29. The Whole Picture Our work revising the standards is only one part of a systemic approach to improve the mathematics learning of our students.

30. ALIGNMENT IS ESSENTIAL Content Standards Classroom Instruction CurriculumTest Development Process Regents Exam FINDING: The Math A content standards are not clear. FINDING: There are technical problems in the test development process, which result in the exams being inconsistent over time. FINDING: There is no agreed upon curriculum. FINDING: Because the standards are unclear, and there is no agreed upon curriculum, teachers look to past Regents exams for guidance. FINDING: THE SYSTEM IS NOT ALIGNED.

31. MATH A PANEL SUMMARY Content Standards Instruction CurriculumTest Development Process Regents Exam The Standards need to be retooled. The Math A Regents exam needs to have technical changes made, and to be linked to the retooled standards. A grade-by- grade curriculum, K-8, Math A, Math B needs to be written and disseminated, with Math A being a one- year course. Teachers need to understand the standards, and need to have enough preparation to teach the curriculum. LINKAGES/PARTNERSHIPS K-12 - Higher Ed Public Libraries Museums Public Television DONE

32. Work Complete Still to be done Technical Changes to Math A Exam Grade by Grade Curriculum Revised Standards (our work) Professional Development to the new standards Stronger pre-service training Linkages

33. The Next Steps Field review of our work, make any necessary changes, and adopt the work. Field review of our work, make any necessary changes, and adopt the work. Curriculum development Curriculum development Professional development for teachers Professional development for teachers Continue to expand linkages Continue to expand linkages Continue to involve members of the Math A Panel and the Standards Committee as we go forward, to prevent unintentional drift and loss of alignment Continue to involve members of the Math A Panel and the Standards Committee as we go forward, to prevent unintentional drift and loss of alignment

34. Summary The solution must be systemic in nature. Our work builds the foundation with new standards, but it is still only one part of the system. High expectations for student performance, alignment of suggested grade-by-grade curricula and assessments, and professional development to the standards must all be in place to ensure success for our students.

35. Summary, continued Ultimately, the goal we must all have is to establish a set of “world class” standards in New York that will guarantee that New York’s children receive the best mathematics education anywhere. We appreciate the opportunity to be part of this effort, and we hope our work has advanced this goal.