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The State of K-12 Student Achievement in Mathematics, 2006 Why new Mathematics Standards? Florida, Math Matters! Mary Jane Tappen, Deputy Chancellor, K-12 Public Schools Todd Clark, Deputy Chief, Bureau of Instruction and Innovation Patrick W. Wright, K-12 Mathematics Program Specialist Keith Sheets, Program Coordinator, Bureau of Instruction and Innovation

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10 th ANNIVERSARY After 10 years, Florida’s Standards needed to be revisited and refreshed The only question was the extremity of the makeover.

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2005/2006 Guiding Documents College Board Review of FL Mathematics standards International Center for Leadership in Education’s review of FL Mathematics standards Fordham Foundation Koret Task Force

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Findings Demand less of students than some other states Minimal program provided for secondary students Lack of emphasis on reasoning, problem solving, applications, and communication Need to identify “big ideas” Need to remove repetition across grades Need to decrease the number of benchmarks Covert in their representation of rigor/relevance Fail to show a progression of rigor in grades 9-12 Grade = “F” Need greater specificity and clear guidelines that describe the knowledge students need to acquire As students approach high school, neither the standards nor the testing system support a level of learning necessary for doing well in high school mathematics

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2006 Florida’s Mathematics Standards Charge Completely re-write the standards Use guidance and the expertise of national and international experts to develop a set of mathematics standards that are rigorous and relevant to career and educational requirements beyond high school Set high expectations for Florida K-12 students in mathematics New mathematics standards will be the basis for rigorous and relevant classroom instruction, state assessment, and teacher professional development in mathematics

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What does the data say?

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FCAT CR Data

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Mathematics FCAT NRT and CR Improvement Since 2001

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Based on NAEP test results, Florida’s 4 th grade students outperform most of the nation.

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th -grade NAEP Mathematics Florida is At or Above the National Average in all Subgroups

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NAEP Grade 4

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The same is not true for 8 th grade Mathematics

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NAEP Grade 8 mm

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Discussions About A NAEP Grade 12 This test would include more Algebra II, Trigonometry, and a greater emphasis on mathematical reasoning What impact would/should this have on the revision of Florida’s mathematics standards?

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SAT

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ACT

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International Math Performance TIMSS (Trends in International Mathematics and Science Study, 2003)

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PISA – Program for International Student Assessment (2003 data)

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Let’s Talk About Other Gaps The gap in performance between our grade levels.

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FCAT Mathematics

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Florida Middle Grade Mathematics

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Retention and Level 1 Performance

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Gaps in College Readiness Florida High School Graduates Requiring Remediation 2003 Students entering our State Universities: 7% in mathematics 4% in reading 4% in writing Students entering our Community Colleges: 54% in mathematics 42% in reading 29% in writing 2004 Students entering our State Universities: 6% in mathematics 3% in reading 3% in writing Students entering our Community Colleges: 47% in mathematics 36% in reading 26% in writing

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Goals of the High School Reform Task Force Goal 1: Increase the academic achievement levels of high school students. a. Increase the percent of graduates prepared to enter postsecondary institutions without remediation. b. Increase the level of rigor of high school mathematics and science instruction. c. Increase the percent of teachers prepared to teach advanced courses at grades Goal 2: Increase the percent of high school graduates. Goal 3: Increase the percent of graduates who begin their postsecondary path to college or career while in a Florida high school.

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Secondary School Redesign Act Students promoted from the 8 th grade have the necessary academic skills for success in high school and students graduating from high school have the necessary skills to success in the workplace and postsecondary.

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Florida K-12 Student Achievement Mission of K-20 Education System …Allow students to increase their proficiency by allowing them the opportunity to expand their knowledge and skills through rigorous and relevant learning opportunities. Goal Lead the nation in improving student achievement Mission Lead the nation in student performance

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What did the experts say at the “Thinkers” Meeting ?

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Achieve American Diploma Project Kay Fargione

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American Diploma Project How well prepared are our students for the world after high school? What does it take to be prepared for postsecondary education and work? What do we expect of our high school graduates? What will it take to close the expectations gap?

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A high school diploma is not the last educational stop required Jobs that require at least some postsecondary education will make up more than two-thirds of new jobs. Source: Carnevale, Anthony P. and Donna M. Desrochers, Standards for What? The Economic Roots of K–16 Reform, Educational Testing Service, 2003.

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Change in the Distribution of Education in Jobs, 1973 v % -9% +16% Source: Carnevale, Anthony P. and Donna M. Desrochers, Standards for What? The Economic Roots of K–16 Reform, ETS, 2003.

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College bound does not necessarily mean college ready Nearly three in 10 first-year students are placed immediately into a remedial college course. Percentage of U.S. first-year students in two-year and four-year institutions requiring remediation Source: National Center for Education Statistics, Remedial Education at Degree-Granting Postsecondary Institutions in Fall 2000, 2003.

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Source: National Center for Education Statistics, The Condition of Education, Most U.S. college students who take remedial courses fail to earn degrees nMany college students who need remediation, especially in reading and math, do not earn either an associate’s or a bachelor’s degree. Percentage not earning degree by type of remedial coursework

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Clearly, we’ve got a problem Students are following all the rules; Meeting all of the requirements for a HS diploma; and still-- Falling through the cracks between high school and the expectations of postsecondary institutions.

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College Ready = Career Ready ADP research found a common core of knowledge & skills in math and English that are necessary for success in postsecondary education and in “good jobs”. ACT Study Ready for College Ready for Work: Same or Different?: whether planning to enter college or workforce training programs after graduation, high school students need to be educated to a comparable level of readiness in reading and mathematics.

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Blue-collar jobs require high- level skills Requirements for draftsmen: Recommended high school courses include Geometry and Trigonometry. Draftsmen may wish to seek additional study in mathematics and computer-aided design to keep up with technological progress within the industry. Requirements for electricians: Recommended high school courses include Algebra, Geometry, Trigonometry and Physics. Sources: American Diploma Project, 2002; The Associated General Contractors of America (AGC)

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Blue-collar jobs require high-level skills Requirements for iron workers: Recommended high school courses include Algebra, Geometry and Physics. Requirements for sheet metal workers: Four or five years of apprenticeship Algebra, Geometry, Trigonometry and technical reading Requirements for tool and die makers Four or five years of apprenticeship and/or postsecondary training Algebra, geometry, trigonometry and statistics Sources: American Diploma Project, 2002; The Associated General Contractors of America (AGC)

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Recommended Math Courses for 16 CTE Career Clusters Algebra I, Geometry, & Algebra II Trigonometry, Pre-Calculus, or Statistics Trigonometry, Pre-Calculus, or Calculus Arts, A/V Technology & Communications Architecture & Construction Business, Management, & Administration Finance Government & Public Administration Hospitality and Tourism Human Services Information Technology Manufacturing Marketing, Sales and Service Transportation, Distribution & Logistics Agriculture, Food & Natural Resources Education & Training Health Science Law, Public Safety, Corrections& Security Science, Technology, Engineering and Mathematics

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ADP Post-secondary Institution Study: Key finding In math, graduates need knowledge and skills typically taught in Algebra I, Algebra II and Geometry, as well as some Data Analysis and Statistics.

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44 states require students to take certain courses to graduate from high school

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23 states require Algebra I

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16 states require Geometry

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Only 8 states require Algebra II

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A strong high school curriculum* improves college completion and narrows gaps *Completing at least Algebra II plus other courses. Source: Adapted from Adelman, Clifford, U.S. Department of Education, Answers in the Toolbox, % 13%

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Students can pass state math tests knowing content typically taught in 7th and 8th grade internationally FL MD MA NJ OH TX Source: Achieve, Inc., Do Graduation Tests Measure Up? A Closer Look at State High School Exit Exams, Grade when most international students cover content required to pass state math tests

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Curriculum Focal Points PK-8— A Quest for Coherence Released September 12, 2006 Dr. Jane Schielack

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The Problem: Two Major Issues to Address Long lists of mathematics learning expectations at the state level with little consistency across states Emphasis on breadth resulting in lack of depth, i.e. “mile wide, inch deep” curricula in mathematics

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The Rationale: How to Address the Issues Identify key mathematical ideas across preK-8 that prepare students for future mathematics, particularly algebra Identify the mathematics that should be the focus of instruction and student learning at each grade level, preK-8

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NCTM Curriculum Principle A curriculum is more than a collection of activities. It must be: coherent focused on important mathematics well articulated across the grades Principles and Standards for School Mathematics p. 14

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NCTM Curriculum Principle “…a well-articulated curriculum gives teachers guidance regarding important ideas or major themes, which receive special attention at different points in time. It also gives guidance about the depth of study warranted at particular times and when closure is expected for particular skills or concepts.” Principles and Standards, p. 16

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A Proposed Solution: Identify Curriculum Focal Points Highlight the most important mathematical ideas for each grade level, preK-8 Describe cohesive clusters of related ideas, concepts, skills, and procedures that form the foundation for higher-level mathematics

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The Process: Defining A Curriculum Focal Point Major mathematical idea for a grade level More than a single objective, standard, expectation, or indicator An important link in the chain of building mathematical understanding, preK-8 Not an element of a list of discrete topics to check off as mastered by students

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The Product: Curriculum Focal Points Three per grade level, preK-8 Often represent multiple content strands Describe the majority of instruction for a specific grade level Taken together across grade levels, provide the major components of a mathematically sound, coherent and cohesive preK-8 curriculum

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The Product: Connections to the Curriculum Focal Points Provide meaningful contexts for the focal points Identify connections between strands and across grade levels Round out a well-balanced curriculum

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The Uses: Curriculum Focal Points and Teachers To design instruction around the question, “What are the most important ideas at my grade level?” To provide information about how ideas at one grade level fit with the important ideas in previous and following grades To prioritize uses of activities, assessments and other published materials

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The Goal: Curriculum Focal Points and Improved Mathematics Education Guidance for schools and states in the design of curricula and assessment that target the most important topics Focus for teachers that gives sufficient time for students to understand concepts and develop and apply skills necessary for future mathematics Clear direction for students and parents on the importance of particular ideas at each grade level

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Center for the Study of Mathematics Curriculum Dr. Barbara J. Reyes

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Publication of State-Level Mathematics Curriculum Standards (as of May 2006) states states states states states states states pre states (FL, 1999)

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Example of Variation in Number of GLEs (grain size) Mean number of GLEs by grade level across all 42 state documents: 47

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At each grade, we recommend a general statement of major goals for the grade. These general goals may specify emphasis on a few strands of mathematics or a few topics within strands. These general goals should be coordinated across all grades, K-8, to ensure curricular coherence and comprehensiveness. Recommendations Identify a small set of primary goals for each grade level.

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Recommendations Limit the number of grade-level learning expectations to focus instruction and deepen learning. The set of learning expectations per grade-level should be manageable given the school year. Along with the statement of general goals and priorities for a particular grade, we suggest that the set of learning expectations per grade be limited to

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Recommendations Develop clear statements of learning expectations focusing on mathematics to be learned. We recommend that learning expectations be expressed succinctly, coherently, and with optimum brevity, limiting the use of educational terms that may not communicate clearly to the intended audience of teachers, school leaders, and parents.

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Recommendations Be clear about the role of technology. Provide guidance within particular learning goals or as part of an overall philosophical statement regarding the role of technology - specifying when it is an appropriate tool for computing and/or developing or representing mathematical ideas.

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The California Mathematics Standards Dr. R. James Milgram

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In California the green dot standards are the focus of most instruction since these topics comprise 85% of the state exams in grades 2 – 7. They were selected by mathematicians, teachers and math educators as the key topics students needed to know

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The Role of the Focus Topics NCTM regards the Focus Topics as a description of how the key elements in an effective curriculum in mathematics should look. But comparing the Focus Topics with most state standards reveals a very poor fit. An exception is California. The Green Dot standards closely align with the Focus Topics. And the emphasis is also about right NCTM recommends 60 – 80% of instruction time be devoted to the focus topics, while 85% of the California assessments in mathematics are on these standards.

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Focus Topics – Numbers

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Focus Topics Fractions

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Focus Topics Fractions, Ratios

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Focus Topics, Algebra, Data

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There are more topics among the green dot standards There are minor differences in the grade levels for different topics between the two documents But there are no substantive differences in the sequencing of the common topics

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And no disagreement that the focus topics are the core subjects that should be given the vast majority of instruction time in K – 8. They should be learned in depth by students as they provide the foundation for all the math and science that follows

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The Quality of U.S. and Florida Math Instruction Compared with Singapore, a Recognized World Leader Dr. Alan Ginsburg

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In fact, U.S. International Math Results Are Below Average At Grade 4 Source: TIMSS 2003 (Mullis, I., Martin, M., Gonzalez, E., and Chrostowski, S. (2004). TIMSS 2003 international mathematics report.

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The U.S. International Math Gap Continues in Grade 8 Source: TIMSS 2003 (Mullis, I., Martin, M., Gonzalez, E., and Chrostowski, S. (2004). TIMSS 2003 international mathematics report.

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Mathematics Are Gateway Courses to College and Jobs COLLEGE. 71 percent of low-income students who took algebra I and geometry went to college, only 27 percent of low-income students who did not take algebra I and geometry went on to college. (U.S. Dept. of Education) JOBS. An applicant for a production associate’s job at a modern automobile plant would have to score roughly 300 points or higher on the NAEP math test to meet company proficiency requirements -- almost half of all 17-year-olds cannot do math at that level. (Murnane & Levy, Teaching the New Basic Skills)

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Is Singapore Too Different from the U.S.? Size: 500,000 Pupils: A little bigger than the Chicago Public Schools and a little smaller than Connecticut. Population: Racially diverse student body: 75% Chinese, 15% Malaysian,and 10 % Indian Work ethic: Singapore students are 2.5 times as likely as U.S. students to receive high-levels of math homework (8 th grade TIMSS).

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Singapore Workers Are Strong on Implementation, Weaker on Innovation “We come from a very conscientious culture. You tell our people what to do, they’ll follow the rules, they’ll do it. The downside is they are not as creative. We fixed that by having a U.S-based R&D team that’s doing more advanced research.” Sim Wong Hoo CEO Creative Technologies Singapore Newsweek Feb. 21, 2005

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Math Standards Should Aim to develop in students a set of desired mathematical proficiencies Logically and clearly organize math topics sequence around the internal logic of mathematics cover a few core math topics in-depth at each grade be specific and clear about content Provide for student diversity in learning math

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Singapore’s Proficiencies Are Centered Around Problem Solving Numbers, Geometry, Statistics, Algebra Computation, Mental Math, Data Analysis Thinking Skills Heuristics

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Singapore Logically Builds-up Math Topics Across Grades: Numbers

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Singapore Logically Builds-up Math Topics Across Grades: Geometry

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Singapore Logically Builds Math Topics Across Grades: Statistics (Note: does not teach probability)

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Singapore Limits Use of Calculators in Early Grades; Florida Does Not Singapore: calculators not allowed grades 1- 6; 2007 will allow calculators grades 5-6. Florida Grade 1: uses calculators to explore addition, subtraction, and skip counting

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Singapore’s Framework Addresses At-risk Students: U.S. State Frameworks (including Florida) Do Not Singapore Identify students for supplementary after-school instruction by a specially-trained teacher (Grade 1+). Weaker math students identified for special track with more math instruction and similar content but at a slower pace (Grades 5-6) Students are streamed based on their Primary School Leaving Exam scores(Grade 7+) U.S. State frameworks don’t differentiate students. Traditionally, compensatory education is often taught by untrained teacher aides. No Child Left Behind holds students to same standards and highly-qualified teachers. No Child Left Behind holds schools rather than students accountable.

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New Directions for Standards: China Integrates Science Into Math to Foster Applications “In math during the middle school and high school period, China tries to link math more closely with science problems. The purposes of this are as follows: To adapt to the increasing tendency of science development. Chinese educators and scientists believe that integration could be one of the developmental directions. To make math more vivid and less boring. Math could not be just logical explanations and abstract signals any longer and might have something to do with everybody’s daily life. To train student scientific spirit. Students shall be prepared to develop creativity and be ready to solve practical problems, not just memorizing this and that. MOE China

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Science Examples Could Support Different Math Strands Geometry: Vectors forces Algebraic equations: F=MA (linear); projectile motion (parabolic) Numbers: Speed of light Statistics and measurement: inquiry science

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Source: A Meaningful Math-Science Example of “Concrete Models & Real-world Problems”

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Singapore’s Relative Strength Is Numbers and Measurement; U.S. Relative Strength is Data and Weakness is Geometry: TIMSS Gr. 8 Source: Mullis et al., 2004

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What We Found At Different Stages of Teacher Development StageSingaporeU.S. Screening of education majors 1 institution with high standards pays students to become teachers Praxis 1 during college Pre-service expectations Approx 12 semester hours math methods Average is one math methods course Certification requirements Completion of course work/no further exam Praxis 2 Induction 20% reductionDiffers by State with full-load common Professional Development Annual target of 100 hours Haphazard prof. devel. Less than 24 hours

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Teacher Preparation to Teach Math: Grades 4 and 8 Source: Mullis et al., 2004

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U.S. Elementary Teacher PRAXIS 2 Sample Questions: 1. Which of the following is equal to a quarter of a million? (A)40,000 (B) 250,000 (C) 2,500,000 (D) 1/4,000,000 (B) (E) 4/1,000, Which of the following fractions is least? (A) 11/10 (B) 99/100 (C) 25/24 (D) 3/2 (E) 501/ On the scale above, the arrow most likely indicates (A) 630½ (B) 635 (C) 660 ½ (D) 670 (E) 685 Source. Ginsburg, Lienwand, Anstrom, and Pollock (2005). What the United States Can Learn From Singapore’s World-Class Mathematics System And What Singapore Can Learn From the United States. Singapore Gr. 6 Exam Is More Difficult Than the U.S. Elementary Teacher PRAXIS 2 Exam

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U.S. Middle School Math Teachers Lack Content-based Professional Development Source: National Longitudinal Study of NCLB: Teacher Survey (2006). U.S. Dept of Education

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Implications and Actions: Bottom Line Our major finding is that the components of Singapore’s system – frameworks,texts, tests and teacher prep – are carefully aligned AND all of these components reflect a higher quality than comparable components in U.S. But there are a few 21 st Century features of the U.S. system that Florida should build upon, but we need to do a better job.

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Adopt highly logical mathematics standards (e.g., Singapore) Define desired student mathematics proficiencies so as to balance mathematics concepts, skills, and strategies Organize standards to clearly and visually portray the sequencing of core mathematics topics across grades Identify fewer mathematics topics per grade and for each topic describe a deeper set of desired mathematics outcomes Sequence mathematical topics across grades to build on prior knowledge rather than repeat topics Consider standards that explicitly recognize the diversity in students’ mathematics performance Leap ahead by incorporating standards that encourage the reinforcement of 21 st Century mathematics proficiencies Implications of Singapore Math for Florida’s Standards Reforms

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Implications of Singapore Math for Reforming Florida’s Mathematics System Standards need to be made instructionally meaningful through aligned textbooks and assessments Teachers will require in-depth professional development in understanding and teaching the deeper mathematics content Consider launching Singapore Math textbook pilots in Florida Benchmarking Promising Practices in highly successful sites to guide improvements

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What was done with this expert information?

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Thinkers Experts from across the nation and representative stakeholders in Florida established a framework for organizing and writing the new mathematics standards September 18 – 19, 2006 STEM Professionals Mathematics Educators (K-20) District Administrators Special Interests (Parents, ELL, ESE, etc)

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What We Need A blueprint for the development of Florida’s new mathematics standards. Standards that will: Lead the nation Prepare students for future success in the workforce they will become a part of Be specific enough to guide the development of rigorous and relevant curriculum and the implementation of rigorous and relevant instruction Be specific and comprehensive enough to develop valid and reliable assessment Lead to the increase in the number of high school graduates that become engineers, scientists, mathematicians, and the problem solvers of the future

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What is the goal for Florida’s standards? The “Thinkers” group agreed that the goal for the “Doers” is the development of “World- Class” standards which will guide instruction, teacher professional development, and the selection of instructional materials.

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Thinkers Consensus Consensus on framework is as follows: Standards drive everything! Standards will be divided into sections K-7 by grade level 8th grade standards with promotion of Algebra I, with Algebra and up written by discipline

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Guidance for K-7 Writing Team Start with the NCTM Focal Points No more than 5 GLEs will relate to each focal point Use the current GLEs to map our current standards to the Focal Points Continuously assess for overlap, continuity, and gaps in content

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Guidance for HS Writing Team Develop standards based on content areas Example:Algebra I, Geometry, Algebra II, Trigonometry, Mathematical Analysis, Linear Algebra, Probability and Statistics, AP Probability and Statistics, Calculus “Big Ideas” are to guide the development of standards Keep in mind the articulation requirements for college and work

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Writers will use examples throughout this process of top-rated standards states such as Indiana, Massachusetts, California and international examples including top-rated Singapore to compare rigor, focus, and specificity and showing progression of content

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Algebra and up will be written while evaluating California and Indiana standards (who take the same approach), College Board comments, and Achieve.org data which describes what a graduate needs to proceed into college without any remediation

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Next Steps The work of the “Doers” will be reviewed by stakeholders through an online system and by the “Thinkers” during a final meeting before it is submitted for State Board Approval

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Next Steps Teacher/Professional Development on the new math standards will be implemented over a 3-year period This teacher training track will line up with the earliest possible implementation of the FCAT, allowing students at grade K to receive instruction based upon the new standards throughout their education

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LET’S DO THIS!

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