Georgia Performance Standards

1. Georgia Performance Standards Aug. 24, 2005

2. The previous Georgia curriculum:Quality Core Curriculum (QCCs) 1986 Quality Basic Education (QBE) Act of 1986 led to the establishment of the Quality Core Curriculum (QCC). 1995 A major revision of the QCCs was undertaken. 2001 The Georgia State Board of Education requested an audit of Georgia’s Quality Core Curriculum. Phi Delta Kappa conducted the audit and found that in several areas the curriculum lacked rigor and was inadequate to guide teaching and to ensure common expectations for all students.

3. Why new standards? In 2002, an external (Phi Delta Kappa) audit concluded that the QCCs were lacking: • too many topics • too little depth • did not meet national standards • could not be covered in a reasonable amount of time (would take twenty-three years—not twelve—to cover the topics in any depth)

4. GDOE was charged with addressing the following concerns • The curriculum needs to be rigorous—more than “an inch deep.” • The curriculum needs to be more focused—less than a “mile wide.” • The curriculum needs to be clearer and more specific about what students are expected to know and be able to do. • Instruction need to be student-centered rather than teacher-centered so that educators can focus on what students are learning.

5. Why an integrated approach in high school? • Integrated approaches are used in most other parts of the world. • Separation is artificial and doesn’t start until Algebra I. • Integration encourages connections between mathematical ideas. • All of Algebra I and part of Geometry are finished by Grade 8, so traditional courses wouldn’t work.

6. Georgia Performance Standards Here’s the official Georgia Department of Education introduction: • Introductory Video

7. Comparison of the Old/New Curriculum

8. Just the numbers . . .

9. Comparing GPS to the QCCs GPS often requires • higher level in Bloom’s Taxonomy (knowledge, comprehension, application, analysis, synthesis, evaluation) • or requires conceptual AND procedural knowledge (Hiebert). GPS are clearer or more specific about what is expected. Difference between laddered and spiral curriculum is evident. Important content (for example, in 6th grade nets, sketches of solid figures) is added. Data analysis and probability strand is strengthened.

10. Social Studies Example QCC, Grade 8 • 14Topic: Influential People • Standard:Identifies well-known and influential Georgians from the colonial era (men, women and minorities). GPS, Grade 8 SS8H2 The student will analyze the colonial period of • Georgia’s history • explain the importance of James Oglethorpe, the Charter of 1732, reasons for settlement (charity, economics, and defense) Tomochichi, Mary Musgrove, and the city of Savannah • evaluate the Trustee Period of Georgia’s colonial history emphasizing the role of the Salzburgers, Highland Scots, malcontents, and the Spanish threat from Florida • explain the development of Georgia as a royal colony with regard to land ownership, slavery, government and the impact of the royal governors

11. QCC: Topic: Integers Standard: Computes with integers using models, manipulatives, and/or rules. Topic: Whole Numbers, Fractions, Decimals, Computation, Problem Solving Standard: Uses addition, subtraction, multiplication, and division (interpreting remainders in context of problem) in computation and problem solving with whole numbers, fractions, and decimals. GPS: M7N1. Students will understand the meaning of positive and negative numbers including rational numbers and will compute with them. a. Find the absolute value of a number and understand it as the distance from the origin on a number line. b. Compare and order rational numbers including repeating decimals. c. Add, subtract, multiply and divide positive and negative rational numbers. d. Solve problems using rational numbers. Note the level of thinking required in each. Note the emphasis on conceptual understanding. Note how the organization helps you identify connected concepts. Note the differences in specificity. Example 1:7th Grade Integers & Computation

12. Example 2:Relations & Functions QCC Algebra I: Topic: Connections, Patterns, and Functions 5   Standard: Connects patterns to the concept of function and uses patterns, relations, and functions to solve problems. 6   Topic: Patterns and Functions Standard: Distinguishes between relations and functions, and identifies the domain and range. Has these two objectives under this topic, along with two on solving equations and nine on linear equations in two variables. All are in a list of 37. M8A3. Students will understand relations and linear functions. a. Recognize a relation as a correspondence between varying quantities. b. Recognize a function as a correspondence between inputs and outputs where the output for each input must be unique. c. Distinguish between relations that are functions and those that are not functions. d. Recognize functions in a variety of representations and a variety of contexts. e. Use tables to describe sequences recursively and with a formula in closed form. f. Understand and recognize arithmetic sequences as linear functions with whole number input values. Note the level of thinking required in each. Note how the organization helps you identify connected concepts. Note the differences in specificity.

13. Example 3:Data Analysis QCC: Algebra I, Topic: Probability 36 Identifies possible outcomes of simple experiments and predicts or describes the probability of a given event expressed as a rational number from 0 through 1. 37 Conducts and interprets a compound probability experiment. GPS: 8th Math M8D2. Students will determine the number of outcomes related to a given event. a. Use tree diagrams to find the number of outcomes. b. Apply the addition and multiplication principles of counting. M8D3. Students will use the basic laws of probability. a. Find the probability of simple independent events. b. Find the probability of compound independent events. Note the level of thinking required in each. Note how the organization helps you identify connected concepts. Note the differences in specificity.

14. Comparing GPS to the QCCs GPS often requires • higher level in Bloom’s Taxonomy (knowledge, comprehension, application, analysis, synthesis, evaluation) • or requires conceptual AND procedural knowledge (Hiebert). GPS are clearer or more specific about what is expected. Difference between laddered and spiral curriculum is evident. Important content (for example, in 6th grade nets, sketches of solid figures) is added. Data analysis and probability strand is strengthened.

15. Process of Developing GPS • Two years ago, teacher teams were enlisted to write GPS. • Writing teams drew on strengths of Japanese curriculum and North Carolina standards. • Teachers produced a draft, which was made public for feedback. • K-8 GPS approved in May 2004.

16. Process of Developing GPS • The Middle School Review Team consisted of three people who met three times. • Middle School portion was approved in spring 2004. • Because the new integrated high school curriculum was so different from the QCC, a group was formed to review it. • High School Mathematics Advisory Committee included teacher writing team members, curriculum supervisors, and higher education faculty (mathematics, mathematics education, and statistics). The group met five times during 2004-2005. • The 9-12 GPS was approved by the BOE in May 2005.

18. Tasks for Georgia Performance Standards

19. From the Executive Summary: • A performance standard has four components: • a content standard, • illustrative tasks, • examples of student work, and • a commentary for teachers. • Together, these components will be the teacher’s guide as to what to teach, how thoroughly to treat a topic, and what some instances of student work that meet the content standard might look like.

20. What are tasks? • A mathematical problem or series of problems that provide an opportunity for students to demonstrate their conceptual knowledge. • Tasks may take minutes or days. • Tasks may be used for a variety of purposes including classwork or assessment.

21. Purpose of Tasks? • Fewer topics, together with sample tasks, student work, and commentary, • provide clear expectations for student performance, • guide instruction, and • allow for a careful alignment of instruction and assessment.

22. What’s in the Teacher Commentary? • Documentation of which parts of the problem assess which standards • Analysis of student work • May also include • Extensions • Notes to the teacher • Suggestions about technology or manipulative use.

23. Process • Committees are working on drafts of the sets of tasks for each grade level or course. • Committees include teachers, mathematicians, mathematics teacher educators, curriculum specialists, and system office mathematics specialists.

24. The challenge? • To pose tasks that give students opportunities to demonstrate their deep understanding. • To provide tasks for instruction or assessment. • Tasks may begin with procedural knowledge, but push towards conceptual or higher levels of Bloom’s taxonomy. • Tasks emphasize connections across mathematics topics. • Tasks encourage use of process standards.

25. An Example Here are two of the 6th GPS: a. Apply factors and multiples. c. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers. • Imagine the typical textbook question. • Take a minute to imagine a question that will help you learn more about the depth of that student’s understanding. Share it with a colleague.

26. Here are two questions from the related 6th Grade Task: • Find the prime factorization of 24. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Find their prime factorizations and compare them to the prime factorization of 24. What do you notice? • The number 5 and another number less than 40 have a least common multiple of 40. What could the other number be? Could there be other answers? If so, list as many as you can.

27. Where are we now? • 6th grade tasks are on the web listed at the end of the standards. • Committees are working on tasks at other grade levels. During the next school year, the emphasis will be on getting sample student work and writing commentaries about them. • At Rock Eagle, check for sessions on tasks for your grade level or courses.

28. Sources of similar problems • New York City Standards • NAEP items • TIMSS problems • FCAT (Florida) problems • More on Performance Assessment Tasks: http://www.aea267.k12.ia.us/cia/ framework/tasks/writing/index.html

30. GPS MATHEMATICS Implementation Plan

31. Textbooks • For grades 6-8, our current textbooks cover most of the GPS, although some supplementing of the textbooks will be necessary. • For grades 9-12, publishers are already expressing interest in preparing textbooks for Georgia’s integrated curriculum.

33. Mathematics Curriculum Timeline

35. Are: Georgia Performance Standards (GPS) What students are to learn, know, and understand An expression of clear expectations for performance A curriculum document Fewer in number Application of content Are Not: New Quality Core Curriculum (QCC) How teachers are to teach Comprehensive school reform An instructional handbook A checklist of objectives Coverage of content Performance Standards. . .

36. Spiral vs. Ladder Curriculum With the Georgia Performance Standards, we are creating a ladder style curriculum that expects mastery of topics - as opposed to our current spiral curriculum, which contains constant review in each grade. This is extremely important – especially in math and science.

37. Spiral vs. Ladder Curriculum “This long duration means that U.S. states include many more topics at each grade than do [high performing] countries. That, in turn, means each topic is addressed in less depth. In general, the state standards increase the duration of a typical topic by introducing it at an earlier grade. For instance, even more demanding topics such as geometric transformations, measurement error, three-dimensional geometry, and functions are introduced as early as first grade. In the [highest performing] countries, these same topics are first covered in middle school.” -Professor William H. Schmidt, Michigan State University Source: A Coherent Curriculum: The Case of Mathematics, Summer 2000 issue of American Educator

38. Characteristics of GPS in Middle Grades • In grade 6, the curriculum begins to address traditional topics from algebra and geometry. • From grade 7 on, the curriculum has four content strands: • number and operations, • geometry, • algebra, and • data analysis and probability. • What strand ends here? Why? • By the end of grade 8, the student will have completed the equivalent of traditional first-year algebra and much of the traditional geometry course.

39. Characteristics (cont.) • In the past, very little new content was introduced in middle grades, making it easy for students to skip a course. • In the new curriculum, new content topics are introduced in every grade in middle school, making it impossible to justify skipping any course. • Acceleration of students with exceptional mathematical talent should be achieved by differentiation, as opposed to skipping or compressing courses. • The rigor of the middle school curriculum allows all students to take in high school the courses they need to enter college.

40. Assessment • The GPS establishes the minimum standards, and does not prohibit systems, schools, or teachers from adding material to it. • GPS will be tested by the Criterion-Referenced Competency Test (CRCT) and the Georgia High School Graduation Test (GHSGT). • Both tests will immediately begin revisions. By the 2nd year of phase-in, both tests will be aligned to GPS. Tasks will be used to design tests.

41. Timeline What other middle school subjects will implement this year? When will you start teaching those students who have been through the GPS in the year before?

42. Sixth Grade Teachers are Heroes!