2. Math Testing as it exists in S. C. now PACT PACT Grades 3 through 8 Grades 3 through 8 Standards-based Standards-based Used to measure academic progress Used to measure academic progress HSAP Required for graduation EOCEP End-of-Course Examination Program Algebra I / Math Tech II 20% of final course grade

3. What’s the difference? PACT (Grades 3 through 8) PACT (Grades 3 through 8) Five strands Five strands Numbers and Operations Numbers and Operations Algebra Algebra Geometry Geometry Measurement Measurement Data analysis and probability Data analysis and probability HSAP (2 nd year of High school) Five strands Numbers and Operations Algebra Measurement and Geometry Data Analysis and Probability Integrated Response (may address one or more of the above strands)

4. What’s the difference? HSAP (taken in the second year of high school) HSAP (taken in the second year of high school) Numbers and Operations Numbers and Operations Algebra Algebra Measurement and Geometry Measurement and Geometry Data Analysis and Probability Data Analysis and Probability Integrated Response (may address one or more of the above strands) Integrated Response (may address one or more of the above strands) Algebra I/Math Tech II EOCEP (taken at the end of Algebra I or the end of Math Tech II) Understanding functions Linear functions Quadratic and other functions

5. What’s the difference? HSAP (taken in the second year of high school) HSAP (taken in the second year of high school) Numbers and Operations Numbers and Operations Algebra Algebra Measurement and Geometry Measurement and Geometry Data Analysis and Probability Data Analysis and Probability Integrated Response (may address one or more of the above strands) Integrated Response (may address one or more of the above strands) Geometry Geometric Structure Geometric Patterns Geometry of Location Geometry of Size Geometry of Shape Other math courses Check your course standards

6. Today’s Focus Information about HSAP Information about HSAP Location of resources Location of resources The link between EOCEP (Algebra I) and HSAP The link between EOCEP (Algebra I) and HSAP What can I do to improve my students’ scores on HSAP? What can I do to improve my students’ scores on HSAP?

7. What types of items are on the HSAP mathematics test? Multiple-Choice (1 pt. each) Multiple-Choice (1 pt. each) Items with four options each will assess the content in Number and Operations, Algebra, Measurement and Geometry, and Data Analysis and Probability. Items with four options each will assess the content in Number and Operations, Algebra, Measurement and Geometry, and Data Analysis and Probability.

8. What types of items are on the mathematics test? Integrated-Response (3 pts.each) Integrated-Response (3 pts.each) These items are designed to integrate the expectations of Number and Operations, Algebra, Measurement and Geometry, and Data Analysis and Probability. These items are designed to integrate the expectations of Number and Operations, Algebra, Measurement and Geometry, and Data Analysis and Probability. These questions ask students to show their work and/or write an explanation to support their answers. These questions ask students to show their work and/or write an explanation to support their answers.

9. What materials are students allowed to use during the test? Each student will be given: Each student will be given: a reference sheet with formulas a reference sheet with formulas a sheet of graph paper for scratch work a sheet of graph paper for scratch work the test booklet the test booklet

10. Can students use calculators during the mathematics test? Students may use calculators during the mathematics test. Students may use calculators during the mathematics test. However, the test questions were written so that they do not require a calculator! However, the test questions were written so that they do not require a calculator!

11. What kinds of calculators may be used? Test takers may use the following types of calculators: Test takers may use the following types of calculators: 4-function 4-function Scientific Scientific graphing graphing Test takers may not use: Test takers may not use: pocket organizers pocket organizers Palm Pilots Palm Pilots handheld PCs that use a writing tablet or QWERTY keyboard handheld PCs that use a writing tablet or QWERTY keyboard calculators that use symbolic manipulation capability calculators that use symbolic manipulation capability Casio FX 2.0 Casio FX 2.0 Hewlett Packard HP 40g or 49g Hewlett Packard HP 40g or 49g Texas Instruments TI-89 or TI-92 Texas Instruments TI-89 or TI-92 calculators that talk or otherwise make noise, such as the AudioCalc calculators that talk or otherwise make noise, such as the AudioCalc

12. The Scoring Process Multiple choice scoring Multiple choice scoring Computer scored by contractor Computer scored by contractor Integrated response scoring Integrated response scoring Scores based on rubric Scores based on rubric Rangefinding Rangefinding Scorer Training Scorer Training Hand Scoring Hand Scoring

13. Integrated Response Scoring Rubric 3 points  Addresses all parts of the task appropriately.  Provides thorough evidence of the student’s knowledge, strategy, and execution (including concepts, techniques, and representations) to meet the intent of the task.  May contain execution errors that do not detract from the overall correct completion of the task.  Clearly communicates the student’s mathematical thinking.

14. Scoring Rubric (cont…) 2 points  Addresses most parts of the task appropriately.  Provides adequate evidence of the student’s knowledge, strategy, and execution (including concepts, techniques, and representations) to meet the intent of the task.  May contain execution errors that do detract from the overall correct completion of the task.  Adequately communicates the student’s mathematical thinking.

15. Scoring Rubric (cont…) 1 point  Addresses some part(s) of the task appropriately.  Provides some evidence of the student’s knowledge, strategy, and execution (including concepts, techniques, and representations) to meet the intent of the task.  Contains an attempt to accomplish some part of the task with little success.  Minimally communicates the student’s mathematical thinking.

16. Scoring Rubric (cont…) 0 points  There is no evidence of mathematical knowledge that is appropriate to the intent of the task.

17. Constructed Response

19. PaperScoreNotes A-13In Part A, the student arrives at the correct answer, with supporting work. He cross multiplies to find the discount and then subtracts it from the regular price. In Part B, the student has a correct answer, with supporting work; he finds the discount and subtracts it from the sales price. In Part C, the student arrives at the correct answer by taking his Part B answer, finding the sales tax, and adding it back to his Part B answer.

21. PaperScoreNotes A-102In Part A, the student arrives at an incorrect answer, with supporting work. He finds the discount, but does not subtract it from the regular price (error that detracts). In Part B, the student has an incorrect answer, with supporting work; he follows through with his Part A answer ($30), finds the discount but does not subtract it from the sales price (error that detracts). In Part C, the student has an incorrect answer; he takes his Part B answer ($3), finds the sales tax, and adds it back to $3.

23. Paper Score Notes A-3 1 The student’s Part A answer and work are correct. He leaves Parts B and C blank.

25. Paper Score Notes A-4 0 The student’s Part A answer is incorrect with no work shown. He leaves Parts B and C blank.

26. Spring 2006 Operational Rank of Domains by student performance StrandPerformance% Total % not adequate Number and Operations (N) Needs improvement 22% 45% May need improvement 23% adequate55% Algebra (A) Needs improvement 10 % 49% May need improvement 39 % adequate 51 % Measurement and Geometry (MG ) Needs improvement 21 % 57% May need improvement 36 % adequate 43 % Data and Probability (DP) Needs improvement 10 % 47% May need improvement 37 % adequate 53 % #1 #2 #1 #2 } } } } #1

33. Links on www.ed.sc.gov Curriculum Standards Course Standards Rubrics Calculator Policy (and how to clear calculators for HSAP) Math HSAP Test Blueprint Algebra I (Math Tech II) EOCEP Blueprint Reference Sheet Practice Test & Key (“Prototype”) and release items Descriptions of Achievement Levels (Below Basic, Basic, Proficient, Advanced)

34. In many schools today…. Many (most?) students take Math Tech II (or Algebra IB) in their second year of high school. Many (most?) students take Math Tech II (or Algebra IB) in their second year of high school. This means that many (most?) students take the EOCEP the same year that they take HSAP. This means that many (most?) students take the EOCEP the same year that they take HSAP.

35. What are the expectations of HSAP? Students should… Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Compute with rational numbers and make reasonable estimates in applied situations. Compute with rational numbers and make reasonable estimates in applied situations. Understand and apply patterns, relations, and functions. Understand and apply patterns, relations, and functions. Represent, analyze, and model situations using mathematical structures and algebraic symbols. Represent, analyze, and model situations using mathematical structures and algebraic symbols.

36. Expectations (cont.) Apply appropriate techniques, tools, and formulas to determine measurements and solve problems. Apply appropriate techniques, tools, and formulas to determine measurements and solve problems. Analyze characteristics and properties of two- and three-dimensional geometric shapes, understand geometric relationships, and apply spatial reasoning using coordinate geometry. Analyze characteristics and properties of two- and three-dimensional geometric shapes, understand geometric relationships, and apply spatial reasoning using coordinate geometry. Use appropriate statistical methods to analyze data and apply basic concepts of probability. Use appropriate statistical methods to analyze data and apply basic concepts of probability.

37. Characteristics of HSAP Standards based Standards based 62 Multiple Choice items (1 point each for a total of 62 points) 62 Multiple Choice items (1 point each for a total of 62 points) Three Integrated Response items (3 points each for a total of nine points) Three Integrated Response items (3 points each for a total of nine points) Untimed Untimed Scores reported as Level 1(below basic), 2(basic), 3(proficient), or 4(advanced) Scores reported as Level 1(below basic), 2(basic), 3(proficient), or 4(advanced) Students scoring at level 1 have not met requirements for graduation. Students scoring at level 1 have not met requirements for graduation.

38. HSAP Test Blueprint – Mathematics Number and Operations 15–16 points Number and Operations 15–16 points N 1: The student will understand numbers, ways of representing numbers, relationships among numbers, and number systems. N 1: The student will understand numbers, ways of representing numbers, relationships among numbers, and number systems. N 2: The student will compute with rational numbers and make reasonable estimates in applied situations. N 2: The student will compute with rational numbers and make reasonable estimates in applied situations. Algebra 19–20 points Algebra 19–20 points A 1: The student will understand and apply patterns, relations, and functions. A 1: The student will understand and apply patterns, relations, and functions. A 2: The student will represent, analyze, and model situations using mathematical structures and algebraic symbols. A 2: The student will represent, analyze, and model situations using mathematical structures and algebraic symbols. Measurement and Geometry 19–20 points Measurement and Geometry 19–20 points MG 1: The student will apply appropriate techniques, tools, and formulas to determine measurements and solve problems. MG 1: The student will apply appropriate techniques, tools, and formulas to determine measurements and solve problems. MG 2: The student will analyze characteristics of two- and three-dimensional geometric shapes, understand geometric relationships, and apply spatial relationships using coordinate geometry. MG 2: The student will analyze characteristics of two- and three-dimensional geometric shapes, understand geometric relationships, and apply spatial relationships using coordinate geometry. Data Analysis and Probability8 points Data Analysis and Probability8 points DP 1: The student will use appropriate statistical methods to analyze data and apply basic concepts of probability. DP 1: The student will use appropriate statistical methods to analyze data and apply basic concepts of probability. Integrated Response Questions9 points Integrated Response Questions9 points Total: 71 points

39. Purposes of EOCEP Promote instruction, encourage student achievement, and document the level of mastery of curriculum standards Serve as indicators of program, school, and school-district effectiveness Be weighted 20% in the determination of students’ final grades in these classes

40. Characteristics of the EOCEP Standards-basedMultiple-choice 50 to 60 items long, depending upon subject Untimed, but about 90 minutes is the estimated administration time Grades expressed on the State Uniform Grading Scale

42. So, how do we teach it all? Some things are obvious: “Apply the commutative, associative, distributive, equality, and identity properties, including order of operations, to simplify mathematical expressions, equations, and inequalities.” (HSAP, Numbers and Operations)

43. Look at the HSAP Blueprint and the course standards for Algebra I EOCEP: “Apply the commutative, associative, distributive, equality, and identity properties, including order of operations, to simplify mathematical expressions, equations, and inequalities.” (HSAP) “Use the commutative, associative, and distributive properties to simplify algebraic expressions.” (Alg I EOCEP)

44. So, how do we teach it all? Some things are not so obvious: Add, subtract, multiply and divide fractions, decimals, percents, integers. (HSAP N2.1 on the Blue Print) There is not a standard like this in the course standards!!

45. First we need to identify which skills are “duplicates” (that is, are covered in both HSAP and in your course standards) Then we will look for gaps

46. Start Getting “In Your Head” What You Have to Teach. Working in pairs or small groups, look at the HSAP Blueprint (blue sheets) and at the SC Course Standards for your course (salmon sheets) to find the shared areas. Write the standard number in the box next to the skill on the blueprint.

47. Now you know which HSAP topics you already address in your course. So what about all of those HSAP “point-earning” bullets that you do not have assigned to any course standards?

48. So, how do we teach it all? Some educators call this scaffolding You can teach = 3 by teaching it as a fraction and as division. –As a matter of fact, the link between division and fractions could be taught/reviewed often as this is a common weak area. You can teach most operations (including converting from one form to another) while solving equations. x 12

49. HSAP + EOCEP Choose from the HSAP Blueprint a bullet that is not addressed in the Algebra I Standards. Decide how you could integrate teaching that skill with one of your course standards. Write a mini-lesson (or lesson outline) that you could use to weave the HSAP skill into a topic in your course. Use a piece of large post-it paper to post your “lesson plan” on the wall.

50. Harriet Pritchard hpritcha@ed.sc.gov Buck F. Brown Bfbrown@ed.sc.gov