Math Testing as it exists in Math Testing as it exists in S. C. nowS. C. now

PACTPACT Grades 3 through Grades 3 through

88 Standards-based Standards-based Used to measure Used to measure

academic progressacademic progress

HSAPHSAP Required for Required for

graduationgraduation

EOCEPEOCEP End-of-Course End-of-Course

Examination Examination Program Program

Algebra I / Math Algebra I / Math Tech IITech II

20% of final course 20% of final course gradegrade

What’s the difference?What’s the difference? PACT PACT (Grades 3 (Grades 3

through 8)through 8) Five strandsFive strands

Numbers and Numbers and OperationsOperations

AlgebraAlgebra Geometry Geometry MeasurementMeasurement Data analysis Data analysis

and and probabilityprobability

HSAP HSAP (2(2ndnd year of High year of High school)school) Five strandsFive strands

Numbers and Numbers and OperationsOperations

AlgebraAlgebra Measurement and Measurement and

GeometryGeometry Data Analysis and Data Analysis and

ProbabilityProbability Integrated Response Integrated Response

(may address one or (may address one or moremore of the above of the above strands)strands)

What’s the difference?What’s the difference? HSAP HSAP (taken in the (taken in the

second year of high second year of high school)school) Numbers and Numbers and

OperationsOperations AlgebraAlgebra Measurement Measurement

and Geometryand Geometry Data Analysis Data Analysis

and Probabilityand Probability Integrated Integrated

Response (may Response (may address one or address one or moremore of the of the above strands)above strands)

Algebra I/Math Algebra I/Math Tech II EOCEPTech II EOCEP (taken at the end of (taken at the end of Algebra I or the end of Algebra I or the end of Math Tech II)Math Tech II) Understanding Understanding

functionsfunctions Linear functionsLinear functions Quadratic and Quadratic and

other functionsother functions

What’s the difference?What’s the difference? HSAP HSAP (taken in the (taken in the

second year of high school)second year of high school) Numbers and Numbers and

OperationsOperations AlgebraAlgebra Measurement and Measurement and

GeometryGeometry Data Analysis and Data Analysis and

ProbabilityProbability Integrated Response Integrated Response

(may address one or (may address one or moremore of the above of the above strands)strands)

Geometry Geometry Geometric StructureGeometric Structure Geometric Patterns Geometric Patterns Geometry of Geometry of

LocationLocation Geometry of SizeGeometry of Size Geometry of Shape Geometry of Shape

Other math Other math coursescourses

Check your course Check your course standardsstandards

Today’s FocusToday’s Focus

Information about HSAPInformation about HSAP Location of resourcesLocation of resources The link between EOCEP The link between EOCEP

(Algebra I) and HSAP(Algebra I) and HSAP What can I do to improve my What can I do to improve my

students’ scores on HSAP?students’ scores on HSAP?

What types of items are What types of items are on the HSAP on the HSAP

mathematics test?mathematics test?• Multiple-Choice (1 pt. each)Multiple-Choice (1 pt. each)

• Items with four options Items with four options each will assess the content each will assess the content in Number and Operations, in Number and Operations, Algebra, Measurement and Algebra, Measurement and Geometry, and Data Geometry, and Data Analysis and Probability.Analysis and Probability.

What types of items are What types of items are on the mathematics test?on the mathematics test?• Integrated-Response (3 pts.each)Integrated-Response (3 pts.each)

• These items are designed to These items are designed to integrate the expectations of integrate the expectations of Number and Operations, Algebra, Number and Operations, Algebra, Measurement and Geometry, and Measurement and Geometry, and Data Analysis and Probability. Data Analysis and Probability.

• These questions ask students to These questions ask students to show their work and/or write an show their work and/or write an explanation to support their explanation to support their answers.answers.

What materials are What materials are students allowed to use students allowed to use

during the test? during the test? • Each student will be given:Each student will be given:

• a reference sheet with a reference sheet with formulasformulas

• a sheet of graph paper for a sheet of graph paper for scratch workscratch work

• the test bookletthe test booklet

Can students use Can students use calculators during the calculators during the

mathematics test?mathematics test?• Students may use Students may use calculators during the calculators during the mathematics test. mathematics test.

• However, the test However, the test questions were written so questions were written so that they do not that they do not requirerequire a a calculator!calculator!

What kinds of calculators What kinds of calculators may be used?may be used?

Test takers may use the following types Test takers may use the following types of calculators: of calculators: 4-function4-function ScientificScientific graphinggraphing

Test takers Test takers may notmay not use: use: pocket organizerspocket organizers Palm PilotsPalm Pilots handheld PCs that use a writing tablet or QWERTY handheld PCs that use a writing tablet or QWERTY

keyboardkeyboard calculators that use symbolic manipulation calculators that use symbolic manipulation

capabilitycapability Casio FX 2.0Casio FX 2.0 Hewlett Packard HP 40g or 49gHewlett Packard HP 40g or 49g Texas Instruments TI-89 or TI-92Texas Instruments TI-89 or TI-92 calculators that talk or otherwise make noise, such as calculators that talk or otherwise make noise, such as

the AudioCalcthe AudioCalc

The Scoring ProcessThe Scoring Process

Multiple choice scoringMultiple choice scoring• Computer scored by contractorComputer scored by contractor

Integrated response scoringIntegrated response scoring• Scores based on rubricScores based on rubric• RangefindingRangefinding• Scorer TrainingScorer Training• Hand ScoringHand Scoring

Integrated Response Integrated Response Scoring RubricScoring Rubric

3 points3 points Addresses all parts of the task appropriately.Addresses all parts of the task appropriately. Provides thorough evidence of the student’s Provides thorough evidence of the student’s

knowledge, strategy, and execution knowledge, strategy, and execution (including concepts, techniques, and (including concepts, techniques, and representations) to meet the intent of the representations) to meet the intent of the task.task.

May contain execution errors that do not May contain execution errors that do not detract from the overall correct completion detract from the overall correct completion of the task.of the task.

Clearly communicates the student’s Clearly communicates the student’s mathematical thinking.mathematical thinking.

Scoring Rubric Scoring Rubric (cont…)(cont…)

2 points2 points Addresses most parts of the task Addresses most parts of the task

appropriately.appropriately. Provides adequate evidence of the student’s Provides adequate evidence of the student’s

knowledge, strategy, and execution (including knowledge, strategy, and execution (including concepts, techniques, and representations) to concepts, techniques, and representations) to meet the intent of the task.meet the intent of the task.

May contain execution errors that do detract May contain execution errors that do detract from the overall correct completion of the from the overall correct completion of the task.task.

Adequately communicates the student’s Adequately communicates the student’s mathematical thinking.mathematical thinking.

Scoring Rubric Scoring Rubric (cont…)(cont…)

1 point1 point Addresses some part(s) of the task Addresses some part(s) of the task

appropriately.appropriately. Provides some evidence of the student’s Provides some evidence of the student’s

knowledge, strategy, and execution knowledge, strategy, and execution (including concepts, techniques, and (including concepts, techniques, and representations) to meet the intent of the representations) to meet the intent of the task.task.

Contains an attempt to accomplish some Contains an attempt to accomplish some part of the task with little success.part of the task with little success.

Minimally communicates the student’s Minimally communicates the student’s mathematical thinking.mathematical thinking.

Scoring Rubric Scoring Rubric (cont…)(cont…)0 points0 points

There is no evidence of There is no evidence of mathematical knowledge that is mathematical knowledge that is appropriate to the intent of the appropriate to the intent of the task.task.

Constructed ResponseConstructed ResponseConstructed Response

78) Lacy’s Department Store marked coats down 40% during a sale.

a) If Janice bought a coat that regularly cost $75.00, what was the sale price of the coat before sales tax? Show your work to support your answer.

Answer:

b) Janice found a coupon for an additional 10% off the sale price. If she used the coupon during the sale, how much did the coat cost before the sales tax was added? Show your work to support your answer.

Answer:

c) If Janice used the coupon and paid sales tax of 6%, what was the total cost of the coat on sale? Show your work to support your answer.

Answer:

Paper

Score

Notes

A-1 3 In 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.

Paper

Score

Notes

A-10 2 In 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.

Paper Score

Notes

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

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.

Spring 2006 Operational Rank of Spring 2006 Operational Rank of Domains by student performanceDomains by student performance

StrandStrand PerformancePerformance %% Total % not Total % not adequateadequate

Number and Number and Operations (N)Operations (N)

Needs improvementNeeds improvement 22%22%45%45%

May need improvementMay need improvement 23%23%

adequateadequate 55%55%

Algebra (A)Algebra (A) Needs improvementNeeds improvement 10 %10 %49%49%

May need improvementMay need improvement 39 %39 %

adequateadequate 51 %51 %

Measurement Measurement and Geometry and Geometry (MG(MG))

Needs improvementNeeds improvement 21 %21 %57%57%

May need improvementMay need improvement 36 %36 %

adequateadequate 43 %43 %

Data and Data and Probability Probability (DP)(DP)

Needs improvementNeeds improvement 10 %10 %47%47%

May need improvementMay need improvement 37 %37 %

adequateadequate 53 %53 %

#1

#2

#1

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}

}

}

} #2

#1

Links on www.ed.sc.govLinks 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)

In many schools today….In many schools today….

Many (most?) students take Many (most?) students take Math Tech II (or Algebra IB) Math Tech II (or Algebra IB) in their second year of high in their second year of high school.school.

This means that many This means that many (most?) students take the (most?) students take the EOCEP the same year that EOCEP the same year that they take HSAP.they take HSAP.

What are the expectations of What are the expectations of HSAP?HSAP?Students should…Students should… Understand numbers, ways of representing Understand numbers, ways of representing

numbers, relationships among numbers, numbers, relationships among numbers, and number systems. and number systems.

Compute with rational numbers and make Compute with rational numbers and make reasonable estimates in applied situations.reasonable estimates in applied situations.

Understand and apply patterns, relations, Understand and apply patterns, relations, and functions.and functions.

Represent, analyze, and model situations Represent, analyze, and model situations using mathematical structures and using mathematical structures and algebraic symbols.algebraic symbols.

Expectations (cont.)Expectations (cont.) Apply appropriate techniques, tools, and Apply appropriate techniques, tools, and

formulas to determine measurements formulas to determine measurements and solve problems.and solve problems.

Analyze characteristics and properties Analyze characteristics and properties of two- and three-dimensional of two- and three-dimensional geometric shapes, understand geometric shapes, understand geometric relationships, and apply geometric relationships, and apply spatial reasoning using coordinate spatial reasoning using coordinate geometry.geometry.

Use appropriate statistical methods to Use appropriate statistical methods to analyze data and apply basic concepts of analyze data and apply basic concepts of probability.probability.

Characteristics of HSAPCharacteristics of HSAP Standards basedStandards based 62 Multiple Choice items (1 point each for 62 Multiple Choice items (1 point each for

a total of 62 points)a total of 62 points) Three Integrated Response items (3 Three Integrated Response items (3

points each for a total of nine points)points each for a total of nine points) UntimedUntimed Scores reported as Level 1(below basic), Scores reported as Level 1(below basic),

2(basic), 3(proficient), or 4(advanced)2(basic), 3(proficient), or 4(advanced) Students scoring at level 1 have not met Students scoring at level 1 have not met

requirements for graduation.requirements for graduation.

HSAP Test Blueprint – MathematicsHSAP Test Blueprint – Mathematics Number and Operations Number and Operations 15–16 points15–16 points

N 1: The student will understand numbers, ways of representing N 1: The student will understand numbers, ways of representing numbers, relationships among numbers, and number systems.numbers, relationships among numbers, and number systems.

N 2: The student will compute with rational numbers and make N 2: The student will compute with rational numbers and make reasonable estimates in applied situations.reasonable estimates in applied situations.

Algebra Algebra 19–20 points19–20 points A 1: The student will understand and apply patterns, relations, and A 1: The student will understand and apply patterns, relations, and

functions.functions. A 2: The student will represent, analyze, and model situations using A 2: The student will represent, analyze, and model situations using

mathematical structures and algebraic symbols.mathematical structures and algebraic symbols. Measurement and Geometry Measurement and Geometry 19–20 19–20

pointspoints MG 1: The student will apply appropriate techniques, tools, and MG 1: The student will apply appropriate techniques, tools, and

formulas to determine measurements and solve problems.formulas to determine measurements and solve problems. MG 2: The student will analyze characteristics of two- and three-MG 2: The student will analyze characteristics of two- and three-

dimensional geometric shapes, understand geometric relationships, dimensional geometric shapes, understand geometric relationships, and apply spatial relationships using coordinate geometry.and apply spatial relationships using coordinate geometry.

Data Analysis and ProbabilityData Analysis and Probability 8 points8 points DP 1: The student will use appropriate statistical methods to analyze DP 1: The student will use appropriate statistical methods to analyze

data and apply basic concepts of probability.data and apply basic concepts of probability. Integrated Response QuestionsIntegrated Response Questions 9 points9 points

Total: 71 pointsTotal: 71 points

Purposes of EOCEPPurposes of EOCEP

Promote instruction, encourage student Promote instruction, encourage student achievement, and document the level of achievement, and document the level of mastery of curriculum standardsmastery of curriculum standards

Serve as indicators of program, school, Serve as indicators of program, school, and school-district effectivenessand school-district effectiveness

Be weighted 20% in the determination of Be weighted 20% in the determination of students’ final grades in these classesstudents’ final grades in these classes

Characteristics of the EOCEPCharacteristics of the EOCEP

Standards-basedStandards-basedMultiple-choiceMultiple-choice50 to 60 items long, depending upon 50 to 60 items long, depending upon subjectsubjectUntimed, but about 90 minutes is the Untimed, but about 90 minutes is the estimated administration timeestimated administration timeGrades expressed on the State Uniform Grades expressed on the State Uniform Grading ScaleGrading Scale

So, how do we teach it all?So, how do we teach it all?Some things are obvious:Some things are obvious:

““Apply the commutative, Apply the commutative, associative, distributive, equality, associative, distributive, equality, and identity properties, including and identity properties, including order of operations, to simplify order of operations, to simplify mathematical expressions, mathematical expressions, equations, and inequalities.”equations, and inequalities.” (HSAP, (HSAP, Numbers and Operations)Numbers and Operations)

Look at the HSAP Blueprint and the Look at the HSAP Blueprint and the course standards for Algebra I EOCEP:course standards for Algebra I EOCEP:

““Apply the commutative, associative, Apply the commutative, associative, distributive, equality, and identity distributive, equality, and identity properties, including order of properties, including order of operations, to simplify mathematical operations, to simplify mathematical expressions, equations, and expressions, equations, and inequalities.” (HSAP)inequalities.” (HSAP)

““Use the commutative, associative, and Use the commutative, associative, and distributive properties to simplify distributive properties to simplify algebraic expressions.” (Alg I EOCEP)algebraic expressions.” (Alg I EOCEP)

So, how do we teach it all?So, how do we teach it all?

Some things are not so obvious:Some things are not so obvious:

Add, subtract, multiply and divide Add, subtract, multiply and divide fractions, decimals, percents, fractions, decimals, percents, integers. integers. (HSAP N2.1 on the Blue Print)(HSAP N2.1 on the Blue Print)

There is not a standard like this in There is not a standard like this in the course standards!!the course standards!!

First we need to identify which First we need to identify which skills are “duplicates” (that is, skills are “duplicates” (that is, are covered in both HSAP and are covered in both HSAP and in your course standards)in your course standards)

Then we will look for gaps Then we will look for gaps

Start Getting “In Your Head” Start Getting “In Your Head” What You Have to Teach.What You Have to Teach.

Working in pairs or small groups, look at Working in pairs or small groups, look at the HSAP Blueprint (blue sheets) and at the HSAP Blueprint (blue sheets) and at the SC Course Standards for your course the SC Course Standards for your course (salmon sheets) to find the shared areas. (salmon sheets) to find the shared areas.

Write the standard number in the box next Write the standard number in the box next to the skill on the blueprint.to the skill on the blueprint.

Now you know which HSAP Now you know which HSAP topics you already address in topics you already address in

your course. So what about all your course. So what about all of those HSAP “point-earning” of those HSAP “point-earning” bullets that you do not have bullets that you do not have

assigned to any course assigned to any course standards?standards?

So, how do we teach it all?So, how do we teach it all?Some educators call this scaffoldingSome educators call this scaffolding

You can teach You can teach = 3= 3 by teaching it as a by teaching it as a

fraction fraction andand as division. as division.

– As a matter of fact, the link between division and As a matter of fact, the link between division and

fractions could be taught/reviewed often as this is fractions could be taught/reviewed often as this is

a common weak area.a common weak area.

You can teach most operations (including You can teach most operations (including converting from one form to another) while converting from one form to another) while solving equations.solving equations.

x12

HSAP + EOCEPHSAP + EOCEP

Choose from the HSAP Blueprint a bullet that is Choose from the HSAP Blueprint a bullet that is not addressed in the Algebra I Standards.not addressed in the Algebra I Standards.

Decide how you could integrate teaching that Decide how you could integrate teaching that skill with one of your course standards.skill with one of your course standards.

Write a mini-lesson (or lesson outline) that you Write a mini-lesson (or lesson outline) that you could use to weave the HSAP skill into a topic in could use to weave the HSAP skill into a topic in your course.your course.

Use a piece of large post-it paper to post your Use a piece of large post-it paper to post your “lesson plan” on the wall.“lesson plan” on the wall.

Harriet PritchardHarriet Pritchard

hpritcha@ed.sc.govhpritcha@ed.sc.gov

Buck F. BrownBuck F. Brown

Bfbrown@ed.sc.govBfbrown@ed.sc.gov