geometry: content and process good ideas in teaching precalculus and…. rutgers march 18, 2011

GEOMETRY: CONTENT and

PROCESS

Good ideas in teaching Precalculus and….

Rutgers

March 18, 2011

SAT UPDATE

• Colleges use the SAT as a way to check against unequal opportunities, variable standards and grade inflation.

• Some colleges use SAT scores for placement and scholarship opportunities.

• SAT scores are only one among many factors that colleges use to make admission decisions.

How Do Colleges Use the SAT®?

*Along with high school grades, the SAT is the best predictor of college success.

The SAT® provides a valid, nationally consistent measure

of what students have learned and how well they apply that knowledge.*

The SAT® provides a valid, nationally consistent measure

of what students have learned and how well they apply that knowledge.*

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Correlations* of Predictors with First-Year College Grade Point Average

*All correlations have been corrected for restriction of range.Sample size: 159,286 students at 110 colleges and universities in entering class of 2007.

Correlations* of Predictors with Second-Year Cumulative College Grade Point Average

*All correlations have been corrected for restriction in range.Sample size: 80,958 students at 66 colleges and universities. Results are based on institutions in the 2006 cohort that provided second-year data.

Another Way to Look at Correlation of .56

SAT Scores: Math + Critical Reading + Writing

Grades Are Increasing*

1990 1995 2000 2005 2009 2010

Art and Music 3.61 3.68 3.74 3.75 3.76 3.75

English 3.08 3.19 3.26 3.30 3.37 3.39

Foreign/Classical Languages 3.06 3.15 3.22 3.26 3.31 3.33

Mathematics 2.91 3.01 3.07 3.11 3.14 3.16

Natural Sciences 3.00 3.12 3.20 3.23 3.25 3.27

Social Sciences/History 3.15 3.26 3.34 3.36 3.39 3.40

Grade Average for All Subjects 3.09 3.20 3.28 3.30 3.32 3.34

Percentage of Students With GPA of A-, A or A+ Is Increasing

1990 1995 2000 2005 2009 2010

A+, A, A- 29% 34% 40% 41% 43% 44%

B+, B, B- 53% 50% 47% 47% 46% 45%

C+, C, C- 18% 15% 12% 11% 11% 10%

High School Grades Shifting Over Time

*Based on four-point system, where A=100Note: 1990 GPAs reflect all Student Data Questionnaire responders, not just SAT® takers. GPAs for 1995-2010 reflect SAT® takers only.

As SAT scores increase, so does the likelihood of a student returning for the second and third year of college.

SAT Scores Identify Students Who Will Return

SAT takers in the class of 2010:

– 42% were minority students– 25% reported that English

was not exclusively spoken at home

– 45% intend to be first-generation, college-bound students

• The SAT is administered by over 6,000 test centers in more than 170 countries!

Who Took the SAT® This Year?

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The 2010 cohort was the most diverse group ever!

The 2010 cohort was the most diverse group ever!

SAT Performance by Core Curriculum Participation

Reading Math Writing

Core Curriculum 518 531 509

Non-Core Curriculum 467 481 459

Difference +51 +50 +50

Core curriculum is defined by at least four years of English, and at least three years of mathematics, three years of natural science, and three years of social science and history.

Reflects SAT takers in the class of 2010 who took the SAT through March 2010.

SAT Performance by AP or Honors English or AP or Honors Math Participation

+59 points

+58 points

+77 points

Reflects SAT takers in the class of 2010 who took the SAT through March 2010.

Mathematics Study by SAT-takers

2010 2005 2000 1995 1990

Four or More Years of Study

76% 74% 69% 68% 65%

AP or Honors 36% 30% 28% 28% 23%

Courses

Calculus 28%* 27% 24% 22% 19%

Pre-calculus 28%* 48% 44% 37% 31%

Trigonometry 12%* 46% 50% 54% 55%

* Highest Level of Mathematics Achieved

Number/Percent of SAT-takers Intending to Major in Mathematics

YEAR PERCENT NUMBER

1975 2% 12,835

1980 1% 10,300

1985 1% 10,105

1990 1% 6,659

1995 1% 5,436

2000 1% 6,150

2005 1% 9,935

2010 1% 14,001

NEW -- Student Web Experience

NEW -- Student Web Experience

The new practice feature Answers Imagined utilizes rich visuals and animations to demonstrate how a student might arrive at the answers to SAT practice questions. (sat.collegeboard.com/practice/answers-imagined)

NEW -- Student Web Experience

Innovative Features, Including Test Day Simulator

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• You have told us that SAT® rosters would make your lives easier … Online rosters will pilot this school year!

Rosters include:– Test Date and Type– Students’ First and Last Names– Students’ Grade Level– Assigned Test Center– Fee-Waiver Status– Absentee Status– And More

SAT® Registration Rosters

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If you would like to participate in the pilot, please contact us: counselorfeedback@collegeboard.org.

If you would like to participate in the pilot, please contact us: counselorfeedback@collegeboard.org.

Why Should Your School Become an SAT Test Center? Benefits …

– Inspires students to connect to college success and beyond

– Fosters a college-going culture

– Offers value-added support for students, parents and the community

– Honorarium for SAT Test Center staff — test center supervisor, room supervisors and proctors

– Reimbursement for some of your school’s test-related expenses

– More staff includedin the college planning process

– Test in familiar surrounding

– Accessible and easy to reach

– Expanded opportunities to connect to the college that is right for them

Become an SAT® Test Center!

… for your students… for your students

… for your school… for your school

… for your staff… for your staff

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• It’s easy to become an SAT test center …• The two most important requirements for a

test center are proper facilities and a professional who is qualified and willing to serve as the test center supervisor. The SAT Program will provide all the necessary training, testing material and support needed to administer the SAT.

Become an SAT® Test Center!

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For more information regarding SAT Test Center capabilities or support in completing your

application process, please contact us:

counselorfeedback@collegeboard.org.

For more information regarding SAT Test Center capabilities or support in completing your

application process, please contact us:

counselorfeedback@collegeboard.org.

GEOMETRY: CONTENT and

PROCESS

SAT Mathematics Content Areas

• Number and Operations (20–25%)• Algebra and Functions (35–40%)• Geometry and Measurement (25–30%)• Data Analysis, Statistics, and Probability

(10–15%) 

Multiple Choice

Key = E

Student-Produced Response

Key = 9.8, 49/5

SPR Answer Grid

● Polygons

● Circles

● Volume of boxes, cubes, and cylinders

● Isosceles, equilateral, and right triangles

● Parallel and perpendicular lines

● Coordinate geometry

● Geometric visualization

● Slope

● Similarity

● Transformations

Geometric Content on the SAT

● Problem Solving

● Representation

● Reasoning

● Connections

● Communication

NCTM Process Standards

Problem Solving

Parallel and perpendicular lines

Problem Solving

Circles

Problem Solving

Similarity

Problem Solving

Volume

Problem Solving

Volume

Representation

Equilateral triangles and circles

Representation

Coordinate geometry

Representation

Geometric visualization

Representation

Similarity

Representation

Transformations

Representation

Geometric visualization

Reasoning

Parallel and perpendicular lines

Reasoning

Geometric visualization

Reasoning

Isosceles triangles

Reasoning

Triangles

Reasoning

Parallel and perpendicular lines

Connections

Volume

Connections

Polygons and triangles

Connections

Polygons

Connections

Triangles

Connections

Coordinate geometry and Slope

Communication

Polygons

Communication

Rectangular solids

Communication

Coordinate geometry

Communication

Circles