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JMP DISCOVERY SUMMITSEPTEMBER 13 – 16, 2011DENVER, COLORADO

Discriminant Analysis of High School Student Mathematics Class Placement

Simon King

simon_king@caryacademy.org

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CARY ACADEMY• Since 2008 - Upper School Mathematics Chair and

Advanced Statistics Teacher at Cary Academy, North Carolina.

• Cary Academy is a grade 6 – 12 independent school, located next to the SAS world headquarters.

• Cary Academy was founded by the owners of SAS.

www.caryacademy.org

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TEACHING USING JMP AS AN EDUCATIONAL AND ANALYTICAL TOOL

• The key focus of the course is the promotion of “Statistical Thinking”• JMP empowers the students to move beyond the “data-crunching”

statistics class of old and focus on analysis of data and interpretation of results.

• JMP is used in the classroom for descriptive and inferential statistics and the discovery or reinforcement of key concepts

• The result is a course that is very kinesthetic• Resources: http://castatistics.wikispaces.com/

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Student Feedback

• “Technology, specifically JMP, enhances learning greatly. Tutorials are posted online to learn how to use it-- very helpful.”

• “We use JMP every day in this course, so technology is pretty much indispensable and I probably wouldn't even be taking this class if it weren't for the technological component. I imagine I wouldn't have liked Statistics if it weren't for the fact that JMP makes it easier to understand and do.”

• “I like having all the notes available electronically and I feel comfortable using JMP software.”

•  ”The JMP software is awesome. It's extremely useful.”

• “We use a lot of technology and it always helps my understanding of the material.”

• “JMP is the key to this course.”

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Part-time M.S. Statistics Student(Online Distance Education)

• ‘Borrow’ ideas, concepts and datasets for Advanced Statistics course.

• Apply concepts learned for data analysis at Cary Academy.

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Data Analysis to measure and improve quality of educational instruction at Public

Schools and Independent Schools

The use of data to guide decisions varies between public and independent schools.

Generally, Public Schools are subject to No Child Left Behind. As a result, students take End of Grade and End of Course examinations in order to progress. These examinations are heavily analyzed for student progress, and school and teacher performance. Teacher bonuses are linked to these scores and constantly poorly performing schools can come under threat of closure.

Use of data in Independent Schools is generally limited to SAT, PSAT, Advanced Placement Examinations and various testing done for accreditation purposes.

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Educational Data Analysis at Cary Academy

• SAT and PSAT data is reported.

• Students in grades 6 through 11 take the CTP4; Comprehensive Testing Program by ERB.

• This exam is taken at the end of the year and is a ‘zero stake test’ – the student results are not analyzed to measure performance or affect teaching and learning.

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The Challenge . . . An average Upper School class (100 students) has about 30 new students joining it between 9th and 12th grades. The challenge is to place the student into an appropriate mathematics class. The choice between a regular and honors class is of particular interest to the student and parents.

• Problem at previous school: “A grade” students not challenged enough or students placed inappropriately.

• Needed a comparison with the Cary Academy student population to decide appropriate placement.

• All students coming to CA had to take a standardized exam (CTP4 or similar)

• Current Cary Academy students might also request to move classes from one year to the next (i.e. regular to honors)

• Classification analysis is a perfect analysis tool for this.

• This process then needs to be disseminated to parents, students and administrators in a simple way they can understand.

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Determine which variables discriminate between different groups and develop a rule in which to classify further data.

Use variables that are good indicators math class placement of Cary Academy and place incoming students using the same variables.

Data set:Discriminant Analysis – Simon King

ClassificationAdditionally, their 9th grade mathematics class placement is recorded. This is our response variable. Students are placed into the following populations of 9th grade mathematics classes: • Algebra I (Y=1) • Geometry (Y=2) • Geometry Honors (Y=3) • Algebra II Honors (Y=4)

Discriminant Analysis

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Data CollectionData is collected for a single grade of 106 students for the following: = Student PSAT percentile (based on college bound students) = 8th grade mathematics class grade = 2010 ERB quantitative test percentile = 2010 ERB Math 1 & 2 test percentile = 2009 ERB quantitative test percentile = 2009 ERB Math 1 & 2 test percentile

All percentiles are based on independent school students only. This better differentiates the students in the population (4th – 99th percentiles) versus national (60th – 99th)

For example, students ranked as 99th percentile on a national scale are ranked 77th – 99th percentile on an independent school scale.

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Student Percentile Inconsistencies

Differences in year on year ERB scores = 2010 ERB quantitative test percentile

= 2010 ERB Math 1 & 2 test percentile = 2009 ERB quantitative test percentile = 2009 ERB Math 1 & 2 test percentile

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Variable analysis – Lack of Multivariate Normality

distribution of variate (PSAT percentiles)

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Logistic Discriminant Analysis

• Fewer conditions to satisfy

• Measure the model fit through ‘misclassification rate’ – percentage of subjects wrongly classified through the model

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Logistic Discriminant Analysisusing variables x1 – x6

Testing Null Hypothesis

Misclassification rate.Percentage of data not correctly classified from theModel.

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Analysis of Misclassification

The diagonal shows the students correctly classified from the model (53 out of 75). The other cells indicate where students were misclassified.

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Classification?

Oneway Analysis of Max Math By Dummy

Analysis – Max. Student Percentile

SLIDE 16

17Bivariate (8th Grade mathematics class grade) by (2010 ERB independent schools quantitative test percentile)

Bivariate Representation

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Three Variable Representation

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Box Plot Visual

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Concluding Remarks

• In previous years, many students were misplaced and either not challenged or “out of their depth” and many changed classes in the first four weeks of a new school year.

• Through good communication, parents, teachers, administrators and students are now able to understand the choice they have and can make a fully informed decision.

• For example, if a student is around 80th percentile, they can look at the side-by-side box plots (slide 19) and understand that in Geometry ( dummy 2) they would probably be comfortable, but in Honors Geometry (dummy 3) they might at times struggle to keep up with the other students.