To review Upper School Mathematics Department Vision, click here

Honors and Advanced Courses

All courses have high expectations, but there are different prerequisites and expectations for Honors and Advanced courses. Compared to regular mathematics courses, students in Honors or Advanced courses should expect to encounter topics at a faster pace, which will be investigated in greater depth. Students in an advanced or honors class can expect a greater emphasis on conceptual understanding and abstract thinking with less focus on review and practice. Beyond the expectations of regular mathematics courses, students are expected to be more self-motivated as well as interested in devoting time and energy towards more challenging and thought provoking problems.

COURSE OUTLINE

AIMS (long-term goals after the course has been completed)

Students will:

understand the importance and consequences of variation in data

be able to explain and interpret data through visualizations

understand the crucial role data plays in business and research

be able to use statistical inference to make interpretations and predictions

be aware of bias in all applications of statistics and analytics

understand the application of probability in statistical inference

be able to work effectively in teams

be able to effectively follow an experimental design process

OBJECTIVES (short-term curriculum goals)

SECTION 1: Introduction to Statistics and Analytics
Students will

understand the importance of citing sources correctly

become familiar with the basic functions of JMP® software

understand different types of variables

have a basic understanding of inference and variation

understand and apply the basic concepts of working in a team

be familiar with simple visualizations of data

be able to use appropriate visualizations to represent data

SECTION 2: Distribution

Students will

know the concept of and be able to calculate the standard deviation

understand the characteristics of different distributions

understand the characteristics of the Normal Distribution

understand the characteristics of the Binomial Distribution

be able to apply and interpret a Wilks-Shapiro test

SECTION 3: Experimental Design and Sampling
Students will

understand and apply sampling methods

be able to identify potential bias and sampling error

be aware of the need to recognize lurking variables

SECTION 4: Introduction to Six Sigma
Students will

understand the significance of variation

know about many areas of Six Sigma applications

become aware of DMAIC and other core principles

apply some Six Sigma principles of decision making as a team

SECTION 5: Sampling Distributions
Students will

understand benefits of sampling distributions

derive The Central Limit Theorem

discover the t-distribution

SECTION 6: Introduction to Confidence Intervals and Testing
Students will

be able to estimate the mean of single sample

test a hypothesized population mean with a single sample

understand the concept of a p-value and level of significance

SECTION 7: Type I and II Errors and Power
Students will

understand Type I and II Errors in statistical inference

understand the concept of Power

SECTION 8: Bivariate Data
Students will

be able to examine the relationships between numeric data through:

correlation

transformations to achieve linearity

density elipses

test of slopes

confidence intervals of slopes

Non-parametric testing

understand the need to explore an entire dataset, rather than just two variables

SECTION 9: Categorical Data
Students will

understand contingency tables and associated visualizations

Apply and interpret Chi-Squared and Fisher's exact test

SECTION 10: Comparing two samples
Students will

understand and apply the sampling distribution for the difference of two samples

SECTION 11: Experimental Design
Students will

understand the basic principles of experimental design

understand the benefits of different designs

be able to design and conduct their own experiments, including factors and levels

be aware of potential issues such as confounding and placebo effect

study simple experimental design ideas through "Predictably Irrational: The Hidden Forces That Shape Our Decisions" by Dan Ariely

To review Upper School Mathematics Department Vision, click hereHonors and Advanced Courses## All courses have high expectations, but there are different prerequisites and expectations for Honors and Advanced courses. Compared to regular mathematics courses, students in Honors or Advanced courses should expect to encounter topics at a faster pace, which will be investigated in greater depth. Students in an advanced or honors class can expect a greater emphasis on conceptual understanding and abstract thinking with less focus on review and practice. Beyond the expectations of regular mathematics courses, students are expected to be more self-motivated as well as interested in devoting time and energy towards more challenging and thought provoking problems.

COURSE OUTLINEAIMS(long-term goals after the course has been completed)Students will:

OBJECTIVES(short-term curriculum goals)SECTION 1: Introduction to Statistics and AnalyticsStudents will

## SECTION 2: Distribution

Students willSECTION 3: Experimental Design and SamplingStudents will

SECTION 4: Introduction to Six SigmaStudents will

SECTION 5: Sampling DistributionsStudents will

t-distributionSECTION 6: Introduction to Confidence Intervals and TestingStudents will

SECTION 7: Type I and II Errors and PowerStudents will

SECTION 8: Bivariate DataStudents will

SECTION 9: Categorical DataStudents will

SECTION 10: Comparing two samplesStudents will

SECTION 11: Experimental DesignStudents will

SECTION 12: Six Sigma IIStudents will