Syllabus
For
AP Statistics

We believe that AP Statistics should be an activity centered course in which students routinely use technology to construct their own understanding of the principles and practices of statistics. Therefore, the following syllabus relies heavily on student's active engagement in doing statistics with appropriate technological tools throughout the course. This engagement is achieved by the use of Workshop Statistics: Discovery with Data, (1995) by Allan J. Rossman as the primary text book for the course. Additional support is provided by the use of The Basic Practice of Statistics, (1995) by David S. Moore. Sequencing of the topics in this syllabus differs from the listing of topics in the AP Statistics Course Description; however, this syllabus will treat all of the topics in the published AP Statistics curriculum.    

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Resources Key:  Rossman = Workshop Statistics: Discovery with Data by Allen Rossman Moore = The Basic Practice of Statistics by David S. Moore Freeman = Statistics, 2nd Edition by Freedman et al. Quantitative Literacy Series = Quantitative Literacy Series by David Freedman.

 

Unit 1: Exploring Data Distributions

Unit 2: Exploring Data Relationships

Unit 3: Designing Samples and Experiments

Unit 4: Sampling Distributions & Probability

Unit 5: Inferences from Data: Principles

Unit 6: Inferences from Data: Comparisons

Unit 7: Inferences from Data: Measurements

Unit 8: Inferences from Two Way Tables

Unit 9: Inferences for Regression

Unit 10:Review and Preparation for AP Test

Time: 4 weeks

Topic & Activities	Resources
1. Data, Variables and Distributions	Rossman - Topic 1
2. Displaying and Describing Distributions	Rossman - Topic 2
3. Measures of Center	Rossman - Topic 3
4. Measures of Spread	Rossman - Topic 4
5. Comparing Distributions	Rossman - Topic 5
6. Readings and Report	Freedman - Chapter 4
7. Introduction to major project

Time: 5 weeks

Topic & Activities	Resources
1. Graphical Displays of Association	Rossman - Topic 6
2. Correlation	Rossman - Topic 7
3. Least Square Regression	Rossman - Topic 8 & 9
4. Interpreting Correlation & Regression	Moore - Section 2.4
5. Meaning of Regression. Why Least Squares	Bohan
6. Readings and Report	Freedman - Chapters 8 & 10
7. Influential Points Activity	Quantitative Literacy Series
8. Contingency Tables	Rossman- topic 10
9. Major Project Work

 

Time: 4 weeks

Topic & Activities	Resources
1. Random Sampling	Rossman - Topic 11
2. Readings and Report	Freedman - Chapters 1 & 2
3. Sampling Distributions: Confidence	Rossman - Topic 12
4. Sampling Distributions: Significance	Rossman - Topic 13
5. Normal Distributions	Rossman - Topic 14
6. Central Limit Theorem	Rossman - Topic 15
7. Designing Experiments	Rossman - Topic 20
8. Major Project Work

 

Time: 3 weeks

Topic & Activities	Resources
1. Probability Distributions	Moore - Section 4.2
2. Sample Proportions	Moore - Section 4.3
3. Binomial Distributions	Moore - Section 4.4
4. Sample Means	Moore - Section 4.5

 

Time: 3 weeks

Topic & Activities	Resources
1. Confidence Intervals	Rossman - Topics 16 & 17
2. Tests of Significance	Rossman - Topics 18 & 19

 

Time: 2 weeks

Topic & Activities	Resources
1. Comparing Two Proportions	Rossman - Topics 21 & 22
2. Major Project Work

 

Time: 3 weeks

Topic & Activities	Resources
1. Inference for a Population Mean	Rossman - Topics 23 & 24
2. Comparing Two Means	Rossman - Topic 25
3. Major Project Work

Time: 2 weeks

Topic & Activities	Resources
1. Two-Way Table-expectancies	Moore - Chapter 8
2. The Chi-Squared Test	Moore - Chapter 8
3. Readings and Report	Freedman - Chapter 28
4. Major Project Work

 

Time: 2 weeks

Topic & Activities	Resources
1. The Regression Model	Moore - Chapter 10
2. Confidence Intervals for the Regression Slope	Moore - Chapter 10
3. Testing Hypothesis of Non-Linear Relationship	Moore - Chapter 10
4. Major Project Work

 

Time: 2 weeks

Topic & Activities	Resources
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The choice of presenting small sample methods prior to large sample methods reflects the treatment of the topics in Rossman's text. This ordering has been approved in consultation with Alan Rossman.

 

Instruction on technology, with particular emphasis on the TI-83 and Minitab, is incorporated into the pursuit of the regular class activities. Some allowances in the time schedule for the early units have been made to accommodate direct instruction within the context of an assigned activity.    

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This course is organized as an activity based experience for the students. Lecture is held to the minimum with the students actively engaged in discovery and exploration of statistical realities and relationships. This design is consistent with the constructivist philosophy of education. The teacher attempts to facilitate and guide the student's explorations and formations of hypotheses. Students learn appropriate statistical techniques within the context of statistical activities and experiences better than they can learn from lecture-based teaching of the techniques.

 

The discovery and exploration are fully supported with technology, particularly the TI-83 calculator and secondarily Minitab statistical software. Students are required to have graphing calculators with a full menu of statistical functions; the Mathematics Department does not require any particular brand or model of calculator. However, mathematics teachers at our school tend to prefer either the TI-83 or TI-85.

 

Much of the course is devoted to developing the students into competent interpreters and investigators of statistical data and information. The activities of decision making and validating/justifying statistical hypotheses are of the highest importance. The goal is to develop competent users and receivers of statistical information; consequently, proof and algebraic justification are restricted to topics for which it has been determined that such activities will serve to deepen the understanding of the students and further empower them in statistics.

 

Our choice of Workshop Statistics: Discovery with Data (Rossman, 1996) supports this approach to learning. As the Preface states,

This book contains activities that guide students to discover statistical concepts, explore statistical principles, and apply statistical techniques. Students work toward these goals through the analysis of genuine data and through interactions with each other, their instructor, and with technology.

Each student is to conduct a major project throughout the entire course. This major project involves a substantial set of bivariate data on which the students will apply all of their statistical techniques and concepts. Students are encouraged to begin the project with real data from their own experience. Suggested sources of data include data that student's parents or guardians have, school data (with proper safeguard for confidentiality), statistical abstracts, etc. Students are instructed that one of the components of the project is to evaluate their data: this evaluation may determine that the data set is not usable. Should this occur, students will have to gather more data in order to proceed with this component of the course. It is our belief that the experience of this project should parallel real-world statistical practice.

 

During the term of the project, each student will analyze each component of their data set, investigate relationships between the components, use the components as the superset for random sampling activities and the basis for hypothesis testing and

interpretation.

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Once the AP Test has been administered, the students explore a variety of statistical topics including an Introduction to Analysis of Variance and other regression models. Time is also devoted to polishing each student's Major Project report.    

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The assessment program for AP Statistics has two components:

 

Traditional Assessment

 

1. Each Nine Week Marking Period:

a) Homework activities are assigned each class and are not graded. They are discussed extensively in class.

 

b) Quizzes deal with the full range of procedures and interpretations for each topic.

 

c) Tests are administered at the end of each unit. The tests cover both concepts and techniques and include AP Statistics type questions as much as possible. Questions include both short answer skill and conceptual items as well as more extensive multi-step analyses and interpretations of analyses.

 

d) Readings and Reports are assigned independently of the normal class work. Students are to submit a brief written report for each of the assignments.

 

e) Major Project evaluation will occur at the end of each 9 week marking period. The project is graded according to how well the student applies of the concepts and techniques of that marking period.

 

 

2. At the end of each semester, a Semester Examination will be administered. This test is designed to assess the more global and interpretative aspects of the curriculum.

 

3. Calculation of the grade:

a) The Marking Period Grade is the mean of the all tests of the marking period. The mean of the quizzes is used as one test. The evaluation of the Major Project is calculated in the following way:

i) 1st and 2nd Marking Periods: worth one test

 

ii) 3rd and 4th Marking Periods: worth two tests

The Marking Period Grade is adjusted based on the discussion as part of the Competency Based Grading System (see below).

 

 

b) The Semester Grade is calculated using the following weights:

i) Each Marking Period grade: 40%

 

ii) Semester Examination: 20%

 

The Final Grade is the mean of the two semester grades.

 

Competency Based Assessment

 

1. At the beginning of the course, each student is presented with a list of competencies (see page 10) for AP Statistics. At the end of each unit, the teacher makes a judgment regarding the status of competencies that were addressed during that unit. The categories of evaluations are Excellent (97), Proficient (92), Adequate (85), Marginal (78) and Unsatisfactory (65). Each student's Competency List is then updated by entering the date of the evaluation in the appropriate column.

 

2. Each Competency Grade is subject to revision at any time throughout the balance of the course. Revision is accomplished either by administration of a retest of that competency or by the presentation of evidence by the student in a conference with the

teacher. This second option is by far the more popular and provides the beneficial requirement that the student must argue for an increase in rating. In addition, a rating may move down if the teacher perceives that the performance of a particular

competency has slipped.

 

3. At the end of each Marking Period, the ratings are quantified.

 

4. Each student then has a conference with the teacher at which time the two evaluations, traditional and competency-based, are reconciled The student and teacher come to an agreement regarding the letter grade that best represents the student's level of understanding and performance and that will be reported to the school. This negotiation session has proved most beneficial in our school's AP Calculus courses.

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Primary:

 

• Allan J. Rossman, Workshop Statistics: Discovery With Data. New York, NY: Springer-Verlag New York, Inc., 1996.
• David S. Moore, The Basic Practice of Statistics. New York, NY: W. H. Freeman and Company, 1995.

 

Secondary:

 

• David Freedman, Robert Pisani, Roger Purves, Ani Adhikari, Statistics, 2nd Edition. New York, NY. W. W. Norton & Company, 1991.
• Gnanadesikan, Landwehr, et al., Quantitative Literacy Series: Exploring Data, Exploring Probability, The Art and Technique of Simulation, Exploring Surveys and Information from Samples, Exploring Measurements. Palo Alto, CA. Dale Seymour Publications, 1986.

* major topics - competency rating calculated with twice the weight of other categories