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COLLEGE OF EDUCATION DEPARTMENTAL COURSE SYLLABUS The College of Education CAREs The College of Education is dedicated to the ideals of Collaboration, Academic Excellence, Research, and Ethics/Diversity. These are key tenets in the Conceptual Framework of the College of Education. Competence in these ideals will provide candidates in educator preparation programs with skills, knowledge, and dispositions to be successful in the schools of today and tomorrow. For more information on the Conceptual Framework, visit: www.coedu.usf.edu/main/qualityassurance/ncate_visit_info_materials.html 1. Course Prefix and Number: MAE 6137 2. Course Title Probability and Statistics for Middle Grades Teachers 3. Regular Instructor(s) Dr. Richard A. Austin Dr. Helen Gerretson Dr. Gladis Kersaint Dr. Denisse R. Thompson adjuncts credentialed by program faculty (Several faculty at Manatee Community College have completed the Ph.D. in mathematics education at USF and will likely help with the teaching of this course.) 4. Course Prerequisites (if any) Admission into the MAT in Middle Grades Mathematics or CI 5. Course Description This course examines in depth topics from probability and statistics appropriate for middle grades mathematics teachers, including historical connections. Topics studied include data collection and display, measures of central tendency and variability, use of tree diagrams to find probabilities, independent and dependent events, combinations and permutations, and sampling procedures. Teachers experience instructional approaches appropriate for use in middle grades classrooms. This course is required in the MAT in Middle Grades Mathematics. Prerequisite: Admission to the MAT program in middle grades mathematics or CI. 6. Course Objectives Upon completion of this course, students will demonstrate the following: 1. The ability to define probability and statistics; 2. The ability to display data using a variety of graphical displays (bar, line, picture, circle, scatterplot, box and whisker, stem and leaf); Probability and Statistics 3. 4. 5. 6. 7. 8. 9. The ability to identify measures of central tendency and situations in which they are appropriate; The ability to identify measures of variability and use such measures to interpret results; The ability to find probabilities of independent and dependent events and to use tree diagrams to find probabilities; The ability to find combinations or permutations as appropriate for the situation; The ability to design an experiment or simulation, collect data, and interpret the results; The ability to discuss different sampling procedures, including the use of random samples; Knowledge of major historical developments in statistics and probability. 7. Content Outline Week 1. Displaying data: discrete and continuous data (bar graphs vs. histograms, picture, circle, line graphs, stem and leaf plots) Historical connections with statistics Week 2. Measures of central tendency Situations in which different measures are most appropriate Week 3. Measures of variability Box and whisker diagrams Using central tendency, variability, and graphs to interpret results Week 4. Definitions of probability Historical connections to probability Using tree diagrams to find probabilities Week 5. Independent and dependent events Week 6. Solving problems with probability Week 7. MIDTERM Week 8. Permutations and combinations Week 9. Counting problems Week 10. Designing experiments – sampling issues Week 11. Random samples Week 12. Hypothesis testing Week 13. Further work with hypothesis testing Week 14. Computer simulations Week 15. Computer simulations 8. Evaluation of Student Outcomes Exams or tests will evaluate students' content knowledge on the major content topics in the course. Students will have to pass the final, comprehensive exam in order to pass the course. (CF #2) Problem sets will evaluate students' ability to explore open and extended problems. (CF #2) Probability and Statistics 9. Historical paper will give students an opportunity to explore the historical background of a topic from statistics and/or probability. (CF #2 and #4) External project will have students engage in a statistics or probability project of the instructor's design or of their own approved design. (CF #2, #4 and #6) A journal will provide on-going evaluation of students' facility with the content of the course and emphasize the importance of writing throughout the curriculum. (CF #4) Grading Criteria Exams or Tests or Quizzes Problem Sets and Journal Historical Paper External Project 50-55% of Grade 15-20% of Grade 10-15% of Grade 15-20% of Grade The university's plus/minus system of grading will be used. USF Policy on Religious Observances "No student shall be compelled to attend class or sit for an examination at a day or time prohibited by his or her religious belief. In accordance with the University policy on observance of religious holy days, students are expected to notify their instructors if they intend to be absent for a class or announced examination prior to the scheduled meeting." 10. Required Textbooks Sample text: The following units from the Connected Mathematics Project are possible texts. Data About Us How Likely Is It? What Do You Expect? Clever Counting (Glenda Lappan, James T. Fey, William M. Fitzgerald, Susan N. Friel, and Elizabeth Difanis Phillips. Menlo Park, CA: Dale Seymour Publications, 1998.) A packet of supplemental readings related to statistics and probability activities and/or historical aspects of statistics and probability will also be used. Sample readings might include the following: Zawojewski, Judith S. and J. Michael Shaughnessy. "Mean and Median: Are They Really So Easy?" Mathematics Teaching in the Middle School, 5 (March 2000): 436-440. Norton, Robert M. "Determining Probabilities by Examining Underlying Structure." Mathematics Teaching in the Middle School, 7 (October 2001): 78-82. Probability and Statistics Note: The actual text and readings will be selected at the time the course is offered in order to permit the most current materials to be used. The above samples reflect the nature of the materials intended for use to help teachers address the content of this course. 11(a) ADA Statement: Students with disabilities are responsible for registering with the Office of Student Disabilities Services in order to receive special accommodations and services. Please notify the instructor during the first week of classes if a reasonable accommodation for a disability is needed for this course. A letter from the USF Disability Services Office must accompany this request. 11(b). USF Policy on Religious Observances: Students who anticipate the necessity of being absent from class due to the observation of a major religious observance must provide notice of the date(s) to the instructor, in writing, by the second class meeting. Probability and Statistics COLLEGE OF EDUCATION DEPARTMENTAL COURSE SYLLABUS Graduate Level Course ATTACHMENT I Please respond to each of the following questions and complete the attached Matrix: 1. Rationale for Setting Goals and Objectives: What sources of information (e.g., research, best practices) support the formulation and selection of course goals and objectives? The aim of the course is to provide middle grades mathematics teachers with a solid background related to the statistics and probability content they would be expected to teach. The course will not only focus on providing a solid foundation in statistics and probability but will approach that content from pedagogical perspectives that are appropriate for use in a middle grades classroom. In this way, teachers experience learning mathematics through the types of approaches they are expected to use when they teach. 2. What aspects of the COE conceptual framework is/are specifically addressed in this course? 3. USF prepares professionals who know the content they teach. USF education candidates demonstrate an understanding of his/her subject field, its linkage to other disciplines, and applications to real world, integrated settings. USF professionals are reflective and analytical problem-solvers. USF education candidates engage in continuous professional improvement for self and school through a commitment to life-long learning. List the specific competencies addressed from the relevant national guidelines. National Council of Teachers of Mathematics 1.5.5 "use both descriptive and inferential statistics to analyze data, make predictions, and make decisions;" 1.5.6 "interpret probability in real-world situations, construct sample spaces, model and compare experimental probabilities with mathematical expectations, use probability to make predictions;" 1.5.11 "use mathematical modeling to solve real-world problems;" 1.5.12 "use counting to enumerate and order; use matrices, finite graphs, and trees to model problem situations; describe basic algorithms for accomplishing tasks;" 1.6 "Programs prepare prospective teachers who have a knowledge of historical development in mathematics that includes the contributions of underrepresented groups and diverse cultures." Probability and Statistics 4. Are there field-based experiences in this course? If so, please briefly indicate nature and duration. No. 5. a. Is technology used in this course? Students will be expected to have access to a graphing calculator throughout the duration of the course. Graphing calculators have built-in functions that will be useful in exploring statistics and probability functions studied in the course. b. Are students required to access and demonstrate use of technology in instruction or record keeping in this course? No. 6. How are issues of diversity addressed in this course? Indicate which aspect of the course (e.g., instructional strategies and/or experiences) provides the candidate the opportunity to acquire and/or apply knowledge, skills and/or dispositions necessary to help all students learn. ("All students" includes students with various learning styles, students with exceptionalities and different ethnic, racial, gender, language, religious, socioeconomic, and regional/geographic origins and achievement levels.) A variety of instructional methods are used in the course to accommodate learning environments with diverse kinds of students. Students will explore historical connections to probability and statistics, including the contributions made by diverse peoples and cultures. Students will be expected to complete a historical paper related to some statistics or probability topic. 7. (For initial certification programs) a. List the specific competences addressed from the Florida Adopted Subject Matter Content Standards or the Florida Adopted Subject Area Competencies. Knowledge of mathematics as problem solving (1-4) Knowledge of mathematics as communication (1) Knowledge of mathematics as reasoning (1) Knowledge of mathematical connections (3) Knowledge of statistics (1-5) Knowledge of probability (1-5) Probability and Statistics b. Describe any component of the course designed to prepare teacher candidates to help PK-12 students achieve the Sunshine State Standards. The Sunshine State Standards are drawn from the national content recommendations from the National Council of Teachers of Mathematics. This course will address aspects from Strand E on Data Analysis and Probability. Probability and Statistics Course Objectives Matrix Evidence of Achievement Accomplished Practices 1.0 The ability to define probability and statistics. Exams Journals #8 Knowledge of subject matter 2.0 The ability to display data using a variety of graphical displays (bar, line, picture, circle, scatterplot, box and whisker, stem and leaf). Exams Problem sets Project #8 Knowledge of subject matter 3.0 The ability to identify measures of central tendency and situations in which they are appropriate. Exams Problem sets Journals #8 Knowledge of subject matter 4.0 The ability to identify measures of variability and use such measures to interpret results. Exams Problem sets #8 Knowledge of subject matter 5.0 The ability to find probabilities of independent and dependent events and to use tree diagrams to find probabilities. Exams Problem sets #8 Knowledge of subject matter 6.0 The ability to find combinations or permutations as appropriate for the situation. Exams Problem sets Journals #8 Knowledge of subject matter 7.0 The ability to design an experiment or simulation, collect data, and interpret the results. Problem sets Project #8 Knowledge of subject matter 8.0 The ability to discuss different sampling procedures, including the use of random samples. Problem sets Project #8 Knowledge of subject matter 9.0 Knowledge of major historical developments in statistics and probability. Historical paper #8 Knowledge of subject matter Probability and Statistics