University of Virginia

School of Continuing and Professional Studies

Office of Mathematics Outreach

Instructor Preparation: Algebra Functions and Data Analysis Grant

Supported with funds through a Virginia Department of Education

Mathematics and Science Partnership Grant

NCLB Title II Part B

Math 6060: AFDA: Mathematical Modeling with Probability and Statistics

Credit: 3-hours graduate level mathematics

Instructor: Pam Bailey

Secondary Mathematics Coordinator, Spotsylvania County Schools

pbailey@spotsylvania.k12.va.us

Course Format: This is a blended course that will include face-to-face class meetings and synchronus online class meetings facilitated through Blackboard, Elluminate Live, and Digimemo2.

Course Dates:

Saturday   Jan 9

Online       Jan 12

Online       Jan 26

Saturday   Feb 6

Online       Feb 9

Online       March 2

Online       March 16

Saturday   April 17

Online       April 27

Online      May 4

Saturday   May 15

Course Times: Saturday Classes meet 9:00 A.M. – 3:30 P.M.

Online Classes meet 4:00-7:00

Course Location: Spotsylvania School Board Office

Course Description and Objectives:

The course is designed to explicitly relate the mathematics content to classroom practice through participants engaging in inquiry based learning as students of mathematics, making mathematical connections to the school division adopted curricula materials, the Virginia Standards of Learning, and using technology as a tool for teaching and learning. Emphasis will be placed upon using the Process Standards (Connections, Communications, Reasoning and Proof, Representations, and Problem Solving) as tools for differentiation and supporting students developing strong connections to other strands of mathematics as well as to real world contexts. In addition, participants will use the Lesson Study framework as a tool for collaborative planning and reflection upon student learning.

In this course participants will deepen their understanding of experimental design and probability and statistics through exploring, analyzing, and interpreting data set. Participants will develop skills using the graphing calculator as a tool to display and analyze data. Data will be obtained from sampling, and observations, measurement, experiments and Internet sources. The course instruction will model facilitating group work, posing questions and facilitating student discourse, developing and implementing lesson designs for active learning, and making connections between multiple representations to enhance understanding.

This course will enable teachers to:

• Deepen their understanding of mathematical modeling as a tool for describing real-world relationships in mathematical terms to obtain solutions.
• Design simple investigations and collect data (through random sampling or random assignment to treatments) to answer specific questions.
• Understand and use a variety of ways to display data.
• Explore, display and interpret data by observing patterns and departures from patterns in data, particularly patterns related to spread, variability, and correlation.
• Anticipate patterns by studying, through theory and simulation, those produced by simple probability models.
• Draw conclusions with measures of uncertainty by applying basic concepts of probability.
• Become aware of current applied uses of statistics and probability.
• Understand and be able to apply the normal approximation, the central limit theorem, and basic procedures of statistical inference and hypothesis testing,

Textbooks/Readings/Other Materials (Provided through the Grant)

Cosenza, G., Gray, P., Horn, J. (2009) Modeling with Mathematics: A Bridge to Algebra II-Virginia’s Algebra, Functions, and Data Analysis. Freeman Publishing, New York, NY. ISBN 10-1-4292-2549-1

Course Requirements:

This course is highly interactive, group activities and discussions are a significant part of each class and it is where much of the learning in this course is consolidated. Therefore, active participation in class activities is crucial to success in this course. Successful completion of the course also requires regular attendance and punctual completion of all class activities and assignments. No points are deducted for the first 3 hours of class absence provided the instructor is notified of the absence and all work is made up satisfactorily and in a timely way. Additional absences from classroom instruction will result in a tw-point deduction from the final grade for each hour of class time that you miss.

Assignments that have been satisfactorily completed are well thought out, mathematically accurate, and reflect the intent of the national and state standards.

Evaluation and Assessment:

The grading scale for this course is:

A 100-93 %

A- 92-90 %

B+ 89-86 %

B 85-83 %

B- 82-80 %

C 79-70 %

F Below 70%

Class Participation (10%) Come prepared to think and exchange ideas in whole group and small group work sessions. During or after each session you will be asked to record your observations, questions, and insights in an ongoing journal. For in-class individual and small group mathematics workshops, satisfactory performance will include active efforts to use and describe the relationships between multiple representations of the problem to include contextual, concrete, pictorial, and symbolic; to reach and justify accurate solutions; and to identify underlying mathematical structure and principles and to articulate mathematical reasoning. As a part of the grant supporting this project, students are required to complete a pre/post content test and beliefs survey.

Lab Journal (20%) Entries will be based on class explorations and/or discussions, whole group and small group classroom discussions, and readings. For a 15-week class, 1 page entries will be collected weekly; for a 2- to 3-week class with 8- to 10-sessions, longer entries will be collected at the end of each week.

Homework Assignments (35%) Assignments will include mathematical exercises, readings, translating work from this course to your own classroom practice, and technology explorations. Problem set assignments will be collected throughout the course for grading.

Culminating Project (35%) The project is to be completed and presented as defined by the instructor. Student work on the final project will be incorporated throughout the course. Additional information will be provided at a later date.

Final Grades: Information about your final grade and your transcript can be accessed at the following link. http://www.virginia.edu/registrar/

University of Virginia Honor Code: All work should be pledged in the spirit of the Honor System of the University of Virginia. The instructor will indicate which assignments and activities are to be done individually and which permit collaboration. The following pledge should be written out at the end of all quizzes, examinations, individual assignments and papers: “I pledge that I have neither given nor received help on this examination (quiz, assignment, etc.)”. The pledge should be signed by the student. Students should refer to the University Graduate Record (pages 36 & 37) for more information concerning the Honor Code.

Special Needs: If you are a student with special needs, you should let the instructor know within the first week of class. Written documentation will be required. You should also visit the following website to review your rights and responsibilities as a student (http://www.virginia.edu/vpsa/rights.html) and the following website for the Learning Needs and Evaluation Center (http://www.virginia.edu/studenthealth/lnec/).