InterMath

Probability and Statistics Course Syllabus, Summer,2004

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Instructor:Jacquie Allison

jallison@mailstart.com


Office Address:

Davidson Fire Arts School

615 12th Street

Augusta, GA 30904

706-823-6924

 

Office Hours: Upon request.

 

Participant List:

Rosa Fields

 

 

Important Information:

InterMath Website

http://www.intermath-uga.gatech.edu

 

 

Click here to get detailed instructions to access and modify your homepage and publish write-ups.

 

 

Resouces

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ClickHere to see a list of probability and statistics articles from MathematicsTeaching in the Middle Grades.

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††††††††††††††† ClickHere to see a list of probability and statistics books with additional activities.

 

ClickHere to see an additional list of probability and statistics related web sites.

 

††††††††††††††† Click Here to find a TI 83 Plus tutorial

 

 

 

Course Policies:

This course will concentrate on using various software applications to solve mathematics problems, to organize pedagogical demonstrations, and to set up problem explorations. All materials for the course are maintained by an Internet Webpage site and students will create and use web documents in the course.

The emphasis is on exploration of various mathematics contexts to learn mathematics, to pose problems and problem extensions, to solve problems, and to communicate mathematical demonstrations.

The following technologies will be used:

GeometersSketchpad 4.04 (from http://www.keypress.com/)

GraphingCalculator 3.2 (from http://www.pacifict.com/)
Spreadsheets (recommend Microsoft Excel)
Hand Held Calculators such as TI-81, TI-82, or TI-83+ (TI: Texas Instruments)

WebPage Browser (recommend Netscape 7.0 or InternetExplorer)
Web Page Authoring Tool (recommend Microsoft Front Pageor Microsoft Word)

2. GOALS ADDRESSED

Participants will:

       Expand and strengthen their mathematical knowledge and capabilities, specifically in the domain of probability and statistics by investigating challenging probability and statistics problems

       Engage in problem solving by identifying patterns, forming conjectures, and developing proofs through the use of technology

       Use mathematics-specific technologies such as dynamic geometry software, graphing programs, spreadsheets, and the Internet to explore probability and statistics investigations

       Write and post online solution processes to the investigations using web page development software

       Develop instructional activities and strategies that incorporate technology-enhanced mathematical investigations

       Develop a network of peer educators available for continued support during and following the workshop

3. IMPROVEMENT PRACTICES

Participants will gain knowledge and practice in developing instructional activities and strategies for teaching probability and statistics in the middle school classroom in order to positively affect student achievement. Participants will also improve their own mathematical competencies in the area of probability and statistics.

4. COMPETENCIES

Participants will be able to:

       Select and use appropriate technological software to explore, analyze, and represent probability and statistics problems

       Communicate their mathematical thinking by expressing their reasoning, analysis, and extensions of the mathematical concepts associated with an investigation in written, verbal, and visual forms

       Modify probability and statistics investigations for appropriate use in classroom

       Make connections between InterMath Probability and Statistics experiences and standards-based reform documents, such as the NCTM standards

5. PERFORMANCE INDICATORS

As a result of this course, participants will demonstrate their ability to:

       Incorporate technology into the learning and teaching probability and statistics concepts

       Communicate mathematical understanding of a variety of probability and statistics concepts in the form of an online portfolio of investigation solutions

       Plan instructional activities based on InterMath Probability and Statistics experiences

6. COURSE REQUIREMENTS& ASSESSMENT

Participants will be assessed on the content and quality of their online portfolios. Feedback and suggested modifications for a select number of write-ups will be provided throughout the workshop. Assessment will be based on use of representation, analysis, appropriate selection and use of technological tools, creation of extensions, and accuracy of mathematics. In addition to the investigation write-ups, the participants will also create two independent mathematics lessons and one group lesson that integrate technology and probability and statistics for use in their own classroom. Students will read and review two articles from appropriate journals. Students will maintain a reflective journal starting with the initial class meeting.

Electronic Journal: As a part of this course, you are expected to maintain a reflective journal. This journal is a log of your experiences within the course. It should include thoughts about new skills and accomplishments that you acquire; critical incidents that occur; and your thoughts and feelings about content (mathematics/probability and statistics investigations) and technology. If you are experiencing difficulty keeping a journal, discuss it with your instructor who can provide you with additional suggestions and assistance.

 

Electronic Portfolio of Write-ups: Each person will develop a personal Web Page for the course. There will be a set of "Write-up" projects. These are the "homework" for the course. Participants are required to create at least six write-ups, three for probability and three for statistics (though some may overlap). Each Write-up will be prepared as a Microsoft Word document and linked to your personal web page.

What is a write-up?

The "write-ups" represent your synthesis and presentation of a mathematics investigation you have done --usually under the direction of one of the assignments. The major point is that it convincingly communicates what you have found to be important from the investigation. A write-up should communicate the essential material you have synthesized from your investigation. The format could be entirely in a word-processing document. Write-ups should be posted to your personal Web Page. If you work as a team on a write-up, post the write-up into each team member's Web Page but label collaborative effort. Criteria should include correct mathematics, use of technology, and how well you communicate. "Solution" might be another word for "Write-up."

 

Clickhere to see a template for write-ups.

 

Electronic Portfolio of Lesson Plans: Participants are required to create two mathematics lessons independently and one mathematics lesson in a group that integrate technology and probability and statistics for use in their own classroom. The "lessons" are to be your creations of material to incorporate technology into classroom lessons. The material can be individual lessons or a unit of material. Your criteria should be on its usability in your classroom or in other peoplesí classroom and something you feel good enough about to share with colleagues over the web.

 

Clickhere to see a template for lesson plans.

8. COURSE OUTLINE

I.Class 1

A. Introduction to InterMath
B. Introduction to Technology
C. Work through a statistics investigation as a whole class using technology
D. Participants engage in probability investigation as a whole class using technology

E. Participants complete their first web page write-ups to include in their online portfolios
F. Continued technological teaching and support (especially with Excel, TI-83Plus, and the structure of a write-up)

II.Class 2

A. Participants engage in investigations dealing with theoretical and experimental probabilities.

B. Counting principles

C. Complementary and Conditional events
D. Participants engage in activities dealing with probability and the calculator to reinforce their graphing calculator skills.
E. Participants complete web page write-ups to include in their online portfolios.

III.Class 3

A. Participants engage in investigations dealing with simulating probabilities.

B. Participants engage in investigations dealing with expected value

C. Participants engage in investigations dealing with displaying and interpreting data
D. Participants engage in activities dealing with statistics and the calculator to reinforce their graphing calculator skills

E. Participants complete web page write-ups to include in their online portfolios

IV. Classes 4

A. Participants engage in the mean, median and mode investigations

B. Participants will investigate conducting surveys and sampling.
C. Participants add write-ups to their online portfolios

D. Participants revisit and revise one or more write-ups in their online portfolio.

E. Each participant creates a technology-enhanced mathematical investigation for their own classroom.
F. Participants are encouraged to collaborate with each other for ideas and feedback.
 

V.Class 5

A. Participants complete investigations based on measures of dispersion.

B. Participants will collect and analyze data using Ranger and calculator
C. Participants add write-ups to their online portfolios

D. Participants will add their lesson plan to their on-line portfolios

VI.Class 6

A. Participants participate in a discussion about the significance of statistics.

B. Participants engage in investigations based on real-world statistics.

C. Participants will write a report based on experimental or observational data.
D. Discuss and brainstorm ideas about modifying InterMath experience for a middle school mathematics classroom 

VII.Class 7

A. Each participant creates a technology-enhanced mathematical investigation for their own classroom.
B. Participants are encouraged to collaborate with each other for ideas and feedback.

C. Participants will add their lesson plan to their on-line portfolios.

VIII.Class 8

A. Each participant presents their instructional activity to the entire class.
B. If the activity was implemented in the classroom, participant will discuss what went well, what was difficult, what can be improved, etc.
C. Each participant will take a mathematics exam

9.MATHEMATICAL CONTENT EXPLORED THROUGHTHE INVESTIGATIONS
(
ClickHere to see a list of selected InterMath investigations clustered for Data Analysis ) 

Probability Objectives

 

P1.   

To identify possible outcomes of a simple experiment and calculate the probability of the event.

P2. 

To identify appropriate counting techniques and calculate possible outcomes.

P3. 

To explore the relationship between experimental and theoretical probabilities including: making predictions of outcomes, conducting simulations, and analyzing results of simulations.

P4. 

To conduct a compound experiment and analyze the results.

P5. 

To model situations using simulations.

P6. 

To apply probability in a practical, real-life setting.

P7. 

To explore concepts of chance.

P8. 

To calculate odds and relate them to probability.

P9. 

To use appropriate technology for computation and exploration of probability.

 

Statistics Objectives

 

S1. 

To explore and use a variety of data collections methods.

S2. 

To formulate and solve problems that involve collecting and analyzing data.

S3. 

To construct, read, and interpret displays of data (i.e. scatterplots, box and whisker plot, circle graphs, histograms, bar graphs, stem and leaf plots, line plots, line graphs, pictographs, frequency distributions).

S4. 

To make inferences and convincing arguments that are based on data analysis.

S5. 

To evaluate arguments that are based on data analysis.

S6. 

To develop an appreciation for statistical methods as a powerful means for decision making process.

S7. 

To select an appropriate graph and scale for displaying data (i.e. scatterplots, box and whisker plot, circle graphs, histograms, bar graphs, stem and leaf plots, line plots, line graphs, pictographs).

S8. 

To describe a set of data using measures of central tendency (mean, median, mode).

S9. 

To select, justify, and use an appropriate measure of central tendency to describe a set of data (mean, median, mode).

S10. 

To describe a set of data using measures of dispersion (standard deviation, variance, range, interquartile range).

S11. 

To select, justify, and use an appropriate measure of dispersion (standard deviation, variating, range, interquartile).

S12. 

To hypothesize outcomes of experiments.

S13. 

To calculate and interpret measures of position (quartiles, percentiles, median, stanine, deciles).

S14. 

To identify, locate, and explore resources for real world data (internet, almanacs, people, census).

S15. 

To design, construct, administer, analyze, and interpret surveys/experiments to investigate real world problems.

S16. 

To calculate measures of central tendency and dispersion using appropriate tools.

S17. 

To make predictions and conclusions based on data displays.

S18. 

To recognize when statistics have been used incorrectly (in the media, in polls, or other interpretations).

S19. 

To use statistics to persuade an audience.

 

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