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Proportional Reasoning**
 
Course Description
    

In this course, participants will learn about different components and levels of proportional reasoning. They will complete classroom tasks that illustrate ways to develop stronger conceptual understanding and target different components of proportional reasoning. They will use video and written examples of student work. They will also conduct a student interview in order to reflect on studentsÂ’ approaches to proportions problems and to identify evidence of proportional reasoning at various levels. For the final project, participants will create a lesson that targets a component of proportional reasoning and that incorporates questioning techniques learned in the course. They will provide a rationale for the lesson that relates to the material learned in the course and reflect on their own learning.

**This course is open to all certified WV educators of mathematics grades 6-8.
 

 
Course Syllabus
    

In this course, participants will learn about different components and levels of proportional reasoning. They will complete classroom tasks that illustrate ways to develop stronger conceptual understanding and target different components of proportional reasoning. They will use video and written examples of student work. They will also conduct a student interview in order to reflect on studentsÂ’ approaches to proportions problems and to identify evidence of proportional reasoning at various levels. For the final project, participants will create a lesson that targets a component of proportional reasoning and that incorporates questioning techniques learned in the course. They will provide a rationale for the lesson that relates to the material learned in the course and reflect on their own learning.

Goals and Objectives

This course will enable participants to:

Understand and identify different components and levels of proportional reasoning

Broaden their repertoire of classroom tasks to use to develop students' conceptual understanding of proportionality

Develop skills and tools for analyzing students' thinking about proportionality

Apply those skills and tools to a lesson on proportional reasoning that is appropriate for middle school students

As a final product, participants will create a lesson plan related to proportional reasoning promoting both conceptual and procedural understanding that can be used in the classroom. The final project should be designed around particular learning goal(s) connected to an area of proportional reasoning. There are two key companion elements to the final project: The Student Interview and The Personal Reflection. The Student Interview is described in Session 4 and is to be conducted in Session 5. The Personal Reflection consists of a series of questions that you will answer throughout the course and complete during Session 6.

Audience

This is an introductory course for teachers, technology specialists, curriculum specialists, professional development specialists, or other school personnel. Participants are expected to have regular access to computers. In addition, participants should be proficient with using email, browsing the Internet, and navigating to computer files.

Course Details

This is an introductory course for teachers, technology specialists, curriculum specialists, professional development specialists, or other school personnel. Participants are expected to have regular access to computers. In addition, participants should be proficient with using email, browsing the Internet, and navigating to computer files.

Session One: Proportional Reasoning - More Than Just Cross Products

Session Two: Recognizing When a Situation is Proportional

Session Three: Understanding Ratios

Session Four: Reasoning About Relationships

Session Five: Questioning Strategies for Uncovering Student Thinking

Session Six: Building on StudentsÂ’ Proportional Reasoning in the Classroom

Assessment

Specific questions about assessment, expectations, or requirements should be directed to the facilitator of this course.

ETLO recommends that the following criteria be used to determine successful completion of this course:

Participation in all session discussion forums;

Completion of the course’s final project, submitted to the facilitator and/or posted in the appropriate discussion forum; and

Completion of the orientation and final course surveys.

Readings and Activities:
Participants are expected to complete the required course readings and activities as posted in each of the session assignment pages. Optional readings may also be completed, but are not mandatory.

Orientation Quiz & Pre & Post Course Surveys: 
Participants must complete an Orientation Quiz with a score of 90% or higher.  In addition, participants are expected to complete both a pre-course and a post-course surveys. The Orientation Survey is to be completed by Sunday during the Orientation Session and the Final Survey is to be completed by Sunday during Session Six.

Discussion Participation: 
Participants will be evaluated weekly on the frequency and quality of their participation in the discussion forum.  Participants are required to post a minimum of one substantial original posting each session in response to the discussion prompt for that session by Sunday evening. Participants are to respond thoughtfully to a minimum of two colleagues' original postings each session by Monday evening. They are to read all original messages by course participants and enough additional responses to make a total of 50% of the messages posted for that session by Tuesday evening. Postings will be evaluated on their relevance, demonstrated understanding of course concepts, examples cited and overall quality.  .

Copyright and Plagiarism

All resources referenced during the course will be properly documented. Copyright guidelines are to be observed throughout the course project and all course activities.  All work associated with course projects, course assignments and course discussions will be original to each course participant. Fair use does not apply to the course project. 

Plagiarism, the reproduction of all or any part of another individual’s or organization’s work, by a course participant of work associated with the course project or other course assignments at any point during the course will result in no credit being awarded for the course.

Grades

All grades in the course gradebook must be a "C" for successful course completion.  A grade of "C" indicates that all work has been completed and the work meets the expectations for that assignment.

The grade scheme for this course will be:
C = all work meets the guidelines provided
I = the work submitted is incomplete and/or does not meet the guidelines provided
N = no work has been submitted

Certificates of Completion

Upon successful completion of this course, Promoting Reading Comprehension in the Middle School, participants will receive a Certificate of Completion documenting successful completion of the course requirements. Certificates are distributed to each qualifying participant as a file attachment to the Session Six Dropbox shortly after the completion of the course.  Certificates of Completion are not recognized as being an official course transcript.

Non-Degree Graduate Credit Information

Participants in this course are eligible to receive non-degree graduate credits from either West Virginia University, Concord University. West Virginia State University or Marshall University. Credits will be awarded at the end of the semester in which the course occurs. Additional information is available on the course News/Welcome Page.

 

Standards

This course will help teachers to enable their students to meet the following Content Standards as identified by National Council for Teachers of Mathematics (NCTM) (http://standards.nctm.org/document/chapter6/index.htm)

Number Strand: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Understand and use ratios and proportions to represent quantitative relationships.

Number Strand: Compute fluently and make reasonable estimates

Develop, analyze and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Algebra Strand: Analyze change in various contexts

Use graphs to analyze the nature of changes in quantities in linear relationships.

Problem-Solving Standard

Solve problems that arise in mathematics and other contexts

Apply and adapt a variety of appropriate strategies to solve problems.

Connections Standard

Recognize and use connections among mathematical ideas

Understand how mathematical ideas interconnect and build on one another to produce a coherent whole

This course will also help participants meet the ISTE Educational Technology Standards and Performance Indicators for All Teachers.

About this Course

This course was developed by EdTech Leaders Online (http://edtechleaders.org) at Education Development Center, in partnership with Alabama Public Television (http://www.aptv.org/), and the e-Learning for Educators project, funded by a US Department of Education Ready to Teach grant. EdTech Leaders Online provides capacity-building training and online courses for school districts, state departments of education, and colleges and universities. Alabama Public Television is the nation's first educational television network and is the lead agency coordinating the eight state E-Learning for Educators collaboration, comprised of state departments of education and public television stations in Alabama, Delaware, Kentucky, Mississippi, Missouri, New Hampshire, Pennsylvania and West Virginia.