Designing an Online Math Course: Questions and Answers

1. Designing an Online Math Course: Questions and Answers Burt Granofsky EdTech Leaders Online

2. Overview: What are we trying to create? • Online PD course for elementary teachers (grades 3-5) about fractions • Help teachers gain specific techniques for teaching fractions to students • Provide teachers with problems that stretch their understanding and allow them to wrestle with the mathematical content • Something more interesting than “methods of solving fraction problems” course • Ultimate goal: Impact student achievement

3. Design Parameters • 6 sessions, 4-5 hours per session • Video, discussion board required • Align content to: • NCTM and state math standards • ISTE standards • Must be interactive, allow for engagement in mathematics • Must fit into a set course design template

4. Design Questions • How do we present fractions in an interactive, non-textbook way? • Do we stress content, pedagogy, or both? • How do we create a course that is mathematically-engaging and that treats teachers in a professional way?

5. Math Questions • How much should we emphasize fraction operations (+, -, *, )? • How much should we emphasize fraction models? • How can we use existing research on fractions to help us shape the course? • How do we create a course that is mathematically-engaging and that treats teachers in a professional way?

6. Design Question 1 • How do we present fractions in an interactive, non-textbook way? • Use video, online manipulatives, discussion board as tools • “Learning by doing” philosophy • Focus on teacher thinking about the math, and using online tools to promote this thinking • Use available technology to get away from “set of problems” model

7. Design Question 2 • Do we stress content, pedagogy, or both? • If focus solely on content, teachers do not learn how to teach • If focus solely on pedagogy, teachers do not learn more about fractions • Needs to be combined approach • Individual math problems address the content • Discussion board, readings address the pedagogy • Videos address both content and pedagogy

8. Math Question 1 • How much should we emphasize fraction operations (+, -, *, )? • Big decision; shapes how course is designed • Assumption: many teachers are not as comfortable with fraction operations as they should be • If operations focus, teachers would leave with concrete skills • Problem: Cannot cover all 4 operations well in 6-session course!

9. Math Question 2 • How much should we emphasize fraction models? • Assumption: Most teachers are not familiar with different models for teaching fractions • If conceptual focus, teachers may leave with more knowledge of models, but does this translate into more content knowledge? • Decision: Through focus on linear and area models, teachers will have more resources to use in teaching, and content knowledge will increase through using models

10. Math Question 3 • How can we use existing research on fractions to help us shape the course? • NCTM 2002 Yearbook: Making Sense of Fractions, Ratios, and Proportions • Basis for understanding how students think about fractions • Liping Ma: Knowing and Teaching Elementary Mathematics • Helps us think about what teachers need to know

11. Math Question 3 (cont’d) • How can we use existing research on fractions to help us shape the course? • Examine different elementary math curricula to figure out how students are being taught • Use a content expert: Andee Rubin • Result: Focus on Area model, Linear model • Area model most prevalent in US education • Linear model emphasized in some of course readings, prevalent in Japan • Not used: Discrete model, Rate model

12. The Big Question • How do we create a course that is mathematically-engaging and that treats teachers in a professional way? • Present fraction problems in a new way through use of online technologies • Require that they struggle with content, while allowing them to share valuable pedagogical ideas over discussion board • Weave thread of student thinking through course, especially through videos, interview • Pedagogy trumps content

13. Now What?(Is the hard work done, or is it just beginning?)

14. Sources of Inspiration (or Frustration!) • NCTM Principles and Standards • National Library of Virtual Manipulatives • Developing Mathematical Ideas Series • Reform Curricula • Investigations (TERC) • MathScape (EDC) • www.arcytech.org • www.learner.org

15. Persistent Questions • How can we best use video in this course? • Show student thinking? • Show good teacher practice? • Small group vs. realistic classroom • Are we providing teachers with a good balance of content and pedagogy? • Are teachers learning something? • If so, it is valuable knowledge? • If not, how can we fix it?

16. Were We Successful? • “This workshop has really put the struggle students have with fractions into perspective.  No wonder they don't like them.  If all they have been told is the algorithm (the way that I learned fractions), then it doesn't make sense.  If you are good at memorizing you are going to get by, as long as someone doesn't ask you why it works. ”

17. Were We Successful? (Part II) • “My ideas about how to teach students about fractions has changed with my experiences in this class.  I honestly didn't know there were so many different ways to model fractions and fraction operations.  I was very familiar with the area model, and not at all with the linear model.  It surprises me how challenging the linear model is for me, however I think it is from lack of experience using it.  I would like to continue tinkering with it for my own learning.”