Conceptual Algebra Project [An Ed391 Web Tech Project]

1. Conceptual Algebra Project[An Ed391 Web Tech Project] Adam Royalty David Tu Autumn 2005, Stanford University

2. Motivation Source: National Center For Education Statistics Trends in International Mathematics And Science Study (TIMSS)

3. Motivation • California State Board of EducationContent Standards • 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

4. Motivation • What is conceptual understanding??? • Concept mapping is a powerful tool for linking knowledge and could be a key to developing strong performance assessments that ought to be designed to generate both an assessment of how students are applying concepts and to assess the deep understanding that students are gaining…[North Central Regional Educational Laboratory]

5. Motivation • Algebra + Concept Map  • CONCEPTUAL ALGEBRA • Help the students form their own conceptual map about Algebra…

6. Dale’s Cone of Experience

7. Objective Statement The objective of this project is to develop a prototype of an E-Learning platform that aims at developing middle school and high school students’ conceptual understanding of Intermediate Algebra, through the use of concept mapping tools. The expected results are four-fold: 1) Create students who can contrast, connect, associate, and define topics in Algebra I. 2) Teach students to solve, calculate, define, and describe the mathematical processes of Algebra I. 3) Give students the ability to apply, illustrate, discuss, analyze, and classify real-world problems, and 4) Motivate students through a more engaging approach to mathematics.

8. ABCD-Audience The audiences are typically 9th grade students in the United States, but open to all middle school and high school students taking Intermediate Algebra.

9. ABCD-Behavior • Positive difference in the level of conceptual understanding of the topic • Positive difference in knowledge gained on the topic • Ability to apply to real-world problems related to the topic • Positive difference in motivation to learn mathematics • Summarize topics studied in the course • Compare and contrast dependence of topics on each other • Define relevant terms • Identify properties of linear equations and polynomials • Connect topics and lessons • Explain mathematical procedures

10. ABCD-Condition The program will primarily be integrated into Intermediate Algebra classrooms in the United States. The requirements for the classrooms are one computer per each/two student(s), with access to the Internet*. The computer requirements are fairly low, primarily limited by the requirements for Internet Explorer 6 and Macromedia Flash 10. As for network requirements, a 56k modem should suffice.

11. ABCD-Degree • Positive difference in the level of conceptual understanding of the topic • Positive difference in knowledge gained on the topic • Ability to apply to real-world problems related to the topic • Positive difference in motivation to learn mathematics

12. Gagne

13. Technology Shopping List

14. Technology Shopping List

15. Technology Shopping List

16. Storyboard

17. Prototype

18. Existing CMap Conceptual Algebra Tools Add Polynomials Simplify Exponentials Divide Exponentials Zoom Exponentials Multiply Exponentials ExistingNodes Next

19. Choice Conceptual Algebra Tools Divide Polynomials ?? Add Polynomials ?? Multiply Polynomials Simplify Exponentials Divide Exponentials FutureNodes Zoom ChoiceNodes Exponentials Multiply Exponentials ExistingNodes

20. Objective Conceptual Algebra The topic covered in this module is multiplying polynomials. We will start by multiplying monomials: Then we will multiply monomials by polynomials: Finally, we will multiply polynomials by polynomials: Tools Key Next

21. Preview Conceptual Algebra After completing this module, you will know how to solve this problem: You will multiply out the components to get this: And then combine terms to reach the answer: Tools Key Next

22. Add Link Conceptual Algebra AddLink What do you need to know to Multiply Polynomials? Add Polynomials DeleteLink X Multiply Polynomials Simplify Exponentials Divide Exponentials Zoom ChoiceNodes Exponentials Multiply Exponentials ExistingNodes

23. Add Link Conceptual Algebra AddLink Add Polynomials DeleteLink X Multiply Polynomials Simplify Exponentials Divide Exponentials Zoom ChoiceNodes Exponentials Multiply Exponentials ExistingNodes Next

24. Review Conceptual Algebra • Lets review a topic that we must understand in order to successfully multiply polynomials. • Power of a product: • Remember when multiplying • like bases, add their exponents Tools Key Next

25. Tutorial 1 Conceptual Algebra Here you will learn to multiply a monomial by a monomial: Remember the power of a product is the sum of the powers: Tools Key Next

26. Exercise 1 Conceptual Algebra Now you try to solve this: Input your answer here: Tools Key Answer… Submit

27. Example 1 Conceptual Algebra • Let’s see another example of multiplying a monomial by a monomial: • Treat fractions like other numbers, • and don’t be thrown off by strange • variable symbols Tools Key Next

28. Tutorial 2 Conceptual Algebra Now let’s multiply a monomial by a polynomial: Use the distributive law: Use the power of a product rule: Simplify: Tools Key Next

29. Exercise 2 Conceptual Algebra Now you try an example: Input your solution here: Tools Key Answer… Submit

30. Example 2 Conceptual Algebra Here is a slightly more complicated example of multiplying a monomial by a polynomial: Tools Key Next

31. Tutorial 3 Conceptual Algebra We now turn towards a key concept: multiplying polynomials by polynomials. To help us remember this process, we will introduce the acronym F.O.I.L. F.O.I.L. stands for First Outer Inner Last Tools Key Next

32. Exercise 3 Conceptual Algebra Now try this exercise: Input your solution here: Tools Key Answer… Submit

33. Example 3 Conceptual Algebra • Let’s view an example similar to the problem you just worked: • F.O.I.L. Tools Key Next

34. Tutorial 4 Conceptual Algebra In our final tutorial, we will F.O.I.L. two more complicated polynomials: Tools Key Next

35. Exercise 4 Conceptual Algebra Here is a familiar problem: Input your answer here: Tools Key Answer… Submit

36. Example 4 Conceptual Algebra Our final example is another problem that requires us to F.O.I.L.: Tools Key Next

37. Add Link Conceptual Algebra AddLink Do you want to add more links? Add Polynomials DeleteLink X Multiply Polynomials Simplify Exponentials Divide Exponentials Zoom ChoiceNodes Exponentials Multiply Exponentials ExistingNodes Next

38. Add Link Conceptual Algebra AddLink Add Polynomials DeleteLink X Multiply Polynomials Simplify Exponentials Divide Exponentials Zoom ChoiceNodes Exponentials Multiply Exponentials ExistingNodes Next

39. Compare Conceptual Algebra Add Polynomials AddLink Student Model DeleteLink Divide Exponentials X Simplify Exponentials Multiply Polynomials Exponentials Multiply Exponentials Add Polynomials Expert Model ChoiceNodes Divide Exponentials Simplify Exponentials Multiply Polynomials ExistingNodes Exponentials Multiply Exponentials Next

40. Assessment Conceptual Algebra Test your skills by solving this problem: Tools Key

41. http://www.zoomerang.com/survey.zgi?p=WEB224UHDVYNQ6 Sample Result A good start, more can be added Be able to explain differences between student and expert models Roll-over node and see example/video of the mathematics Survey for User Testing