Conceptual Algebra Project [An Ed391 Web Tech Project]

1
Conceptual Algebra ProjectAn 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 gainingNorth
  Central Regional Educational Laboratory

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Motivation

• Algebra Concept Map ?
• CONCEPTUAL ALGEBRA
• Help the students form their own conceptual map
  about Algebra

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Dales Cone of Experience
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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.

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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.

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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

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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.

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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
EVENT PROCEDURE-ACTIVITY
1. Gaining attention Begins w/ Concept Map
2. Informing the learner of the objective A screen with goals before each exercise
3. Stimulating recall of prior learning Show current node structure
4. Presenting the stimulus material Worked examples
5. Providing learning guidance Vertically layered explanation with side notes
6. Eliciting the performance Dispersed questions
7. Providing feedback Summative assessment and comparison w/ expert CMap model
8. Assessing performance Summative assessment
9. Enhancing retention and transfer Node connection links ideas
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Technology Shopping List
  Producer Host Consumer
Hardware IBM desktop computer Ö Linux servers in a Beowulf Cluster Any desktop/notebook computer that can support the software Ö
Network Connection Speed DSL Kbps Ö Speed T3 Kpbs Speed DSL Kpbs Ö
Software Microsoft 2000, Apache, Web Server, MySQL, PHP, Flash Player, JavaScript Ö Redhat Linux, Apache Web Server, MySQL, PHP, FTP Internet Explorer or Safari or FireFox or Mozilla (on any OS), Flash Player, JavaScript Ö
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Technology Shopping List
  Authoring Hosting Delivery
Curriculum N/A N/A N/A
Course MS Word, MS Excel, Photoshop, Flash, PHP, Javascript Redhat Linux, Apache Web Server, MySQL, PHP Internet Explorer or Safari or FireFox or Mozilla (on any OS), Flash Player, JavaScript
Lesson MS Word, MS Excel, Photoshop, Flash, PHP, Javascript Redhat Linux, Apache Web Server, MySQL, PHP Internet Explorer or Safari or FireFox or Mozilla (on any OS), Flash Player, JavaScript
Topic MS Word, MS Excel, Photoshop, Flash, PHP, Javascript Redhat Linux, Apache Web Server, MySQL, PHP Internet Explorer or Safari or FireFox or Mozilla (on any OS), Flash Player, JavaScript
Content Module MS Word, MS Excel, Photoshop, Flash, PHP, Javascript Redhat Linux, Apache Web Server, MySQL, PHP Internet Explorer or Safari or FireFox or Mozilla (on any OS), Flash Player, JavaScript
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Technology Shopping List
Product Group or Supplier Questions
Linux servers in a Beowulf Cluster Reliability, Redundancy, Backup Cycles, Contingency Plans, Compatibility
ISP Reliability, Speed, Contingency Plans
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Storyboard
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Prototype
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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
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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
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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
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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
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Exercise 1
Conceptual Algebra
Now you try to solve this Input your answer
here
Tools
Key
Answer Submit
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Example 1
Conceptual Algebra
Lets see another example of multiplying a
monomial by a monomial
Treat fractions like other numbers,
and dont be thrown off by
strange variable symbols
Tools
Key
Next
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Tutorial 2
Conceptual Algebra
Now lets multiply a monomial by a
polynomial Use the distributive law Use
the power of a product rule Simplify
Tools
Key
Next
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Exercise 2
Conceptual Algebra
Now you try an example Input your solution
here
Tools
Key
Answer Submit
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Example 2
Conceptual Algebra
Here is a slightly more complicated example of
multiplying a monomial by a polynomial
Tools
Key
Next
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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
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Exercise 3
Conceptual Algebra
Now try this exercise Input your solution
here
Tools
Key
Answer Submit
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Example 3
Conceptual Algebra
Lets view an example similar to the problem you
just worked

F.O.I.L.
Tools
Key
Next
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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
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Example 4
Conceptual Algebra
Our final example is another problem that
requires us to F.O.I.L.
Tools
Key
Next
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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
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Survey for User Testing

• http//www.zoomerang.com/survey.zgi?pWEB224UHDVY
  NQ6

• 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