Conceptual Online Linear Algebra

The goal of this project is the development of conceptually-based, online linear algebra modules that combine the power of platform independent applets and cognitively-guided activities in order to build a local cognitive theory for various concepts in elementary linear algebra. These modules are designed for students to explore, experiment, conjecture, discuss, and extend their understandings from the concrete to the abstract. Except those applets dealing with Gaussian elimination, these tools are not typically for computation since applets for computation can be found at the Linear Algebra Toolkit web site. For samples of student work with some of these modules, see Meel & Hern (2005).

Anticipated Instruments:

- Module 1: Systems
of
Equations
- Applets:
- Cognitively-guided activity:
- Local Cognitive Theory: TBA

- Module 2: Linear
Transformations
and
Composition
of
Transformations
- Applets:
- 2D Transformation Explorer [updated]
- Transformer3D_v2 [new]
- Multiplier
- Non-square Transformer [in development]

- Cognitively-guided activity:
- Local Cognitive Theory: TBA

- Applets:
- Module 3: Vector
Spaces
- Applets:
- GridMaster_v2 [updated]
- Linear Dependence Detector [in development]

- Cognitively-guided activity:
- GradMaster activity [updated]
- In
search of the elusive matrix (paper by Meel (1999), from
*MAA Online*)

- Local Cognitive Theory:

- Applets:
- Module 4: Eigenvalues,
Eigenvectors,
Diagonalization,
and
Discrete
Dynamical Systems
- Applets:
- Cognitively-guided activity:
- Local Cognitive Theory: TBA

- Module 5: Singular-Value
Decomposition
- Applets:
- Cognitively-guided activity: TBA
- Local Cognitive Theory: TBA

- Module 6: Application-based
activities
for
Linear
Algebra
- The Projects:

- Rubric and Scoring sheets: