Advanced Search
All Posts : Applications, Examples and Libraries

I'm back from presenting work in the "23rd Conference on Applications of Computer Algebra - 2017" . It was a very interesting event. This first presentation, about "Active Learning in High-School Mathematics using Interactive Interfaces", describes a project I started working 23 years ago, which I believe will be part of the future in one or another form. This is work actually not related to my work at Maplesoft.

At the end, there is a link to the presentation worksheet, with which one could open the sections and reproduce the presentation examples.
 

 

Active learning in High-School mathematics using Interactive Interfaces

 

Edgardo S. Cheb-Terrab

Physics, Differential Equations and Mathematical Functions, Maplesoft

 

Abstract:


The key idea in this project is to learn through exploration using a web of user-friendly Highly Interactive Graphical Interfaces (HIGI). The HIGIs, structured as trees of interlinked windows, present concepts using a minimal amount of text while maximizing the possibility of visual and analytic exploration. These interfaces run computer algebra software in the background. Assessment tools are integrated into the learning experience within the general conceptual map, the Navigator. This Navigator offers students self-assessment tools and full access to the logical sequencing of course concepts, helping them to identify any gaps in their knowledge and to launch the corresponding learning interfaces. An interactive online set of HIGIS of this kind can be used at school, at home, in distance education, and both individually and in a group.

 

 

Computer algebra interfaces for High-School students of "Colegio de Aplicação"  (UERJ/1994)

   

Motivation

 

 

When we are the average high-school student facing mathematics, we tend to feel

 

• 

Bored, fragmentarily taking notes, listening to a teacher for 50 or more minutes

• 

Anguished because we do not understand some math topics (too many gaps accumulated)

• 

Powerless because we don't know what to do to understand (don't have any instant-tutor to ask questions and without being judged for having accumulated gaps)

• 

Stressed by the upcoming exams where the lack of understanding may become evident

 

Computer algebra environments can help in addressing these issues.

 

 

• 

Be as active as it can get while learning at our own pace.

• 

Explore at high speed and without feeling judged. There is space for curiosity with no computational cost.

• 

Feel empowered by success. That leads to understanding.

• 

Possibility for making of learning a social experience.

 

Interactive interfaces

 

 

 

Interactive interfaces do not replace the teacher - human learning is an emotional process. A good teacher leading good active learning is a positive experience a student will never forget

 

 

Not every computer interface is a valuable resource, at all. It is the set of pedagogical ideas implemented that makes an interface valuable (the same happens with textbooks)

 

 

A course on high school mathematics using interactive interfaces - the Edukanet project

 

 

– 

Brazilian and Canadian students/programmers were invited to participate - 7 people worked in the project.

 

– 

Some funding provided by the Brazilian Research agency CNPq.

Tasks:

-Develop a framework to develop the interfaces covering the last 3 years of high school mathematics (following the main math textbook used in public schools in Brazil)

- Design documents for the interfaces according to given pedagogical guidelines.

- Create prototypes of Interactive interfaces, running Maple on background, according to design document and specified layout (allow for everybody's input/changes).

 

The pedagogical guidelines for interactive interfaces

   

The Math-contents design documents for each chapter

 

Example: complex numbers

   

Each math topic:  a interactive interrelated interfaces (windows)

 

 

For each topic of high-school mathematics (chapter of a textbook), develop a tree of interactive interfaces (applets) related to the topic (main) and subtopics

 

Example: Functions

 

• 

Main window

 

• 

Analysis window

• 

 

• 

Parity window

• 

Visualization of function's parity

• 

Step-by-Step solution window

The Navigator: a window with a tile per math topic

 

 

 

• 

Click the topic-tile to launch a smaller window, topic-specific, map of interrelated sub-topic tiles, that indicates the logical sequence for the sub-topics, and from where one could launch the corresponding sub-topic interactive interface.
• 

This topic-specific smaller window allows for identifying the pre-requisites and gaps in understanding, launching the corresponding interfaces to fill the gaps, and tracking the level of familiarity with a topic.

 

 

 

 

 

The framework to create the interfaces: a version of NetBeans on steroids ...

   

Complementary classroom activity on a computer algebra worksheet

 

 

This course is organized as a guided experience, 2 hours per day during five days, on learning the basics of the Maple language, and on using it to formulate algebraic computations we do with paper and pencil in high school and 1st year of undergraduate science courses.

 

Explore. Having success doesn't matter, using your curiosity as a compass does - things can be done in so many different ways. Have full permission to fail. Share your insights. All questions are valid even if to the side. Computer algebra can transform the learning of mathematics into interesting understanding, success and fun.

1. Arithmetic operations and elementary functions

   

2. Algebraic Expressions, Equations and Functions

   

3. Limits, Derivatives, Sums, Products, Integrals, Differential Equations

   

4. Algebraic manipulation: simplify, factorize, expand

   

5. Matrices (Linear Algebra)

   

 

Advanced students: guiding them to program mathematical concepts on a computer algebra worksheet

   

Status of the project

 

 

Prototypes of interfaces built cover:

 

• 

Natural numbers

• 

Functions

• 

Integer numbers

• 

Rational numbers

• 

Absolute value

• 

Logarithms

• 

Numerical sequences

• 

Trigonometry

• 

Matrices

• 

Determinants

• 

Linear systems

• 

Limits

• 

Derivatives

• 

Derivative of the inverse function

• 

The point in Cartesian coordinates

• 

The line

• 

The circle

• 

The ellipse

• 

The parabole

• 

The hyperbole

• 

The conics

More recent computer algebra frameworks: Maple Mobius for online courses and automated evaluation

   

 


 

Download Computer_Algebra_in_Education.mw

Download Computer_Algebra_in_Education.pdf

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft
algebra

Please Wait...