Geogebra

GeoGebra

Introduction: What is GeoGebra and How Does It Work?

Background Information About GeoGebra

GeoGebra is dynamic mathematics software for schools that joins geometry, algebra, and calculus.

On the one hand, GeoGebra is an interactive geometry system. You can do constructions with points, vectors, segments, lines, and conic sections as well as functions while changing them dynamically afterwards.

On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors, and points. It finds derivatives and integrals of functions and offers commands like Root or Vertex.

These two views are characteristic of GeoGebra: an expression in the algebra window corresponds to an object in the geometry window and vice versa.

GeoGebra’s User Interface

GeoGebra’s user interface consists of a graphics window and an algebra window. On the one hand you can operate the provided geometry tools with the mouse in order to create geometric constructions on the drawing pad of the graphics window. On the other hand, you can directly enter algebraic input, commands, and functions into the input field by using the keyboard. While the graphical representation of all objects is displayed in the graphics window, their algebraic numeric representation is shown in the algebra window.

The user interface of GeoGebra is flexible and can be adapted to the needs of your students. If you want to use GeoGebra in early middle school, you might want to hide the algebra window, input field, and coordinate axes and just work with the drawing pad and geometry tools. Later on, you might want to introduce the coordinate system using a grid to facilitate working with integer coordinates. In high school, you might want to use algebraic input in order to guide your students through algebra on into calculus.

Drawing Geometric Figures and Other Objects

Preparations

• Hide the algebra window and coordinate axes (View menu).
• Show the coordinate grid (View menu).

Drawing pictures with GeoGebra

Use the mouse and the following selection of tools in order to draw figures on the drawing pad (e.g. square, rectangle, house, tree,…).

	New point
	Move
	Line through two points
	Segment between two points
	Delete object
	Undo / Redo buttons
	Move drawing pad
	Zoom in / Zoom out

Square Construction

In this activity you are going to use the following tools. Make sure you know how to use each tool before you begin with the actual construction of the square:

	Segment between two points			Polygon
	Perpendicular line			Show / hide object
	Circle with center through point			Move
	Intersect two objects

Construction process

1. Draw segment a = AB between points A and B
2. Construct perpendicular line b to segment AB through point B
3. Construct circle c with center B through point A
4. Intersect circle c with perpendicular line b to get intersection point C
5. Construct perpendicular line d to segment AB through point A
6. Construct circle e with center A through point B
7. Intersect perpendicular line d with circle e to get intersection point D
8. Create polygon ABCD.
   Hint: Don’t forget to close the polygon by clicking on point A after selecting point D.
9. Hide circles and perpendicular lines
10. Perform the drag test to check if your construction is correct

Week 8

Date:
8 March 2010 (Mon)

Details:
Using Mic.Excel to record student's marks, grades, calculate average and standard deviation.


Here i attached the example we have done in lecture. You can click on the image to make it larger.

Week 5

Date:
10 Feb 2010 (Mon)

Details:
We are given a group task on Composite Function. Our group members are Saras, Dayang and myself.

Composite Function

Week 5

Date:
8 Feb 2010

Details:
Exploring Power Point to create slides for teaching. We can insert images, sounds, animations, videos, hyperlink, etc to make the slides look more interesting to students.

Week 3 (ii)

Date:
3 Feb 2010 (Mon)

Details:
We are required to use Math Equation in Microsoft Word to make some math questions.

Example: Matrices

Week 3 (i)

Date:
3 Feb 2010 (Mon)

Details:
Today we learned about instructional design models suitable for teaching mathematics.

Information below is taken from:
http://web.hku.hk/~jwilam/PCEd_FT_2003_IT/crsware.htm#bm_2


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Instructional Courseware

Today, teachers are utilizing computers in their classrooms for more than the basic productivity tools of word processors, spreadsheets, and databases. A new breed of software, instructional courseware, may be exactly what you are looking for to spark students' interest and to teach challenging subjects to your students.

Overview of Instructional Courseware

Several terms have been used in recent years with respect to instructional courseware, but one that is particularly well suited for our purposes is computer-assisted (or aided) instruction (CAI). CAI may be used as a supplement for your instruction or as a complete lesson.With CAI, the computer can assist the teacher in implementing any or all of the four essential phases of instruction:

# presenting information
# guiding the student
# providing student practice
# assessing student learning

Commercial software vendors release new instructional courseware titles in ever increasing numbers. As a teacher, you must determine when to implement CAI in the classroom and what CAI to use. Additionally, you can create your own CAI with authoring tools that are readily available and relatively easy to use. An authoring system is a computer program that lets you create instructional software of your own. In cases where no suitable CAI exists, this may be your only option to provide your students with instructional courseware.
Return to Table of Contents

Types of Courseware

Generally speaking, there are five types of CAI. Each methodology has its own particular strengths and are discussed briefly below. The five types are:

# Tutorials
# Drills
# Instructional games
# Simulations
# Tests

Tutorials

Purpose: Present information and guide the student
Example: This lesson on courseware

Tutorials strive to provide sequenced, interactive material, to the learner. The learner is engaged in direct and continual two-way communication with the computer, i.e., an active participant. A tutorial is ideal for presenting new material, allowing students to progress at their own pace, and reviewing previously learned subjects.

You can design a tutorial in linear fashion (like a book) or with branching that allows students to control the lesson by their choices. Regardless of the type of design, tutorials should include embedded questions and remediation loops to ensure learners master material before moving on to more difficult concepts.

Advocates of tutorials suggest that they can facilitate learning better than a teacher because of the one-to-one learning. Many tutorials permit students to learn at an individualized rate. When you choose to incorporate a tutorial into your lesson, make sure that it matches your objectives, goals, and content. Review of tutorials prior to using them in class will ensure that they meet your needs. Tutorials are often combined with other types of computer assisted instruction such as drills.

Drills

Purpose: Provide student practice
Example: Math Blaster; Reader Rabbit

Computer-based drills can take the practice previously found in workbooks and flash cards to a higher level. When used in conjunction with other computer assisted instruction, usually a tutorial, drills are not intended to teach new material. Drills are designed to give students the opportunity to practice what they've already learned. Some of the arguments for using the drill software is that the software can determine the proper level of difficulty based on student ability, ensure completion, provide feedback to mistakes, suggest supplemental activities, and depending on its' design, record student results. Some drill software lets you incorporate randomly generated questions, interactive graphics, pacing and time measured responses, and student progress updates.

Many drills are used in subjects such as mathematics, foreign languages, spelling, grammar, and vocabulary, but they are suitable for practically all subjects that require the student to memorize facts.

Instructional Games

Purpose: Provide student practice and present information
Example: Where in the world is Carmen SanDiego

Instructional games provide students a means to practice previously learned material or gain new information. But unlike drills, games are competitive by design, pitting the student against the computer, another player, or time. Instructional games are difficult to design, and all too often, even those which are professionally designed turn out not to be fun and become another piece of unused software. Instructional games come in many varieties such as adventure, arcade, board, card or gambling, combat, logic, role-play, psychomotor, TV quiz, and word games. Like drills, these can be adapted to any subject that requires repeated practice.

Simulations

Purpose: Present information, guide the student, and provide student practice
Example: Oregon Trail

Simulations are unique in that they attempt to give the student a chance to participate in a real-life decision-making situation. They are an effective way of learning because. they require problem solving and decision making. Also, they provide a non-threating learning safe environment. Students can easily work in groups to solve simulation problems. Whole class discussions can assist in helping students prepare for the simulation and help them understand what happened after the simulation.

When utilizing simulations, it may be difficult to assess student learning using traditional evaluation methods. Alternative assessment strategies may be required to ensure that the objectives of instruction have been fulfilled.

Tests

Purpose: Assess student learning
Example: Graduate Records Examination

Using the computer to construct or administer tests offers the advantages of automatic scoring, randomly generated test items, testing at students' convenience, cross reference of test items to learning objectives, and ease of test bank maintenance. There are numerous testing software packages that can be utilized in the classroom.


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Week 2

Date:
27 jan 2010

Details:
Lesson plan

Lesson Plan Sarah Liza