Tag: GeoGebra

Posted in Geogebra

Pathways to mathematical understanding using GeoGebra

Posted on by

You may want to check-out the first-ever book about the use of GeoGebra on the teaching and learning of mathematics: Model-Centered Learning: Pathways to Mathematical Understanding Using GeoGebra by Ligguo Bu and Robert Schoen.

Supported by new developments in model-centered learning and instruction, the chapters in this book move beyond the traditional views of mathematics and mathematics teaching, providing theoretical perspectives and examples of practice for enhancing students’ mathematical understanding through mathematical and didactical modeling.

Designed specifically for teaching mathematics, GeoGebra integrates dynamic multiple representations in a conceptually rich learning environment that supports the exploration, construction, and evaluation of mathematical models and simulations. The open source nature of GeoGebra has led to a growing international community of mathematicians, teacher educators, and classroom teachers who seek to tackle the challenges and complexity of mathematics education through a grassroots initiative using instructional innovations.

The chapters cover six themes: 1) the history, philosophy, and theory behind GeoGebra, 2) dynamic models and simulations, 3) problem solving and attitude change, 4) GeoGebra as a cognitive and didactical tool, 5) curricular challenges and initiatives, 6) equity and sustainability in technology use. This book should be of interest to mathematics educators, mathematicians, and graduate students in STEM education and instructional technologies.

STEM – Science, Technology, Engineering, Mathematics

Wikipedia on model-centered instruction:

The model-centered instruction was developed by Andre Gibbons. It is based on the assumption that the purpose of instruction is to help learners construct knowledge about objects and events in their environment. In the field of cognitive psychology, theorists assert that knowledge is represented and stored in human memory as dynamic, networked structures generally known as schema or mental models. This concept of mental models was incorporated by Gibbons into the theory of model-centered instruction. This theory is based on the assumption that learners construct mental models as they process information they have acquired through observations of or interactions with objects, events, and environments. Instructional designers can assist learners by (a) helping them focus attention on specific information about an object, event, or environment and (b) initiating events or activities designed to trigger learning processes.

I’m not sure if the book cites research cases that show how using Geogebra or interacting with applets help students build those mental models. It would be interesting if somebody will really do a study on this.

Posted in Algebra, GeoGebra worksheets

What is a coordinates system?

Posted on by

This is the first in the series of posts about teaching mathematics and Geogebra tools at the same time. I’m starting with the most basic of the tools in GeoGebra, the point tool. What would be a better context for this than in learning about the coordinate system. Teacher can use the following introduction about geographic coordinates system and the idea of number line as introduction to this activity.

A coordinates system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric elements. An understanding of coordinate system is very important. For example, a geographic coordinate system enables every location on the Earth to be specified by a set of numbers. The coordinates are often chosen such that one of the numbers represent vertical position, and two or three of the numbers represent horizontal position. A common choice of coordinates is latitude and longitude. Sometimes, a third coordinate, the elevation is included. For example:

Philippine  Islands are located within the latitude and longitude of 13° 00 N, 122° 00 E. Manila, the capital city of Philippines is 14° 35′ N, 121º 00 E’.

In mathematics we study coordinates systems in order to describe location of points, lines and other geometric elements. The numberline is an example of a coordinates system which describe the location of a point using one number. The coordinates of a point on a numberline tells us the location of a point from zero. But what if the point is not on the line but above of below it? How can we describe exactly the location of that point? This is what this activity is about: how to describe the position of points on a plane.

You would need to familiarize your students first about the GeoGebra window shown below before asking them to work on the GeoGebra worksheet.

Click here to go the GeoGebra worksheet – What are coordinates of points?

 

Posted in Algebra, Geogebra, High school mathematics

Embedding the idea of functions in geometry lessons

Posted on by

GeoGebra is a great tool to promote a way of thinking and reasoning about shapes. It provides an environment where students can observe and describe the relationships within and among geometric shapes, analyze what changes and what stays the same when shapes are transformed, and make generalizations.

When shapes or objects are transformed or moved, their properties such as location, length, angles, perimeters, and area changes. These properties are quantifiable and may vary with each other. It is therefore possible to design a lesson with GeoGebra which can be used to teach geometry concepts and the concepts of variables and functions. Noticing varying quantities is a pre-requisite skill towards understanding function and using it to model real life situations. Noticing varying quantities is as important as pattern recognition. Below is an example of such activity. I created this worksheet to model the movement of the structure of a collapsible chair which I describe in this Collapsible  chair model.

Show angle CFB then move C. Express angle CFB in terms of ?, the measure of FCB. Show the next angle EFB then move C. Express EFB in terms of ?. Do the same for angle FBG.
[iframe https://math4teaching.com/wp-content/uploads/2011/07/locus_and_function.html 700 400]
Because CFB depends on FCB, the measure of CFB is a function of ?. That is f(?) = 180-2?. Note that the triangle formed is isosceles. Likewise, the measure of angle EFB is a function of ?. We can write this as g(?) = 2?. Let h be the function that defines the relationship between FCB and FBG. So, h(?)=180-?. Of course you would want the students to graph the function. Don’t forget to talk about domain and range. You may also ask students to find a function that relates f and g.

For the geometry use of this worksheet, read the post Problems about Perpendicular Segments. Note that you can also use this to help the students learn about exterior angle theorem.

Posted in Conferences and seminars

Announcement: Seminar-Workshop on GeoGebra

Posted on by
It is the offial seal of the UNIVERSITY OF THE...

width=”126″ Image via Wikipedia

The University of the Philippines National Institute for Science and Mathematics Education Development (UPNISMED) will conduct a three-Saturday seminar-workshop on using GeoGebra in the teaching and learning of high school mathematics on August 13, 1320, & 27, 2011 at UP NISMED. This is a first level seminar and will cover the basic tools of GeoGebra. Sample lessons, activities,  applets will be presented. The participants are expected to develop at least one activity/ GeoGebra applet for high school mathematics lessons as output.

For more information, fees, and registration procedures visit this link. To Filipino math teachers, please share this post in your Facebook.