Posted in Geogebra

GeoGebra and Learning Mathematics

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GeoGebra is a great software for teaching and learning mathematics. It offers geometry, algebra and calculus tools in one environment, a great support indeed for linking mathematical concepts. On top of that it is free and an open-code software. Click here to download the latest version of the software.

 Is it easy to use? Yes and No. Yes, for math teachers because they know the mathematics and can therefore easily understand the ideas and logic behind the tools. Yes, for students who have been instructed on how to use the tools and understand the mathematics and logic behind it. They can use it in solving problems and for investigating mathematical relationships. But, for the majority of students, especially those who have not learned the basic of graphing, equations, and geometric relationships, the use of GeoGebra is limited to manipulating ready-made GeoGebra applets. (Click here for my posts on solving problems about quadrilaterals or here for introducing function using Geogebra applets.) Well, yes, GeoGebra applets are easy to use but most of the time if you do not know the  mathematics behind the construction or can’t construct it yourself, then the learning of the mathematics may be superficial.

Construction of math models using the software is not accessible for many younger students just starting to learn basic Algebra and Geometry. In order for them to construct a model, they  will have to follow a set procedure (constructed by the teacher) without really understanding why they do what they do. So I thought why not teach GeoGebra tools and mathematics at the same time? This is a challenge I set for myself and I have no idea if it will work or not. I am thinking of doing a research of it later in the year. GeoGebra is free and faithful to mathematics so for countries like us that can’t afford to  buy licensed softwares, we get the same quality teaching tool with Geogebra. I think all students need to know how to learn mathematics with it.

Posted in Geometry

Problem Solving Involving Quadrilaterals

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‘To understand mathematics is to make connections.’ This is one of the central ideas in current reforms in mathematics teaching. Every question, every task a teacher prepares in his/her math classes should contribute towards strengthening the connections among concepts. There are many ways of doing this. In this post I will share one of the ways this can be done: Use the same context for different problems.

The following are some of the problems that can be formulated based on quadrilateral BADF.  You can pose these problems to your class but the best way is to simply show the diagram to the students then ask them to formulate the problems themselves.

quadrilateral

Problem #1. What is the area of the quadrilateral? Show different methods.

The solution to this question depends on the grade level of students. The one shown below can be done by a Grade 5 or 6 student. Continue reading “Problem Solving Involving Quadrilaterals” →

Posted in Curriculum Reform, Mathematics education

Understanding by Design and Pedagogical Content Knowledge

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If you know where you are going, it doesn’t always follow that you also know how to get there. Understanding by Design (UbD) supports the first part of the statement: knowing where you are going. Its three-stage curriculum planning framework is useful as a general guide for identifying where to lead the students in terms of understanding what they are supposed to be learning.

In Stage 1: Desired Results, teachers think about what goals they would like their students to learn. They also jot down the “big ideas”, “essential questions”, and what students should know after the lesson.

Continue reading “Understanding by Design and Pedagogical Content Knowledge” →

Posted in Algebra

Teaching and Learning Algebra Blog Carnival

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I am hosting a special edition of Math and Multimedia Blog Carnival. This special edition will be all about the teaching and learning of algebra at all year levels.

A blog carnival is like a magazine. Checkout the following carnival to give you some ideas:

1.) Mathematics and Multimedia Carnival #1

2.) Let’s Play Math Carnival #24

3) Carnival of Maths

Articles, lessons, tasks and activities, algebra problems,  learning and teaching algebra in multimedia format, your experiences with algebra as teacher or student, etc are welcome. Teaching and learning prealgebra topics are also most welcome.

To submit, email me the link to your post.

The carnival will be posted in December 2010. Yes, you have time to write.

Thanks.