Posted in Algebra, Geogebra, GeoGebra worksheets

Teaching mathematics with GeoGebra

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GeoGebra constructions are great and it’s fun ‘watching’ them especially if you know the mathematics they are demonstrating. If you don’t and most students don’t then we have a bit of a problem. Even if the applet demonstrates the mathematics to students I don’t think there’ll be much learning there. No one learns mathematics by watching. We know that ‘mathematics is not a spectator sport’. You have to play the game. In Geogebra  and Mathematics I proposed that if GeoGebra is to help students in learning mathematics with meaning and understanding, then students should know how to use it. But these GeoGebra tools will be most useful only to students if they know the mathematics behind the tools and why they work and behave like that.  And so we teach students the mathematics first? Where’s the fun in that?

I believe (Translation: I’ve yet to do a study if my theory works) that it is possible to learn mathematics and the tools of GeoGebra at the same time .  I will be sharing in this blog GeoGebra activities where students learn to use GeoGebra as they learn mathematics. The main objective is of course to learn mathematics. The learning of GeoGebra is secondary. I will start with the most basic of mathematics and the most basic of the tools in GeoGebra: points, lines, and the coordinates system.

The lesson includes four GeoGebra activities:

Activity 1 – What are coordinates of points? Read the introduction about coordinates system here.

Activity 2 – What are the coordinates of points under reflection in x and y axes?

Activity 3 – How to describe sets of points algebraically Part 1?

Activity 4 – How to describe sets of points algebraically Part 2? (under construction)

Posted in Math blogs

Guest post to share your math teaching ideas

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If you want to share your ideas about teaching, this blog accepts guest post about teaching and learning k-12 mathematics and other issues relating to mathematics teaching. Articles about teaching specific content topics in mathematics are most welcome. You may want to read some of the posts in  this blog so you have an idea what sort of topics are discussed here. I reserve editorial rights and the right to accept posts.

If you have a blog you can guest post and link your article to your blog posts. For articles that will have links to commercial sites, fees will apply. Thank you.

Email me or click this link to take you to submission page. You can also use the form below. It can be expanded.

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Posted in Mathematics education

Learning research study module on analyzing understanding of function

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Just recently the National Centre for Excellence in the Teaching of Mathematics (NCETM) of the UK released a set of learning research study modules to support continuing professional development of mathematics teachers online. One of the modules is based on my paper Growth Points in Students Understanding of Function in Equation Form. This paper was published in 2009 in Mathematics Education Research Journal (MERJ). MERJ is an international refereed journal that provides a forum for the publication of research on the teaching and learning of mathematics at all levels. It is the official journal of the Mathematics Education Research Group of Australasia, Inc. (MERGA). The papers in the journal used to be downloadable for free. Since last year I think they are now published through Springer link, no longer free. I have tried to share ideas from the paper in my posts How to assess understanding of function and What is a function in my attempt to provide teachers another thinking tool by which they can analyze students understanding of function and of mathematics concepts in general.

The learning research module about analyzing understanding of function was developed by Anne Watson, professor of Mathematics Education at Oxford University. NCETM presented it in power point presentation platform. I love the way Professor Watson turned my otherwise boring research paper into a thought provoking learning module for teachers. I have downloaded the presentation and sharing it here so other teachers can easily access it. Of course you can also go to the NCETM site. Teacher educators can learn from the style of presentation of the research study modules. This is a great way of making research results accessible to teachers. Kudos to NCETM for this project.
Professor Anne Watson is also one of the editors of the book New Directions for Situated Cognition in Mathematics Education (Mathematics Education Library). The book is a great reference for those doing research about mathematics teaching and learning.