Representations of Linear Growing Patterns Cluster Launched

It is with a lot of pleasure that I am able to announce the launch of a new cluster of CLIPS.

Representations of Linear Growing Patterns is based on research conducted by Ruth Beatty at the Institute for Child Studies in Toronto. Although it does not flesh out the experiences that students would have in Grades 4-6 with concrete materials, it certainly alludes to them. Students take pictorial representations, based on coloured tiles, of a pattern and develop graphical representations and algebraic rules. They then explore the role of the constant and multiplier in the pattern rules. One Near North teacher blogged about the change it made in her understanding and about her experience trying it in her classroom.

Among the material created for the cluster are a graphing tool and an open-ended tool to explore the relationships between the representations, including stories and the algebraic equation. The graphing tool is described carefully in Clip 2, Activity 4: Practice Graphing. The Rainbow DSB is conducting a "book study" of this cluster. I hope that soon we can feature some innovative ways to use the Exploring Representations tool resulting from their work. I am hoping to engage the Web 2.0 math teacher community to address the question "What can we do with this?".



The cluster movie is quite different from the "Who Cares?" movies developed for Fractions and Periodic Functions. The overview movie, which should be viewed after working through the development, summarizes the cluster nicely.

There are several improvements to the CLIPS "wrapper", including the ability to set a volume level or mute that is respected throughout navigation and a new scene selector. The major videos can be viewed fullscreen without downloading a huge source file. Trish Steele narrates a new 12-minute introduction to the wrapper that is well worth the time.

Since the activities are primarily flash animations (SWF) with embedded narration, the files are relatively big. The design of CLIPS does not depend on any server technology. Teachers or students who wish to use the activities, but don't want to depend on an internet connection, can download the entire thing and point to the index.html file at the root, for local use.

We thought it would be done earlier and there are still some rough edges (please use the Feedback link at the top right to record anything that you notice) but we are very happy to now have the work officially in circulation.

Some Nuggets from my Reader

Summer has not been a great time to absorb the material being fed to my Google Reader account. In fact, I have been practicing marking items read that aren't and unsubscribing from feeds.

I found four recent things quite interesting though.

1. Tim Hawes' post about Willingham's contention that learning styles don't exist. Have a look at the video posted at Tim's site and some of the references quoted in my comment. I will look forward to reading your musings on Tim's post.

2. Geoff Day, another commun-it blogger, pointed me to an interesting study about how counting is not dependent on having language to name numbers. It made me think of the EQAO tests.

3. At the recent GAINS-CAMPPP, I subscribed to a news feed about Keith Devlin, who commented on my recent post. There I found a long and interesting article from the San Francisco Chronicle about what algebra should be taught in schools. It also has some interesting quotes. My favorite was:

"Algebra ... the intensive study of the last three letters of the alphabet."

4. A post by Gary Stager suggesting ways to better the teaching of geometry (including use Sketchpad, use Logo (but not Scratch)).

Math Manipulatives

In April of 2005, a group of teachers from North East Ontario got together for a regional Leading Math Success working session and created introductory videos and powerpoints for six Math manipulatives. These were then used in local training events. When I let the participants know that they had been posted to a popular video sharing site, I got lots of replies and recollections about how worthwhile a professional development experience people thought it was - fodder for Judy's resume! The full collection of files has been posted for a while.

Algebra Tiles



Colour Tiles



Connecting Cubes



Fraction Circles

My contribution was a Geometer's Sketchpad sketch - a Fraction Circle tool and virtual manipulative.



Geoboards



Pattern Blocks

A little shameless self-promotion

Now that Amazon.com has accepted my edit, adding me as an author (yup - that's my name at the bottom), it is a good time to let you know that a book that I helped to write is available at the Key Press site.

Math Wars, The Pre-eminence of Algebra and the Presidential Math Panel

The blogosphere has been abuzz with opinions about the Presidential Math Panel report. Five good ones are found at the Pulse blog. Gary Stager's opinion includes the following:

Not only is the progression from arithmetic manipulation of fractions to Algebra tenuous, but neither of the assumptions underlying the value of teaching fractions or Algebra are ever questioned. The President’s Math Panel, like most of the math education community maintains a Kabbalah-like belief in an antiquated scope and sequence. Such curricular superstition fuels a multigenerational feud in which educators fight over who has the best trick for forcing kids to learn something useless, irrelevant or unpleasant.

and

The Report of the National Mathematics Advisory Panel
does not dispute that teachers spend lots of time teaching fractions. The report merely urges that teachers do even more of the same while hoping for a different result. A definition of insanity comes to mind.

I wonder if Math teachers are so unwilling to question the supremacy of algebra because they are worried that they will lose market share in the high school curriculum and lose sections at summer school.

Yet Another Computer Algebra System

I have been exploring Yacas for a little while now. It is extremely powerful and is free. Students can download it or run it directly from its web site. There is an interactive tutorial available from the main set of tabs.

On the related links page, there is a link to mavscript, which uses yacas to perform calculations directly in text or OpenOffice Text documents. Maybe I am a geek, but being able to differentiate, graph and factor directly inside a text document warmed a cockle in my heart!