bodmas blog

Are there patterns to learning in Maths? Are these different in different subjects?

Patterns and pattern languages are used to think about writing computer software that works quickly. I’ve noticed that when students are learning (say) directed numbers in Maths, the adding and subtracting is learned fine, and then the rules for multiplying and dividing. Mixed problems can be sorted using varied examples. But then they have to solve problems with multiplying out brackets – application of the multiplying and then the adding rules on a single problem – and there is nearly always some relearning needed.

My pattern would be something like

• Context: students applying directed numbers to symbolic algebra
• Problem: they need to switch between the multiplying rules where the sign of the answer can be inferred from the signs of the terms to adding where the size of the like terms being collected matters
• Solution: Remind students of the rules in a familiar context – quick examples using numbers. Add the directed numbers table on the right hand part of the whiteboard for easy reference

A concrete example of what I’m on about is the Writer’s Circle patterns page on the c2 wiki – but that looks more like a lesson plan or set of rules. Conservation Economy Net has a nice looking mind map come pattern language for sustainable development.

Global Nerdy blog, The World Needs More Dialog Boxes Like This

Amen

Seashore is a graphics editor for Mac OS X. It is based on the Gnu Image Manipulation Program but runs native under the Aqua window manager on Mac OS X, it does not need X11 loaded.

Seashore provides a subset of the functions present in The Gimp, but the subset is well chosen for those of us composing images for use on Web pages and processing scanned material. The application comes with a brief but useful manual in PDF form. The program runs noticeably more quickly than The GIMP on my iBook. Installing the optional SVG importer allows me to draw masks and grids in Inkscape and import them as bitmaps with a choice of scale.

Perhaps an example of ‘just enough functions’ rather than ‘everything we can think of and 20 layers of menus’?

• Seashore Web site
• Flickr photoset of St Brides typography museum found via the We Made This blog.

Just in case anyone wants to install a copy on their own computer. Most college networks will need admin rights to install this software.

• Hot Potatoes home page
• Registration page [ Registration is free but you need to put quizzes on public Web sites ]

“A family of immigrant workers from Kosovo living in Switzerland has installed a big computer screen in their living room, for example, and almost every morning they have breakfast with their grandmother back home, via a webcam. It is migrants, rather than geeks, who have emerged as the “most aggressive” adopters of new communications tools, says Ms Broadbent. Dispersed families with strong ties and limited resources have taken to voice-over-internet services, IM and webcams, all of which are cheap or free. They also go online to get news or to download music from home. In the case of a Spanish family living in Switzerland, the daughter often does her homework with her aunt—but over a free Skype video-link, since the aunt lives in Spain.”

From Home Truths about Telecoms in the Economist, via Seb Schmoller’s mailing list. Now, why not doing some tutorials this way? We need to find some way of making Skype like systems available within FE Colleges for teachers to use with remote students.

“After all, most users don’t know or care whether their computer has a 65nm dual-core CPU or a tiny midget wizard squatting in their cases. All they care about is how it works and how quickly it does the tasks we most often ask it to do.”

From Apple Mac Plus vs AMD Dual Core by Hal Licino. It is the beginning of what UK journalists call the ‘silly season’ where there isn’t much news so you have to make some up. Hal and his friends decided to compare a current production Dual Core Intel based computer running Windows XP and Vista with a 1980s Apple Mac Plus, and they based their comparison on everyday tasks that real people perform.



I remember using an Acorn A3000 to surf the Web and do e-mail in the early to mid-90s. A 12MHz 32 bit ARM chip ran the whole machine including what would now be called ‘integrated graphics’. What amazed me then (and still does) was the !Draw module that was part of the RISC-OS operating system. Draw handled all printing and image rendering from files and provided a common standard so that Web pages could be saved as Draw files – vector files mark you – and then printed, or imported into the !Draw application and edited. It all worked a bit like PDF on Mac OS X does.

Enough of the ‘good old days’ and I’ll be posting GCSE Revision links over on gcsemaths.org.uk over the weekend – its too late for the non-calculator paper now so I’ll be working on the usual calculator paper topics. Back to Maths here on bodmas as well.