Of course the actual lesson activities are an essential feature of any e-portfolio, both for yourself and others,  because these are the practical ideas that will be applied in classrooms.

The benefits of social bookmarking are similarly a collaborative learning tool for teachers since teachers can find other like-minded teachers who have links of interest. Also it is a nice place to keep all of the websites you might find in one place.

Excel spreadsheets are a good pedagogical tool because they are so common and easy to use and access. Formulas can be inserted and assigned to cells fairly easily and to great effect. It is imperative to be aware of all shortcuts and to be very familiar with using the program, otherwise tasks can quickly become tedious.

I have also been told that there are attachments that can be linked to the calculator so that continuous data can be inserted. For instance a thermometer can be connected to the graphics calculator and the heat will be automatically shown on the screen. I’m sorry about the sketchy details, but it does sound like a good idea.

The technology merges hands on and visual learning techniques, benefiting multiple student leaning styles.

Anyway, I think that since Mathematish does have a certain form of grammar that obeys a set of rules that we are teaching students to use another language. The main difficulty I see for students is in translating word problems into Mathematish. The use of the word ‘translate’ when discussing word problems could be beneficial for students to understand that they are indeed dealing with alternative forms of language, which is difficult. Hopefully this will result in the complaint of  “I’m not good at Maths” meaning something more like “I find it difficult to read/speak/translate in Maths”.

A good point was made that it is the teacher’s oral communication that helps students to construct meaning from written Mathematical words and symbols. This has great implications for explanations will impact on the students’ “internal chatter” and how they think about language. Teachers need to be very careful and precise in explaining language use because this is the initial source that students form understanding from.

I really can’t see the use of one-ty one, one-ty two etc. catching on because although it makes sense and may be easier to learn, we simply don’t use it in our lives. We are brought up with the traditional use of eleven and twelve etc. A complete overhaul of how we pronounce numbers would be more trouble than it is worth. Why not completely create uniform of expression and start saying that the winner of a race finished in “oneth” place? It ‘aint broke – it’s just the way things are.

I also completely disagree with the author’s preaching about using zero more to promote it as a number. It seems completely bizarre to me to say that a baby is zero years old. If a child has not yet lived a year, then they have lived months! Or weeks! Zero years is not a useful description and would be taking things to extremes.

Dismounting from my high horse, the second reading got me thinking about triangular roots of numbers and whether or not it would be a useful problem for students to have a go at to better understand why square numbers have developed. Having students apply knowledge of squaring to (equilateral) triangles could be a good way to reinforce understanding of the ways that some particular natural numbers can be arranged into squares (4, 25, etc.) while the operation of squaring can be applied to numbers in general.

Here is a link to the Chess activity.

Strengths

• Task has good Knowledge Integration with history (cold war)
• Uses research as a teaching strategy
• Relevant links are included for students to read more about different aspects of the task
• Plenty of technology incorporated with links to films and opportunities for students to create part of web pages
• Students have the chance to play chess with one another

Weaknesses

• Irrelevant to maths syllabus
• Research is only of interest to chess fans and requires a degree of background knowledge of chess
• Task 4 is more suited for D&T where design and ease of use is important
• Seems to be a trivial activity aiming at chess promotion
• Outcome is not mathematical and does not require higher-order thinking (more a structured writing task)
• No meaningful motivation for students
• Purely individual work – lost opportunity for collaboration

For anyone interested in learning chess from a grandmaster, here is a blog on the games of Karjakin Sergey.

Giving the circle a perimeter rather than a circumference might be a good idea just because the standardising could make composite shapes easier to interpret. Then again maybe circles and ellipses do deserve a reserved title for being curved. Yes the fence is comfortable, thanks for asking.