EDUC4105

What are the key features of a teachers’ e-portfolio are general information and lesson ideas. It is important to provide some general information such as teaching philosophy so that teachers are able to find other teachers with similar views and like-minded in their general approaches. This also gives the included lesson plans some context of how and why the lesson has been produced.

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.

The Webquest is a useful form om planning a lesson activity that involves using information presented on the internet.  As a form of lesson planning it is a good framework since teachers are guided to think comprehensively about the task, how it will work and how to assess it.

Dynamic geometry software packages such as GeoGebra and the Geometer’s Sketchpad have the distinct advantage that points and lines can be manipulated on the screen. in particular points can be moved along a curve to see what happens at every point. Not to many disadvantages that I can see.

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.

My views on graphics calculators is that they are a great tool to use when teaching any data topic. It is relatively easy to input data and to produce a scatter-plot and other forms of data processing techniques. This is where I personally would use this technology in classrooms.

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 interactive whiteboard offers the benefit that objects can be moved around on the board. By manipulating the items on the board students can play around with ideas which could create a bit of interest in the information presented.

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

As I started to read this paper, I couldn’t help but think that the symbols the authors refer to as ‘Mathematish’ form proper English sentences and so isn’t really another language. It wasn’t until the section of comparisons of Mathematish and English that I became more convinced. The sentences formed by equations do have certain structure whereby there must be meaningful symbols on either side of the = symbol/sign. That is an interesting point - why do we use the word ’sign’ to describe Mathematical symbols in general communication?

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”.

It was interesting to read about the multiple registers that all contribute to create meaning in Mathematics. The combination of written language (including technical words and symbols) and oral and visual representations need to be interpreted by learners of Mathematics to understand instructions, exercises and problems.

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.

The first reading was yet another reading on the inconsistencies of Mathematical language. It did however avoid the ‘doom and gloom’ by making some recommendations for teachers to deal with the problems.

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.

The following is the opinions of a small group of university students on a webquest activity. We are all viewing the contents as beginning Mathematics Teachers.

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.

I think I will jump on the bandwagon from now on and start using “oblong”. It seems like a good idea for a square to be a rectangle, but not an oblong, to better distinguish between the two shapes.

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.