Geometry has always annoyed me, actually until circle geometry in year 11 which was pretty awesome. I find dynamic geometry to be the most frustrating thing on the planet and I don’t think I will use it very often at all just because I get so annoyed by it. However, i would like to use it because I actually think it is an amazing pedagogical tool. I would definitely want my students to be able to use it because it makes you think about how shapes are made up and what are actually the important features of shapes. For example, drawing a square on paper is easy. Drawing a square using sketchpad or geogebra is a nightmare. A nightmare in which you have to think about what constitutes a square and how you can transfer this knowledge onto the program. And a square is the simplest shape Ican think of! No wonder I get so angry with it.

I actually get really angry because I’ve been trying to make a rectangle so that the perimeter stays the same but the area changes as you move it around. I found an example on the internet after much searching, and tried to copy it for days without much luck. Or much skill. Every time I thought I knew how to do it it turned out that I still couldn’t. This is the kind of technology that causes teacher burnout, but also causes a deep respect of any student who can master it.

I am definitely willing to use dynamic geometry in the classroom, but i think I will need a lot more trainign and practice to make it.

The attributes of a short term WebQuest are:

The attributes of a long term WebQuest are:

Components of a WebQuest
Every WebQuest has six basic components:

The Benefits of WebQuests
Using WebQuests in our classrooms can help build a solid foundation that prepares them for the future. The First WebQuests In 1995, San Diego State University’s Bernie Dodge and Tom March developed a type of lesson plan—what they termed a “WebQuest”—that incorporated links to, from, and along the World Wide Web. Students were presented a scenario and a task, usually a problem to solve or a project to complete. The students were given Internet resources and asked to analyze and synthesize the information and come up with their own creative solutions. Over the next three years, teachers wrote their own WebQuests, and instructors began to teach WebQuests in their workshops and classes.Fortunately, this proliferation of curricular materials convinced many teachers that it was all right to publish their own WebQuests for others. Most teachers have included their e-mail addresses, which allow a WebQuest user to contact the teacher and discuss quest results. Additionally, WebQuest sites have sprung up and continue to grow on the Internet.

Before starting to create an account, you need to decide on your Topic, Subject and the Grade Level of your WebQuest. Once we determine these three items, the rest will be easier.You will need to answer the following questions:

Planning Components of a WebQuest

Discuss Excel spreadsheets as a pedagogical tool. What are the advantages and disadvantages and why?

Take Out Your Aggressions in Excel

I have never really used excel before now, and I must say I was pleasantly surprised with its uses. I have yet to master the program, actually I only really know how to do a few things, but even that has helped with my views of how I am going to teach in the classroom. The more technological tools I am brought face to face with, the more exciting lessons I can imagine.

When I asked a few of my friends if they had ever used excel in the mathematics classroom, they proclaimed that they hadn’t and they wouldn’t advise it. This made me put off using excel until the last possible moment, but now that I have I believe it will be a useful tool in the classroom and I encourage all teachers to embrace it.

Excel can basically do what a calculator does, but you can display as many answers as you want on the screen simultaneously. This in itself is enough to excite me as someone who always does one calculation at a time to avoid using brackets or having too long an equation in the calculator for fear of error. It can also produce graphs, which is helpful because who wants to draw a graph when the computer can do it for you?

Discuss the webquest as a form of lesson planning. What are the advantages and disadvantages and why?

Webquests are an extremely good invention because they draw on students’ recreational love of and ability with computers in order to help them learn. Using the internet to discover information is what people do when they want to know anything. Why should schoolwork be any different? 

Webquests help students learn that the teacher is not the only source of information, and that teachers are aware of the internet and its uses. A well thought out Webquest will grab each student’s attention, even if they are usually restless in class and find it difficult to concentrate normally. Webquests can improve students’ self-efficacy and can give a break from other monotonous elements of the classroom, especially in maths where routine and practice out of the textbook is usually the name of the game.

Webquests are probably the best idea for assignments, especially group assignments. Group assignments are already usually all over students’ emails as they send them back and forth – why not leave them there? Webquests done in class are a brainwave for late in the term, year or even week when even thinking about doing exercises out of the textbook gives you a headache. They can also be a break for the teacher.

I will definitely be using Webquests as a teacher because I believe that students are so used to learning from the internet that they won’t even realise they’re actually doing maths work

What (if any) pedagogical benefits do you believe graphic calculators offer and why?

Graphics calculators are a quick way to check graphs and to compare different graphs. They are difficult to master, but if you use them all the time it’s not too difficult to use them for creating most graphs and to input data so you don’t have to plot it out yourself. It’s also got the advantage of being small and portable, which other technological devices such as Maple and Excel don’t ahve.

Graphics calculators allow you to chack your work and also complete work much faster. Students take a long time to draw their own graphs and a lot of the time it isn’t necessary for them to draw it. Unless the specific idea of the lesson is teaching them how to draw graphs, there’s no reason to waste more time making them create a simple graph that they already know how to draw. More time looking at the graph and less time drawing it means there are more possibilities to discuss its implications and any deeper concepts that arise.

What (if any) pedagogical benefits do you believe the interactive whiteboard offers and why?

I guess Smartboards are pretty handy in most classrooms, because you can write in different colours and get students to come out and play with multimedia things and write with their fingers or whatever.

I don’t think I will be using the Smartboard much as a teacher just because doing a Smartboard lesson means that what you’re doing is pretty much set in stone and there’s not that much room to breathe or to go off on (useful and informative) tangents.

I think an occasional smartboard lesson would be great, as long as it’s not used all the time. I think I would use it more for the junior classes and probably not much for senior classes, unless I thought it was actually the easiest way to present something, such as 3D diagrams.

Smartboards are an effective learning tool though, especially for students who get distracted easily. Visual learners don’t really get much satisfaction from maths normally, and the colour and liveliness of a smartboard would be a welsome change from the monotony of the textbooks.

The thing with Smartboards is, you don’t like them unless you use them a lot, and you don’t use them a lot unless you already like them. I guess gradually over time, if you use them a little bit for each of your classes, you’ll build up an effective way to use them, know when to use them and also build a database of Notebook files that you can adapt and reuse all the time. That is one very good point to using Smartboard – you can keep the lesson plan and just roll with it again.

What are the key features of a teachers’ e-portfolio and why? Discuss the potential benefits of social bookmarking as collaborative learning tool for teachers.

An e-portfolio is a digitised collection of artefacts comprised of text-based, graphic or multimedia elements archived on a web site.

An ePortfolio is a purposeful collection of work and information that:

• represents an individual’s efforts, progress and achievements over time

• is goal-driven, performance-based and indicates evidence of the attainment of knowledge, skills and attitudes

• includes self-reflection

• is a tool for facilitating life-long learning and career development

E-portfolios, like traditional portfolios, can facilitate students’ reflection on their own learning, leading to more awareness of learning strategies and needs.

Social bookmarking is very useful for seeing what other people find relevant or useful for specific things. Bookmarking tools such as del.icio.us help weed out useful technologies by letting you know how many other people have bookmarked a site and the tags they used for it. This saves time because you know what the site consists of without having to explore too much.

In week 8 tutorial you will be allocated one of these Geometer’s sketchpad lessons to evaluate. You are to carry out the lesson and evaluate it (with a link to it included) on your blog. Ask yourself questions like: What part (if any) of the NSW syllabus would this lesson be appropriate for? What is the benefit of using the Geometer’s sketchpad software in this lesson? Could the lesson be taught any other way? If so, how? How could the lesson be improved? Are the instructions for the lesson clear?

Finding Relationships Between Area and Parallel Lines in Triangles

This lesson was alright. I couldn’t find the “Label Options” thing, so I don’t know if it was for a different Geometer’s Sketchpad than the one I was using. Apart from the slight differences, the instructions were very clear.

I guess the lesson is useful in cementing the idea of why area=1/2 the base times the perpendicular height. If students just remember the formula A=1/2bh they may not remember that the “h” stands for perpendicular height and may measure some obscure kind of height. This lesson proves that even if the triangle is incredibly stretched out, the height is still the same, and the formula tells us this because the base is staying the same, therefore if the height changed the area would change, but it doesn’t.

Trying to do this lesson without the help of Geometer’s Sketchpad would be very difficult. I think it is very handy in allowing students to see the ramifications of the formula for the area of a triangle in action. You really do need the software to move the point around and see that it doesn’t change. Drawing a billion different triangles within parallel lines with the same base would be tedious and not worth it.

OK, so I actually did the readings for last week (I read them on Friday actually but today I’m bored hanging around uni waiting for my carpooling buddies – perfect blogging opportunity). I actually found I do have some things to say.

Number1: Zero is not and never will be a counting number. According to me. If you have none of something, you don’t count it. If you’re doing that fence thing, you will have to realise that there is a post at the point 0 and add it on. It isn’t difficult. You definitely should not count the post as 0, because then you are saying that one post is zero posts!!! WHAT!!!!! No. I actually do say babies are 0 years old. Because I’m rounding down. To the nearest 2 years. Not because they are actually 0.

I don’t actually have the readings here with me so I might not remember everything I hated about the readings, which by the way were tedious and I did skim read them because they were dense and mainly the same as every other reading, except worse.

Number 2: North/South, up/down thing. I don’t remember what it actually said, mayhap I will edit this post later. But this ridiculous statement actually went on for like 2 pages, as I recall. It was too much.

This post is dedicated to Sarah P, Pru, Marjorie, Chris, Geoff, Dave, Nick and Ben. Love your work guys!

All of the articles in the course to date are starting to show similar ideas. Teachers need to discuss mathematical applications and use of mathematical language. Students need to see where problems can occur in the use and talk of mathematics and find ways to conquer these problems. Mathematics is a language in itself, and yet we try to explain it using another language. Problems arise when we use words that have relatively straightforward meanings in colloquial use, yet we use these same words to describe quite complex concepts. Conceptual complexity and apparent contradictions in mathematics language, and the artificial symbolic nature of mathematics, with its reliance on many non verbal ways of representing information, often acts to disturb students. Using background knowledge, using multiple teaching methods (for students from different learning styles) is helpful.

We need to be able to describe what we are doing in non-mathematical language as well as mathematical language. This use of students’ own understanding and explanations when dealing with new ideas is important as it connects the new knowledge with established structures that can later be refined to be more in line with conventional definitions. Though we should encourage students to talk in mathematical English, at times it is appropriate (and neccessary) to talk about examples in normal English to aid discussion and the deeper understanding that comes from such a free flowing discussion.

This week’s readings have a similar message to previous weeks; the language of maths conflicts with everyday use of the English language. They also offered similar suggestions for handling the difficulties that can arise for students. Mathematics “borrows words that already exist with everyday meaning” and in doing so changes the context of the word and therefore changes the meaning. cause a lot of difficultly and impatience for the untrained mathematical mind.

For example starting with a number and imagining that it is the area of a square, the square root gives the side length of that square, which is something that gives students a real example of how to view the square root. Teachers need to foster the use of correct mathematical language in the mathematics classroom at all times. Correct mathematical language should be prevelant in any mathmatical discussion. I also disagree that zero should be used as a number. For example, “zero years old” is not a useful description and would be taking things to extremes.

Students need to participate with the language, that is they need to be using it both orally and in its written form. It is usually agreed that mathematics cannot be learnt by watching, therefore it makes sense that using correct mathematical language cannot be learnt by simply reading and listening.