DYNAMIC GEOMETRY SOFTWARE

Dynamic geometry software such a Geogebra or Geometer Sketchpad have many excellent applications in the mathematics classroom. This software is so great for classrooms because it is so versatile. You can use it for functions, geometry, coordinate geometry and many many more applications. It is also flexible in how it can be used, for example, the teacher can demonstrate a consept visually via a projector, the students can interact with the software individually at a computer, it can even be used in conjunction with the internet or the teacher can use it to create diagrams for handouts. Pedagogical benefits include student engagement, higher order thinking and promotes creativity and interaction. Even if the software is only used to demonstrate one thing or for one activity during the lesson, it will still enhance the knowledge. There is also a lot of online rescourses for teachers to save time. The only limmitation is the availability of computers for students (which hopefully will drastically improve within the net few years). I  cannot think of another negative point, I really love this software and plan to use it at every chance where it is appropriate. See this video for a little demo of Geogebra:

Geogebra

WEB QUESTS

Web Quests are an educational tool to allow students to discover knowledge using the internet and technology found on the computer. It may be a fun activity for the students and be an effective form of lesson planning. However, care needs to be taken to ensure that the technology is used in the right way. For example, if the Web Quest entails students searching the net for notes and formulas, then the lesson will have the same effect as working out of a text book. It should requre the students to interact with the technology in a meaningful, fun way, allowing them to construct the knowledge. Even though the teacher can plan well in advance, it still takes up a lot of time searching the internet and preparing the site. Therefore, a Web Quest should only be used if a teacher has a good idea to match a particular outcome with some particular activities on the internet (and this may or may not be often). Realistically, if a teacher could prepare one Web Quest per topic for the most relevat outcome, this would enhance students’ understanding of the topic.

 Here is a Weq Quest that shows disadvantageous use of technology: Calculus Mission

Alternatively, here is a Web Quest that better engages students with technology: Poverty in the U.S

It may seem like a subtle difference as both Web Quests require students to find information and present it. However, Calculus Mission asks for regurgitation and could easily be completed with a text book, while Poverty in the US asks for synthesis and creation and could not be taught without the internet and spreadsheets. So, Web Quests are a quality learning tool if used in a way that enhances the content with the use of technology and cudos to teachers who make the time to create a fun learning experience for their students.

GRAPHICS CALCULATORS

Ofcourse graphics calculators have pedagogical benefits for mathematics teaching. They allow students to engage with technology while learning maths. However I believe that there are some limmitations for the use of graphics calculators. For them to be useful in advanced topics, students need to have built up a repitoir of skills on the calculator. Otherwise, the lesson time will be spent on procedural tasks and not engaging with the content of the lesson. Students also need to be comfortable working independantly with the calculator ie having built up skills to sort out their own problems rather than having to ask the teacher many times for help. This means that the teacher’s time is allocated to teaching the lesson and getting the point accross, not losing focus going around the classroom helping individuals for the majority of the time.

If students have skills in using the calculator and are comfortable to work independantly then the graphics calculator can be used to enhance students’ knowledge in most areas of maths. For example, functions, trigonometry, geometry, coordinate geometry and the list goes on. Teachers can also challenge students as the calculator can perform advanced tasks for example, asking the students to program a short formula. Also you can have a bit of fun…

PEDAGOGICAL BENEFITS OF INTERACTIVE WHITEBOARDS

Research has shown that benefits of usising interactive whiteboards in classrooms include:

• Engagement and motivation
• Student interaction
• Improved engagement with students with special needs
• Relevance to students who are engaged with technology in everyday life

Technology can further enhance the effectiveness of interactive whiteboards in the classroom. For example, learner feedback systems where the students use a remote device to give an answer.

It should be pointed out that consideration must be given so that the technology enhances interactivity and does not carry on traditional methods. For example, using it as an electronic whiteboard to display notes or Powerpoint presentations. Teachers and student teachers will need to practice their skills and explore the technology to fulfill its potential in the classroom.

E-PORTFOLIOS

An eportfolio is an effective way to showcase a teacher’s personal and professional side in one convenient and attractive location. A basic structure of an eportfolio can be seen here:

More detailed elements found at Institutional eportfolios include:

• A statement of teaching philosophy
• Representative course syllabi
• A summary of teaching methods and strategies
• Feedback from students, colleagues and seniors
• Reflections on the feedback and self-reflection
• Evidence of professional development (e.g. participation in conferences, publications, awards)
• Personal goals and objectives for the next several years
• Products of teaching (e.g. samples of students’ work)

An eportfolio with these features will show that the teacher is passionate, professional and well worth hiring.  

SOCIAL BOOKMARKING

Social bookmarking sites such as Delicious are important because there is so much information out there that many quality sites get lost in the traffic. Searching using Delicious allows you to take advantage of the work that colleagues have already done, sifting through engine searches. It also allows you to contribute to the online community by adding your own useful sites you have found.

For example, a simple search for ‘geometry’ in Delicious yields numerous useful sites in order of popularity. While the same search in Google yields sites which are vague and not immediately useful for teachers for example, Wikipedia. If people have bothered to tag a site in delicious then more often than not it will be worth a look- it saves you time! Here is something fun to puzzle early finishing students I found on Delicious in less than 10 seconds:

EVALUATION OF A GEOMETER SKETCHPAD LESSON

Sum of Interior Angles of a Polygon by Sara Otis

This lesson requires students to see that the angle sum of a triangle is always 180, consruct polygons, divide the polygons into triangles, add up the number of triangles and then devise a general formula for angle sum of a polygon. This lesson would be appropriate for year 8 or 9 geometry.

Strengths

• Geometer Sketchpad makes it easy for students to quickly construct polygons and manipulate them.
• Students are given a chance to discover the formula.
• Students would find it fun to use the computer instead of constructing shapes on paper. This could lead to high student engagement.
• The lesson instructions are clear and easy to follow.

Limmitations

• Students are given two consepts to take in - the angle sum of a triangle is always 180 and how to work out angle sum of a polygon. This may be difficult for students to gain a deep knowledge of both consepts.
• This is a common way of presenting this outcome however there needs to be some extension for students who would find this task a little tedious. For example, asking them to construct a proof (or an argument for a proof) as to why the formula holds foor any polygon.
• The lesson could easily be done without Geometer Sketchpad.

This is a good lesson and students will achieve the outcome of discovering the angle sum of any polygon. However the lesson does not harness the potential for geometer sketchpad and the lesson could be improved by including some higher order thinking.

I think this might be a good representation of how many kids think of maths. For example, as performing calculations, recalling pi and getting the answer right. Hope we can change this. Ps. I think he might have too much time on his hands…
Download Video: Posted by SumersetInc at TeacherTube.com.

This weeks readings had some useful ideas and some not so useful ones. Gough makes some good points- that mathematical language is arteficially constructed with unusual combinations and juxtapositions. The idea of taking words that already exist and giving them new  meaning(s) seems odd but yes this is what we do in maths. I wonder why mathematicians have done this for so many years… Also it is interesting to think about ESL students and whether they actually have equivalent words in their first language. If they don’t, this must cause great confusion.

However the ‘zero’ argument is a little strange. Speaking of babies who havent turned 1 yet as zero year olds kind of makes me think they are not alive yet as we usually speak of them in months such as 6 month olds. But I guess this is just the confusing nature of our language. (Although before taking this subject I thought everything was fine!)

Here is an evaluation of a Web Quest lesson. This lesson requires the students view sites about proofs of Pythagoras Theorem, then design an onramp for cars to drive up. Overall, the task was vague and would not be recommended to use in a classroom to gain deep knowledge. Here is a more detailed evaluation: 

I think this weeks reading by Lee was just what we needed - a positive view of the use of language in the classroom with practical examples. Key ideas include talking as a way to learn mathematics; its OK to say a wrong answer; the more students use mathematical language, the more natural it will become and how language is useful to the teacher for assessment. And to start using these ideas in lessons, let the students vocalise the words and then think about how they could use them to express mathematical ideas.

This article has made me think of a few things about students. Many kids don’t like to sound too smart in-front of their peers, so when asked to give a mathematical answer they may reply with ‘um that thing miss’ for example. However, if ideas as discussed previously were used in a classroom and all students were using mathematical language aloud, then it would be socially acceptable to have a go and sound smart! Also many students don’t have a go at giving an answer, even when prompted by the teacher because they are afraid of giving a wrong answer in-front of the class. When in reality, if one person doesn’t understand a concept then there is a good chance there are others too. If discourse is opened up between students, then they can realise that they are not the only ones to need help and making mistakes is part of the learning process.

An important point from the Tapson article is that language is always changing. Speaking of change, if maths teachers are able to overhaul the way mathematics is taught and produce a generation of kids who love maths, what happens when they get to uni? They will see the ugly side of how maths used to be taught. My point is, I think if teachers can change then lecturers can too!