1. Our students must be actively engaged.
2. There must be opportunities for group interactions (surely the use of collaborative software establishes this).
3. There must be frequent feedback. I see this as common sense. If students are constructing knowledge in any form, we must check to ensure they don’t form misconceptions.
4. Our students must be connected to real world experts.

I guess the final point is an interesting one which we need to consider. It implies that we do not need to be an expert in every technology, as the nature of online technology means that our students will be able to seek help from real experts across the globe.

Original Photography: ‘One Of These Buttons Will Get Me+Out+Of+Here‘

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I guess this means even those teachers with little technological ability will still be able to implement technology by connecting, or letting their students connect, to experts outside the school community.

podcast

As part of my immersion activity with Nigel, we looked at Microworlds and in particular the implementation of SimCalcs MathWorld in a Mathematics classroom. Another example is ThinkerTools which looks at Newtons laws of motion (discussed here).

MicroWorlds are seen by Jonassen as beneficial for students as they are an active learning environment which contain simulations of real world situations which the students manipulate.

Jonassen provides the example of students matching the velocity and displacement to motion. It can also be highly interective, with the right equipment, students can even model their own movements.

Research has also statistically examined the benefits of MathWorlds. It has been shown to improve Algebra results, in particular in more difficult concepts, and motivate students (Trotter, 2007). Overall, I see these as an interesting area to try to utilise next year to help improve student learning and engagement. Surely it is more motivating to learn algebra in real world simulations than on a blackboard:

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Whilst MathWorlds is one example, there are surely numerous alternate software available on the world wide web. I found ThinkerTools (KLA: Science) in minutes.

There is a free 120 day trial for MathWorlds for those interested.

Trotter, A. (2007). Project on Algebra Software Seen to Show Promise. Eduction Week. 27(5), 10. Retrieved October 23, 2008, from ttp://web.ebscohost.com.ezproxy.lib.uts.edu.au

Whilst this site apparently allowed you to create sketchcasts, it doesn’t appear to be working at the moment. For those interested in learning more, see the following tutorial on how to create a sketchcast using a range of desktop and internet applications. The key to creating a sketchcast is having a mic, a screen recording tool and a sketching pallat, the most basic of which I can think of is Paint.

Anyway, I think this idea could be useful in a classroom. We could use it as a teacher directed aid, however to be more beneficiall to our students, we could get our students to create there own. This could take the form of an overview of a topic or as a solution to a question, as suggested by the blogger. In this way the technology would be implemented using a constructionist approach to learning. This is underpinned by Pappert’s theory that students learn best when they are the designer and builder, as discussed by Harel.

Whilst a true sketchcast involves a sketching pallet, I do not see why this idea cannot be extended to include recordings of software such as Geogebra that will allow more complex ideas to be examined. See my amateurish version below on constructing an angle in a semicircle using geogebra. This was created using Geobra and Debut Video Capture Software.

Note: For a true sketchcast  I should also record sound to explain what I am doing. 

Note: If you can’t see the embedded video below (I couldn’t see it), see it on YouTube.

Nico talks about the dynamic nature of such constructions i.e. “when constructing the bisector of an angle, dragging the arms of the angle and therefore changing it don’t change the fact that the bisector still divides it in 2 equal angles”. I just wanted to mention that this has been a researched benefit of such software. The dynamic nature allows students to see the generalisations of a construction. Or if you like, it aids the student in seeing that a property doesn’t just hold for one example, rather it holds in all cases (Kissane, 2002). This overcomes the problem of a student questioning the validity of a proof, as it shows that the property holds in more than one instant.

Within our curriculum, I see this as particularly useful in the area of circle constructions where a large number of difficult constructions are necessary. For example, the image below shows a construction which the students could generate to construct their own knowledge that the angle in a semicircle is a right angle. 

Kissane, B (2003). Using Technology in the best possible ways. Reflections. 27(1). 2-11.

In my practical experience, too often computers were used as the dreaded “teaching machine”, with little difference in such a lesson to completing textbook activities. Indeed some just involved completing an online quiz. Is there a purpose to this?

Rather, we must have a purpose and try and let our students program the computer rather than the computer program the student. Often when utilising Excel in mathematics the students on prac just had to copy code and answer some fairly straightforward questions. Instead, as research points out, why not have a purpose of using Excel, or other spreadsheet programs, to improve the students understanding of the relationships or concepts involved. If we get the students to program their knowledge into excel by converting known mathematical properties into code or formula, they need to utilise higher order thinking.

Don’t just give them a worksheet, with the formula given as below. Let them think creatively for themselves to improve their own understanding.

Overall we need to think seriously about our implementation of technology. Don’t just mimic textbook activities, engage our students and extend them beyond routine ideas.

This was one topic I was considering for my immersion activity and felt it warranted some greater exploration on my part. For me personally, I couldn’t see the value in commercial games and only thought benefits could exist in educationally produced material.

But this view has altered. Upon viewing the video Why Games , it became apparent that even commercial software has potential. Possibilities mentioned included the physics involved in Half-life through to the historic perspectives offered in games such Age of Empires. Or my own thought, could physics or engineering be examined by using flight simulators?

Original Photography:  ’mac flight’

But why are games so useful as educational tools. The key mentioned is that they are ENGAGING. Additionally, feedback included that: 

§         They can be open-ended or non constrictive, unlike standard workbooks or textbook work

§         They can allow you to make your own creations.

§         They can allow you to examine the impact of certain actions to build your understanding.

More formal commentary suggests the added benefits of modified mainstream games to include additionally educational elements. These games are still engaging but also provide opportunities for students to think more broadly, such as an understanding of chemistry in the modified DoomEd game. Its also interesting to read that games are not only being used by students but also actively created.

I feel the need to be careful when using games to model real-world phenomenon or those which examine historical perspectives. As research has pointed out, there needs to be a sound level of accuracy so that we will be comfortable using them in a classroom. For example, games where you can somehow jump from a 10 story building and then keep running could create dangerous misconceptions in a child’s mind.

As part of immersion we are required to create a mindmap.

When utilising this tool (we used bubbl.us) it was apparent that it enabled us to logically organise our thoughts on the types of ‘mindtools’ available to us as educators.

Indeed this is the reason why mindmaps are beneficial in helping our students learn. In producing a mindmap a student is required to engage in “critical thinking” to analyse the relationships between concepts that may initially appear isolated. (See Jonassen). In this way they are constructing their own links between concepts that may otherwise appear unrelated.

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For a teacher, I believe there are more important divisions other than age. For example great divides exist within the current generation of “digital natives”.

It seems inappropriate to classify someone as a digital native purely on their age. I personally know 18yr olds have as much ability as a monkey when it comes to utilising technology. Is this person a digital native? Surely Taniak is more of a native than this person?

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I believe to us as future teachers, motivating and engaging such students like this 18yr old will be one of the greatest challenges when implementing technology in a classroom.

Additionally, this gap in knowledge may be increased as many such students may be unwilling to ask for assistance due to the stigma attached to a lack of ability with technology. (McFarlane, 2008)

McFarlane, S. (2008). The Laptops Are Coming! The Laptops Are Coming!. Rethinking Schools Online. 22(4). Retrieved September 25, 2008 from http://www.rethinkingschools.org/archive/22_04/lapt224.shtml

On some further digging through the archives of ERIC, I discovered several papers one of which I will mention here. Pugalee (2001, see reference below) examined the impact of using technology is a constructivist environment when students learn algebra and functions with the use of graphics calculators.

 

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Whislt the results don’t give specific details of percents gained in terms of marks, it discusses other aspects of learning that had improved. It allowed the students to make their own connections (connectedness, an element of the QTM) and refine and extend their own understanding.

So while there does appear to be instances of successful implementation of constructivist approaches, I tend to believe his concluding question and see the need for a balance between constructivist and direct approaches mainly due to the time constraints evident in the teaching of mathematics in secondary schools.

Pugalee, D. (2001). Algebra for All: The Role of Technology and Constructivism in an Algebra Course for At-Risk Students. Preventing School Failure, 45(4), 171-176, retrieved August 31, 2008 from http://web.ebscohost.com.ezproxy.lib.uts.edu.au