Whight’s view on technology, maths and education.

Research discussed on Edutopia has found 4 key components of learning that need to be evident when we utilise technology in the classroom to enhance learning.

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.

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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.

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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

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?

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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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Bakhoum (2008) has studied in some detail the effect of using flash animations within a mathematics classroom. On average 65% of the students achieved better scores when using flash animations whilst 98% of students believed they has a better understanding.

One creative example presented examines the formation of an understanding of velocity. The user of the program drags a car along the top of the screen at variable pace and a distance verse time graph is produces. This would enable a student to examine the variation and “steepness” of such a graph with alterations in the speed of the car.

Whilst in this study, the primary creators of the animations were the teachers; I can see no reason why students cannot create their own animations or just use the teachers own creations to build there understanding of mathematics.

A great example of a Java Appelet allows a student to examine the displacement, velocity and acceleration graphs of a man as the user drags him along the screen.

For your own knowledge, tutorials on creating flash are available at Flash and Maths .

Bakhoum, E. (2008). Animating an equation: a guide to using FLASH in mathematics education. International Journal of Mathematical Education in Science and Technology, 39(5), 637-655, retrieved August 31, 2008 from http://web.ebscohost.com.ezproxy.lib.uts.edu.au

While reading several articles on implementing technology, I find myself questioning whether good teaching practices are still required with the increased usage of technology.

Romeo has discussed in some detail the benefits of technology including:

• Technology can bring real world problems into the classroom. I see this as allowing students to build skills and knowledge that are important part of operating within society. One of the aims of the curriculum.
• Technology gives the students opportunities for reflection, revision of work; which can build a stronger understanding.
• And lastly it means that teachers also need to be learners, and enables opportunities for teachers to reflect on their own practices. This hopefully will lead to better teaching practice.

But what about teaching practices? Romeo puts forward the ideal example of a classroom (Scenario 2) which, although somewhat unbelievable, highlights the need for good teaching practice. For example, we need to allow opportunity for and ensure students collaborate (group work in mathematics), reflect and revise. It is up to teachers to utilise technology to scaffold learning, connect to real life problems and promote learning communities which exist due to technology.

I don’t see technology as being utilised in every lesson due to time constraints within the curriculum; however it does present us with opportunities to provide enriched experience to our students and give relevance back to school work, providing us with an important role in our students’ learning.

Romeo makes an important conclusion. We as teachers can make a difference to our students’ educational experiences. For it is the magic we weave that will remain in students memories, not the use of technology.

When I look in a textbook suitable for high school, the examples of implementing technology are little more than a step by step guide to getting the right solution. On my practicum, one student was so caught up in trying to copy the formula given for Excel, that by the time the solution came out she could not relate it to the area being examined, financial mathematics and in particular simple and compound interest.

They represent what Harel refers to as traditional instruction approaches where the student absorbs the information. Computers are seen as teaching machines, where right and wrong answers in maths are required in a program or a Scholar passes on information to the students (Harel).

Papert is keen to highlight that Constructionism is not a teaching strategy, but rather a focus on how students learn and is a theory that students learn better by doing. In mathematics this revolves around giving the students opportunities to learn mathematics as part of something that is real. Harel expands on this that students learn best when they are the designer and builder. Harel points out that with technology in a classroom, when learning with Constructionism, the student would program the computer, rather than having the computer program the student. An added dimension of technology by utilising this strategy is that it allows the students to expand, reflect and share their constructions (Harel 2).

A great example of implementing this strategy is presented by Harel. Primary school students were designers of their own learning. They expanded their knowledge of fractions by building software to teach the year below them about fractions. In the process the students became engaged in the process and discovered for themselves that there is more than one way to represent a fraction. Additionally they were able to make connections between fractions and where they were used in the real world. I feel this approach could also be applied to areas in high school in which students have difficulty with. Possibilities include algebra, fractions and decimals.

Eg. One Twelth is the same as the slice of the clock representing 1 hour. (Picture to come)

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Back to the initial situation of the students utilising Excel with financial mathematics. Perhaps a task could be designed around the students examining differences between simple and compound interest by building their own knowledge and formula within the computer program.

A teenager chatting on her cell phone, using a Mac and completing her homework all at the same time is an image presented by Wallace. I question how anybody can possibly successfully do this. However then again, I come from a non-multi-tasking generation and as Prensky points out, I, as a digital immigrant, fail to comprehend how the teenagers from today can successfully learn whilst multitasking as I myself can’t. However researchers mentioned in Wallace point out that the quality of output deteriorates as one attends to more tasks. But then again, I assume these researchers are digital immigrants.

Wallace points out some multitasking situations that have been utilised for generations. This highlights that I do multitask but just not in the same manner as teenagers from the digital generation. For example, I have driven and listened to music for years. The difference is that teenagers are now multiprocessing, not just multitasking.

Disregarding my views, if a student can multitask in such a way as suggested, perhaps we, as educators, can tap into this and develop interlocking tasks for a classroom that can be completed simultaneously. But the question remains, if students can complete two tasks at once by dividing their attention, will they save time allowing for deeper investigation of a topic? Or would two tasks that would take 1 hour each to complete individually, take 2 or more hours to complete when done simultaneously? According to research presented in Wallace, when multitasking, errors go up and it takes far longer to complete tasks when compared to doing them individually.

Another view, and one I am more inclined to believe, is presented by Rainie. Perhaps teenagers aren’t so much as doing two things at once; rather they scan several pieces of technology at once and attend to where the action is happening. This is further backed up by research mentioned by Wallace. Rather than truly multiprocessing as previously mentioned, teenagers are actually rapidly switching between different tasks. Also of note is that a human’s ability to do this appears to diminish with age.

The final point is although multitasking appears to diminish performance, research presented in Wallace suggests that a little stimulation, such as music can improve performance. So perhaps an IPOD in the ear in a classroom isn’t something to be frowned upon.

Multitasking:

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Split Attention

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Reference:

Wallis, C. (2006, April). The Multitasking generation. Time. 46-54.

The concept of blind devotion concerns me as an educator.

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A student on a video by The MacArthur Foundation questioned why there was a need for books anymore. Why was this so? It was believed that all books are on the net so all the information you could possibly need is on the net.

Rainie points out that for students the first step for an assignment is to browse the internet and then if they have queries to ask they go on a social networking site for advice.

What concerns me about this is the free access users have to the internet and the fact that information on sites can be from dubious sources to say the least. Students appear to believe whatever is put before them on the internet, perhaps because it represents technology? My other concern is that not all resources are available on the internet and as such students are limiting their experiences in education.

But the question remains, how can we remove these blindfolds so that our students perspectives can be expanded and enable our students to question the authenticity of what they find on the internet? Would our interference in this area be seen as an action to attempt to minimise their use of such technology?

The “Monkey Wrench Conspiracy” is a game discussed by Prensky as an example of how imagination can be utilised to produce a creative and engaging environment to learn in.

But why am I discussing such a concept?
According to Prensky, from generation to generation there have always existed changes which have revolved around style or current fashion trends and the language utilised by the teenagers of that generation. Oh how things have changed. Prensky in fact sees students as having fundamentally different processes of thinking and interpreting information. According to Draper, they spend large quantities of time blogging, pod casting, emailing and in general utilising technology.

But what are the implications for educators?
First and foremost we need to recognise that our current teaching strategies need to be adapted for this digital generation. Draper highlights some statistics:
- 28% of Year 12 school leavers see school work as meaningful
- 21% find school work interesting
Prensky points out that we cannot assume that teaching strategies that have worked in the past will still work today; we need to talk in the technological language that is relevant to our students and relate our work to the future which will heavily involve technology. Perhaps in the form of software, robotics and nanotechnology.

This brings me back to the “Monkey Wrench Conspiracy” game. This was used to teach engineers how to use new computer aided design software (CAD) and is a prime example of how we can utilise a technology which students engage in to get them to learn new ideas. Draper presents other ideas such as using pod casting and blogging in lessons. In Mathematics in particular, Prensky points out that we need to utilise calculators and computers to give useful applications of mathematics. To do this all we need imagination.

Summary:

From the old style teacher to

teaching maths theorems on IPODs or other technology.