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.

Upon reading some posts in the global blogosphere (is that a word) I came across a rather thought provoking piece that reminded me of incidents on my practicum. The post concludes on the need to thoughtfully implement technology so that it is utilised as a purposeful tool.

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.

I refer to another bloggers discussion  on the lack of research on the success of constructivist techniques. Personally I felt I need to examine this area to see if I could find specific success in my KLA of mathematics, as I too had found some of the claims made to be unsubstantiated.

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

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.

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.