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September 2010
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How to make mathematic more interesesting

The other day I was attending a seminar at the local school about how to make mathematics more interesting.

Since I’m somewhat engaged in the use of technology within learning, education and training. I had some expectations about how the seminar would encourage the use of learning resources as tool for more interesting and engaging mathematic education. I was somewhat disappointed after the seminar.

Use of computers was mentioned once: “You should learn your kids spreadsheet because that will be assessed at the 10th grade”.

Use of other technologies was mentioned at the end of the seminar: “We have agreed to ban use of cellphones during classes”.

And that was it – no more mentioning of use of technology to make mathematics more interesting – for the three hours duration of the seminar.

However we got many practical examples:

  • the use rubber-band to exemplify different trigonometrical forms, and how that could be used to get a better understanding of sizes, and the relationship between sizes.
  • And when walking in the forest with the kids, we should challenge them in finding the longest, smallest, something bigger, something smaller to develop a understanding of sizes.
  • We could make (or buy) a set of sheets with numbers and a dots on indicating the value of the number, to develop a understanding of the numbers and its value.
  • We could make (or buy) a set of trigonometric figures to be used in developing a understanding about 1/1, 1/2, 1/3 and so on, and how they relate to each other.

One good thing was that Matematikk senteret was mentioned as a place to go for more examples and illustrations for us as parents, however they forgot to mention all the digital resources at Matematikk.org.

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Accessibility and Learning, Education and Training

The other day I was made aware of the blog of Martyn Cooper from the Open University in UK.

Martyn have several blog posts that raises some important views when working with accessibility and learning, education and training.

What these blog posts made me realise is that we might have focused to much on accessibility to technology, and not necessarily to the learning, education and training per se.

It is widely agreed that there is a link between effective pedagogy and effective use of technology. There may also be therefore, a link between pedagogy and accessibility. Whilst the link may be complex, it would seem to be worth exploring further, particularly with a view to ascertaining whether pedagogical tools have a role to play in the development of accessible e-learning and accessibility practices;

So if the technology is used effectively, we would also have more effective pedagogy. Maybe this is a topic that should be explored – and maybe it is so that if the technology is made more accessible – the pedagogy could be more accessible as well? avoiding drop-outs and foster greater involvement.

However – making learning accessible do also provide some challenges:

2. Another standard accommodation, providing diagram descriptions, leads to a particular challenge in the assessment context. It is all to easy for such descriptions to simply give the answer away. So here accessibility is a pedagogic issue as well as a technical one.

To avoid this kind of mishaps, and to ensure that accessibility features fits the purpose as a -resource, -assessment, -process the teachers must be educated in accessibility issues and how to use technology and create content so that no one is excluded.

In Norway the legislation that regulates the Universities, and University Colleges requires the learning environment to “follow principles of Universal design” (§4.3 i), as the universities is relying more and more on the use of digital learning environments – the focus on how to make these environments universally designed is almost absent.

Based on Martyn Cooper’s blog post I have realised that accessibility is not only important with regard to technology but to pedagogy as well, and there is a chance that if we make the technology accessible the pedagogy could still be inaccessible.

We need to be aware of the combination of technology and pedagogy and make bot equally accessible.

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Universal design – some principles

The last year I was fortunate to get some funding from IT-Funk (Norwegian Research Council, and the RTD program on ICT for the disabled) to investigate challenges on universal design to web based information and services. For a more complete list of findings and results – do not hesitate in contacting me.

We found that the main principle in ensuring universal design is – Predictability – and that the ICT environment is familiar and recognisable, so that when we move from one information domain to another – some of the common functionality is predictable, and there is no need to learn a new interaction design and interaction logic for each domain – or each service.

The Predictable Web Project was established as a result of new legislation in Norway, the “Discrimination and Accessibility Act”. According to this act, all new ICT should be “universally accessible” by 2011, and existing ICT systems should be “universally accessible” by 2021.
The goal of the predictable web project was to identify areas that need standardisation and common specifications, to ensure that web based information and services would be universally accessible.

Types of accessibility

When discussing accessibility to web-based information and services, we have identified at least three different approaches that have to be met to ensure universal accessibility.

Syntactic Accessibility.

This is the coding sent to the browser device used for presenting the information. This is usually information that is – or should be – in compliance with the W3C/WAI criteria, such as WCAG and ARIA. This accessibility approach is managed from a “sender’s perspective” on accessibility: Coding is added to accommodate different assistive technologies, used by people with disabilities. It is quite easy to check for syntactic accessibility, because there is coding embedded in the information sent to the browser; and normally the browser is replaced with an automatic engine checking for accessibility-enabling elements and accessibility attributes.

Semantic Accessibility.

It is not sufficient that a person can access the information; the capability to understand and interpret the information is equally important. To ensure semantic accessible information and services, the systems providing the information must behave in the same way and behave more predictable with respect to basic elements, such as how menus are organised; where the different semantic elements are located on a page.

The reason for this requirement is to avoid that a person entering a new web-domain or a service should have to use time to learn to navigate and use these services. This is important, especially with regard to elderly and people with cognitive problems.

It is also important that similar concepts and functionality are called the same, i.e. use the same vocabularies and terminology.

It is also important to acknowledge the fact that Europe is a multicultural society, and many Europeans have another language as their mother tongue than the official language of the government. To ensure that everyone can interpret the information, different scaffolding solutions are needed, such as automatic translation and specific terminology explained in different languages and adjusted to a proper cultural context.

Procedural accessibility.

Another important dimension in universal accessibility is how you interact with the information system. This is especially important with regard to public (eGovernment) services. Procedural accessibility ensures that similar services have the same sequencing of events and the same patterns of interaction based on the information entered into a system.

As an example: When you are paying your bills using an on-line banking service, there is no reason why the sequencing of events and how you enter the necessary information are different among all on-line banking systems. If you have investigated a lot of time to be able to use a service efficiently, you are not likely to change to a different provider that have a different set of sequence for performing the same task. The same goes for all services.

All three dimensions; syntactic, semantic and procedural accessibility must be addressed to ensure that a web-based information system is universally designed and can accommodate most users, including people with disabilities.

Individual accessibility and adaptability

In addition, there is a new standard, ISO/IEC 24751:2008, that offers a different perspective, where the users are in the centre. This new standard provide a mechanism for users to specify how they would prefer that information are presented. The users could specify a range of different properties indicating how information should be presented to ensure that they could access the information. There are also provisions for a service and a resource to specify which of the personal preferences that could be met by this service. This could be used as a way of filtering out systems and resources that are not capable of meeting the preferences of a user.

Combining this new standard with principles mentioned for universal design would increase the accessibility to web resources.

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Collaborative learning and Creative Commons

Recently I read a note on the Norwegian Creative Commons email reflector about choosing a CC license for learners when they publish information on the internet.

Then I realised that this is an important topic, and that a by-nc-sa license is pivotal for schools.

More and more of pupils work are published online, more and more are based on remixing of available information. In many cases development of material is done in a collaborative manner.

Collaboration will break if material used for remixing and material produced are not available with an open license.

I would recommend that schools work towards a default BY-NC-SA license to be used on all material produced by learners.

There are projects in Europe today e.g. Science Created by You where the learners are collaborating in producing learning resources, and where the idea is that these learning resources should be further developed and enhanced by others. To make this work the resources and objects produced have to be BY-NC-SA.

I’m quite sure that there will be some discussion on “NC” – and that we in the future will find that user generated content would provide a commercial value for some institutions, or that teachers could take resources produced by learners and publish them as commercial learning resources…

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Learning Resources and Learning Resource Repositories

When I meet teachers, I always ask them how they use learning resources and learning repositories. In most cases they do not understand my question… Then I ask them how they use computers in the classroom, how do they decide on what to use and where do they find this? In most cases I’m told they just go to a “home page” of a colleague and use what this colleague have found and recommended. But usually they are a bit reluctant to use computers, because using the “computer room” is tedious and it usually takes about 5-10 min (20% of the class-time) to get everyone starting. In many cases the computer that are available in the class room is not connected to a projector (there are no projectors in the room).

If we assume that the computers are easily available – the question still remains, why are most teachers not using learning resource repositories?

I think there are several reasons for this, and would like to start with the following:

In the design of Learning Resource Repositories – the user and the need of the user is not thoroughly addressed. Who the user of the repository is in most cases unclear; is the user a learner(pupil) or a teacher?

My assumption is that the learner and the teacher have different needs when searching for a resource:

  • A learner would use the repository looking for resources that could help them solve a task assigned.
  • A teacher would use the repository to find resources that would be used for the next class, or a series of classes.

If my assumptions on the user of a repository is correct. Why are repositories not designed with this in mind?

If the repository is intended for the use by learners to solve a task, it would be a nice feature if the teacher could do some preparations for what to search for, and to make sure that the learners would find resources that could answer the assignment. The learner should do its searching and browsing within a sub set of resources, where the sub set is defined by the teacher.

If the repository is intended for use by the teacher, there should be a strong link to the national curriculum.
The advantage of the book is that it provides a set of resources (chapters/sections), and if you follow the structure of the book – the school year is more or less covered for.
The learning resource challenge is that they do not ensure that a school year is covered, most learning resources are for a specific topic with a specific scope.

If the use of learning resources is to be common in the schools, the learning resource repositories need to provide functionality for helping the teachers in planning their classes. The repositories need to make the working day of the teacher easier. The repository need to provide for a proposed set of resources that are suitable for a complete curriculum (even maybe suggest online and off-line resources – based on how to teach a topic with the highest learning outcome) providing a proposed sequencing of resources.

The learning repositories I have looked at – do not provide this service to the teacher. The system is based on the idea that the teacher are the one responsible for finding the most suitable resource for teaching the next class. My argument is that most teacher do not have sufficient resources (time) to do that for all their classes, and therefore the use of the traditional text book will prevail.

When the learning resource repository provides tools that makes the working day of the teacher easier most teachers will use digital learning resources in their classes.

The question to ask is:

  • Who should decide on what resources are best fit to meet the requirements in the curriculum?
  • The repository?
  • Professional editors?
  • Collaboration among peers?
  • How would this affect metadata used for describing learning resources?
  • How do we connect learning resources to curricula?
    • Are the focus on curricula wrong?
    • Should there be a focus on more curricula atoms?

    Disclaimer:

    • I know that many teachers are using digital learning resources in their classes today – successfully. The challenge is how to ensure that all(most) teachers are using digital learning resources?
    • My statements here are not scientifically founded; however they are based on observations and from talking to teachers in different social contexts.

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