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The 7 Zones


This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 23 February 2011 by ncetm_administrator
Updated on 11 March 2011 by ncetm_administrator

Skill Zones for the Successful use of ICT in Mathematics

This skill list has been structured so that it could form a convenient home for ICT activities to be referenced. Potential trainers could also be asked to reference their own ICT competences to these zones.

Zone 1 Classroom Hardware

Although ICT department staff are normally the ones to be concerned about classroom hardware, they are often unaware of the special needs of mathematics teachers. It is important therefore that mathematics teachers have a good understanding of how the classroom should be setup, so that the software and hardware that they do have is not compromised.

Mathematics staff should be aware that these are issues that need to be addressed in setting up/taking over a mathematics classroom:

  1. Connecting desktop and/or laptop to a projector and interactive whiteboard
  2. Projector controls: use of ‘blank’ and ‘freeze’; setting the contrast correctly (default setting invariably loses graph grid lines); adequate speaker system
  3. The vital importance of getting aspect ratio right (circles and ellipses!); problems associated with mixed systems (4:3, 16:9, 16:10), and checking that the graphics card can cope.
  4. Screen resolution: lower the better to achieve a clear image for the pupils in the back row. Need to know about the wide-screen equivalents of 800x600.
  5. Use of a tablet PC (with associated wireless projector link, and bandwidth problems)
  6. Use of wireless graphics tablet. These devises generally connect seamlessly to laptops, but need a Bluetooth dongle for a desktop connection.
  7. Classroom lighting: control of lights vis-à-vis the whiteboard; control of sunlight.
  8. Lo-tech classroom requirements: plastic ruler and protractor (though not to be used with a Smartboard); mini white-boards, etc
  9. the provision of a lectern so that keyboard and mouse can be used standing up
  10. PC-Mac issues (for some).

Mathematics staff may also become involved in IWB purchase issues, and here would need to consider

  1. Installation and usage issues
  2. Making decisions: pen-driven, finger-driven, or both, how the software varies on the different boards and how the interaction is different (pros and cons of the different makes); conversion between different file types

Zone 2 Interactive Whiteboards

A large proportion of classrooms in England have been equipped with IWBs, some pen-based, some finger-based, and more recently some are a bit of both! It is important that this investment is not wasted, and that the teachers learn to put these tools to good use.

  1. At the board, on the desk, in the head: maximising the effective use of the IWB for mathematics teaching
  2. The IWB software as the management (i.e. organisational) tool for all electronic resources in a lesson
  3. Pedagogy of the IWB
  4. Converting from one IWB software type to another (when this is possible and when it is not possible)
  5. Using the IWB software tools specific to the board including: mathematical tools e.g. (compass, protractor ruler); grid creation; camera; hyperlinks; video recorder etc.
  6. Use of virtual manipulatives, Teachers’ TV, and other resources within IWB files
  7. Creation of animations (i.e. video resources) using IWB software.
  8. Use of IWB software for use in mathematics - ActivStudio, ActivInspire; Smart Notebook
  9. Use of learner response systems for specific IWB

Zone 3 Strategies for lessons on laptops, and lessons in the computer lab

It is highly desirable that students get to experience the power of ICT for themselves, and increasingly they will be able to do so at home. At school, the choice of hardware is changing fast, but for now is still likely to be classroom laptops or a laboratory of desktops. The teaching strategies for these different situations need careful planning.

  1. A changed pedagogical practice and the dynamics of the classroom
  2. Planning and problems of implementation
  3. Alternative technologies: Smart phones and e-readers
  4. issues with the widespread use of wireless internet connection; contention ratio

Zone 4 Wordprocessing for Mathematics

Mathematics teachers need to be able to produce high quality worksheets, both on paper and onscreen. In addition to general word processing skills, teachers need to be able to create high quality mathematical diagrams and mathematical expressions.

There are now many WP options now, falling into two categories:

  1. traditional word processors (e.g. MS Office, Open Office). MS Office is still evolving and there are significant interface differences between versions. Office 2003 has toolbars and menus, whereas Office 2007 (and now Office 2010) has threads and ribbons. The MAC version is also different.
  2. in the ‘clouds’ (e.g. Google Docs) – where documents can be easily shared and
    co-authored online, but some features are lost.

The following techniques need to be mastered for any system in use:

  1. How to create one-line mathematical expressions as text, without using an equation editor. These make use of the large number of font independent Unicode symbols that are available. Either use “Insert Symbol” or use the Autograph on-screen keyboard. e.g.: y = |x| ± √(4 – x²)
  2. How to create multi-layered mathematics expressions. These are created as a graphic object (ie not text). An ‘Equation Editor’ can be used for this, or many WP systems have a sophisticated equation tool; there are alternatives such as FX-maths pack, and MathType.
  3. Creating mathematical diagrams; use of shift (to make figures regular), and ctrl (to make figures centred); use of Ctrl-D (to duplicate figures in a controlled way).
  4. Creating hyperlinks to other files and URLs
  5. Pasting images from the web
  6. Careful use of the right-click
  7. Creation of pdf files.
  8. Putting mail-merge to use to create multiple documents based on spreadsheet data.

Zone 5 Spreadsheets for Mathematics

Although designed for use in commerce, spreadsheets can be used in a wide variety of way to support mathematics teachers. They can be as useful in teaching situations, where mathematical concepts can be modelled, as in day-to-day administration.

  1. Managing cells, formulae, series, charts; statistical operations (including filters, pivot tables, frequency counts, histograms and tables)
  2. Making a spreadsheet interactive with slider bars, conditional statements and self-checking methods
  3. Knowing when Excel goes wrong, or does not quite get it right!
  4. Handling large datasets; selecting columns of data
  5. Converting data pasted from website when necessary using “Text to Columns”
  6. Sorting data; filtering data

Zone 6 Internet Resources and Related Issues

The availability of a fast internet connection in the classroom is becoming something most teachers in this country are fortunate to be able to expect. This ability to ‘bring the world into the classroom’ can leave many teachers overwhelmed by the quantity and the very variable quality of what can be accessed.

  1. Awareness of internet resources for mathematics, e.g. www.tsm-resources.com
  2. How to drive Java and Flash web apps, and to embed in other digital resources
  3. Ability to retrieve data (into Excel) and images (into Paint or Autograph) and everything (into IWB software) from websites
  4. Using Teachers’ TV, YouTube, etc.; converting to FLV for offline showing
  5. Software to create and edit podcasts, videos and animations.
  6. Use of video resources (eg ‘Jing’ for on-screen recording, or files from digital cameras)
  7. Understanding the vulnerability of information on the web, eg Wikis.
  8. Email lists; forums; social networks
  9. Virtual Learning Environments: contributing material and accessing resources.
  10. Creative use of games
  11. Ensuring that sites with mathematical input (e.g. NRICH, Mathletics) are used creatively

Zone 7 Specialist Software

Primary level

There will be a need for specialist software trainers to train the trainers in the effective use of primary software. Some of the secondary packages have junior versions (e.g. Cabri and Geogebra).

Secondary level

There will also be a need for specialist trainers in the main secondary software packages, including:

  1. Geometry
  2. 2D: Geometer’s Sketchpad, Cabri II, Geogebra
    3D: Cabri 3, Yenka
  3. Dynamic Coordinate Geometry
  4. 2D and 3D: Autograph.
  5. Statistics
  6. Autograph, Excel, Tinkerplots, Fathom
  7. Graphic calculators (with and without CAS)
  8. Casio, TI, HP and Sharp
  9. Programming languages
  10. Scratch, Logo

Trainers need to be aware of the basic principles of ensuring that dynamic software is used effectively:

  1. The judicial use of parameters.
  2. The use of student prediction before the computer does anything.
  3. Awareness that learners do not have a lifetime of ‘traditional’ mathematical study on which to ‘prop’ visual images. A visualisation that excites a teacher may well not excite a learner.

Mobile Technology

Teachers and trainers need also to be aware of the rapidly changing facilities on mobile technology. Learners are likely to have increasing access to a large number of mathematically based ‘apps’ on their phones and ‘pads’, and should be encouraged to explore their studies using them.

 


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Comments

 


11 March 2011 14:13
About the Promethean voting devices, I expressed concern that dynamic interactive software is zone 7 of 7. I see this is the resource which maximally allows teachers to engage learners dailogically and hence the most importnat resource. Voting systems (of the type shown) allow very limited or multiple choice input and therefore represent a qualitatively different pedagogy. I wanted to draw attention to the choice NCETM made in the resource it wished to illustrate digital technologies with.
By cjolley
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10 March 2011 20:26
this is really interesting and many thanks for your input. As Colin says, we do look at all comments seriously, and the immediate changes to the formatting, we shall make as soon as possible.

further changes, to the content, does have to go through the general NCETM editorial process, and we welcome every inout, but cannot guarantee that every suggestion will be acted upon. I think that this shows a plus point about the NCETM portal - it is a living thing, with the opportunity for any registered users to make comments and contribute to its development.

finally, we have to use images around the site and yes, they do sometimes show various commercial products. This is not an endorsement, but just an illustration of such products. If we were to show an interactive whiteboard being used, then one of the companies would be pleased, the others less so. We do try to get a balance and ensure we don't have any bias.

and finally, finally...

please continue the conversations about how best to use digital technologies - either here, or in the ICT forum.
By Tim_Stirrup
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10 March 2011 15:17
I will certainly have a go at this. However, the issue for me is that the NCETM chose to advertise this page as it stands in their March update. So the message will have been given. The image in the advert was a Promethean voting gadget, which conveys a message about the sort of model of teaching and learning the NCETM wishes to promote. I hope it will be possible to promote the full launch in post 'place holder' mode in a future update and hopefully with a different image. Both TI-nspire and GeoGebra are interesting to watch as they are both aiming for a fully integrated model with 2D/3D, CAS, graphing and statistics all in one package. This means that (a) the teacher only needs to learn one piece of software and (b) as with all good mathematical exploration, we are not limited in the maths modes available. For developing real mathematical dialogue in classrooms, this seems an exciting opportunity. We just have to ensure that the omnipresence of assessment (unless to guide and sustain learning) doesn't prevent teachers from grasping the possibility.
By cjolley
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10 March 2011 14:47
Just to note that GeoGebra is more than a Dynamic Geometry software app. It already has a spreadsheet and many algebraic and statistical functions available. The latest beta version is in the final stages of testing; there is a CAS facility, a simplified version for primary school use and a 3D version is being developed.
By kathrynp
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09 March 2011 18:55
Hi cjolley thanks for your very helpful note and offer of help. Your post has helped us identify a small technical bug that we were unaware of that Tabulation changes when you switch from a word file to an HTML file, we hadn't picked that up when proofing the original report so apologies for some of the earlier mixing up of detail (and thanks again for spotting it). Your later comments about which tools applications and bits of software are referenced in which sections are exactly the sort of discussion we are hoping to promote. As the NCETM started its review of digital mathematics it became clear that to have some sort of taxonomy or classification system would be worthwhile in order to be able to link or group families or threads of mathematics and technology. I am making an assumption that in suggesting gaps and re-classifications you have accepted the overall value of the principle of classification and of the classification groups themselves?

If you would like to re-write the section as you suggest I will be pleased for you to do so. I chair the NCETM Digital Mathematics committee and this document is a "place holder" in so far as it was written during 2010 and agreed as the current state of affairs at a certain date (October 2010) Of course things move on and you comments clearly indicate, as well as mis- classifications there are gaps. If you re-post your suggestions in this thread I will ensure that the authors of this section and of the Digital Mathematics report have a full discussion about your contributions as part of the process leading to changes.

Kind regards, Colin
09 March 2011 11:19
Hi cjolley thanks for your very helpful note and offer of help. Your post has helped us identify a small technical bug that we were unaware of that Tabulation changes when you switch from a word file to an HTML file, we hadn't picked that up when proofing the original report so apologies for some of the earlier mixing up of detail (and thanks again for spotting it). Your later comments about which tools applications and bits of software are referenced in which sections are exactly the sort of discussion we are hoping to promote. As the NCETM started its review of digital mathematics it became clear that to have some sort of taxonomy or classification system would be worthwhile in order to be able to link or group families or threads of mathematics and technology. I am making an assumption that in suggesting gaps and re-classifications you have accepted the overall value of the principle of classification and of the classification groups themselves?

If you would like to re-write the section as you suggest I will be pleased for you to do so. I chair the NCETM Digital Mathematics committee and this document is a "place holder" in so far as it was written during 2010 and agreed as the current state of affairs at a certain date (October 2010) Of course things move on and you comments clearly indicate, as well as mis- classifications there are gaps. If you re-post your suggestions in this thread I will ensure that the authors of this section and of the Digital Mathematics report have a full discussion about your contributions as part of the process leading to changes.

Kind regards, Colin
08 March 2011 15:20
For progressive maths educators, I would have thought that putting specialist software (and subsuming graphing calculators into it) as the last zone is a little dismaying. It is hard enough to encourage teachers to teach in a dynamic and engaging way with ICT anyway. Please reconsider.
Also, TI-nspire is not a computer algebra system. It is a software and hardware combination that contains all of items a up to f. It does also contain the a CAS being Derive. Mathematica (and Maple) are also well known examples of CAS.
Also, Casio, Texas Instruments, Hewlett Packard and Sharp all make graphing calculators. They all make different models with and without CAS.
Also, there is no such thing as geoGebra 3D and by Cabri 3, I assume you mean Cabri 3D (which doesn't really belong in the 2D section).
Also Autograph is not dynamic geometry. It is graphing software. (Which handles algebraic and statistical data).
I will happily rewrite this section for you, so that it has the same accuracy and level of detail as the others.
By cjolley
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