## Using ICT In Primary School Mathematics

Any views expressed here are my own but based on my experience. However I’ve seen enough good practice to know that success is often a product of the teacher’s personality as well as sound pedagogy. In short, there is no single right way. Good practice is dynamic and varied.

In the UK we seem to be expected to teach mathematics like we speak to foreigners when we’re on holiday. If it doesn’t work at first say it slower and more loudly. Rather than pressing on with new and innovative ways of working we look back to imagined golden ages. Was it the 1980s? We had the Cockcroft Report examining the problems of learning and teaching in maths.

Further back? “… a large proportion of entrants (to trade courses) have forgotten how to deal with simple vulgar and decimal fractions, have very hazy ideas on some easy arithmetical processes, and retain no trace of knowledge of algebra, graphs or geometry, if, in fact, they ever did possess any.” A Mathematical Association Report of 1954

Further still? “…accuracy in the manipulation of figures does not reach the same standard which was reached twenty years ago. Some employers express surprise and concern at the inability of young persons to perform simple numerical operations involved in business. … It is sometimes alleged … that the teacher no longer prosecutes his attack on this subject with the energy or purposefulness for which his predecessors are given credit.” A Board of Education Report of 1925.

Even further? “In arithmetic, I regret to say worse results than ever before have been obtained – this is partly attributable, no doubt, to my having so framed my sums as to require rather more intelligence than before: the failures are almost invariably traceable to radically imperfect teaching.” From reports by HM Inspectors 1876. So, dumbing down in the 19^{th} century!

So it’s time for something new and we have a brand new age in terms of technology to help us.

The new National Curriculum for England tells us, “In both primary and secondary schools, teachers should use their judgement about when ICT tools should be used.” A strange statement. Are we to imagine that no judgement is called for when choosing other resources or that teachers will otherwise make random choices?

Ofsted make their own actually quite exciting statements about what outstanding practice looks like: “Problem solving and investigative approaches are central to learning for all pupils.” They also talk about independence, perseverance and learning from mistakes. So have we got the wrong message about an emphasis on content?

So why embrace technology? First I ought to say that technology is not a magic bullet. It is a teacher that makes the difference; the technology is the tool that, if used well, makes the good teacher even more effective.

Technology, in those circumstances:

- enhances learning;
- allows you to do something that can’t be done any other way;
- makes life easier (without damaging standards);
- connects with children’s lives outside school.

These bullet points are generic rather than relating solely to mathematics. It must also be remembered that technology needs to be planned and targeted rather than being a token use.

I also want my tech to help me use different strategies in my lessons. Paragraph 243 of the Cockcroft Report was good in 1981 and is still good today.

Mathematics teaching at all levels should include opportunities for:

- exposition by the teacher
- discussion between teacher and pupils and between pupils themselves
- appropriate practical work
- consolidation and practice of fundamental skills and routines
- problem solving, including the application of mathematics to everyday situations
- investigational work

My decisions on what technology to use will be informed by the above and my own personal beliefs based on experience.

- Learning on tiptoe (the learner is the best (s)he can be)
- Learn regularity not tricks
- Learn by heart and not by rote
- All activities must be connected to other learning and activities
- There should be a variety of approaches
- No one is completely unable to do every part of something (When a learner says “I can’t do…” there is often one facet that needs addressing that is blocking progress)
- There are some hidden basics in maths. These are items not covered in curricula but vital from an early stage to many areas that are. Examples:

– Inverses

– Area as covering surfaces

– The meaning of =

Lastly I’d think about how technology can help learners climb Bloom’s Revised Taxonomy.

**Calculators**

Let’s look first at calculators, that most reviled of resources. First of all no sensible person would use a calculator to perform a calculation they could do more quickly another way. Children should be as good as they can at mental calculations, as good as they can at written calculations and able to estimate and approximate to be able to use a calculator effectively. Then they should know exactly when to use one of these alternatives.

- Tables card games. See #4 in https://icttalk.wordpress.com/2010/09/23/not-by-rote-but-by-heart-how-to-learn-multipl/
- Prepare a worksheet with sets of questions like:

1.6 x 10

3.8 x 10

7.2 x 10

23.5 x 10

and

2.45 x 10

8.32 x 10

9.01 x 10

17.74 x 10

The learner must answer each in turn, check it on the calculator and use the result to inform their answer to the next question. Sets of four are usually sufficient.

- Find how many different numbers less that, say, 30 you can make with four 4s and any symbols (This is the father of the 3+3×3-3+3 question that was on Facebook a while back)

Which of the reasons to use technology listed above did you spot in these ideas?

**Spreadsheets**

I’ve used them for modelling situations where doing it by hand takes far too long and detracts from the mathematics and the ability to experiment. Creating a chart and watching the effect as the data changes is fantastic. We all have a blind spot (I hope) and mine was cumulative frequency. I could never get my head round it until I created a chart and manipulated the data.

- Maximising area problem (see area and perimeter can be different in NC)
- Using graphs

Of the apps, programs and environments listed here others are available which are equally as good. The examples, while good, are meant to be generic rather than a claim to be the best.

**Environments**

Here are three very different environments.

The Khan Academy has had a bad rap in some quarters. It’s not designed to replace teachers but brings something else to the table. Students can practice, extend and watch the videos again and again and again and … It might have its place in a flipped classroom but this begs the question as to whether watching a video is necessarily always best as a solitary activity.

Geogebra is best described as a dynamic geometry environment but is rather more. It has a cut down version for younger users and works on just about every platform known to mankind. I confess to using it in a rather trivial fashion to model vertically opposite angles and what happens as one changes. It beats holding two slippery rulers across your chest!

Beluga Learning is an environment where users have to solve challenges as they move through it so it is neither a learn and practice activity nor a model.

I’ll tag on to this the sort of virtual tool that is available online, in IWB software and on tablets for example a protractor, base 10 materials and a virtual pinboard. I’m happy to debate the inclusion of the latter, apparently somewhat trivial resource.

**Programming**

Daunting for non-programmers but as Conrad Wolfram said, “If you really want to check you understand math then write a program to do it.” Scratch will bring computing and mathematics together as will the still free offering from EducationCity, Code Crunch. Go on, be subversive, make a calculator!

**Expertise and collections**

If it’s expertise and experience you’re looking for with excellent resources based firmly in good practice look no further than the Association of Teachers of Mathematics (ATM) and NRICH.

**From the environment**

There’s a lot of maths in the virtual world too. The recent freezing temperatures in the USA threw up lots of data in news feeds, real life maths features http://www.teachersmedia.co.uk/videos/interpret-and-construct-tables-food-scientist and my holiday pictures revealed a fantastic number square on the wall of the Sagrada Familia in Barcelona.

**Short applications / programs / tools**

I haven’t said a lot about practice here but there is a wealth of tablet apps that fill this space. The ICTMagic site has more than enough resources for even the most enthusiastic teacher and the Primary National Strategy programs are still alive and well. Try letting the children use them learning instead of using them for teaching.

**Screencasting**

Last but not least consider screencasting where learners make an electronic product to demonstrate an area of mathematics. You can build up a library for other learners to view over the years and the process can really enhance the learning process when the producer finds themselves having to explain something to another person.

And if you must teach Roman numerals…

Lastly, my own social bookmarking for mathematics.

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