## Thursday, August 18, 2011

### Why is maths different when it comes to laptops?

Continuing the series on 1:1 laptops in the mathematics classroom. This post may be a little uncomfortable for all of us, but the factors considered come up again and again for all mathematics teachers - even those of us (like myself) who have drunk the Cool-Aid and are eagerly looking for ways to enrich our teaching through use of technology. In later posts we shall consider the wonderful and amazing things mathematics teachers can  do with laptops - but first we need consider some of the barriers.

In the previous post, we looked at what for many people is an unexpected finding: mathematics teachers have their students use laptops much less than teachers in other subjects. Some reports put this figure at 50% less than other subjects.  When all other factors are taken into account - access to technology, training, confidence, skills - we still find a reluctance to use the 1:1 laptops in the mathematics classroom. And so we ask: Why do maths teachers make these decisions? Is there something different about mathematics?

My research has led me to conclude there is indeed something different when it comes to mathematics.

 Mathematics teacher beliefs + mathematics teacher practices : a powerful combination which often acts as a barrier to using technology.

A core set of beliefs about mathematics and mathematics teaching in conjunction with some strongly entrenched mathematics teaching practices act together as a powerful barrier to widespread use of the laptops in mathematics classrooms.  I see the three key themes at work:

• "Maths is something you do on paper"
• "Laptops aren't suitable for low achieving students"
• "The teacher leads, the student follows"

I make no explicit comment on the validity or otherwise of these commonly held mathematics teacher beliefs and teaching practices - but there is no getting around their effect on 1:1 laptop programs.

"Maths is something you do on paper"

When you ask mathematics teachers what 'real' maths is, and how you 'really' learn it - pen and paper, and I really mean pen and paper the physical media - eventually emerge as a key requirement. Software may be fine to demonstrate and maybe explore mathematics (for some mathematics teachers)- but it's not properly learnt until it's done on paper.

Now consider the very strongly established practice of managing student learning by working in and monitoring output in the student exercise book. Learning outcomes aren't tangible - can't be verified until they are seen in the exercise book.  Entire sequences of classroom practice, homework, outcomes tracking are based on physical movement in and around the student exercise book. You won't find this combination of beliefs and practice in most other subjects. No-one would say you don't understand science, or history, unless you do it on paper. And other subjects are much more receptive to accepting digital learning artifacts as evidence of learning.

Unfortunately there is also a technical hurdle : unlike other subjects, writing in the language of our subject with a computer is hard. It's actually very awkward to write a continual flow of mathematical ideas with standard or even specialised software.
Try writing this  $\large \int_{-\pi}^{\pi} \sin ^2x dx$ without taking a software detour. Now do twenty lines of it. For now at least, the technology gets in the way of expressing the ideas. While there is powerful and non-intrusive software such as GeoGebra for exploring and demonstrating some parts of mathematics, actually writing long sequences of mathematical language is hard work on the computer.

So: combine the belief that real mathematics is done on paper with a key teaching practice based on writing in exercise books and there isn't much space left for using laptops beyond peripheral extension activities.

"Laptops are not suitable for low achieving students"

We have a real problem in secondary school mathematics: many students are not achieving the learning outcomes. It's no surprise these students don't enjoy maths and are looking for other ways to occupy their time and energy during maths class. Now ask mathematics teachers if using laptops might help make the classroom more engaging, or possibly even provide new ways to help these students with learning mathematics. The answer is a pretty resounding 'no' - there is a widely held belief that laptops are not suitable for low achieving students. Two lines of reasoning are offered: the low achieving students are actually incapable of using the software; and the low achieving students are using the laptops to escape from mathematics and instead engage in off-task behaviour - watching videos, listening to music, playing games. Not like the high achieving students who want to use their laptops for maths.

Some mathematics teachers strongly believe it is in their lower achieving students' best interests to turn off the laptops. These students need to do more maths, and allowing them to use the laptops, which provides more distraction, is actually harming them - teachers motivated by care and compassion for their students make the decision to block use of the laptops. Personally - I don't agree with this approach - indeed I believe the laptops offer us possibilities to re-engage students with mathematics - but this reaction is understandable and consistent with those teachers' beliefs.

Now consider the strongly entrenched teaching practice of  ability streaming, used in mathematics faculties across the country almost without exception, and to a degree not seen in any other school subject. We put the highest achieving students in one class, and then progressively lower achieving students into progressively "lower" class groups, creating entire classes of disengaged, low achieving students.

Combine the belief that low achieving students can't or won't use the laptops for learning with the practice of ability streaming, and we have effectively created entire classrooms where the laptops just will not be used. And indeed this seems to be the case.  Chances are when it comes to secondary mathematics, you will see the laptops being used almost exclusively in the top achieving classes.

And finally, we consider the strong prevalence in secondary mathematics education of the idea that the teacher should show-and-tell, and that students should follow-and-practice. While it would be an overstatement to say this is always the case, it is the prevalent belief among maths teachers.  A student armed with a laptop can be disruptive to 'teacher leads, students follows' - and although the presence of the laptops doesn't automatically guarantee a change in pedagogy, the benefits of the laptops seem to me to be diminished if they are merely used to automate lead-and-follow practices.  This combo of belief+practice isn't unique to mathematics teaching by any means, but I do think we are more likely to follow traditional teaching and learning approaches than other subjects.

In conclusion ...
So by considering these three powerful belief+practice combinations, which are to a large degree unique to secondary mathematics education, we can begin to see just why laptops are used at up to 50% less than in other subjects. I find that even in my own practice, keen as I am on using technology with my students, I'm often falling into these memes: I do worry about not doing the maths on paper - "is it real maths?", I do worry about exercise books, and I do find myself dismissing using the laptops with my lower achieving students. And I catch myself 'holding the mouse' often.

Am I optimistic about using technology in the mathematics classroom? Absolutely. But I also recognise there are powerful beliefs and practices in our subject domain - and these contribute to making using the laptops harder in mathematics teaching and learning.

This post is high level summary of research I conducted during 2010. The study examined the use of the laptops in mathematics classrooms at five schools, looking at usage levels, how the laptops are used and the role of teacher skill, confidence, knowledge and beliefs factors. The work builds on a body of knowledge as found in nearly 100 published papers on technology in education, mathematics teaching using technology, and mathematics teaching beliefs and practices. An academic paper is currently in preparation.

1. This is quite a disturbing blog post in this day and age. I have been working hard with low ability Maths students all year using laptops 98% of the time and find tht although it does take more time to teach them to use the programs the ultimate outcome is worth it and they end up experiencing for themselves all the benefits they fought against in term one. Thing are quicker, neater and often more efficient yet still covering the same Maths skills when done on the laptop.

The other Maths teacher uses laptops for about 98% of his lessons too and he has the top yr 9 class. Yes there are technical difficulties to work around but there generally is once if you keep looking and for the 2 of us that's the fun and challenging part of our days at school- how can we teach this skill/concept in the best possible way using the laptops.

2. In my school last year the Maths department had the highest across faculty use of laptops than any other subject. We worked as a team to write specific units of work and share between us to enable all faculty members to integrate laptops into their lessons. This school is bottom heavy in the ability level of students and the concentration of laptop use is greater at the bottom than top. I personally used the laptops for a portion of EVERY lesson with my mid/ low ability year 10. Otherwise the students feel resentful for carrying them each day without purpose.

3. It's great to hear examples of positive results which go against these rather negative beliefs - and I would strongly urge you to publicise these stories. One of the things I discovered in my research (and doesn't take much insight to realise this :-) ) is that teachers who are more skeptical about using laptops are much much more likely to consider different views when they are presented by their peers - that is - by other mathematics teachers, teaching in classes like their own, sharing actual true-life practice stories in schools.

I'm interested how you deal with the 'maths is learnt on paper' aspect for the classes using the laptops so frequently.

4. Another hurdle we face in spreading the message: the people who might benefit from hearing about successes using the laptops aren't reading about them online - because many of these teachers aren't online.

5. Maths is about process and problem solving. How is the learning of this specific to the use of a particular medium? If I wrote a shopping list on a scrap of paper or typed it on my phone, I wld have the same recall of the items (very little in both cases hence why I record it in the first place). I've seen students struggle to verbalise an explanation for how to solve problems and wonder if figuring out a good one then voice recording it would be worth about 10 examples of qns in a book. To me the paper thing is no biggy- one note (particularly for low classes) can be used in exactly the same way (if u have to) and you can have the equivalent of a textbook n exercise book on your laptop with way more functionality.

Maybe these teachers need to see it in action! Why dont they get pl time to visit schools such as the anonymous one above and check it out- or do vcs to chat with teachers about what they're doing or even do a vc lesson with another teacher where all students use laptops.

6. You and I have the same view on what maths "is", and what "doing maths" is. :-) But it's not the commonly held view among the majority of math teachers. I am almost daily told by a well meaning colleague I'm doing "mathotainment" and that it makes no difference - kids either get it or don't get it. This is an extreme view, but silently held by many teachers.

7. And dare I say it, a view encouraged by the way we are mandated to assess our students.

8. I read your '1:1 Laptops' serial here... made me a bit sad. I hope you will eventually try the Math-o-mir software and change your opinion. I also hope you will try it with your students - would love to hear your/their comments.

You wrote: "When you ask mathematics teachers what 'real' maths is, and how you 'really' learn it - pen and paper, and I really mean pen and paper the physical media - eventually emerge as a key requirement."

I understand: the math is a craft and one must doing it in order to learn it. But I see no reason why you really mean "pen and paper the physical media". It may be that you insist on this 'physical media' because math notation is born by 'pen and paper' and it would be awkward to write it any other way. As you said "...actually writing long sequences of mathematical language is hard work on the computer". This awkwardness of on-computer-math-typing is, in my opinion, the most important reason why computers are not much accepted in math classroom

Since 2009. I am struggling to change the physical media the math is written on and to somehow increase efficiency of PC input devices (keyboard and mouse) for math typing. I believe that math typing with the mentioned software is now fluid enough and does not distract a mathematician while he/she is doing math.

One more comment... Also the math notation will change to better suit computer input devices. I have no doubt about it - the math wants to be written.

Danijel Gorupec

9. Dear Daniel, Thanks for the comments. Please don't think however I agree with the barriers raised by others to the use of technology in mathematics! :-) I'm reporting the findings of my work and while I believe I understand why maths teachers hold these views, and see why they impede adoption of laptops, that's doesn't mean I fully accept them. My current thoughts are that the use of a touch pads with a stylus or finger should, with the right software, overcome the 'math input' problem. Indeed, once we go digital, we can *improve* on the math input through the use of context sensitive computer algebra systems and inbuilt tuition.

10. This story also makes me very sad. I am a high school math teacher trying to use laptops, but feel lost. I have tried to implement a thing or two here or there, but would really benefit from more specific examples of how teachers are using their laptops for learning. I think it can be done, but I am not sure how! Any help?

1. Don't be too sad - it is difficult! I do have some ideas and strategies to help out - will write a post hopefully this weekend or the next based on a presentation I delivered to the DER 2012 conference on this subject.

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