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 CoolAid 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. Noone 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
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 nonintrusive 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 offtask 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 reengage 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.
"Teacher leads, student follows"
And finally, we consider the strong prevalence in secondary mathematics education of the idea that the teacher should showandtell, and that students should followandpractice. 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 leadandfollow 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.