For many years, mathematics education specialists have joined forces with software and hardware developers to create new tools for learning. But still, decades on, the mathematics classroom remains one largely about teacher exposition and bookwork practice. Technology has made little impact.

Yet, technology in mathematics can help to de-abstract-ise the subject. All those apparently meaningless processes that we have all been taught at some point in our lives can suddenly be made to come to life. Just watch a Gapminder animation or use a virtual manipulative and you will see what I mean. No longer does the mathematics teacher have to explain some new concept while drawing inadequate diagrams that contradict their words. Technology can solve this. So why hasn't it?

The answer is simple: the technology, although the solution, has also been the problem. Teachers, even those most adventurous and brave, will give up when the technology is a blocker, and until now it certainly has been – whether that be the unreliability of hardware, the sheer confusion of understanding the operations of a programme or the lack of logical pathways through a piece of software.

But touch technology, in the guise of an iPad or the like, brings with it what good design always should – an intrinsic understanding of how to operate it. There are no longer blockers. Through touch, interfaces suddenly make sense. They become natural when well written apps come to life.

The trouble, at the moment, is that no-one yet has taken the step of creating a truly difference-making, meaningful, student centered, pedagogically sound app for mathematics. But they are coming.

I have talked (ranted) for years now about the need for someone to create such an app and bemoaned the deluge of opportunistic, superficial apps that have flooded the market in anticipation of securing a slice of the enormous student/teacher/parent purchasing power cake. There are many apps for mathematics, but none that bring anything new to the equation. So I have been really excited recently by a group of developers that I have met who are creating a mathematics app that will up the ante and change the face of learning apps.

Through touch-tech, there is no longer the need to prelude the learning with lengthy instruction on using the technology or learning operating systems or the idiosyncrasies of a particular piece of software. The children in our schools are already at ease with using the devices and technology is a routine part of their lives.

So we can now take the step that was always the hope for technology in the classroom – to enhance active engagement, interaction, feedback, micro-teaching, analysis and problem-solving skills, make connections across and within subjects and contextualize and internalize the learning in a way that connects to students' own realities.

The tech can at last meet the curricular objectives.

Technology, and particularly hand-held technology, can create an environment where the teacher is effectively split into 30 individual teachers. With each student having access to information, prompts, reflections, guidance, challenges and support any time they need it. Students are no longer bounded by the need for a lesson to be timed for a group of children with wildly different abilities. The technology can take them on the learning journey, while teachers guide the experience like an orchestra conductor. The teacher is in turn freed up to actually teach – not just transmit information – they can work at the individual and group level. The student remains engaged in learning for a much greater proportion of the time because they have instant access to progression.

The relationship between student and teacher can be greatly enriched when technology is integrated effectively. This takes a shift-change in pedagogy, but teachers can take on the role of advisor, knowledgeable other, and mentor.  This shift-change will require investment in terms of time and money for teacher professional development - for every penny spent, I think the breakdown should be 20% on tech, 80% on teacher professional learning.  This is not just about how to use devices, but about what the pedagogical implications are for changing from the traditional transmitter of held knowledge to one of an artist creating the right environment for children to be knowledge creators.

And in mathematics, we can finally move towards what the subject is truly about. The technology can make school mathematics less focused on calculating and more on sythesising, modeling and interpreting. Students at any age can see visualisations of the most complex mathematics and draw inferences from them – mathematics is suddenly opened up as it should be.

With the internet, students are able to access any information that they need. Information is no longer the preserve of the teacher. So students can learn from external sources, or knowledgeable others, so that they themselves can become knowledge creators.

Unlike many technological devices of the past, touch-technology becomes simpler and more intrinsic as we move forward. In many aspects of life, touch-tech is now the interface that we meet. It is epitomised by its simplicity, by its universal approach of guiding the user through the process. This removes the apprehension that many people feel about technology. And this is a key point, for it is only those of us that are adults that feel this apprehension. To children in our schools it is simply part of their life. So through touch-tech, teachers are now able to feel comfortable about creating a tech-based learning envinronment, where they do not have to understand the technology or learn how to use a keyboard or mouse.

Touch technology is what mathematics education has been waiting for. It is the conduit that will allow the generations to come together and will remove teacher bias towards their comfort zone. We're not there yet, because appropriate apps have not yet been written, but they are just around the corner. Over the coming year, I believe that a product for mathematics will enter the market that will help us all to take the last steps to integrating technology in the classroom.