In Sparks’s 2010 article reporting results studies of primary mathematics curriculum she used the term “math wars” in relation to the battle of pedagogies. That is traditional mathematics teaching (direct instruction, rote memorisation of facts and formula and skill-based practice) versus more social-constructivist approaches (referred by Sparks as “reform based”). These “math wars”, unfortunate as they are, are healthy for improving our teaching and learning of mathematics.

As Roblyer (2016) writes:

- Do students learn mathematics best from explicit, teacher-directed explanations followed by individual practice?
- Do they learn best when they are engaged in student-centred learning where they construct the conceptual ideas through hands-on activities that help them build their personal understandings as in the constructivist approach?
- Or, do they learn best when they are involved in group work and discussions with other students using a more social-constructivist approach?

As I argued in previous posts (see my post 4th Nov 2014 There is a place for everything) each of these questions are valid and there is both evidence and research (albeit limited, we need more!) to support and refute each of them. Why? In my opinion it depends too much on the individual learners and the teacher. If you take a teacher whose epistemology and pedagogical approaches are aligned completely with direct instruction and transfer of knowledge then they will not be as effective when forced to teach another way, and vice-versa. You’ll see it in their body language, you’ll hear it in their voice and their side comments to other staff and students, of course, will pick up on this lack of authenticity and the learning won’t be effective.

**But why do I bring this up in a blog post that is meant to be about the relative advantage of integrating technology in Mathematics teaching? **

The same is true for teaching with technology. If the teacher doesn’t use it regularly or “believe” in its relative advantage in the classroom then that will come across, students will see it for what it is. This is why frameworks such as SAMR or TPCK are so important. They help both teachers and students see whether technology has been integrated properly and is useful.

So what are some of the key ways that integrating technology in to your Maths classroom can improve learning? What is the relative advantage? There are many, but I believe the most significant one is the ability we now have to make Mathematics dynamic. Historically it was static. Numbers were read off tables, calculations were all to a set number of places due to these tables and arithmetic approaches were given in a “one method” only approach.

Through technology students can now graph functions live online, insert variables and test their hypotheses instantaneously. See the example below for the equation of a shifted circle. Students can manipulate the sliders for the values of *h*, *k* and *r *to determine what they actually mean. It is a virtual manipulative using the incredible free online tool http://www.desmos.com.

https://www.desmos.com/calculator/bjkkisu8eo

Physical manipulatives are the ones I’m sure we all remember from our own primary school education, Cuisenaire rods, coins, dice, blocks – real objects. Roblyer (2016) tells us that these help students bridge the conceptual distance between concrete and abstract mathematical concepts. The same should apply in senior schools and throughout one’s learning. If educators can help students bridge the gap between the abstract concepts and tangible concrete / physical phenomena then we can deepen understanding.

According to Li and Ma (2010), research has found that virtual manipulatives have a positive impact on both attitudes toward mathematics and student achievement. However, as with many of these studies the research is often heavily focused on primary and early mathematics education. But, Lee and Chen (2010) also report that virtual manipulatives can improve high school student’s attitudes towards mathematics. This is where the rubber meets the road, engagement, attraction to Mathematics, enjoyment of learning. If we as educators loose students from the STEM fields because it is seen as “boring” or not relevant than it is us who have dropped the ball, not our students. Technology is a tool, but it is a tool that can help teachers simulate activities from the real world or an abstract mathematical one that is often hard to understand. Making mathematics tangible, real and enjoyable is surely as important as just getting the right answer.

**References**

Lee, C., & Chen, M. (2010). Tiwanese junior high school students’ mathematics attitudes and perceptions towards virtual manipulatives. *British Journal of Educational Technology, 33*(3), 333-337.

Li, Q., & Ma, X. (2010). A meta-analysis of the effects of computer technology on school students’ mathematics learning. *Educational Psychology Review, 22,* 215-243.

Roblyer, M. D. (2016). Integrating educational technology into teaching. (7th Ed). Allyn & Bacon

Sparks, S. (2010). Early-grade math programs go head-to-head in study; ongoing federal research shows an edge for some widely used curricula. *Education Week, 30*(11), 11.

Hi doug, you are perfectly correct……no model works for all students, especially when their learning backgrounds are so different – the teacher they had, the parents who looked after them, the friends they have….it is a smorgasbord and a really good teacher recognises the need to have multiple delivery strategies….keep it up!