Transforming Maths Practice & Practise

Why Use Digital Tools in Mathematics?

• Immediate feedback
• Infinite patience
• Personal (individual//automated) differentiation
• Less marking, more monitoring (dashboards)
• Dynamic interactive models (what if)

SAMMS
Situated: work anywhere, any place any time. No carting around text or exercise books, all you need is scrap paper and a pen or pencil. Students can work out the own pace in their own space without having to do work pitched at a group of students in order to make the management of the task practically feasible for the teacher. No more having to set 'homework', now the homework is the classwork continued, and vice versa. As the results feed into one dashboard, you can see the results of an entire class/classes in one view, updated in real time.

Access: videos and tutorials from some of the greatest Maths teachers on the planet is only a click away. Not to mention access to a wider range of strategies, and ways of explaining. Leverage the computer processing power of automated marking; faster, and more efficient than a human, freeing teachers to focus on marking the stuff computers cannot, and freeing time for teaching/planning. No longer do students have to wait several days to find out whether the work they did is correct or incorrect, they know as soon as they submit an answer and are able to work on each problem until they get it right without the need for teacher intervention.

Multimodality and Mutability: beyond text and static images to illustrate, they can use video to explain, and animations (animated gifs) to demonstrate visually/aurally, in ways that allow rewind, repeat, retry, as often as is needed. Interactive dynamic models allow students to really explore mathematical models, with 'what if' experimentation. Got it wrong? Try again. No limits, no stress, no strife. Undo, try again, repeat.

Socially Networked: via an online space, students can share their questions, clarification, celebration. Teachers and students alike can can help one, help many. The fact that students can receive so much of the mathematical support via digital resources and via each other means the teachers actual face-to-face time can be used far more efficiently to work with smaller groups that would benefit more from the personal touch that computers cannot replicate.

Who Says?

Well, there’s lots of research, but let's just focus on a few for the sake of brevity. I reckon the points they made (some time ago, I might add) will convince anyone who has any passion for the teaching of Mathematics that their argument make sense.

In Principles and Standards for School Mathematics (NCTM 2000), the Technology Principle asserts: “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning” (p 24). More specifically, a technology-rich environment for mathematical learning influences five critical features of the classroom (Hiebert et al 1997): the nature of classroom tasks, the mathematical tool as learning support, the role of the teacher, the social culture of the classroom, and equity and accessibility. An essential question when working in a technology-rich mathematics environment is how technology can be used (appropriately) to enhance the teaching and learning of mathematics.

An effective way to optimize the mathematical thinking opportunities presented by technology is to plan the mathematics task focused on the five Process Standards (NCTM 2000): Problem Solving, Reasoning and Proof, Communication, Connections, and Representation.

...

Learning environments that take advantage of virtual manipulatives offer a number of ways for students to develop their mathematical understanding. The authors identify the following as five primary benefits:

1. Linked representations provide connections and visualization between numeric and visual representations. 
2. Immediate feedback allows students to check their understanding throughout the learning process, which prevents misconceptions. 
3. Interactive and dynamic objects move a noun (mathematics) to a verb (mathematize). 
4. Virtual manipulatives and applets offer opportunities to teach and represent mathematical ideas in nontraditional ways. 
5. Meeting diverse learners' needs is easier than with traditional methods. 

Enhancing Mathematical Learning in a Technology-Rich Environment
Teaching Children Mathematics / November 2008


Then there’s this from the Centre for Research in IT in Education (CRITE) Bray & Tangney (2013):

An examination of the extent to a which recent technological interventions in mathematics education make use of the educational opportunities offered by the technology and the appropriate pedagogical approaches to facilitate learning, focused on digital tools classified as follows:

• Outsourcing of Processing power 
• Dynamic Graphical Environments (DGE) 
• Purposefully Collaborative 
• Simulations/Programming 

These are the guiding principles that have the potential to form the basis of a 21st Century model for the integration of technology into mathematics education. An appropriate and innovative technology intervention in mathematics education should:

1. Be collaborative and team-based in accordance with a socially constructivist approach to learning. 
2. Exploit the transformative as well as the computational capabilities of the technology. 
3. Involve problem solving, investigation and sense-making, moving from concrete to abstract concepts. 
4. Make the learning experience interesting and immersive/real wherever possible, adapting the environment and class routine as appropriate. 
5. Use a variety of technologies (digital and traditional) suited to the task, in particular, non-specialist technology that students have to hand such as mobile phones and digital cameras. 
6. Utilise the formative and/or summative assessment potential of the technology intervention. 

Students often wait days or weeks after handing in classroom work before receiving feedback. In contrast, research suggests that learning proceeds most rapidly when learners have frequent opportunities to apply the ideas they are learning and when feedback on the success or failure of an idea comes almost immediately (Anderson, 1996).

The sheer autonomy that online tools like Khan Academy provide for students, is radical in and of itself, a radical departure from the traditional textbook centred, non adaptive model that anyone older than 40 would have experienced at school. As Jo Boaler explains, these tools allow students to 'become self-regulatory learners, so that they are not dependent upon following somebody else's plans':

Assessment for Learning
A4L is based upon the principle that students should have a full and clear sense of what they are learning, of where they are in the path towards mastery, and what they have to do to become successful. Students are given the knowledge and tools to become self-regulatory learners, so that they are not dependent upon following somebody else's plans, with little awareness of where they are going, or what they might be doing wrong. (My emphasis)

Boaler J (2009)

References

Aibhin Bray, Brendan Tangney Centre for Research in IT in Education (CRITE), School of Education and School of Computer Science & Statistics, Trinity College Dublin, Ireland

Anderson JR, 1996. The architecture of cognition. Mahwah, NJ: Lawrence Earlbaum Associates, 1996.

Boaler J (2009). The elephant in the classroom: Helping children learn and love maths. Souvenir Press)

Bray, A., & Tangney, B. (2013, May). Mathematics, Technology Interventions and Pedagogy-Seeing the Wood from the Trees. In CSEDU (pp. 57-63).

Hiebert, James, Thomas P. Carpenter, Elizabeth Fennema, Karen C. Fuson, Diana Wearne, Hanlie Murray. Making Sense: Teaching and Learning Mathematics with Understanding. Portsmouth, NH: Heinemann, 1997.

National Council of Teachers of Mathematics (NCTM). Principles and Standards for School Mathematics. Reston, VA: NCTM, 2000.