Why do many teachers see benefits in the use of graphing calculators to improve learning in the classroom?

When it comes to using graphing technology in the classroom, we know that opinions vary between teachers. Some remain sceptical, some are undecided, while others are fully convinced of the benefits but face obstacles to adoption within their schools.

We believe the fx-CG50 graphic calculator really shows its value as a source of support and a tool to enhance learning, yet we understand that our perspective alone may not justify transitioning to graphing technology. What advantages are other schools experiencing? Additionally, what insights have been gathered from the all-important student feedback?

Overcoming concerns about technology

For those with doubts about the fundamental idea of graphic calculators, one experienced teacher said it’s useful to think about how they can be used, rather than if they should be used.

Melios Michael, Assistant Headteacher at Hamstead Hall Academy, spoke about how calculators become much more than a tool for simply checking answers when they’re used to encourage curiosity and exploration.

“It’s a tool that we can use for investigation, to introduce topics and to explore the maths,” Melios said. “If we start to use it like that and embed that within our teaching, then you see a lot more thinking and problem solving.”

We also heard from Rose Jewell, a senior examiner and area coordinator with the Advanced Mathematics Support Programme. Rose highlighted the Distribution app on the Casio fx-CG50 graphic calculator as a specific example of how the functionality of the most advanced devices improves learning and understanding.

“The app opens up the topic of probability distributions in a way that you just don’t get with older graphic calculators or with scientific calculators, because every time you use it for a calculation, it shows you the corresponding graph straight away,” she said.

“Students can get further insight by looking at how that distribution works graphically, and it’s giving them more information and more intuition into the topic.”

Rose was also keen to stress that the calculator is not a substitute for mathematical understanding. Students still need to show algebraic solutions and grasp the underlying theory, but they should also know what the calculator can do to support them, particularly in exams.

Fairness and finances

Given the tightness of school budgets and the importance of equal opportunities for all students, there are understandable questions to be asked about the fair and financially-responsible rollout of graphic calculators.

The advice from Rhiannon Rainbow, School Improvement Lead for Maths at the Greenshaw Learning Trust, was to start small.

She recommended speaking to relevant people within your school, such as your Senco and stakeholders responsible for raising equity standards, to explore what budgetary support might be available for a pilot.

Melios echoed this point, noting that you can start with a limited number of graphic calculators and roll them out gradually.

“You don’t have to get lots of devices at the same time,” he said. “Starting small also gives you an opportunity to see the outcomes with a specific group of students, and build teachers’ skills at the same time.”

Rhiannon recommended speaking to Casio about potential options to improve access to graphic calculators for all students, such as loan sets. She argued that all learners can and should be able benefit from the technology, regardless of their level of attainment or financial background.

“I’ve seen graphic calculators used really powerfully with some of the most vulnerable and most disadvantaged students in mathematics,” she said.

Showing the evidence for graphic calculators

For teachers who are facing the challenge of convincing their colleagues of the value of graphic calculators, Rhiannon said it can help to think in terms of evidence that proves the advantages.

“Show them how it works, get them talking to others, show them students using it and the benefits that come from it,” she suggested.

Bernard Murphy, a maths teacher and education support specialist, said his eyes were opened when a fellow teacher presented him with a very complex-sounding equation, before displaying it on a graphic calculator to show that it was in fact a straight line.

Changing a single coefficient in the equation then created an entirely new line of investigation, encompassing concepts such as implicit differentiation and binomial expansion.

“All sorts of ideas came together, purely from the technology motivating a question that surprised us,” Bernard said. “It’s an example of where I have thought differently about mathematics and become a better mathematician, because of the way the technology made me think.”

Embracing change and new methods

If you’re still undecided about graphic calculators, the first-hand experiences and enthusiasm of the teachers we spoke to could give you food for thought.

When it comes to the time required to learn the technology, Bernard said this is absolutely a worthwhile investment when you see how big an impact it can have and how it can transform thinking and understanding.

Moreover, you might be surprised by how quickly you can grasp the basics of using a graphic calculator. This is particularly true when you have the natural curiosity of students to spur you on and access to resources such as free introductory training from Casio.

Building on Bernard’s point about time concerns, Rose noted that teachers often, by necessity, revert to how they learnt themselves or how they have taught in the past. But there comes a point where ignoring the potential of technology to aid learning and make tasks easier – for teachers and students – is counterproductive.

“Nobody these days thinks we should go back to doing calculations with log tables, because calculators have been around for so long,” she said. “I think the next layer of things to go will be, at A-level, once you’ve simplified a problem to the point where it’s a quadratic equation, then it’s a machine’s job to solve it.”

And that’s not to say the power of graphic calculators in any way discourages mathematical investigation; quite the opposite in fact. As Rose pointed out, the calculator can keep up with you as you indulge your curiosity and continue to ask that quintessential mathematician’s question: “What if…?”.

To learn more about graphic calculators and their potential to aid teaching and learning, explore the Casio Education blog and resources centre, or contact us to discuss your school’s technology needs. Our team of ex-teachers and practising industry leaders are here to support UK schools, teachers and educators in the teaching of mathematics.