I recently presented some professional development sessions to teachers in Dubai, Amman and Cairo. During these sessions we talked about active and student-led learning and what it requires of both students and teachers. It was clear from the sessions that teachers highly value approaches that encourage interactive and hands-on learning. But it was also clear that they sometimes struggle to find a balance between the demand that students perform well in tests and exams, and their own approaches to teaching and learning.
As always, in discussions with teachers, there was much interesting debate and some (very!) challenging questions that got me thinking more about active learning, its implications for academic achievement and practical ways of building it into maths lessons. This blog post teases out some of that thinking.
Active learning in the maths classroom
Active learning is about engagement. And when we engage with something we are trying to learn – for example, by talking it through, trying it out, or making and fixing mistakes. Through this, we are much more likely to grasp and understand it.
In turn, that makes us feel more confident and that means we are more likely to succeed when we put the learning to the test. This is backed by research (specifically into mathematical achievement) that has produced several studies showing that ‘active learning has a direct effect on students’ success and consequently their achievement’. The American Mathematical Society (AMS) reports that ‘active learning has a strong positive impact on a wide range of students’ and that ‘active learning does not harm, and may further benefit, already high-achieving students’.
So, given the evidence, what simple steps can we take to build more opportunities for engagement into our maths lessons?
Creating opportunities for engagement
Give students regular opportunities to reflect and ‘think about their own thinking and learning’. In her blog, Pauline Stirling writes: ‘There is a strong body of research from psychology and education demonstrating the importance of metacognition and self-regulation for effective pupil learning.
The Education Endowment Foundation (EEF) found that the use of metacognitive strategies was a high impact and low cost intervention that can be worth the equivalent of 7 months’ additional progress.’
Here’s an example of what that might look like:
(Cambridge IGCSE™ Core and Extended Mathematics, page 133)
Try inquiry- or problem-based learning tasks like these to help students develop critical thinking and problem-solving skills, while also reinforcing maths concepts:
Use interactive technology tools such as walk-through examples, maths games or simulations to teach or reinforce concepts.
Cambridge Online Mathematics provides specially tailored online resources linked to their courses. The activities increase engagement, so students are not just passively scrolling – they fill in steps, make choices, complete activities and get instant feedback to guide their progress. In addition, teachers can personalise learning by creating different paths through the material for groups or individual students.
Consider using some of the rapidly evolving artificial intelligence (AI) technologies such as ‘teaching assistants’ or ‘classroom buddies’. Online resources like Wolfram Alpha, Khan Academy and ChatGPT can all be useful in an inverted (flipped) classroom approach.
Students can work independently to find out about a topic or learn how to do something. That frees up class time for active learning tasks and developing the topic further.
‘There is emerging evidence that a flipped learning approach in mathematics is achieving success in relation to increasing student engagement due to the increased autonomy that allows students more access to learning resources’.
Build in opportunities for collaboration and communication to promote higher-order thinking skills. This might take the form of discussions like the one below, but it can also involve dual-coding activities in which students translate between different forms, for example from a graph to a table, or from a written problem to a visual representation like a bar model.
Acknowledge that not all learning activities will be student led. Discussions with teachers show that many of them are concerned that active learning means they cannot cover the same amount of material and that students won’t learn the maths if the teacher doesn’t tell them what they need to know. My response to this is that maths is cumulative and that it involves more than just content transmission.
I used to go into my class every day and write a + a = 2a and a X a = a2 on the board, and despite that daily reinforcement, many students continued to demonstrate that they had not learned this distinction (much to my dismay and frustration!). Since then, my ideas have changed considerably and I think that how students learn often determines what they learn and how well they learn it.
Tweaking direct instruction to be more active
The good news is that even direct instruction can be engaging. Here are a few ideas that you can try:
- Silent worked example – explain to the students that you are going to demonstrate a step-by-step worked example in silence (this is so you don’t break their attention) and then you are going to give them a similar example to work through on their own. Once they have done this, they can compare and discuss their solutions and ask questions.
- Use the think-pair-share approach regularly. Ask students a question and give them a minute to jot down their responses. Then have them talk about these in pairs before taking feedback from the class.
- Ask questions as you teach the material. Consider questions that just require students to raise their hands to agree/disagree, and include more thought-provoking questions like ‘are you sure?’, ‘how do you know?’, ‘what else could you do?’.
- Use educational technology to vary the ‘instructor’ and to offer different approaches from your own.
- Build in feedback processes (self and peer assessments) that are specific, encouraging and actionable.
In general, it is useful to think in terms of ‘I > We > You’ where you move the lesson from teacher to collaborative work as a class and then to students working independently. This allows for scaffolding and questioning and it allows you to gauge student progress and understanding. The Derek Bok Center for Teaching and Learning at Harvard University has an interesting article about this.
I hope this short blog shows that there are many ways to engage students in their own learning. While teachers must find a balance between exam performance and their own pedagogy, incorporating active learning strategies (even in a small way) can make learning more engaging and effective, and have a positive impact on achievement.
