Engaging vs Engaging

If I asked you to imagine an 'engaging' maths lesson what would you expect to see and hear?

For many years I believed that this would be the same for every teacher. 

Turns out this isn’t the case.

What your mind's eye pictures depends on how you define engagement.

I have been thinking about engagement a great deal lately. One reason is because I am currently supervising a student who is doing some fascinating research in this area for his PhD. Over the past few years we have had many discussions around his findings and this has challenged me to think deeply about engagement.

Engagement is a word that gets thrown around a lot in Maths Education, but its exact definition can be a little 'blurry'. 

This blurriness can cause issues as it means two teachers can be looking at exactly the same classroom scenario with different points of view.

I was listening to a podcast the other day where an educational researcher was sharing some research she was doing on the explicit teaching of vocabulary in maths (I would put the link in here, but I can't remember which podcast it was- I listen to so many different ones!😲).

I found the topic of this research very interesting, as I strongly believe exploring vocabulary should form a critical part of our maths instruction.

After the teacher experiment had concluded, the teachers who had taught the vocabulary program were asked to report on whether they thought the students were 'engaged' in the lessons. All three teachers reported 'low engagement'.

The researcher spoke about how this really surprised the research team, as they were watching the lessons and according to the metric they were using, engagement was seen to be 'high' amongst the students.

This is where I observed a disconnect.

The researchers defined engagement in terms of joining in and responding. They were counting the number of responses the students were making. They found they were responding at least 7 times per minute. To them, this was high engagement.

While the researcher in the podcast didn't provide more detail about why the teachers considered student engagement to be 'low', this made me wonder what the teachers may have been seeing.

This is the perfect example of two people looking at the same 'scene' but through a different lens.

This brings me to Professor of Maths Education at Western Sydney University, Catherine Attard.  Catherine is well known for her extensive research in the area of engagement. This blog provides a summary of the excellent framework she developed for engagement within Mathematics (FEM) (Attard, 2014).

Catherine notes in the blog above that students who are engaged are more than 'on task', they are 'in task'. She highlights the importance of students being cognitively engaged (thinking hard), operatively (working hard) and affectively engaged (feeling good about maths). I think these 3 parts of Catherine's framework allow us to more succinctly define engagement.

If we think back to the podcast example, the researchers may have been looking at the cognitive aspect of engagement, while the teachers were foregrounding the affective aspect. 

As teachers we naturally want to see smiles on the faces of our students, we want them to enjoy their learning and we want them to develop a love of maths. 

BUT, we also know that 'enjoyment' doesn't automatically equate to learning.

Professor Robert Coe points out, in this presentation (Slide 12), that 'engagement' can be a poor proxy for learning. This basically means that just because students are 'engaged' doesn't mean they are definitely learning (I would suggest that this depends on how engagement is defined). 

This brings me to an activity called 'array city' that I have seen taking place in classrooms. The photo below is a student sample.

Some may argue that this is an 'engaging' maths activity. And if you observed a class doing this activity, they maybe affectively engaged (smiling, enjoying the art aspect), BUT I would question the level of cognitive engagement.

By spending 40 minutes on this activity are they going to significantly increase their knowledge and understanding of multiplication?

For me, there are too many other skills required (cutting, pasting, design). These are getting in the way of the actual 'maths'.

Don't get me wrong, I am not saying don't do this activity.

It is a great art lesson which can link to the work your class has been doing on multiplication!

In my opinion it is just not a great use of your precious maths teaching time.

We need to remember that just because students are having fun, doesn’t mean they walk out of the lesson with the knowledge they need. Similarly, if there is an absence of affective engagement in our maths program, we need to think about how this impacts our students outlook on maths.

So, as always, I believe we need to find a happy medium, use our teacher judgment and make considered pedagogical decisions around our maths instruction.

This week I encourage you to have a think about student engagement. Firstly, what does engagement look like to you, and secondly, are there some small tweaks you can make to ensure your maths lessons are cognitively, operatively and affectively engaging so we can maximise student learning?

Have a great week!

Ange🎲🎓