Paying attention - issues with online lessons

Ensuring students are paying attention to things that are relevant is important in the classroom, but even more so if trying to teach lessons live online.

‘Paying attention’ can mean a number of different things.  This blog explores four of them:

1)      Not being distracted

2)      Completing the task

3)      Thinking about what mathematics is involved in the task

4)      Focusing on a particular feature of the mathematics

1)      Not being distracted

This might be seen as “not being naughty” and is perhaps the traditional “pay attention everyone” version.

Distraction can happen in the classroom in lots of ways.  Pupils distract each other.  They can be distracted by a display, or a word they are unfamiliar with, or noise outside the classroom, or snow, or … .

When working at home our students can face additional distractions.  Family members in the same house may be playing music, making noise, talking to each other, talking to the student, etc.  A younger sibling might be playing a computer game, or an older family member might be watching TV.  This is exacerbated if the students doesn’t have their own bedroom and their own working-space.  If there is a shared family computer that is in a communal area of the house then that may make things difficult too.

Friends may still be a distraction (via apps and social media) and there is also the need for will-power to avoid watching Netflix, playing games on a phone, etc.

If we want students to learn online, there are inevitable distractions on the very device they are using to access the lesson.  Email alerts may sound, for example.  This is such an issue that Word now has a ‘Focus’ button at the bottom of the screen.  This makes the document fill the whole screen (which is useful) but also stops email alerts from interrupting.

If we are teaching live and online, it is next to impossible for us to be sure that students are not doing other things at the same time and really are paying attention.

2)      Completing the task

Paying enough attention so a task can be completed accurately now starts to focus on the mathematical work carried out in a lesson.  This might not necessarily involve the student in thinking about the mathematical structure of what is going on, though. 

For example, an exercise of questions to find the size of a missing angle on a straight line might look something like this:

It is possible (likely?) that a student who starts by applying the rule “angles on a straight line add up to 180°” will quickly shift so they are finding a number which adds to the number given to make 180.

This is different from the original task.  The second version is akin to having a table and asking for complements to 180.

Number	Complement to 180
42
79
117

It is possible to answer the questions in the table without having any understanding of angles.

So it is possible to complete a task in the classroom without doing the intended sorts of mathematics and this clearly possible at home too.

How else might students aim for task-completion rather than the intended learning?  A calculator might be used for things that were designed to encourage thought.  Graph drawing software might be used when not necessary (for algebraic graphs and for statistics).  Research tasks intended for students to learn a new mathematical idea might merely be used to find the answer to a particular question.

3)      Thinking about what mathematics is involved in the task

The next level of ‘paying attention’ in my list is to have to think about what mathematics to use.  This might be selecting the maths to use when solving a problem.  Here’s a problem tweeted recently by the UKMT:

Problem Of The Day. Good luck, everyone!#UKMT #UKMathsTrust #ProblemOfTheDay pic.twitter.com/OmTIKq2kQ6

— UK Mathematics Trust (@UKMathsTrust) March 31, 2020

When I started work on that task I started thinking about cube numbers but then thought about factors; I had to choose which maths to use.

If our angles questions involved more than one rule there would be a need to think about the scenario and to consider what mathematics to apply.

Alternatively, we could include some questions that still only focus on a single idea but require thought in the way this is applied.  There are now two more questions in the exercise:

D cannot be calculated.  In E we need to ignore some information (and can work out another angle too).

These then are some ways to demand a greater level of ‘paying attention’ to the mathematics.  Are they different if students are working at home?

In some ways they are not.  It is still possible to have a well-chosen set of questions or tasks for students to work on.  It is likely to be more difficult for students to work on this, though.  Are they used to the idea that some questions cannot be answered owing to a lack of information?  Are they used to ignoring information in a question?  Are they used to needing to use mathematics from different areas of the curriculum?  Do they need the teacher’s reassurance that they are doing the right thing?

4)      Focusing on a particular feature of the mathematics

We might want students to focus on certain ideas within the mathematics.  For example, the idea that in cube numbers all factors are repeated several times is important. 

If we are considering angles on a straight line, students can consider the mathematical features of these scenarios.  In the first, we can calculate angle F without needing to know that “opposite angles at a vertex are equal”.  We can work out the size of G as 149° (because it’s on a straight line with the 31°) and can then switch our focus to the other straight line and can say that F and 149° lie on a straight line, so F must be 31°.  A more sophisticated way to look at this would be to avoid working out that angle G = 149°, perhaps saying if G + 31 = 180 and G + F = 180, then F must equal 31 (without solving simultaneous equations!). 

An extension to this might involve looking at the relationship between the two given angles in the triangle and the size of angle H.  (It is interesting, and possibly cultural, that we see the first of these as being important enough to be a named geometrical rule at GCSE, even though it can be worked out, while the second is not.)

This sort of ‘paying attention’ is where a lot of mathematical thinking takes place.  This can be guided when it happens in the classroom.  The teacher can easily pick up on things the students are saying, methods they are using, things they are noticing and, crucially, the things they are paying attention to. 

It seems much harder to do this online.

Resilience and individual working

In many ways we are encouraging our students to work more independently.  This might end up being a positive result of the lockdown … for some students.  How do we support students who don’t have access to a quiet space to work (where they can pay attention to the things they are supposed to be thinking about)?  How do we support all students to stay on-task from a distance?

Key themes from above are about the sorts of tasks we can ask students to do.  I worry there is a danger we might end up with tasks that only require students to use the first two types of attention that are noted here.