Why grades and not just a rank order?

As I understand it, the system for awarding grades for GCSE and A-level in summer 2020 will be broadly as predicted. 

1)      Teachers will be asked to provide predicted grades for each student in the subject (so if there are several classes/teachers these will need to be combined into a single list), and then to rank the students within each grade.

2)      The awarding bodies will look at the past few years of value-added data in a school and the baseline scores for the current students and will move students up or down accordingly, using the rank of the students (so if they decide there need to be 3 more students getting a grade 9 then the top three with a teacher grade of an 8 will be moved up).

3)      The students and teachers will find out the moderated grades.

This leads to the question of why it is necessary for us to put down grades.  If the data will specify a particular number of grade 9s, then a rank order of the students would have allowed the awarding bodies to put in the grades they have determined.

Here are my thoughts:

Teachers have an understanding of what each grade in their subject ‘looks like’.  We don’t have that sort of feel for where someone is in their year group.  This means it will be easier to compare across classes.  It will also be easier as a starting point for deliberations within school.

This leads to an obvious way of ranking students: start with the grade for each student, then decide whether they are a middling version of that grade, or just scraping into the grade, or nearly at the grade above.  Then rank the students within that sub-grade.  (To be clear: I don’t think this will be a quick job and I don’t think it will be easy to get the ‘right’ grade, let alone the right third of a grade, but this seems less bad than any other system.)

It fits with existing data.  We are likely to have some of the data we will use to help us to make and justify our decisions as grades already, such as mock exam results, predicted grades, etc.

It will help us as teachers to gain a better knowledge of grades for the future.  If all of our predicted grade 6s are moderated down to become grade 5s then we might need to redraw our mental grade boundaries in future (or the system used here might be flawed).

It will help us to explain things to pupils and their parents.  I don’t know what sort of comeback there might be after the grades are moderated and published.  For example, might we be called on to explain how we reached particular decisions about grading?  I will, clearly, have evidence I can use to justify my suggestion of a particular grade.  It would be possible for me to present that information to parents and pupils.  If they are then unhappy that their grade has been moderated downwards then that is a matter for Ofqual and the system they have put in place.  It would be much harder for me to justify why I have ranked a particular pupil as being number 94 in the year group if there were no grades involved.

It will be interesting to see how easy this will be to do and what proportion of grades are moderated (and in which direction).

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.

Online learning - early experiences

I had a conversation with a group of trainee maths teachers just before Easter about their experiences of the first two weeks of the closure of schools due to coronavirus.  Here are some of the things that cropped up.  It seemed worth sharing them because they represent views of what is happening in 19 different schools.

1) Teachers are working phenomenally hard

I don’t find it easy to set cover lessons in school.  Leaving sufficient material for a 50-minute lesson that the pupils can all access and learn from, without me being there, is difficult.  It needs to be tailored to the needs of the pupils, and something that a non-specialist teacher can lead.  It probably means not introducing much new content.

Teachers are setting what amounts to three or four lessons of cover for each class every week now.  (They are cover lessons in the sense that the teacher isn’t there in the room with them.)  Some teachers are juggling family commitments alongside their planning.

2) Schools are using different systems

• Some are using Microsoft Teams as a way to communicate with pupils.
• Others have Google Classroom.
• Show My Homework or Go4Schools is being used by some schools as a way to alert pupils (and their parents) to the work that has been set.
• Sometimes work is set that involves a subscription site, such as HegartyMaths, Mathswatch or MyMaths.
• Some teachers are making videos or are narrating PowerPoint presentations.

In all cases, it seems that pupils are finding it easier if they are being asked to use a system (whether Google Classroom, Mathswatch or Show My Homework) that they are familiar with already.

3) Structure is important

It seems to me that Easter holidays have come at the right time.  We have had two weeks of remote working and can now take stock before beginning again after the holiday period.

Some schools have been following a timetable and setting work for when the pupils would have had lessons in that subject.  This was felt to be good for a number of reasons:

• It helps children to organise their time, both in terms of when to do the work and how long to spend on it.
• It gives structure to their day and demarcates ‘work time’ from ‘social time’ or ‘family time’ or ‘playing time’.
• If pupils work on ‘lesson times’ it perhaps stops it from feeling like they have 5 pieces of homework to do each day.

The alternative, which has been happening in some schools, is for the week’s work for each subject to be issued at the start of the week and for the children to need to structure their own time.

The more structured version was felt to be better because it gave the children more support and a realistic idea of how much they should achieve.  It also meant they were likely to be fresher and less tired than if they left their work until the evening.

4) The amount of work that is set has been over-ambitious

After a fortnight of doing this, teachers have realised that setting a full lesson’s worth of tasks is not realistic or fair.

• There is a need to factor in time to access the work, to download files, print, etc.
• 1 hour of worksheet work is too tiring and is not productive. This wouldn’t usually happen in the classroom (for a reason!).
• It is important to set other types of activities too.
• Schools with 50-minute lessons are aiming to set 40 minutes of work.

5) Access is an issue

There are concerns about disadvantaged children.

• Children without a device (computer, tablet) at home cannot access material that is issued daily. If they have a device but no printer, then this will hamper some tasks.
• Children who share a family device (computer, tablet) will not have access throughout the day. If they have school-age siblings then they will need to share time on the device. If two or more siblings need to spend the entirety of 5 hour-long lessons using the computer then this makes life difficult and they certainly can’t all work during their ordinary lesson times.
• Children without a quiet space to work will find any sort of school work difficult (they might share a bedroom, or other family members might be playing music or watching TV or playing games elsewhere in the house).

6) Assessing online is hard

Other than small-scale monitoring using tools within HegartyMaths, MyMaths or Mathswatch, this is an area that hasn’t been explored in detail yet.  We can know how many questions a pupil has answered and how many they got right, but can’t pick up the usual things we would in class about what the students are struggling with, what errors they are making, etc.

7) Very few schools are doing live teaching

A limited number of schools are doing live lessons with older students, but very few do this with younger ones.  This is not a surprise:

• It is hard to do and different from the way a lesson would usually be planned, organised and taught.
• Access issues are exacerbated. The students have to be online at a particular time.
• The teacher can’t do classroom management, check engagement, can’t easily pick up misconceptions, etc.
• Schools have concerns about safeguarding (and concerns about Zoom meetings being hacked mean they are right to worry).

One benefit of having live lessons is that queries can be asked and answered immediately.  This has led some schools to have lessons that are provided via an online platform or PowerPoints, but then to offer live online ‘surgery’ times during which question can be raised by students.

As to how these are structured, a common method seems to be for the teacher to use the visualiser from their classroom, with a mini-whiteboard or a piece of paper underneath it. 

8) There will be long-term effects of learning remotely

At the moment it is all exciting and new but there are concerns as to whether/how pupils will stay motivated in the longer term.  There is a danger that pupils might receive 5 hours of lessons each day, from 5 different teachers, that involve them watching a PowerPoint and answer questions online for every subject.  This will force the students to be in front of a screen for much of the day and will become very samey. 

It will be increasingly important for pupils to receive feedback; some are already starting to ask “what’s the point in doing this task?”.

When work is set with a deadline, rather than being provided for a specific lesson time, the students are spending different amounts of time on it.  This will hit disadvantaged children the most and the learning gap will only increase in the long term.

The teacher cannot give thought-provoking extension questions, or targeted support to specific pupils.  This means there will inevitably be a change in how pupils are learning and the sorts of things they think are important.  It will take a while to settle back into learning in school again.

We had a long discussion about independent working skills, with some seeing it as a good thing that pupils will have the opportunity to develop these skills, while others are concerned that this is a difficult thing to do and that access to a quiet working space, structure and access to resources will be important for this to be possible.  Many children will need a considerable level of support to become more independent. 

Where do we go next with this?

It will be interesting to see how things continue to evolve over the first few weeks after Easter and whether schools switch to a model of having a tighter structure to the week for pupils and an encouragement for teachers to set different types of activities that might take pupils away from a computer.