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USing AfL strategies in Maths?

Discussion in 'Mathematics' started by mongus, Sep 26, 2009.

  1. I am L&T co-ordinator in our school and am struggling to get our MAths dept to adopt AfL strategies wholeheartedly. They insist that Maths does lend itself to formative assessment, only summative and that is too difficult to do one piece of closely marked, target driven comment marking every 1/2 term. They argue that they need to mark everything with a grade/level/mark rather than comment as the answer is either right or wrong.
    ~~~Please would anybody share ideas of how they use AfL within their depts?
    I really don't want to fall out with the team and want to make sure that what they say is not correct before pushing it further.
  2. I am L&T co-ordinator in our school and am struggling to get our MAths dept to adopt AfL strategies wholeheartedly. They insist that Maths does lend itself to formative assessment, only summative and that is too difficult to do one piece of closely marked, target driven comment marking every 1/2 term. They argue that they need to mark everything with a grade/level/mark rather than comment as the answer is either right or wrong.
    ~~~Please would anybody share ideas of how they use AfL within their depts?
    I really don't want to fall out with the team and want to make sure that what they say is not correct before pushing it further.
  3. First of all, last year's Ofsted report on Mathematics Teaching highlighted the problems caused when school-wide policies were imposed on Mathematics. Maths is a different subject, and I despair whenever I hear someone assuming every other subject is like English or History; in these subjects comment based marking is far easier, as there are always good points to an (for example) essay, and always areas in which improvements could be made. I hear members of our SLT telling me our comments should always have suggestions for how students could have improved a piece of work - but how do you do that if the student got 100%
    BUT: the principles of AfL can be used in Mathematics. It is simply not true that every piece of Mathematics homework must be graded/levelled. Why should it be necessary to grade everything? Tests, yes, but homeworks? Classwork?
    In our department we were very resistant to AfL as we could not see how SLT's ideas (which sound very like yours) could be applied to Maths, and also because of the time it would take. However, we did try comment based marking on homeworks. Although percentages are recorded in markbooks, they are not shared with the students - instead they have constructive comments on their work. Sometimes these comments might be short, if the work is very good, but when necessary the comments are longer showing students how they could have answered certain questions better. Of course it goes without saying that every answer gets a tick or cross, but this is inevitable and does not seem to get in the way of comments.
    Our concern remains time taken to mark, especially from those in the department who right long comments in every homework. But, overall, I am glad we went for comment based marking on homeworks.
    So how do you get your Maths department to adopt AfL - well for a start listen to them and realise that Maths is a unique subject. Then scour the web for good examples of AfL in Maths. Get the department to start small - which we did - ask each teacher to try some AfL with one class, and then get them to discuss the pros and cons.
  4. I do think that Maths is different to many subjects and that AfL techniques from say English cannot always be used in Maths. I have resisted the attempt to enforce a unified approach to AfL across the school but, as a department, I believe we have adapted our methods of teaching to incorporate AfL.
    1. We make extensive use of pupil whiteboards. Although these might be used at any time in a lesson, I find them invaluable at the start when I can ask a few questions about the last lesson's work and get instant feedback on what has been remembered. I see AfL as a feedback loop. Students feel comfortable giving answers on the boards which they might be uneasy about if I asked them to say an answer. If they honestly don't know they can show me a blank board and, as I tell them, the others in the class cannot see what they have written so there is no embarassment. Without identifying pupils I can consider some of the wrong answers and address popular misconceptions. If there are a lot of blank boards I know that I may have to go over a topic again. Once I have addressed misunderstandings I then give another similiar question and I keep going through this loop until I am happy that all understand the work. (Occasionally I might leave 1 pupil to work 1 to 1 with an LSA if there is a deep problem!)
    I find the whiteboards particularly useful when I am revisiting a topic so that I can take it further because I can identify at what point I need to start the teaching. e.g. I wanted to expand double brackets. They had done single brackets last term. Whiteboards showed that 3(2x +5) was not a problem, x(4x-3) required a little reminder about powers, and -5(2x-3y) needed some work on multiplying negatives. About 5 minutes later we were ready to learn how to expand double brackets successfully. I believe that the use of these boards is the biggest improvement in my teaching in 10 years.
    2) Marking I must admit that I will still sometimes give a mark for work as well as a comment, but it is the comment that really counts. I find that when pupils mark in class they often give themselves marks anyway and they enjoy this measure of success. Students do a lot of marking of own work or of other pupils work. I find this particularly useful when they are doing exam type questions as it allows them to see how marking schemes work. I know some colleagues get pupils to comment on each others work. I have done this but haven't really got into it. I think it is a matter of looking at a variety of AfL techniques and deciding which you feel comfortable with.
    3) Traffic Lights Last year I used a traffic light system where pupils could give me feedback on how they thought they were doing. I made laminated strips of the 3 colours which I put on desks and collected in at the end of lessons.I haven't done it this year because I wasn't happy with the way it was organised ( strips got lost, damaged etc.) but I do feel that it would be good if a school adopted a standard method so that pupils knew what to do. e.g. If there planners had a red/orange/green laminated section so that they could always have traffic lights with them rather than the teacher have to give them out.
    4) Making posters to summarize a topic is AfL
    5) I use Tarsia jigsaws to practise topics. The pupils enjoy them because they are different to noraml writen exercises. Whether this counts as AfL I am not sure but I see I as part of the bigger picture of changing how we assess work and encouraging discussion.
    To answer your question. I sympathise with your department if they are being forced to "do one piece of closely marked, target driven comment marking every 1/2 term." This sounds too much like the way that AfL works with subjects which have extended pieces of work e.g. History, Geography, D & T, English. Generally in Maths most work tends to be split into bitesize chunks.
    I would suggest that as subject leader you should aim to introduce AfL techniques which can clearly be seen to work and make sure that your "AfL co-ordinator" is aware of how you are doing it. Often it is just a matter of educating other teachers.
    Good luck.
  5. A little ironic that some comments regard AfL as not really applicable to Maths! oneof the founder members of the research team was actually a Maths teacher, who reported that Maths was an ideal tool for AfL strategies. In my experience, and not wating to be controversial at all, but if Maths teachers think outside of the box ( amd particularly away from pages of calculations and text books) AfL is an ideal part of the tol kit for raisiing student achievement.
  6. I agree with your views. Unfortunately, I fear that what constitutes AfL has got distorted (or been misinterpreted) somewhere along the way by some of those in schools who are in charge of it.
    I have also heard the dictum, "one piece of closely marked, target driven comment marking every 1/2 term." as being the key indicator that a department is incorporating AfL into a subject. As I think I suggested earlier, this is suitable for some subjects but not all. Maths is well suited to AfL and I agree that it is an ideal part of the tool kit but the "one piece of closely marked, target driven comment marking every 1/2 term" just doesn't do it for me!
    I wonder if the original poster and colleagues are being put under pressure to adopt a system which might not be the most appropriate one for maths. There is often a tendency to try to make 1 size fit all and not realise that there should be flexibility. I suggest that the poster encourages the department to use AfL techniques most appropriate to Maths and if it isn't "one piece of closely marked, target driven comment marking every 1/2 term" then don't worry. As long as what is being done is good for student's learning then the AfL co-ordinator could hardly complain. When we started to analyse how we taught Maths we realised that we had been doing a lot of AfL for years. We just hadn't realised that it was called AfL.
  7. As someone who had recently finished PGCE, one of the areas where I achieved satisfactory mostly (instead of good or outstanding) was AfL. I did eventually find that using a number of strategies during lessons did help.I think the tricky part of it was tracking progress of all pupils during a lesson. With homework and set tasks it was easy but making sure that all pupils progress, especially those ones that are quiet or not willing to ask for help, is quite tough.
  8. Maths is entirely suited to AfL - and more frequently than once per half term as well! I think the problem is that your SLT has taken a 'one side fits all' approach. I know when I am faced with that I see the bit that does not fit in with me & then it is hard to recognise that other aspects of the plan might actually be benficial.
    Most of Maths marking can, and in my opinion, should be comment only. I don't see the point of recording a mark whilst students are in the process of learning a topic. If, for instance, if a student gets all of an exercise wrong because of one misconception, which is identified & sorted out with that pupil so later on, in a test, he can prove that the problem has gone, I don't see the point of having it recorded that a few weeks ago he couldn't do it? Conversely, a mark of 100% for an exercise that is repetitive practice of a technique covered in class is not really worth recording until you can see that it is fully understood and retained later on when other topics have been covered as well.
    There are some AfL approaches that don't work in Maths but others that are easier to apply in maths than other subjects. Maths definitely lends itself to student self correcting which is really good AfL.Sometimes I mark work by just highlighting the point where mistakes have been made but without correcting them. At the start of the next lesson, students have 5-10 minutes to try to work out what the mistake is & then do the correction - ideally in pairs if they will work well together. If the same error occurs throughout the work. you could write the correction for the 1st one & then just highlight all the ones that are wrong for the same reason. This makes the students engage with the errors they have made & makes it more likely to that they will remember them. I would usually have a puzzle on the board for pupils who complete this more quickly to have a go at (UKMT Maths challenges are good for this) Of course, time is always the enemy with this approach as it takes time out the lesson but it is well worth doing as often as possible and making it part of a homework task if you can't afford the class time (once you get used to it, it makes the marking quicker as well as you don't write so much - just asterix in certain places where the errors are. You don't even have to mark the whole piece of work. If you have highlighted 3 errors, there is no point doing much more as there is only so much the pupil will get out of each piece of work)
    I try to get my department to identify the purpose of each piece of work. Most of the work they do should be about increasing their learning not measuring it. Maybe once per half term you would want a test that measures current performance but everything else should be about increasing learning. Marks do not do that & the research that has shown that includes Mathematics classes.
    I do have sympathy with the 'target' bit. I have really tried with that but agree that maths rarely benefits from setting particular targets for a piece of work with the exception of certian aspects of logical presentation.
    If there are aspects of the whole school policy that your Maths department really don't want to do (for me it would be the target-driven bit) they need to convince the SLT that they are not resistent to change and improvement but have found a better way to do it in Maths. They need to get to grips with exactly what the purpose of AfL is, identify how it will best work in maths & put together a plan to implement it. If this is presented to SLT, together with how/when it will be monitored and evaluated, I am sure it would go down well. Perhaps you can convince SLT to tell all departments that they can opt out of the 1/2 termly target driven thing if they can come up with an AfL plan that will be better in their subject & prove that is has been implemented That could be a real incentive for everyone to really engage with what AfL is trying to do rather than just throw in a few extras that they don't really believe in.
    Obviously I am in my own little utopia where everyone has loads of time to meet, discuss develop and evaluate great educational strategies but I'm sure something could be done.
    Also - your SLT needs to accept that AfL takes time to embed. You can't expect people who have been teaching in one way for years to completely change their approach over night - especially if what they have been doing for years seems to have been pretty much OK.

  9. In my school, we ask the kids to draw a column about 12 or so squares (depending on how big the squares are) in their books, which they use for key information, self assessing their work (how confident they are with a topic or what they struggled with) the teacher would also respond using this columns. We ask the kids to write their corrections in this column as well. This allows a quick guide for revision also as it contains key facts, hints and correct workings.
  10. weggster

    weggster New commenter

    In response to the OP:

    you can't force the issue if the department is so unwilling and they hold the view that AfL techniques don't work. However, if it is just the issue of the one piece of work per half-term couldn't they do one short investigation per half-term (2-3 lessons plus on HW) that can be assessed and formative comments made regarding their approach? This also ties in with the functional maths issues coming up.
    It would also tie in with student APP sheets from kangaroo maths, three birds one stone.
    On the subject of AfL surely mini-whiteboards, quality open questions, short term targets, traffic lighted registers at the end of the lesson, e-registers that also use conditional formatting to highlightwhole class issues, macros within your assessment summaries that give each student an individual print out of their marks per question that they can then use to fill in targets on their own target sheets stuck into their diaries, prompt posters with key questions for the students to consider, etc etc

    All of these are available on the iternet (for free) and take minimal time to do while improving your teaching, learning and even results.
  11. 'All of these are available on the iternet (for free) and take minimal time to do while improving your teaching, learning and even results.'
    Many thanks weggster for your input. Where are these free resources?
  12. The head of maths will have been attending the termly LEA "Subject Leader Meetings"??? These have been on the go for years now and all the ideas in these posts are discussed during these meetings. If the head of maths is not seeing AfL in a positive light I assume they have portrayed AfL to the rest of the department in a less than favourable way. You're only asking them to do what they should already be doing.
    What is your background? Are you on SLT? Do you possess the leadership skills necessary to get people to do what you require? Have you done LFTM/Leadership Pathways?
    Do they dislike you because come from a non-core subject? You've led a smaller department and they are teaming up against you to try to prove you are powerless? They view that you don't understand what it's like to be under pressure getting all students in a year group ready for GCSE?
    As a head of maths I found this useful:
    -Choose something from department development plan
    -I source enough different ideas and present them (preferrably having tried them out myself)
    -Staff use the bits they liked
    -Staff are asked to discuss what they have done at a department meeting. This gets them fired up and they will try out more ideas.
    Is AfL on their department development plan? Perhaps it's too early in their development? Perhaps they have another focus this year?
  13. What you say not only makes so much sense, but is inspiring, and reminds us what AfL is really about - the focus on learning. I really agree with your reminder for us to make the distinction between learning and measurement of learning.
  14. The above comment refers to post8 "maths is entirely suited to AfL
  15. Maths is not suited to AfL?! Shame on them! Let's remember that, by definition, AfL takes place in every classroom, every day (not once per half term - naughty SLT). I listened to Prof. Dylan Wiliam (of Wiliam and Black fame) speak last week about this very issue. Some ideas...
    1) Hand back books in groups of 4, with four separate comments written on slips of paper. Students have to look through each other's books and decide which comment goes with which book (e.g. "When designing your survery, you have asked leading questions. You must try to minimise bias.")
    2) Share marking criteria for investigations before students attempt the work. Have students mark their own work and each others against the criteria.
    3) Whiteboards and traffic lights definitely work. I use them every day. My classroom is covered with traffic light posters! I have three baskets (G/A/R) that students leave their books in at the end of the lesson. Works a treat!
    4) Once a half term I give a 'learning review' which, in essence, is a test made of context (dare I say 'rich'?) questions. I mark this and then students complete a self-evaluation of that unit of work. Their evaluation includes a 'RISK' assessment (for each error made was it a Reading, Interpretation, Silly or Knowledge error). Students then discuss strategies for minimising this next time. I ask for feedback about which lessons students feel they learnt best in. All of this, of course, can be kept in their KS3 portfolio as evidence for the end of KS level.
    5) For each topic I make a set of 'rich' questions. These explore what students already know. I don't assume anything! I use whiteboards to get answers and then base lessons around what I learn (e.g. 'why 7 an example of a prime number?' or 'why is it true that 2 is the only even prime number' instead of simply 'what is a prime?').
    6) In maths, a 'No Hands Up' policy is essential. Why allow students to opt out of learning? Part of the AfL agenda is that students are absorbed in their learning so, for me, it's mini whiteboards, pair discussions and group presentations all the way!
    Hope this helps. Be positive with the department, encourage them to visit other schools and let them start small. They absolutely should have an AfL policy in the department handbook so the curriculum leader needs to get on top of that one. For the SLT deriven half term assessment let them give a test and have the students themselves write their targets!
  16. Do you mean to come across as being patronising?

    How do you get the time to do all of this?

    Compare and contrast: "Why is 7 an example of a prime number?" & "What is a prime?" How exactly is the first question 'richer' than the latter one?

    Ah, the "No hands up" garbage again... I really do wonder what planet these people are on? I ask a question of the class, the hands go up - BUT it doesn't mean I have to ask just those with hands up. Somehow, despite the hands up, I manage to ask questions of a range of students: the quiet and not so quiet, the high-fliers and the strugglers.
  17. I simply hoped to provide some useful ideas and certainly do not wish to patronise colleagues. I think the point with well thought out questions is that a series of planned questions often produce better thinking than 'off the cuff' questions. It is the combination of these questions that provides richness.
    With regards to no hands up, we shall have to agree to disagree! Again, I think the important point here is not what the teacher is doing but the way in which students are encouraged to think about their learning.
  18. walby1993

    walby1993 New commenter

    I think that is easy to forget what AfL incorporates. I am still training but one of the things I do in every lesson is circulate and check students work at random. A lot the time I will just look at it and say "OK, why did you do this?" or "Can you explain why you didn't do.... instead?". I say this whether the answer is right or wrong as it is a way to gauge understanding, not just the ability to follow rules.
    Also, summative assessment can be AfL if the results are used appropriately. If a large majority of the pupils got the same few topics wrong and the teacher decides as a result to spend some extra time on these subjects then this can be AfL. Perhaps this might be a good way to persuade your Maths department to move forward (could be a simple list of the topics covered in the test with a tally of the number of pupils who scored less than 50% for that topic, for example)
  19. I feel that there are plenty of AfL techniques that can be, or already are, naturally embedded within most Math's teachers lessons;

    Differentiation: I often allow pupils to choose their own starting points during an exercise (this lends itself to 'traditional' teaching).

    Questioning: Asking open ended questions, targeting particular pupils.

    Self Assessment: does pupil's ticking their own answers at the end of an exercise count? Do pupils reflect upon their wrong answers, should time be built into the lesson to do this? What will the pupil's with 100% correct do?

    Objective led lessons: surely every maths teacher is now doing this?

    I certainly lack skills in written feedback and helping pupils identify their own next steps, and how they can act upon this within a scheme of work which encourages a frequent change of topic.

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