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Mixed Ability Teaching of Maths in A Secondary School

Discussion in 'Mathematics' started by brookes, Jan 26, 2012.

  1. I'm intrigued by mixed ability in maths. There's been some discussions in the past, so it'd be worth you searching this forum for "mixed". Out of curiousity, whereabouts are you teaching?
  2. Guish

    Guish New commenter

    I think that success will depend on how you can differentiate among the students when you set assignments or any other kind of work. Set the best students the hardest worksheets and try to check on all the students. The strategy works well when you assign work but one cannot do a high profile lecture because the students are mixed ability ones. Therefore, the best students will have to be independent learners. I always ask the best ones to log on my forum and read additional stuff so that they can stretch themselves.
  3. But what about when some of the students need to learn something new, rather than consolidating with a worksheet? What if they don't have the self-discipline, skills or literacy to read up on something?
    And how about the more able students who are not the most self-motivated or independent of learners?
  4. BWALSH479

    BWALSH479 New commenter

    I find that by their 3rd Yera of following this process the "High Achievers" have tended to be lazy and are shocked by the pressure placed on them in their first year of attempting GCSE high level.
    We have maintained our GCSE A*-C grades but 39% of the year 12 group got grade C .

  5. DBizzle

    DBizzle New commenter

    I teach mixed ability secondary, and to be honest i find there aren't that many topics where massive differentiation is required. As my school doesn't do national curriculum levels there is no real sense of the wide ability gap (that certainly exists in the class) amongst the students. Maybe I'm wrong, but generally I find that a lot of topics at GCSE and below don't require too much differentiation at the low end, and I can usually find suitable extension tasks for the brightest on nrich. The only time I've really broken it down so far is when teaching linear equations. We all did converting words to algebra together, then tried a few basic linear equations. I then let the kids split into different tables depending on how they rated themselves, (need to practice the basics, are ok and would like to try some tricky questions, and really confident) and gave them different sheets.

    But this is the only time so far I've had to do such a split, and whilst it worked quite well, I do actually like the mixed ability set, as you often see the brighter ones helping to explain to the weaker ones, which benefits both sets pupils.

    Having said that, whilst there are certainly some very keen and capable mathematicians in the set I don't have any supergeniuses, which I imagine would make things much harder.
  6. carriecat10

    carriecat10 Established commenter Community helper

    You might find it useful to talk to your primary colleagues as they are well practised in mixed ability teaching.
    One of the most effective ways to support each group of children at the most appropriate level would be through guided group work.
    Carrie [​IMG]

  7. "One of the most effective ways to support each group of children at the most appropriate level would be through guided group work." With respect Carrie, isn't that just setted with ability groups on different tables rather than in different rooms?
  8. DBizzle, I'd love to hear more. I think that if we weren't so obsessed with students' levels our classes would *be* more mixed ability. You certainly wouldn't be able to tell most of my highest ability students from most of my lowest ability because they share variation in so many ways - literacy levels, motivation, how they talk, behaviour, interests out of school and success in other subjects etc. But how do you manage with students who who can do trig in the same group as students who can't distinguish a quadrilateral from a triangle?
  9. carriecat10

    carriecat10 Established commenter Community helper

    Guided work doesn't necessarily have to mean children sitting around in ability groups. It will look very different in different settings, however it is about teachers supporting a target group during each maths lesson, so that every child has the opportunity for some focused support from a teacher at least once a week.
    Carrie [​IMG]

  10. DBizzle

    DBizzle New commenter

    Maybe I'm just lucky enough not to have pupils that can't distinguish quadrilaterals from triangles (in shape if not in name). I do have some pretty weak pupils though; there are children who still don't understand what even numbers are (I have to admit, trying to teach pupils primary level maths is something I really struggle with..). Yet frankly that doesn't stop said pupils from scoring 70% in tests on adding algebraic fractions (as one did last week) or from doing Pythagoras or basic trig.

    I really think that GCSE content can be taught in such a way that anyone can understand it (bar some of the most advanced topics like circle theorems or completing the square), and as long as the pupils aren't constrained by the concepts of levels, they should all be able to achieve decently. I.e. I taught algebraic fractions as just the next bit of our fractions topic, not a "some will achieve a level 7 skill of adding algebraic fractions", so the pupils just took it as another bit of maths. I do think this lack of labelling is the key to mixed ability maths teaching, combined with having pupils sit in groups, where you really do see the bright pupils help the less able to understand.

    But then again I am just an NQT, so for all I know I may well be entirely wrong and doing more harm than good, let's hope not!
  11. afterdark

    afterdark Lead commenter

    That is fairly big.
    By whom? the SMT/SLT ? do you have a senoir staff without any academics on?
    Does anyone on the SMT understand the word cummulative in context of a "cummulative subject"?
    • Gradiated exercises.
    • Handicap approach [golf style handicap] each student has a target.
    • Find out who on the SMT is driving this **** for their MA course [or whatever] and sabotage them. Once you establish who is driving this it is then a simple step to ask "for whose benefit is this being forced upon the children and teaching staff at your school?"
    What I don't understand is why people think that they know better despite mathematics being taught in sets and/or streams for a considerable number of decades. The wild experiments of the 20th century were abandoned for a reason... they fail a significant group of children. Often the most able were the most disadvantaged.
    Apparently 82% of teachers in England agree that ability groups are better than mixed ability groups.
    Good luck,
    Continue to fight the good fight.
    And find the Sith in the SMT.

  12. carriecat10

    carriecat10 Established commenter Community helper

    and why do these teachers think teaching in ability groups is better? Better for whom? Where is the evidence that setting is more effective?
    Carrie [​IMG]
  13. afterdark

    afterdark Lead commenter

    Did you not read the rest of my post about referring to mathematics cummulative subject?
    The majority of pupils. And for staff...
    I would have thought it was common sense really...
    There is always a range of ability in any class. All setting and/or streaming does is attempt to reduce that range of ability to a minimum.
    All the arguments against it, presented so far are inaquecies of the implementation which could equally happen with mixed ability teaching.
    Your link carrie coffee cup... does exactly this
    "the best teachers being allocated to the top sets, despite evidence that high quality teaching is more beneficial to lower attaining pupils"
    that is a function of the judgement league table system and poor choices made by SMTs
    " curriculum polarisation, which meant that moving between sets was very difficult because they followed different syllabi"
    again poor choices made at leadership level and links into next point...
    "unreasonable expectations of the top sets, reflected in a fast, procedural teaching style
    a lack of differentiation within sets,"
    let me repeat that one "a lack of differentiation within sets" ...isn't that part of the point of sets to reduce the need for differentitation?
    "Most schools entered all pupils in a set for the same tier at GCSE, resulting in all pupils in the lower sets being entered for exams where the highest possible grade was D. This caused disaffection. In the top sets, many girls and boys were unhappy and felt they would learn more in a lower set. "
    Two problems there, one is the system that governments have allowed to continue with tiers results in tears.
    Borderline students are a perennial problem in terms of which tier to enter them. No matter a school does there is whining about if only.
    Demotivation if the lower tier can only get a grade D? Sorry but that is a problem with the exam boards and the external system which I thought has now been addressed.
    I am not a primary teacher.
    To go back to the orginal question
    Experience...decades of experience.

    I teach from low ability KS3 to A level and I can honestly say it is deeply rewarding to see these children progress. Would the low ability set gain more more mixed ability group? I would put the emotive motivational argument in reverse...I think it would greatly demoralise and demotivate them to see the most able KS3 students complete tasks at level 8 whilst they struggle to move from level 2 to 3.
    I would be interested to see the mathematical analysis and ANOVA on the data claiming that mixed ablity improves secondary results irrespective of ability.
    I doubt that the ANOVA has been done correctly.
    Every few years I hear some spurious claim about mathematics teaching...it appears we are no longer overdue for one.
  14. googolplex

    googolplex Occasional commenter

    I'm not sure I do either.....
  15. googolplex

    googolplex Occasional commenter

    Afterdark, how do you explain the fact that the two most successful comprehensive schools in our area, on any measure you care to choose, both teach mixed ability maths?
  16. afterdark

    afterdark Lead commenter

    I don't. Nor do I need to. Do they have violent disruptive pupils for instance?, how big is your area?
    Would you care to address my fundamental point that all groups contain some range of ability and alll setting and streaming do is attempt to reduce that range.
    I think I see hints of bad teaching and terrible managerial choices being blamed on something that has nothing to do with either.

  17. DeborahCarol

    DeborahCarol New commenter

    I cannot see that mixed ability could be anything but a disservice to at least those at the lower and higher ends of the ability scale.
    Take Year Eight for example. Some can do simultaneous equations (or higher) easily.
    Others take a VERY long time to get the answer to 8+6, and don't know their 3x table.
    It would be sheer daftness to attempt to teach these ability levels together and anyone who feels they are doing so, successfully, is kidding themself.
  18. If this is your experience then you probably work in a school with lttle variation in ability between kids.
    How am I supposed to teach cosine rule to some in the class and others in there find it difficult to find the third angle in a triangle. How do you differentiate that? I'm not cherry picking one topic here either, there are lots of examples of this. Targets of A* to G in the same class (that is our ability range) - I'd probably leave teaching if this was the norm.

  19. BWALSH479

    BWALSH479 New commenter

    I totally agree.
    No one would disagree that it is possible to teach Maths in a Mixed Ability setting but is it the ideal?
    Personnally I think it does a disservice to the students.
    When the children enter Secondary school they are presented with a variety of situations that can lead to anxiety and our programme for year 8(Our First Secondary) is ideal for the students and I can tolerate the students being taught in their mixed ability setting.
    However from Second year they need to be taught in a morely tightly streamed setting with the provision for movement between classes as progress is made.

    The reality in our situation is that Teachers are taking extra classes at 8 a.m. and also every day after school to enable the students to achieve their full potential.

    I am sure that some one will now criticise our teaching methods and suggest better management would negate the need for these extra classes but I have taught for 28 years and have found this situation to being the most frustrating !
  20. googolplex

    googolplex Occasional commenter

    Why should we choose our mode of grouping to suit the needs of violent/disruptive students? What has the size of my area got to do with it!?
    OK. Setting and streaming is indeed an attempt to reduce the range of ability and, so long as teachers remember they are still teaching mixtures of abilities, and continue to differentiate accordingly, it works well. The problem is that so many teachers use setting for their own expedience, for example, as an excuse to teach one lesson, and to hell with anyone who can't cope and many others who could do with extension work. In so doing, setting potentially causes as many issues as it attempts to solve, such as creating a number of groups of students, towards the bottom of each set, who often think they are useless at maths since the work is always pitched above their level.
    Mixed ability grouping can work where it is managed extremely well, with carefully designed resources and teachers who devote necessary time to developing a curriculum which meets the learning needs of all students. Of course, you don't teach cosine rule to students who are struggling to understand G grade work. However, you can plan resources which enable different groups to progress at different rates. That is, in essence, what NRICH have recently been doing recently through their professional development work. The schools I know of use these techniques extremely effectively, and have higher value added rates than any other comparable school in our area, all from non-selective starting points. What mixed ability forces teachers to do is to plan fully differentiated work and this is the real issue which puts off many.
    Don't get me wrong; I don't teach in one of these schools. I'm HoD at a neighbouring school thinking through the consequences of each particular method of grouping based on the fact that we achieve worse results than them.
    A few years back, I showed a German maths teacher around our school. He simply couldn't countenance our method of grouping by sets. In his system, it was perfectly normal for students of all abilities to be grouped around tables, working on different projects, but on hand to work with each other as necessary. It works for them.
    I think many of the responses to this thread have been dismissive of mixed ability teaching without fully considering evidence that exists that proves that mixed ability teaching can be made to work exceptionally well. The two schools that actively practise mixed ability in our area, are both deemed 'outstanding' by the Omen, and provide all the proof you need that mixed ability can work.
    Whilst I suspect, I'll continue to use setting by ability when organising my department, I hope I'm open minded enough to learn from those schools which successfully practise this mixed ability approach.

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