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Learning Objectives in Maths

Discussion in 'Mathematics' started by Andrew Jeffrey, Jun 12, 2015.

  1. Andrew Jeffrey

    Andrew Jeffrey New commenter

    I'd be interested in hearing your thoughts, as I feel that they are something of a double-edged sword. Specifically:

    Thoughts - both random and variable...

    For many years I have been encouraging schools to re-think the often non-negotiable policy of writing a &lsquo;learning objective&rsquo; or &lsquo;learning intention&rsquo; on the board at the start of the lesson, and of requiring children to copy it into their books. I have even heard arguments defending the poor L.O. along the lines of &ldquo;Otherwise how are they meant to know what to learn?&rdquo;

    I would argue that we have come a long way, and some schools have seen the light. Worryingly, many teachers have confessed to me that they agree BUT they would be &lsquo;failed&rsquo; if they stopped doing this. It is a sorry state of affairs if teachers can no longer have an honest debate about good and bad practice without being seen as trouble-makers. We rightly call ourselves a profession, yet too often professionals are prevented or discouraged from behaving as such.

    This article is designed to explain why I think this policy needs to be re-visited carefully. If you are in a school that still insists on it no matter what, then I hope this article will provide a measured argument to help schools look at this a little differently.

    I will outline four concerns. (Admittedly there were only three until I spoke to Anna, a KS1 teacher, recently, who reminded me of #4.) You may agree with all, some or none at all of what follows, but I hope it will at least stimulate some debate.


    First: Concept or Label?

    In every lesson I teach, I need to have a learning objective. If not, I have thought more about teaching than learning, and as we know from Gattegno, teaching must always be less important than learning. Whether or not I need to reveal it my learning intention to the children before the lesson is highly questionable. What if I have more than one? Surely that must be acceptable, and even desirable, since mathematics is, to quote the National Curriculum2, &lsquo;highly inter-connected&rsquo;.

    Suppose my intention is to teach children about prime numbers. Simply saying &lsquo;learn about prime numbers&rsquo; will not help children grasp the concept of a prime, and for two groups of children it risks doing them a dis-service.

    The first group is children who already have a working definition of &lsquo;prime numbers.&rsquo; They decide before the lesson even begins that this lesson is not for them, since they already &lsquo;know&rsquo; about prime numbers.

    The second group are the children who are nervous, and who have no idea what prime numbers are. For them reading the L.O. merely confirms in their own mind what they are already thinking &ndash; maths is hard, and full of words and ideas I don&rsquo;t understand.

    Instead, we might give children 6 square tiles and ask them to make as many rectangles as they can. They can make just two, and the dimensions of these rectangles (1,2,3 and 6) can be seen as ways to split up 6. In mathematical language, these are known as the &lsquo;factors&rsquo; of 6. We might then give the children one more tile and ask them to repeat the exercise. This time, with 7 tiles, they find that they can now only make 1 rectangle. Give them another tile &ndash; again they can make 2 rectangles, with dimensions 1,2,4 and 8, meaning that 8 has four factors. Give them another tile and now they will discover that they can make two rectangles once again, but one of them is a square! Later on, at a time when children are ready, we can explain that 9 is known as a square number because they were able to make a square from it. 7 is one of the numbers from which it is possible to make just one rectangle &ndash; these special numbers have a special name &ndash; they are called &lsquo;prime numbers.&rsquo; And so on. The difference is clear &ndash; in the first example, the LO creates either complacency or fear, while the second allows deep understanding for all, and a hands-on approach that aids the learning. Only after learning the CONCEPT should we presume to ascribe a LABEL &ndash; the L.O. has this totally the wrong way round.

    Second: &lsquo;Only awareness is educable&rsquo;.

    Caleb Gattegno3 famously said that &lsquo;only awareness is educable&rsquo;. If this is true (I believe it is) then this has profound implications for the way in which we teach. This includes those of use who are privileged enough to teach teachers. As I reflect on this more and more, I continuously change the way I do CPD; this inevitably means that I think harder about the tasks that I will give teachers, and I aim to speak less and listen more.

    How can pre-determining my learning sit easily with this philosophy? The short answer of course is that it cannot; to learn means firstly to become aware of something I do not yet understand (Gattegno again), and to work in such a way as to build my understanding. This could not be further from the &lsquo;here&rsquo;s a statement, now learn it&rsquo; approach, and puts the responsibility to learn firmly where it belongs &ndash; with the learner.

    Third: The joy of discovery.

    If I asked you to accompany me on a journey, and promised you a great view at the end &ndash; but then showed you a picture of the destination instead &ndash; I have effectively deprived you of making a wonderful discovery. For example, if I tell you that Pi is equal to 3.14, and then show you how to use it to work out some areas, circumferences and so on, I have in essence taken away any sense of discovery or joy of achievement from you. Far better to refrain from any learning objective such as &lsquo;learn that Pi is approximately 3.14&rsquo;, and move instead to the sports pitch, getting children to measure around and across centre circles, then divide one result by the other, and discover that the size of the circle makes no difference to the result of this division &ndash;in other words, the ratio is a constant.

    Fourth: it frees up teachers to plan and teach rather than spend time ticking boxes

    What&rsquo;s more, it doesn&rsquo;t waste pupil or TA time (either writing out or sticking in) objectives that will be forgotten all too soon. I have been in countless classrooms where the teacher feels duty-bound to get children to have a copy of the learning objective in their book, and this can waste a disproportionate amount of valuable lesson time. As Sir Ken Robinson has noted4, teachers spend too much time proving rather than im-proving, and I am convinced that removing the need to make a learning objective explicit in EVERY lesson will help with this.

    But what do OFSTED think? Often I hear comments such as &lsquo;Yes I agree but OFSTED won&rsquo;t like it&rsquo;. If ever the cart was before the horse, it is in comments like these. But I have good news. In their excellent document, Made to Measure, OFSTED report that it is not always necessary to reveal learning objectives at the start of the lesson. In writing!

    In conclusion &ndash; lesson objectives are, at best, your hopes for how the lesson will go. Some children will learn things you never dreamt they would learn &ndash; embrace that.
    Often it is better to withhold your reasons for choosing particular tasks, in order to give children the time to raise their awareness of a new idea.
    Finally, never forget the joy of an undiscovered piece of reasoning, or a surprising relationship &ndash; such patterns are the building blocks of maths, and should never be rushed.
    Enjoy your maths &ndash; and your children will do the same!


    1. Department for Education (2013) Mathematics programmes of study: key stages 1 and 2 National curriculum in England
    2. Gattegno, C. (1987/2010) What we owe children. New York: Educational Solutions Worldwide.
    3. OFSTED, (2012), Made to Measure.

  2. strawbs

    strawbs Established commenter


    PS I looked at the title of your thread and my first thought was "On no", or actually, a more unprintable version of that!
  3. MisterW

    MisterW New commenter

    For me the objective really just serves as a title. I don't have a title in addition to the objective so there are only two things to write down at the start of the lesson: objective and date (and my objectives are pretty short).

    I find it useful in many ways since it makes it easy for me to identify when each lesson begins when I am marking exercise books and it means there is something for the pupils to be doing the moment they enter the classroom so it helps the class to settle. You make a good point about Ofsted - I think often there are positions attributed to them that they do not actually hold and learning objectives may well be one of them.
  4. googolplex

    googolplex Occasional commenter

    Of all the various fads in education since the age of political interference, Learning Objectives have been one of the most enduring yet pointlessly futile. My approach right from the start, when I bothered/remembered, was simply to turn the usual title into an LO. I've survived over 25 years of SLT visits and Ofsted directives telling us various pathetic things about how things must be done. I still often forget to give LOs. As for WALT an WILF and all that Could and Should nonsense - none of it has ever seen the light of day in my classroom. But kids always know what we're doing, since there's always a point to the lesson. Fortunately, I've reached the stage where I really couldn't give a damn about directives from on high so long as kids in my dept learn well - and they do perform well, usually 2nd quintile + on these latest data dashboard things. If they sack me, good! Early retirement with a reduced pension sounds better than the alternative.

    The point is that no one is ever going to convince me that a Learning Objective has made the slightest difference to educational standards.
  5. bombaysapphire

    bombaysapphire Star commenter

    We were told by one county adviser that all pupils should write in their exercise book at the start of each lesson "I do not know how to .. blah.." followed at the end of the lesson by "I now know how to ....blah.." I flatly refused to waste time on such drivel and when I had a course with Ofsted's chief Maths inspector I asked her about it. She was horrified.

    I resisted learning objectives for years but decided in the end that they were a lesser evil that the above. I also don't use ones like "To discover the value of pi." If we are discovering some thing then the objective is "To be discovered." I now work in an independent school and very few of my colleagues use learning objectives. Despite this our results are impressive.
  6. PaulDG

    PaulDG Occasional commenter

    Exactly. This nonsense is stuff we've allowed people who know less than us to inflict on us because we won't stick together in the face of it.

    Ofsted never asked for it.

    Yes. Almost unheard of in the Independent Sector.

    (Though, even there, there are 'Learning managers" who are dredging round the Internet desperately trying to find something to fill their half-day CPD slot and they tend to find this sort of thing, together with Learning Styles, etc.

    Luckily for the kids the SLT in Independents tend to be focused on results and not on the flim/flam.
  7. Andy.Pipkin

    Andy.Pipkin New commenter

    If you are going to use WALT and WILF, remember that, at the end of the lesson, kids should be writing the abbreviation for "We All Now Know" in their books. SLT will be delighted, I am sure.

    I don't do LO (be they Lesson Objectives or Learning Outcomes or Lesbian Orifices) :)
  8. mature_maths_trainee

    mature_maths_trainee New commenter

    Yep, I certainly agree they are over-used, but I have been astounded at how many teachers seem to 'like them'.

    It seems another one of those things whose original motivation may have started out as being completely reasonable (that students should, in general, know what it is they are going to learn to do), but has been widely mis-applied by absolutely thoughtless leaders to the ''individual lesson' granularity of learning.

    Another serious failing (to add to Andrew's list) is that WALT-type L.O.s are incredibly de-motivating to lower set classes. They give the false impression to students that they *should* be able to (say) 'learn how to add and subtract directed numbers' in a single lesson. When students see (essentially) the same L.O. for a lesson a year later (with the spiral curriculum), they immediately sub-consciously feel a failure because they've 'done it' and the L.O. language rarely describes learning i.t.o. a process to master, but overwhelmingly as a boolean attribute in the student to be persistently activated during a single lesson.

  9. PaulDG

    PaulDG Occasional commenter

    Many teachers who currently survive in the profession were "brought up" with nonsense like LOs as being the "normal" thing.

    They don't know this stuff is time wasting rubbish - it's part of the magic to them.

    Most who dared to ask if the Emperor was wearing any clothes were driven out.
  10. The last 3 schools I have worked in their has always been an 'expectation' that we have to write a LO at the start of every lesson. Although, it has been more like a rule, as if it wasn't seen in an observation you were pulled up about it. As we have little choice therefore, I tend to have the LO as a title, like googolplex, but prefer to put it in a question form. Makes more sense when you return to it later in the lesson.
  11. I have been at my new place for a year.

    In that time we have gone from "must have one learning objective", through (briefly) "try three learning objectives", finally to "no learning objectives shall be used".

    We have also gone from "lesson plans are essential" (because they are somehow vital) to "no lesson plans are required" (because they are now a waste of productive time).

    Front of book stickers also appeared, took a vacation, then reappeared again.

    Each time, there has been an Ofsted consultant type come in the day before.

    I find it quite entertaining, to be honest.
  12. Andrew Jeffrey

    Andrew Jeffrey New commenter

    I too would find it quite entertaining Bobble90, if it were not for the fact that it is wearing down good teachers and stopping good quality teaching from happening, as teachers spend time trying to avoid sanction rather than act in what they believe to be the best interest of their pupils.
  13. lou1990lou

    lou1990lou New commenter

    I don't always write Learning Objectives, but I have NEVER had the students write them into their books... The amount of time that would take for some of them would waste so much time. As well as the fact that the main title/ sub titles I use cover them as much as I beleive necessary.

    Instead at the end of most topics I try to give out a RAG thing that has an outline of all the objectives we have covered... or could have covered. (Green/smile = confident , Amber/straight face = need practise, red/sad face = No idea.) There's then a space at the bottom for them a EBI and WWW. The whole thing is intended as a guide to help them when it comes to revision.

    For many of my topics if I decide I want to have LOs (and only if I have them on a powerpoint) then I try to use All, Most and Some.

    "All" is what was covered in the starter: the fundametal concepts of the topic we'd be covering that lesson or revisiting what they had done last lesson.

    "Most" is what we would be doing that lesson (as I am aware that some of them wouldn't be able to access the tricky topics but if it was something I personally deemed accessible by all it would also come down into the "All" Obj.

    "Some" is the extension activitiy.
  14. lou1990lou

    lou1990lou New commenter

    What I have most recently done actually (and only remembered once I started doing it today) was the use of "will" "should" and "might".

    In place of "all" "most" and "some".

    Mainly because it made the objectives themselves sound better and also reinforced the main point of the lesson and helps them to take responsibility for their own learning.


    By the end of the lesson you:

    *Will be able to simplify a ratio

    *should be able to share an amount in a ratio

    *might be able to find a missing value in a ratio.
  15. PaulDG

    PaulDG Occasional commenter

    LO/ Titles? Doesn't matter which. At least not until the LO becomes policy. Then it becomes a way to beat decent teachers to death and prevent learning.

    And what LOs would we have them write for the next 6 lessons where they practise ratios until they master them?

    "Same as Yesterday only more"?

    How will SLT see that when they do their "learning walks" and "book scrutinies"?

    LOs are part of how we've sacrificed everything in the goal of appeasing a fantasy of "visible progress every 20 minutes".

    That's why they're dangerous.
  16. @Andrew Jeffrey interesting the way you introduced the concept of prime numbers.but is it possible to teach every math topic using manipulatives,if so please guide me
  17. Andrew Jeffrey

    Andrew Jeffrey New commenter

    Great question. Certainly almost every calculation can be modelled, using things such as Dienes, Numicon or Cuisenaire.

    Calculation with fractions takes a bit more thought but is still possible - I recommend the work of Caleb Gattegno in this regard, or Cuisenaire textbooks, (or the excellent videos on NCETM) or even the Numicon manuals if you work with primary age children.

    Also I have a free fractions resource on the free gifts page of my website but last time IO tried to share it my post got deleted by the TES moderators, so I guess you'll just have to search for it!

    Pattern blocks are commercially available and children can reason all sorts of things about shape, angles, rotation, reflection symmetry etc. using this equipment.

    Percentages - funnily enough Dienes is particularly good for modelling this. I showed something to this effect in my free maths teaching newsletter earlier this term. Again, I daren't post a link for fear or irrational deletion!

    Area - I use square transparent coloured tiles, and also use these to teach about factors, multiples etc.

    Algebra - there is not much to beat Cuisenaire for this in my view but I may be wrong; we jump too soon to algebraic notation before thinking about the concept and this can put a lot of children off.

    Maybe others can suggest more?

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