More on memory.. Making sure that they know what I want them to know…

Further to Kevin’s last post on memory, I have been thinking more about this.

You just need to google image search Knowledge Organiser to know that this is popular, but let me start by saying that nothing in this blog is new.  Those of you that remember Mrs Nicholls, will remember that she had loved key word lists.  Those of you that remember Abbi’s presentation last year on memory will know the Ebbinghaus forgetting curve and the need for spacing learning; it is something that we have talked a lot about. As a result, I have spent some time thinking about it and have read  Why don’t students like school – Daniel Willingham and Make it Stick – Brown and Roediger) This has now begun to affect my teaching; having always been been taken with the idea of constructivism (see my blog on Style over substance) I have focused hard on making learning meaningful for students. Yet, whilst I still maintain that this is helpful – students need something to link their new knowledge to, I am now far more focused on knowledge. This is partly inspired by Daniel Willingham ‘memory is the residue of thought’, and the understanding that the new syllabus for GCSE and A Level are going to include much more stuff to learn, I have to make sure that my students are ready for this.  So, I am making a slight change in pedagogy:

  1. I make sure that I know what I want the students to know. (I know that sounds silly, but sometimes I can get carried away with doing the fun stuff!)
  2. I make sure that they think hard about what I want them to know
  3. I make sure that I know that they know what I want them to know.

We have, for a while, been focused on memory at school and I have been focusing on cue cards.  My GCSE Year 11 group have hundreds of them that they have created since the beginning of Year 10 and they know that they need to use them to revise.  They have cue cards for Bible Verses and key words of all the topics.  However, I wonder if my students spend more time making the cue cards rather than using them, some of them lose the cards AND the quality of the cue card is dependent on the maker.   So, I have taken some inspiration from some of the people I follow on Twitter and have created knowledge organisers* for each of the topics that I teach for the exam (I do 5, AE does the others).  This is not to replace the cue cards or mindmaps, or past papers, but to supplement them.

Screen Shot 2016-04-06 at 19.00.39

Each Knowledge Organiser is a one page summary of the very minimum that they need to know.  Obviously, some will know far more than this, but it does mean that every student will have the basic definitions and knowledge to build upon. I plan to use these in my revision lessons over the coming weeks. The one above has a list of all the key words for the unit, Bible verses and key information that they must know.  It also has a list of what the specifications says that they must know.  I have numbered each of the definitions.  So, I can ask the students to cover the word, and then quiz them on the definition or vice versa.  I can ask them to cover the Bible Verse and quiz them on those and so on.  I can set them learning homework and then we can then focus in class on exam technique and applying the knowledge that they are learning at home.

*Check these out if you haven’t heard of knowledge organisers before; they write much more coherently than I! @joe_kirby Joe Kirby Knowledge Organisers and @Jamestheo Knowledge Organisers – James Theobald.

If these are helpful to my current GCSE group, I plan to create these for our new GCSE schemes of work before I start teaching them… Does anyone else do anything similar? I would be interested to know?


Need to jog your memory?

kevin 1

Working Memory

For many of us, working memory is helped if what is being spoken or demonstrated is supported by VISUAL PROMPTS. These can be referred to by students throughout the lesson.

Much of what we teach can be turned into a question. As instinctively curious animals, we want to find answers to questions. It also helps to create a purpose for ACTIVE LISTENING.

To ensure that working memory is developed, students need to PROCESS the information they are receiving. The more PROCESSING the better.

The first process is ACTIVE LISTENING. It is crucial and obvious that students should be listening to (concentrating on) everything that we say, not simply writing as we speak. As they are listening they are trying to make sense of what we are saying/showing, hence the need to keep explanations short before another process takes place.

This could be VERBALISING. Students could Pair and Share and show their understanding of what they have just listened to by responding to a question.

Now they are in a position to PERFORM that understanding and test how far it is installed in their working memory.

Finally students need to REINFORCE their learning through revision so that the knowledge and understanding rests comfortably and accessibly in the LONG TERM MEMORY.

It’s as simple as that!


kevin 2


Paired Observation Update


At the last Teaching and Learning Staff meeting, we talked in groups about our experiences with Paired Observations and at this week’s Staff Meeting, we were reminded that we should really be thinking about our second observation.  With that in mind, I thought it would be worth giving some feedback what observations have happened on also on what different departments are doing.

The following graphs give us an insight into what we have observed – we are obviously really good at questioning!  We will be able to use infographs like these to help plan our CPD, so the BlueSky form is really helpful  (Click on the graphs to make them clearer.)

From your feedback, overwhelmingly, paired observations are seen as a good thing.  Having looked at them all, common themes were:

  • Knowing that everyone can improve by watching others and we learn more from observing than being observed
  • Focus on development, not grading
  • Discussing solutions to common problems
  • A break from the norm
  • Learning about new strategies
  • Beginning to feel less worried about being observed
  • Being able to see someone else teach the same class gives me a different point of view on my students
  • Confirmation of good practice
  • Seeing new ways of doing things that I can try in lessons
  • Talking about teaching strategies
  • Talking about behaviour management strategies

Next Stepsnext steps

So, what is the next stage?  There are some really great things going on.

Lesson Study

Some teachers are doing a kind of lesson study.  Teachers plan a lesson together, they then watch one of them teach the lesson (or if time, watch more than one teacher deliver the same lesson) and then discuss what they find.  This type of co-planning will be invaluable in the coming year when planning new specifications.  If you want to know more about Lesson Study, here is an interesting blog to get you started.

Shared strategies

Some staff have been observing across departments, looking for strategies that will work with the same students across subjects.  One example of this is three teachers who have identified three things that they want to focus on with the same group:

  • Shared approach to behaviour management
  • Shared approach to lesson structure (focus on making the last 10 minutes count)
  • Shared approach to teaching paragraph structure.

Collaboration like this is enabling students to benefit from the same structured approach, but also helps the teachers to be able to know that others are aiming for the same outcomes with students.

Opportunities to observe others

If you want to observe someone who is doing something you would like to focus on, please speak to KR, RH or your LT Lead.  We now have the start of a great database of information about all the great stuff that is going on in our classrooms and should be able to point you in the right direction.  Similarly, if you don’t quite ‘get’ what you need to be looking for in observations, and would like to have some coaching on more experience in paired observations, please also speak to KR who can arrange for you to have a 1:1 session on what to look for in observations.

Paired observations are making a real difference to our classroom practice.  It would be great if someone would blog about what they have seen/tried in response to this idea.  Please let me know if you can find some time to write up your findings!


The Science of Learning

Quite a few of us have done some reading around Memory and the Science of Learning since AA’s excellent inset on it last year.  I have read these two books, which are excellent material on the subject.  However, today, I have found a short article that summarises a lot of current thinking and research on Memory.

I wonder if you would like to read it too and then get together to discuss the impact of these ideas on our classrooms.  If you are interested in a #teachergeek natter over a cuppa, please let me know.

Deans of Impact – The Science of Learning


Skemp’s Theory for teaching Maths

Skemp’s Theory for Teaching Maths 


I found this really interesting from as part of my Teaching Advanced Mathematics Masters Course at Warwick University this academic year. For me the theory is more important than ever with the advent of more demanding problem solving elements in the GCSE and particularly the forthcoming A level changes in maths which are to demand a greater aptitude and flexibility in solving issues arising in questions.

 Skemps theory basically highlights the difference between and instrumental and relational learning in the maths classroom.

I have to say this resonated with my own views on the teaching of the subject.

It is easier and tempting to teach techniques in a non-relational instrumental manner which even if successful in helping a student pass an exam will will soon be discarded after the exam and not provide a firm foundation for a students to build on in their further education.

A summary of the theory appears as as follows:

Skemp’s theory

Richard Skemp was a mathematician who later studied psychology1. He drew on both these disciplines to explain learning in mathematics. The main ‘thrust’ of his argument is that learners construct schemata to link what they already know with new learning. According to Skemp, mathematics involves an extensive hierarchy of concepts – we cannot form any particular concept until we have formed all the subsidiary ones upon which it is depends. Skemp also suggested that emotions play a dominant part in the way in which we learn.

Skemp suggested that there are two kinds of learning in mathematics:

Instrumental understanding2: a mechanical, rote or ‘learn the rule/method/algorithm’ kind of learning (which gives quicker results for the teacher in the short term), e.g. writing 10 would be understood as “This is how we write 10” in instrumental terms.

Relational understanding2: a more meaningful learning in which the pupil is able to understand the links and relationships which give mathematics its structure (which is more beneficial in the long term and aids motivation), e.g. writing 10 would be understood as “This is why we write 10 like this (in terms of place value)” in relational terms.

Both are deemed important for mathematics.

Relational Understanding and Instrumental Understanding

The article Relational Understanding and Instrumental Understanding was written by Richard Skemp and originally published in the December 1976 issue of Mathematics Teaching. The article was reprinted in the November 1978 issue of Arithmetic Teacher and in the September 2006 issue of Mathematics Teaching in the Middle School. The article is available from NCTM at and from JSTOR at


In this article, the author defines relational and instrumental understanding. He then explains the impact he feels these two disparate goals have on the attitudes and understanding of students. We believe the reader will find his ideas about the teaching and learning of mathematics remarkably contemporary and thought-provoking.

Summary of Relational Understanding and Instrumental Understanding

In Relational Understanding and Instrumental Understanding Skemp contrasts two perspectives of mathematics. Using the terms relational and instrumental from Stieg Mellin-Olsen, Skemp introduces relational understanding as “knowing both what to do and why” (p. 89) and instrumental understanding as the ability to execute mathematical rules and procedures. Skemp asks:

If it is accepted that these two categories are both well-fitted, by those pupils and teachers whose goals are respectively relational and instrumental understanding (by the pupil), two questions arise. First, does this matter? And second, is one kind better than the other? (p. 89)

Skemp admits his longstanding assumptions that relational understanding is better, but questions then when so many mathematics teachers and texts focus on instrumental understanding. Concerned about conflicts between the two views, Skemp hypothesizes two mismatches:

  1. Pupils whose goal is to understand instrumentally, taught by a teacher who wants them to understand relationally.

  2. The other way about. (p. 90)

Skemp sees the first mismatch as a short-term problem while the second is much more serious, as a student focused on relational understanding will get little or no assistance from the teaching. Similarly, a mismatch between teacher and text could also lead to conflicts. With the perspectives and conflict made clear, Skemp admits that “I used to think that maths teachers were all teaching the same subject, some doing it better than others. I now believe that there are two effectively different subjects being taught under the same name, ‘mathematics’ (p. 91).

Despite his preference of relational understanding, Skemp proposes three advantages of instrumental mathematics that make it preferred amongst many mathematics teachers: (a) within its own context, instrumental mathematics is often easier to understand; (b) the rewards for following a procedure and getting a correct answer are more immediate; and (c) because less knowledge is involved, it’s often correct answers come more easily and reliably. In contrast, Skemp identifies four advantages to relational mathematics: (a) it is more adaptable to new tasks; (b) it is easier to remember, (c) relational knowledge can be effective as a goal in itself, and (d) relational schemas are organic in quality.

The preference or use of instrumental mathematics by teachers are many, say Skemp. In some cases, instrumental understanding comes more quickly, and for a particular calculation in a class or on an exam it may be all a student needs. The expectations about the nature and amount of content presented in a course can also influence a teacher’s use of instrumental mathematics if they feel pressure to cover many topics. Teachers may also prefer instrumental understanding because it is what they themselves possess, or they have difficulty recognizing relational understanding in their students’ thinking and written work.

To set up a theoretical explanation, Skemp proposes an analogy. He imagines visiting a town for the first time and needing to navigate to particular locations. He compares two strategies: (a) learning specific routes that take him from where he is staying to his destinations or (b) exploring the town in a way that allows him to form a mental map of significant landmarks and features. For getting from point A to B the first strategy will be efficient but limited to that route. The second strategy might result in a longer trip from A to B, but he will be more prepared to find other destinations and is less likely to get lost. Skemp relates the first strategy to instrumental understanding, where learning to navigate consists of learning an increasing number of fixed plans. Relational understanding is like the second strategy, where learning “consists of building up a conceptual structure (schema) from which its possessor can (in principle) produce an unlimited number of plans for getting from any starting point within his schema to any finishing point” (p. 95). Skemp therefore distinguishes relational understanding from instrumental understanding in the following ways:

  1. The means have become independent of particular ends to be reached thereby.

  2. Building up a schema within a given area of knowledge becomes an intrinsically satisfying goal in itself.

  3. The more complete a pupil’s schema, the greater his feeling of confidence in his own ability to find new ways of ‘getting there’ without outside help.

  4. But a schema is never complete. As our schemas enlarge, so our awareness of possibilities is thereby enlarged. Thus the process often becomes self-continuing, and (by virtue of 3) self-rewarding. (p. 95)

I would argue as maths teachers that although instrumental teaching has its place we should always be thinking about maximising relational learning opportunities for our students.

I hope you enjoyed thinking about this as much as I have done these last few months and would love to hear any thoughts you have on the subject.


Deputy Head of Maths

Able Gifted and Talented Coordinator

Learning for Life?

Year 7 seem to be the most enthusiastic when it comes to science lessons, especially this week as it was the first time I’ve met a certain Year 7 group in our science rotation.  I had a lesson with them Weds, then on Thursday at start of lesson asked them to write (anonymously) on a post-it note which of the two things discussed in the previous lesson was their ‘favourite’, and why.  Even though it seemed a bit of a strange question, they did it enthusiastically. However, when I had a look at what they’d written later on the thing that stood out was that several of them had written “Option X is my favourite, because I know more about it.”


Reflecting on this, this seems to be the thing that teachers should be challenging. If they are truly to learn, and to be self-motivated to learn (and to really embrace ‘learning for life’), they’re going to have to switch from being more comfortable with the known to being excited about the unknown because there is the potential to find out something new.  My experience with older students (“Just tell us what’s going to be in the exam” etc.) is a sign that this only gets worse with age. There’s a bit of an improvement with the lower sixth, as that’s a group of self-selecting students (i.e. those with little or no intrinsic thirst for the subject  opt out) but by this stage most seem to have lost the thirst for learning, and instead either have a weary ‘I must learn it for the exam’ attitude, or perhaps collapse into thinking ‘I’m just no good at physics, so I won’t even try’.

I’m not really sure how I’m going to address this in my own practice, but it might help if I’m explicit with them about this*. My speculation is that  we bring them up through an education ‘system’ that routinely tests them, so they associate having knowledge with success and confidence and shun the unknown as something that will bring fear and shame on them.


*Perhaps we should look more into Growth Mindset (ed)

Are you talking too much?

Teacher Talk


It’s possibly the one thing we take most for granted and think least about unless we’re being observed and then, suddenly, we think about every word we’re saying and speak far too much. The following is a response to issues raised from a real observation regarding teacher talk. This was my initial response, via email:

KR: My immediate thoughts are, it’s all about how effective teacher talk is in enabling the students to make progress. 30 seconds at the wrong pitch could be too long. The two issues are: Does the teacher, by talking too long, lose the engagement of the class/prevent them from thinking for themselves and secondly, when the teacher does talk, is it effective in explaining/clarifying/stretching challenging/linking learning together? We should be wary of a hard and fast rule. There may be occasions where more (effective) teacher talk is necessary but the teacher needs always to be aware of how it is “going down with the kids”.

I want to add to that now:
KR: First of all, unless our intended audience is listening, it doesn’t matter what we say. Secondly, what we do say is crucial to learning so it really is the most important aspect of our teaching. We use it to build rapport; build relationships, praise; discipline; inspire; explain; clarify; check; question; stretch; challenge; link learning together.

Dave also responded to the comments raised by the observation. I have included his thoughts and given my reply:

DP: Whilst a teacher is talking, students are (hopefully!) listening. Listening is an important but essentially passive activity as opposed to doing (e.g. writing, drawing, reading, making, performing, running). That’s the main reason to ensure that we only use it when necessary.

KR: We can turn listening into an active activity if the students know that they are going to have to do something in response to what they have heard. In other words, they must process the information. After an explanation, get them to do something with it first, e.g. P&S, rather than simply write it down. In a practical lesson, students can check understanding before practising or after practising.

DP: I’d also pose the question: what types of classroom activities lead to greater independence? I wouldn’t necessarily put listening at the top of the list, but you could argue that having to listen to a teacher for a significant amount of time would require greater resilience.

KR: Effective teacher talk, leading to greater student knowledge and understanding could and should lead to students being able to be more independent in the future. We would also hope that, usually, at some point in the lesson, there are activities that help to develop independence.

DP: On the point of how much and when? That depends entirely on the lesson objective and the structure of the lesson. There can be no hard and fast rule, therefore. Although, the overriding principle remains – only use teacher talk judiciously.

KR: If they’ve started to glaze over, stop talking. We might think what we have to say is important, they obviously don’t.


David Didau in an excellent book ‘What if everything you knew about teaching was wrong?’ investigates the use of teacher talk. He says ‘If students are going to learn anything worthwhile, teachers absolutely must talk… Pupils’ academic progress depends on their ability to think in academic language… Effective modelling us impossible if teachers are afraid to speak. Instead of trying to shut teachers up, maybe we should be training them to improve the quality of their talk.’

Ask yourself three questions this week:
Am I talking too much?
Could someone else say it?
Is what I am saying helping the learning (but not too much)?

Any comments for discussion?