My interest in the idea of sharing pedagogical purposes comes directly with the contact I have had with the Project for Enhancing Effective Learning at Monash University in Australia. Now each of these teachers were very active in establishing learning agendas with their classes. The impact they were having was inspiring. Each classroom tool can have a purpose beyond delivering content, and this needs to be shared.
I suppose the purpose of this website is collate, crystalise and open dialogues about how to increase this within classrooms. As the quote from Carl Bereiter illustrates this classroom methodology can empower our students.

Thursday, 5 July 2018

Unpicking a successful task design.

A little context.

I designed this task for my 10x5 students. They find science and maths difficult and all are the most forgetful students I have ever taught. They are robust and willing and richly deserve some success. Every calculation I have done with them , has been very difficult and the prospect of having to perform a three part calculation on something as abstract as specific heat capacity was a little daunting. However, this worked, and one student even could rearrange the formula to calculate mass, specific heat capacity and temperature change. 

Why I think it worked.

This for me is a clear success of the bar model, which provide a student friendly (and owned) scaffold for this calcualtion. 

Ben Rogers excellent blog posts really helped.

Other features that supported the students in their learning was:
1. Managing the complexity of the task.
2. Increasing the number of operations the students had to do to complete each calculation.
3. Practice.
4. The use of examples.
5. Removal of scaffolding.

I have tried to annotate a students worksheet to show where these features apply. 

Thursday, 14 June 2018

What does Nuthall really say about multiple exposures?

I made this table in 2014, it is based upon a now unsearchable document, namely the now illusive
"Nuthall, G. A. (2001a). Manual: Procedures for identifying the information content of student classroom experiences and predicting student learning."
If anyone has one lying around I would love a copy.

What is it? Well, these are the codes (albeit slightly incomplete, and slightly compiled from other Nuthall research documents) used by Nuthall and his fellow researchers to analyse the interactions students had with a concept. Their purpose was to allow them to predict if learning would occur based upon the "kinds" of interaction.Astonishingly they could oredict if learning would occur to an accuracy of 88%. This is to an extent that it will certainly do for me!

These may be a researcher’s tool, but they certainly illuminate a teachers understanding of how learning takes place, and as such are worthy of a little thought by teachers. It is indeed these research tools that presented us with the multiple exposure rule that if a concept is engaged with three or four times, depending upon the concepts difficulty and the students, then it will be learned. But they might tell us even more.

The codes are categorised into two types: A full set of information that is required for a concept to be learned, here coloured green. Sensationally the other category is a partial set of information that includes important information about the concept being learned.   Here these are shaded blue, and you will see that these are of several different forms. 

Full set of accessible information needed to learn a concept: picture, words.
The exact information that that students need to hear, read, see, discuss or use in an activity. Information that must be engaged with.

Students need the chance to identify and extract relevant information.

Any prior knowledge they express is very much part of this.

Partial set of information with some important parts about a concept.
As above, but just not the full information.

  • Chunked explanations.
  • Corrections to work.
  • Relevant prior knowledge that they express too.

Working out Information.
Information that can lead to an inference or deduction.

Implicit use of key terminology.

Concept use when teaching another concept.[??1] 
Background information

Such as:
  • definitions
  • analogies
  • examples
  • non-examples
  • personal experiences

Activities that lead to a full use/view of the information.

These activities are more than just reading, writing and talking about a concept.  

  • Science practical
  • Making a model

The information is clearly about the concept
Activities that lead to a partial use/view of the information.

These activities are more than reading, writing and talking, but in this case do not give the full information. This may be information that can be used to lead students to make inferences and deductions.

It must first be noted that students not gaining access to a full set of information is not the result of crap teaching. There are numerous valid, and beneficial reasons why we would not want to present everything all at once: complex ideas need breaking down, or we may be helping students think through the content via definitions, analogies,  examples and non-examples and so forth. This information provides students with useful background information so that they can work out the meaning of concepts through induction and deduction.

 The partial information works in different ways: sometimes it provides a context for the learning and potential sources of useful prior knowledge, and sometimes we give information that will allow students to work out what the concept is in a more direct way.

 Nuthall then pieced together through observation, and interviews when and how students interacted with or engaged with information about a concepts. This really is a marvel. As a teacher you rarely get to see where and when students actually interact with the ideas behind a concept, our classrooms are too busy, with too many students and too many ideas being learned (and forgotten) all at once. So this schematic view of it is certainly worth pondering the interactions our students take in a process of a lesson: When? Where?  How?  How many? First exposure? Second? Did they think? Did they infer? Did they copy? Of course this is impossible to know as much of the important interaction  hidden in the mind of the learner. 

Nuthall used the categorisations

  1. Full set of information FSI
  2. Partial set of information PSI
  3. Activity that leads to a full set of information ALF
  4. Activity that leads to a partial set of information ALP
  5. Back ground Information BI
  6. Working out Infromation WOI

 to work out what was needed for a concept to be learned as summarised in the next table.

Interaction/ Exposure number
Additional information
Learned occurs with

Only four required
Learned occurs with
Only four required.
Any one of the blue.
Learned occurs with
Any combination of blue .
Learned occurs with
any combination of blue.
Learned occurs with
And any combination.
Learned occurs with
And any combination.
Nuthall himself said “ Provided a student is able to piece together, in working memory, the equivalent of three complete definitions or descriptions of a concept, that new concept will be constructed as part of the students long term memory” From the table It suggest that four  Full sets of information (FSI) will do the job, as will three provided there is an additional set of partial information.

If there is less than two full sets of information then students will require a total of five interactions with partial information sets.

This makes it essential for teachers to be aware what a full set of information may look like. This is difficult to achieve for every fact and idea you want students to learn.  Ergo, I do not think this is a planning tool, but a key piece of pedagogical content knowledge that will help us plan better teaching sequences.
 This research primarily suggests some useful planning suggestions. So that for learning to take place, students must:
  • interact with a full explanation of concept at least once.
  • interact with the information on at least four separate occasions.
 and that:
  • the more often they interact with the full picture the better for their learning.
  • perhaps breaking down concepts is not always the best strategy as more exposures will be needed for learning to occur for each of the smaller parts and then for the big idea you intended to teach.
  • related information can be deduced, collated and learned from many pieces of information.
  • we have to remember that, no matter how much we manage knowledge, we are entirely reliant upon students engaging with it!
The importance of a full set of information is problematic for teachers as We instinctively strive to break down immense potential complexity into neat, bite-sized chunks appropriate for student consumption. Sadly, this well-intentioned process may not actually benefit student learning; as the most effective teaching activities are often linked to big questions or ideas. This is probably best defined by David Perkins who, in his book “Making Learning Whole”, labels the breaking down of learning into small chunks, rather tongue in cheekly,  as a disease, naming it ‘elementisis’. The problem with elemetisis is that students never get to join the elements back together after they have been broken down for them, so that they may see how the knowledge works as part of a whole.

 Graham Nuthall 2007 The Hidden Lives of Learners NZCER page 127.
 Graham Nuthall Vol. 99, No. 4 (Mar., 1999), pp. 303-341 The Elementary School Journal The Way Students Learn: Acquiring Knowledge from an Integrated Science and Social Studies Unit
David Perkins - making Learning Whole 

Thursday, 7 June 2018

Defining self-regulation and metacognition.

Self-regulation and metacognition share a complex relationship:  both are useful in short term learning and both can be considered long term education goals. Those of us who have strong mechanisms for self-regulation and self-control learn more with less effort, enjoy learning more and go onto live happier and productive lives 
Student academic outcomes are also positively influenced by the use of metacognitive strategies, while good self-regulation is a strong predictor of academic achievement throughout school, for instance preschool children who are good self-regulation are more likely to be more proficient at Maths and reading. Therefore, both self-regulation and metacognition must be viewed as a boon to learning content and not merely an addition. In fact, there can be are “enormous” consequences for ours students in both academic endeavours and in social relationships if they fail to develop robust self-regulatory skills.
Thankfully, self-regulation is a learnable skill, and as such requires practice and feedback as would learning content knowledge. And so…
The next section is about the role of metacognition in the acquisition of declarative and procedural knowledge.
Right now, you are probably thinking along one of three lines:
1.       Great, that sounds really interesting, or
2.       Great, that sounds awfully difficult: or
3.       Great, I already know something about that!
Instinctively, at the very inception of learning our metacognitive monitoring process kicks in. In retrospect, you will recognise all of these thoughts from your experience as a learner, but recognising them and controlling and using them are different matters. For instance, thinking that this section will be difficult could lead to the decision to go off to make a nice cup of tea, and thereby avoiding the effort you think is needed to read this. Alternately, it may be the spur to concentrate, to make sure that you get it. Self-regulation and metacognitive thinking are clearly wrapped up with motivation and its subsequent decision making
Self-regulated learning is our ability to understand and control our learning environment, and involves goal setting, selecting strategies and monitor our progress. The following diagram neatly summarises self-regulation. (adapted from Schraw et al 1996)
The simplest, and perhaps most potent definition of self-regulation is our “ability to inhibit automatic responses” This requires control over our emotions, the ability to focus and refocus our attention onto tasks and on our longer- term goals. When this is in place we can then choose the right cognitive process that will help us best complete the task. 
Metacognition is perhaps the most intriguing part of self-regulation for teachers, as having well developed metacognitive strategies are “the distinguishing quality between good and poor learners” It is quite often given the prosaic thinking about our thinking tagline, that undersells its value. Metacognition simply means “beyond knowing”, inferring that it is about what we know, what we do not know, and the thinking that monitors and controls the learning process. In a sense, it involves us becoming the audience to our own performance. Flavell, the originator of modern educational views of metacognition neatly summated it as “a critical analysis of thought”, in which our knowledge about our own cognitive processes and products (or indeed anything related to them), are seen as something that can be used to regulate and orchestrate these processes. Thus, leaving us with a noble definition for metacognition as the abilities of individuals to adjust their cognitive activity in order to promote more effective comprehension.
Flavell’s model of metacognition helps to define what is useful in practical classroom terms. In Flavell’s model both cognitive and metacognitive processes interact to form our metacognitive knowledge about ourselves, the task at hand and potential useful strategies. The cognitive goals set the context for the thinking to be undertaken and are also the end point. 

Monday, 4 June 2018

The problem with misconceptions

Misconceptions and how students respond to them are key bits of a teachers PCK. This post aims to outline the difficulties they pose to learning and teaching. 

Where do misconceptions come from
Misconceptions can have a strong grounding in our students’ everyday experiences. Misconceptions can lie in the use of everyday language, or they may be partially formed ideas that have persisted as they haven’t yet been challenged. In some cases students have actually seen the phenomena with their own eyes! And seeing, as we know, often results in believing. The word ‘belief’ tells us that our students’ misconceptions can be deeply held to the point of feeling as if they are unquestionable. The importance of this is brought to bear by Graham Nuthall in writing, “What is learned depends upon the prior knowledge the student brings to bear to understand the [new] information.” Here, he is saying that students use their prior experiences and what they know to interpret and make sense of any new ideas being presented. If this ‘knowledge’ is actually incorrect, then the students will not make the correct interpretation of this information and learning simply will not happen. This model of learning suggests that, for learning to take place, there must be enough information to be assimilated into the students working memory before it can then be transferred to the long-term memory. If insufficient information is available - and misconceptions will reduce the amount of correct information - then the new information is either thought of as a different version of a known idea and is absorbed into it, or, alternatively, is simply forgotten.

How are misconceptions different to mistaks?
Although this may sound a trifle hair splitting, there is a useful distinction to be made between misconceptions and mistakes. Misconceptions are genuinely held beliefs:  as a result, they can be difficult for students to spot and to address. Their roots are in preconceived notions and stereotypes, our misinterpretation of concepts and facts, and our confusions common and technical use of language. Mistakes, on the other hand, are often a result of carelessness or of the fact that the thing being learnt is pretty difficult.  Misconceptions often  appear as the  important things to address, and mistakes seem  less so. As teachers we can therefore dismiss mistaks as being less unimportant- “They just made a mistake.” But this is not necessarily the case. We must therefore consider the content being learned and its potential difficulty to determine if dealing with mistakes should be as important dealing with misconceptions

Many factors can go to contribute to conceptual difficulty (as shown in this chart). Knowledge which can be described by any of the conditions on the left-hand side are easier to learn than those found on the right-hand side. Based upon Perkins. .

Beliefs are strong.
Beliefs are also notoriously difficult to shift by logic and reason alone so, more than ever, we need to structure our students’ interactions with the right (and wrong) conceptions. Pedagogical content knowledge, or more precisely our knowledge of potential misconceptions, gives us a decent start point here. Detailed information about subject specific misconceptions is easy to search for, is readily available on the internet and will become well known to you the longer you teach your subject. After a couple of years teaching, you will often find yourself thinking, “They always do that”. It is a genuinely sensible thing to wonder why they always do that. Each teacher experiences these moments, so asking colleagues about common student misconceptions can be a treasure trove too. Once we are aware of them, we can then go on to help students become aware of their own misconceptions; we can scrutinise resources for potential errors; we can design our instruction to reduce the chance of students misinterpreting the information we’ve provided; we can therefore avoid reinforcing or forming misconceptions.

Learner avoidance tactics
Learners do a version of all of these things when faced with a new idea that conflicts with something that they previously believed. Even when the idea presented to them is as true as the passing of time.  Some spot the beauty in the new idea and accept it readily. But not many. Most will either ignore it, reject it, exclude it, hold it in abeyance, or reinterpret it. Few will readily accept the new idea as their new belief as it overrides what they hold as true.

What can teachers do?
Posner and Strike (1992) suggest that the following conditions must be met if students are to correct their misconceptions (or to have them corrected):
  • There must be some dissatisfaction with the student’s current understanding. Students are unlikely to be aware of these, and it therefore falls to us to make them purposefully aware of the ones they hold. This can be difficult, as theories” work for them perfectly well in their everyday lives, and we have to tutor students to become critical of their own thinking.
  • The new conception must be intelligible or understandable to learners. This is where our skill in representing ideas specifically tailored to the learning needs of the students in front of us comes to the fore. Our assessment practices need to allow the students (and teachers) to see that they are ‘getting it’.
  • The new conception must appear initially plausible; it must seem to be a better possible answer than the misconception. Keeping our instruction ‘real’, rooted in what is known (i.e. their prior knowledge), making connections clear and using concrete examples all help students to alter their understanding of things.
  • Finally, the new conception should suggest the possibility being fruitful or useful to them as learners. We can do this by helping students transfer their new understanding and applying it to new examples.

Five things to consider during planning the tackling of student misconceptions:
1.            How can we make students aware of misconceptions?
2.            How could deliberately leading them towards a moment of ambiguity help?
3.            How does making our teaching ‘real’ and connected help?
4.            Why should we keep misconceptions the focus of our assessment?
5.            How might the development of student’s critical thinking help?

[1] Chinn and Brewer 1993- The Role of anomalous data in knowledge acquisition- Review of Educational Research   Vol. 63, No. 1, Spring, 1993

[2] Posner and Strike 1992- A revisionist theory of conceptual change. In Philosophy of Science ed. Duschl and Hamilton.

[3] David Perkins- Making Learning Whole 2009

Friday, 25 May 2018

Using PCK to plan teacher explanations: Keys and Sequencing

In this sequence of blog posts, I have been interested in two ideas: Teacher Clarity of Explanation and Pedagogical Content Knowledge (PCK), and thus far never the twain shall meet. But this is simply not the case. The difference between a good teacher explanation and a poor one is PCK. PCK is not just an understanding of your subject, but also of good general pedagogy. They inform one another. What I hope to do in this post is to exemplify this interaction. It begins with a general idea and will become more specific. So what do we need to know about what makes a successful  teacher explanation.
Understand that there are three factors in making a great explanation” Brown
At the heart of this is an understanding that every good explanation has important constituents: an explainer, a problem to be explained and some explainees (otherwise known as students). For each explanation, we must consider the problem the content itself presents as well as the knowledge and skills of the students so that the input is pitched correctly. We must display sensitivity both to the elements of the explanation the task itself demands and to the social situation of each teaching problem (“how do I teach x and y to Bob?”). In considering both we break down the problem the explanation presents so that the solution can be strategised about and planned.
To plan explanations, the following sequence seems prudent: (modified from Brown)
1.    Analyse topics into main parts or ‘keys’.
2.    Establish links between parts and consider their "best" sequence.
3.    Determine rules (if any) involved.
4.    Specify kinds or purpose of explanation required (context setting, interpreting, thinking, unpicking examples, describing, linking cause and effect and so forth).
5.    Adapt plan according to learner characteristics
How well teachers identify the “Keys” of the explanation is central to their ability to explain; more effective teachers use a greater number of keys. Five kinds of  “key” have been described. For research purposes, Brown and Armstrong assigned each key a cognitive level (1 the least, 5 the most), and I have left these in place as they found that good explainers tended to make higher cognitive demands on their students. This does not mean that they always use for example level 4 type explanations, however; they tend to use a wider variety, and in doing so include more at a higher level.

Cognitive Level
Explanation - Key types
Stating, defining, describing (simple e.g. what something is), classifying, designating.
Comparing, descriptive explanation describing process or structure in detail (e.g. how something works), interpretive (clarifies, exemplifies the meaning of things).
Reason giving, causes, motives.
Conditional Inferring (If…then…).

In order to best sequence may or may not be as straight forward as how the content presents itself. Beware that although certain content appears to naturally fit one of the sequences, it may not be the model that serves the learning of the content that best of all. This is particularly problematic if you aren’t aware of all the other options. For years, I’ve taught the topic of digestion by  applying the logic of that the process itself begins in the mouth and so that my teaching should begin with the mouth and then work down through the digestive tract. The result of this was that, however well the students could identify the organs, they still struggled to explain the big idea of what digestion is. It was not until I re-jigged the sequence of teaching from a part-to-part-to-part structure to a whole-to-part structure did my students start to become competent in both. So now I begin with digested food molecules in the blood being absorbed from the small intestine because they are small enough to pass through its lining. This then naturally leads to a teaching sequence based on what happens to food to make the its molecules small enough to be absorbed. I now find that each organ that I teach about is easily linked to that original idea, giving my teaching a clearer purpose and  that the students have a full understanding of the holistic process of digestion.

The all important alternatives have been succinctly summarised by Rothwell and Kazanas, who propose 9 approaches to sequencing instruction. Each sequence will serve a different type of content knowledge and will help to  place each learning task into a context set by what goes before it. It also provides a useful set of options when you feel that your current order of explanation is not working for your students.

1.      Chronological sequencing.
2.      Topical sequencing.
3.      Whole-to-part sequencing.
4.      Part-to-whole sequencing.
5.      Known-to-unknown sequencing.
6.      Unknown-to-known sequencing.
7.      Step-by-step sequencing.
8.      Part-to-part-to-part sequencing.
9.         General to specific sequencing.
Further Reading.
Brown and Armstrong in Wragg Classroom teaching Skills
Rothwell and Kazanas 1998 Mastering the instructional design process: a systematic approach
E C Wragg and G Brown (1993) Explaining Routledge

Wednesday, 23 May 2018

Trawling for our PCK: A tool.

Planning lessons is so much more than just creating structures and frameworks. Good planning involves us employing our pedagogical content knowledge; it dances at the intersection of our knowledge of:

  • Our subjects.
  • How our subjects are learned: the common misconceptions, threshold concepts and difficult ideas.
  • How students learn.
  • How (or whether) specific teaching strategies work.
Consider the following PCK extraction device as a net to cast over the recesses of your mind to capture  the nuances of  how we need to be able to teach a concept/ idea well.  It is based upon the bloody marvelous tools developed by John Loughran in ‘Understanding and Developing Science Teachers’ Pedagogical Content Knowledge:  though it’s not just for science teachers, this tool has a finely tuned "Cod End" in which the tasty teaching morsels can be captured. A good net is always going to be a compromise between having holes  which are too large and everything can merely pass clean through, and one with too small holes that captures everything in the most cumbersome fashion possible. I believe this set of questions provides an useful balance for  thinking and planning. It’s not a checklist, and there’s no need to use each question: choose which prompts are most useful to you, your students and the content,  as although the example below gives many questions that appear helpful, it’s best targeted at areas where important, difficult concepts or misconceptions lie.

Aspect of PCK
What is the concept to be learned? (a single concept works best for clarity)
What should students know before learning this?
What might they already know?
What misconceptions might they have?
How will you find out about student ideas?
What will they find difficult? Why will it be difficult?
How can this be made easier to learn? Is this idea so important that you will deliberately manage the number exposures over coming lessons?
How will you represent this knowledge so that it is unambiguous to students?
Why is this knowledge important? Is this one of the main concepts of your subject?
Where is this knowledge going? How might it be used in future learning?
How will teaching and tasks/activities help students engage with this idea?  Why have you chosen these activities?
What caution do you need to exercise? How might you teach a misconception?

What else might influence student thinking on this? How might they know what they know?

Although the example given below is a science one many of my colleagues across all areas of the curriculum have found it a useful prompt to thinking about their teaching and a way of pulling ideas together before they plan lesson sequences

Aspect of PCK
Science example
What is the concept to be learned? ( a single concept works best for clarity)
How dissolving takes place. Year 7 beginner science.
What should students know before learning this?
Particle model will help students understand how this process takes place.

Key terms: Solvent, solute and solution
What might they know?
Lots of examples of things that dissolve things and things that are dissolved.
What misconceptions might they have?
That the material being dissolved disappears when in solution.
Students find the change of state of the material being dissolved confusing, often think of it as melting.
This is exacerbated by
How will you find out about student ideas?
Ask them to predict the 100ml of water to 100 ml of ethanol. Do they know taht particles can be different sizes in different materials? How aware are they with the spaces between the particles?
What will they find difficult? Why will it be difficult?
Visualising what is happening to the particles do when in solution.
Distinguishing the key terms due the similarity.
When materials dissolve they, on the surface, look like they have disappeared.
How can this be made easier to learn? Is this idea so important to manage the number exposures over coming lessons?
Rice and Pea model will help visualisation.
Multiple exposures over several weeks to the terminology.
Work from concrete (examples) to the abstract (particle model)
Will have a venn diagram activity (on stand by for this lesson) for when we study changes of state to distinguish between dissolving and melting
How will you represent this knowledge so that the it is unambiguous to students?
Rice and Pea model.
Concept map of key terms.
Discuss examples of solutes, solvents and solution before defining them.
Why is this knowledge important? Is this one of the main concepts of your subject?
2/3rds of the earths surface is a solution. Living things rely upon solutions for transport and function.
Lots of complex science is based upon this.
Where is this knowledge going? How might it be used in future learning.
Students will soon learn about the factors that affect the rate of dissolving.
Students will use this knowledge to separate the soluble and insoluble substances (i.e. is a property)
Later students will study ideas about concentration, osmosis, rates of reaction.
How will teaching and tasks activities help student engage with this idea?  Why have you chose these activities?
Rice and pea makes what is happening accessible and a reference point. As does the simple summary solute+solvent=solution.
A brief practical on dissolving ( and its subsequent write up) allows for plenty of application of new  language and ideas.
What caution do you need to exercise? How might you teach a misconception?
Care must be taken when talking about the rate of dissolving. Using terms such as “fastest” are misleading, but will be part of student every day language.
Important for the knowledge to be applied in different situations so it does not become “inert”. Practicals will help with this.
What else might influence student student thinking on this? How might they know what they know?
Lots of TV adverts proclaim fast action, when they mean in a short period of time.
Kitchen/cooking experiences maybe provide some useful start points.
Reminding of the taste of sea water will remind them that solutes do not disappear.
What signs might students show that they are “getting it”? What questions might they ask that anticipate next steps?
Students refer to “the solute” as opposed to sugar/ salt, and “solvent” instead of a water

Are all solvents liquids?

Are only solids dissolved?

So are some particles smaller than others?

Are the solute particles fitting in between the “gaps” between the solvent particles?

 Understanding and developing Science teachers Pedagogical Content Knowledge by John Loughran et al. 2006 Sense Publishers.