What can teachers do to tackle student misconceptions? An example.

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.

I would humbly add that the role of planned multiple exposures to the correct conception is also essential. Undermining hard held believes is going to take time to shift. 

Strategy 1: Encouaging dissatisfaction.

These tasks are designed to make students ware of the misconception, in a way the makes it absolutely clear that the student did not know that they did not know. For this to happen the alternate answers must at least seem plausible and contain the same kind of content as the correct answer.
The following example, fails to do this with only one plausible answer as John Fashanu, Noel Edmonds and Skeletor did not ride the Tour de France until the 1980's. That was a joke by the way, I point out this not as way of being facetious but as a way of emphasising that it is quite easy to accidently teach a misconception. 

For more on the design of multiple choice question I highly recommend this from Vanderbilt University

In this science example, students often think that the current comes from the battery, jumping out when the circuit is connected. In addition this misconception is linked to another where student believe the current is "used up".  So this dealing with this first will allow this idea to be transferred and applied to this situation. It is therefore going to be fruitful, and be part of a sequence of multiple exposures to the correct concept.

Note that only three options are given in this question , but importantly all answers are plausible.  So rather than sticking to a steadfast rule of  say "I will always give 5 options", the plausibility of the content takes precedence. 

When deliberately trying to exposure a misconception, I tend to do so with a whole class discussion. Using techniques that involves as many students as possible, for instance: asking for hands up fro each response, before asking a few students why they think what they do. Interestingly this year I had one student, almost instantly,  asking " is this about a metals delocalised electrons?" He knew the answer but was not confident about, so exposing it and reinforcing the correct answer can help those with and without significant prior knowledge on the content. If he had of been confident my tactic would have been to  defer my answer in an attempt to create a bit of ambiguity, to encourage dissatisfaction, and further thought. Normally stuidents think ( and they did even when this student spoke up) that the current comes from the battery. I try to avoid telling them that they are wrong, as I wan them to doubt it themselves first. So ambigous responses such as "mmm interetsing" help do this. 

Although, I may use a similar or even the same question in a Pre Quiz to a module, when attempting to incite some dissatisfaction with the student’s current understanding it is important that we focus on one concept at a time whenever possible. Clearly some misconceptions will have complex and interconnected reasosn so this is is not always possible. 

Strategy 2: A plausible and intelligible alternative

The next slide has my follow up to this discussion, I plan to not give the definitive answer until after the students have discussed the next slide. This slide is intended to make clear in the simplest possible terms what the correct idea is. In this case that the electrons that form the current are already present within the components of the circuit, and that on completion the battery provides a 'push' to make these charges flow. The visual shows this, and the open switch, allows for discussion of what the battery does. 

I often ask prompting questions, more or a less in this order:

1. What are the blue circles representing? 
2. What charge do they have?
3. Are they "flowing" or moving in this image? How do you know? 
4. What if the switch was closed, what would then happen? 
5. What do you notice about the amount of current before and after the component? 

This section of the lesson of the lesson attempts to do to things. Firstly have the students acknowledge that their origional think was indeed a misconception and, secondly,  present them with plausible and intelligible. Many students "get it" once they see the image and begin to articulate why they are wrong. 

I often go back to the origional question and ask who wants to change their mind. This is an importamt classroom cultural moment as praising this encourages thinking in what Doug Lemov would describe as a "culture of error". 

This image is a screen shot from the wonderful phet simulation. At this point the students are in now in need of a succinct and clear teacher summary of the correct answer, the simulation provides the perfect backdrop to this. 

Strategy 3: Realness.(Where possible)

In this lesson the students would then build a simple series circuit and measure the current at two points to show that this phenomena is real. This is also another exposure to this idea.

Strategy 4 Multiple exposure (within the lesson).

The lesson has a review based upon another model of current, comparing the bike chain to current and circuits. 

Students very quickly work out through discussion that the pedals represent the battery, the back wheel would be the component and the chain the wires. With minimal prompting they start to associate the links associate the links with the charge. following this further insights into the behaviour of current become clear. The links are evenly spaced; they dont move until they are pushed; they do not jump around the chainring (battery) if there is no pushing. This concrete example ( and therefore more plausible) helps students see their new knowledge as fruitful and leading to new understanding. 

Strategy 5: Multiple exposures (across lessons). 

As this topic develops other concepts must be added such as potential difference and resistance. These are opportunities to build on what hopefully will have become prior knowledge. A good example from future lessons is this classic teaching image. In the image the current is labelled as Amp and needs the push from the Potential difference (volt) to get moving. 

Strategy 6: Feedback.

Students are asked to describe in writing the relationship between the current, potential difference and resistance that is encaspsulated within the picture. They are asked to use the leave a line between each one that they write.  This provides a space where they can reflect on what they have written correct wrong ideas and add missing ones in the light of a model example; class discussion; teacher prompts; or teacher written feedback. 

A copy of the lesson resources are available here 

An update on the Meta-cognitive wrapper. Why and How to use them.

The metacognitive wrapper in many ways is the perfect storm of a metacognitive strategy, in both its structure and procedure. It structure utilises prior knowledge, and engages both strategic thinking and motivation, while it’s procedure beginning before a task or lesson has begun allows students to gain some form of control over their thinking and emotions from the off, and then orchestrate their thinking over the duration of the lesson. The wrapper wraps around the lesson or task, ensuring that reflection occurs and that long term metacognitive behaviours are valued, promoted and developed.

Put simply a metacognitive wrapper is a task that is completed at the beginning and at the end of an activity or lesson, and is designed to help students plan or at the very least consider their thinking over a lesson. The integration of thinking and content and the opportunity for forethought have big impacts on learning ^[2] Studies have shown the metacognitive behaviour of self-questioning to have the biggest effect if carried out before the lesson, while slightly lower after the lesson and much lower during the lesson^[3]. Common sense would suggest that trying to be self-questioning during a lesson could be distracting to all but the most able learners. Echoing what we know about the types feedback most useful to beginner learners that complex feedback while learning can be overwhelming, and should be corrective in nature and focussed upon content knowledge. The wrapper caters for this by emphasising metacognition before and after the act of learning.

Wrappers tend to have a consistent of design although the components are not always equivocal, and some will not be useful for every task.

Designing the wrapper

1. Learning intention should be referenced.

A wrapper should firstly include a statement to make clear what the students are about to learn. This should be broad terms with only sufficient detail to make clear the types of ideas and thinking that may be useful.

2. Prior knowledge should be prompted.

The first question should always prompt useful content knowledge. It is preferable to phrase this speculatively as in:

“What might you already know about …? 

The “might” helps keep possibilities open early in the lesson granting opportunity to come back to these original thoughts, so that students can validate, dismiss or correct them or even become more confident in their own thinking. Although it must be noted that becoming less confident in their knowledge is just as valid a response, as they could either be unlearning a misconception, which is a difficult process or be questioning why they believe something rather just accepting something is right. That is to say, they can practice being metacognitive.

3. Student goal setting.

The third element is a target setting one that could be the visualisation of a success criteria or the setting of a self-reward for success. This could this be a way of tapping into the intrinsic learner motivation? Findlay and Cooper (Locus of control and academic achievement ) demonstrated that those students who are internally motivated perform better than those who delegate this responsibility. An alternative focus may be to ask about the usefulness of what is being is learned, as task value is a powerful metacognitive strategy (DeBoer)

What do you want to learn about “Electromagnets” today?

Or

How will you know that you are being successful today?

Or

Why is it important that we understand why “earth quakes” happen?

4. Prompting Strategic thinking.

Students will benefit from help in working out concrete ways of engaging with the learning task.  This may be structuring their thinking or how they could go about completing the task. For example:

What steps will you need to take to complete this task?

or

What ways of thinking might help you solve this problem?

5.Affective control: Learner attributes.

The final element to a wrapper is to focus on a learner attribute such as motivation or being resourceful. This is often the quickest win for the students and for the teacher.

How motivated are you today?

or

How resilient are you feeling today?

Finally prepare the end part of the wrapper by changing the tense of the questions. So What do you already know about…?” turns into “Was the knowledge you had useful?”, or “How might you plan your work to ensure quality?” turns into “did your plan help you structure your work in a high quality way? The premise here is to allow them to recognise changes: in what they know,: in  how confident are they in this knowledge In how to go about solving this kind of problem, after all change is learning.

Procedure for using a wrapper.

The process of using a metacognitive wrapper is a simple one, albeit with nuance. It starts with

1.Student individual thinking time.

Have the questions selected available at the start of the lesson. You may need to introduce the lesson topic, the purpose of these questions and to make clear the idea that it is OK to be wrong at this point in time, but little more. Allow the students 4 or 5 minutes to ponder and note down their ideas.

2. Whole class response.

Randomly select a few responses for each of the posed questions and record upon the board thereby make their thinking visible. Make a point after the initial trawl of asking if anyone has something to add. There is no need to judge any responses as right or wrong at this point even if their response is a negative one such as "I'm not motivated today ", as they have already engaged in the type of thinking you require. The important part here is that we communicate through the procedure that “your motivation matters and it is your responsibility.” However, be aware of bandwagon jumping with negative comments. Peer culture is very strong, and if you find yourself with growing negativity and students playing to the crowd. If so, challenge it by making it clear what the culture for learning needs to be like for their success. This may not happen overnight, but must start somewhere. Why not here? The students are voicing opinion of their schooling, they are engaged in what you want them to be engaged in.

Seeking multiple responses provides the students with a palette of choices they can make. Simple phrases like “You can steal any of the ideas you hear.” encourages students to begin to reflect on best methods of working and make active choices.

3.The lesson or the task.

Although the procedure does not require the teacher to actively promote metacognitive thinking, you will be sensitised to how the students are going about the learning process. alongside the teacher led conversations of a classroom, you will have opportunity prompt some individual students in controlling their metacognition. The language of choice and the use of ambiguous responses to their questions, such as “could be”, encourages student ownership of the problem at hand, and therefore gain some experience in utilising their metacognition. Some students will require highly structured choices, as in “you can either do A, B or C” while others will be able to respond to “So what are your options here?” Ultimately the students must make the decision of what they do next.

4. Individual reflection.

Using the end wrapper questions, once again a moment to reflect and prepare responses. Ask the student to note down their responses.

5. Whole class debrief.

Again, selected at random, although through the discourse of the lesson you may want to highlight particular students who may have been successful (or not) in controlling their thinking, changing their minds, getting unstuck or being resilient. There is no need to record their responses as what important here is the conversation that debriefs their process. You are likely to hear are stories of improvement and by highlighting these attributes within a specific learning activity helps makes them more visible to all learners. Each part of this review is important: the content, the strategies, the feelings, the attributes, as all are intertwined in the experiences of the students (Nuthall)

The motivation to engage is a vital part of the process, so I tend to use this as one of the prompts more often than not. The conversations around motivation are always interesting and often highlight its fluctuating nature as the lesson ebbs and flows, but how if we are aware of it we can begin to learn how to control it. It is best summarised by an anecdote from a first-year teacher following a training session. He had a busy day, a full teaching day, coursework marking with a looming deadline, a lunchtime mentor meeting and then an afterschool training session on the charms of metacognition. He said as much as we started. All I could do was to thank him for his response and for being there. The session went well and we concluded by going back to the wrapper task. He could not wait to respond to this. At first, he accused (in the best sort of way) me of “tricking him into being motivated”, We revisited the original questions and as we did the conversation became centred around who had made it important. He responded “it was me, I made it important, I was tired and had didn’t want to be here, but I realised that my motivation was important and I had to find a way of being motivated”. The focus became how he as learner had taken control of his thinking and actions. he had become metacognitive. Learners often just need the chance to catch themselves doing it, if I had challenged the unmotivated response of the teacher or of students then I could prevent any chance of this experience and realisation taking place. In essence, the teacher needs mechanisms to keep themselves out of the way to allow students to practice self-monitoring while completing tasks and learning. So, the next step in increasing student self-regulation and metacognition is to increase student control.

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[1] https://serc.carleton.edu/NAGTWorkshops/metacognition/teaching_metacognition.html Accessed 29/07/17

[2] Hattie, Biggs and Purdie 1996: Effects of Learning Skills Interventions on Student Learning: A Meta-Analysis

[3] Huang 1991: A Meta-analysis of Student Self-questioning strategies

Assessing learner confidence.

“Doubt is the origin of wisdom.” Descartes.

It is sometimes useful to question a student’s confidence about a certain piece of knowledge so that we can find out the difference between what they actually know and what they have been able to deduce It is pretty easy to spot a student who ‘doesn’t know what they don’t know’. It is also fairly easy to spot their antithesis: the student who ‘knows what they know’. It is with the students in between these two poles who can form a grey area that can be tricky for teachers to interpret. The following crude table may help untangle students’ knowledge and their confidence in it. From this we can start to figure out what the next teaching steps could be, as students who are confident in their knowledge of a concept have different requirements those who are less confident.

Student’s knowledge is …	Confidence in this knowledge …	Also know as …	Potential initial teacher response
Wrong.	High.	A misconception (or in correct belief)	Make it clear why the answer is wrong. Provide lots of evidence/ ideas of the correct answer. Move them to wrong knowledge/ low confidence.
Wrong.	Middling.	Uncertainty.	Ask them why they think this? Make clear what their doubts are. Move them to wrong answer/low confidence.
Wrong.	Low.	A wild guess.	Give a clear correct explanation.
Right.	High.	Students know they know as well as how they know it. Expert.	Move on. Connect this knowledge to new knowledge.
Right.	Middling.	Students think they know this, but are uncertain.	Reinforce, review, reflect, and rehearse.
Right.	Low.	A lucky guess or hypothesis.	Praise correct answer. Ask why they think this? Move them to right answer/middling confidence.

How to get information on student confidence

To get information on student confidence in a concept, we must look beyond what is said and begin to look at how they are saying it. Here we are in similar territory to Radio Four’s ‘Just a Minute’ in which the panel must speak for a minute without “hesitation, deviation or repetition”. When we listen to (or read) student responses, we are constantly and subconsciously judging the confidence they have, instinctively clarifying things for those who appear confused, nodding in encouragement of those lack that are struggling with confidence. But this remains a process that operates at a liminal level of our consciousness; rarely do we ever bring these actions into being consciously, nor do we exploit the students’ responses as a form of data to inform our planning for them.

It is relatively straightforward to obtain information from these sorts of interactions that you and your students will find helpful. Again, like the light bulb example, the content needs to be significant for this to be worth doing.  Two helpful ways of structuring our assessment of student confidence are:

1. Making it explicit by using self-assessment.

2. Making it implicit within the task or question.

The first method, making it explicit, can be as simple as a multiple-choice question with an attached check box in which the student can indicate their level of confidence about their answer. Look at this number sequence, as an example:

-8.8, -9.0, -9.2, -9.4 …

What is the next number in the sequence?

A -8.6	I am ●     Sure about this ●     Fairly sure ●     Guessing
B -9.5
C -9.6
D -10

.The student complete the problem, and ticks the statement that best represents their confidence, which provides the teacher with two pieces of information to make decisions about what to do next. We can see how we would move student on who were correct and confident, where we may ask students to explain how they derived their answer for those who were correct but not confident in their response. For in correct responses we may decide to re-teach the concept. 

An alternative way of structuring pre-quiz questions to assess confidence is to simply make it as a potential student response in a multiple-choice question. By adding an “I don’t know” option allows students, to express doubt, rather than guess. Remember a correct guess will hide the information that you are seeking about student prior knowledge. 

An example question.

Which of the following are true?

A) In order to reduce manufacturing costs, companies make their products smaller.

B) In order to reduce manufacturing costs, companies computerize their production.

C) In order to reduce manufacturing costs, companies run nightshifts.

D) Both A and B.

E) Both A and C.

F) Both B and C.

G) No Idea.

The “I think this “ grid.

A more sophisticated structure may reveal useful information and engage student reflection about what they know and how well they know It can be drawn from this  well-designed tick grid. Consider this task taken from a History classroom.

Why was the Enabling Act so important?

Statement		I am sure this is right	I think this is right	I think this is wrong	I am sure this is wrong
A	It allowed Hitler to become President
B	It meant that Hitler had won the election
C	It allowed Hitler to make laws without the Reichstag
D	It gave the Nazis a majority in the Reichstag

This simple structure can be illuminating for teachers to base their classroom decisions on evidence that is there. Students that are sure about the correct statements may not reveal as much as students who are sure about incorrect ones, but perhaps the most useful aspect will come from the number of “ I think..” responses given. This begs the question for the teacher “How do I help the students become surer about the things they know?” and “Have the students been exposed to the information sufficiently to allow them to be confident? The seemingly simple structure, engages students in thinking about the content and how well they understand it. 

Tackling Misconceptions.

Encouragingly this simple technique, with questions focussed upon misconceptions and known student difficulties, can help provide one of the conditions needed for students to correct their misconceptions. Once more, a teachers Pedagogical Content Knowledge provides the insight necessary to design these questions.

This following Science example utilises some common misconceptions, and confusions to do this. There are also two correct answers, which adds a richness to the activity. If, as in most multiple choice questions, there was only one correct response, once figured out the students would stop thinking. To avoid student means end thinking these tasks should be introduced by stating “ All of these statements may be true, they may all be false or any combination of true and false” Ultimately we wish for students to be confident about the correct answer and the wrong ones. Why do solid ionic compounds do not conduct electricity?

Statement	I am sure this is right	I think this is right	I think this is wrong	I am sure this is wrong
The ions do not have enough space in between them
The ions can not move
There are no delocalised electrons
There are strong electrostatic forces of attraction

As Posner and Strike (1992) highlight that for students to overcome misconceptions there must be some dissatisfaction with their 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. By enabling students to doubt what they think, or doubt what the answer is, we can begin this process. From doubt the journey to wisdom begins.

How good am I at explaining?

As teachers, our audience, our students can be a great source of feedback upon our craft. They see you teach more than you do. So one way to develop our ability to explain things well is not only in their understanding of the subject, but also in identifying what aspect(s) we need to improve upon. This may be a structural, signalling, clarity or supportive feature of your communication. Further details can be read here and here and here.

These features are broken down in the following student voice survey. As always I worry that a checklist in the wrong hands turns into a management tool, and that is not the intention here. So if anyone tries tell them to do one. This is a professional reflection tool, for teachers to check their own classroom practice on their own or with some feedback from their classes.
A downloadable version can be found here.

My teacher...	Always	Mostly	Sometimes	Rarely	Never
explanations are clear and understandable
goes at the right speed
teacher makes clear points
teacher loses track of what they are saying
teacher says urr, um, em during their explanations
teachers explanations emphasise important ideas
explanations contain extra, unhelpful, statements
Explanations review or summarise  key ideas
Makes mistakes when explaining
Finish the explanation
Build up/ breakdown complex ideas into chunks.
Remind me of what we have already studied
link ideas together
Make clear what they are about to explain
Make useful notes on the board
Point/ highlight key parts of diagrams or idea on the whiteboard