February 12, 2018

An example of how research can benefit your practice – Vicki Cook

As a newly qualified teacher, research has been key in helping me to develop my practice. I have found that research can be particularly useful when trying to resolve issues that arise in the classroom.

For example, as we progressed towards October half-term, I found that behaviour in my classes started to slip. Students would enter the classroom in drips and drabs and were slow to settle. Often, a quarter of the lesson would go by and only the register had been completed. I was giving out over 10 warnings every lesson, and adding time to each lesson for all students. It was clear that my students were not motivated and I was concerned that the students were not progressing as they should.
Although I had asked for advice from members of staff at the school, the various strategies that I had tried were not effective in the long-term. At this point, I decided to turn to research to help me. As teachers, we often focus on the behavioural problems in front of us, not the cause. I needed to find a way to improve behaviour, by tackling the motivational issues that were causing them in the first place.

Research showed me that too often, there is a focus on what not to do in class, as opposed to what to do (Becker, Madsen, Arnold and Thomas, 1967). This is reinforced by more recent evidence, showing that when we punish a person for behaving badly, we leave it up to them to discover how to behave well (Maag, 2001). According to Kaplan, Gheen and Midgley (2002), emphasising mastery goals in class reduces the likelihood of students disrupting lessons. Positive reinforcement can be used to manage classes and enhance skill performance (McLeod, 2015). Students take rules and responsibilities more seriously when there is a common approach, from which they benefit.

I introduced a reward based system called Class Dojo with my groups. Students can be awarded for positive actions, but points can also be deducted for negative behaviour. I believed that this system would have three main outcomes. Firstly, I hoped it would motivate students. The incentive of parental contact for students with the most points led to healthy competition within my classes. As well as this, my expectations would be reinforced every lesson, as Kaplan et al. (2002) had suggested. Each time a point was given out, students would know what it had been given for and why. Finally, I wanted there to be an attention on positive behaviours, as opposed to negative.

Very quickly I found that this system was having a positive impact on my lessons. The number of warnings that I gave out each lesson was reduced, as was the number of detentions. I rarely added minutes to the end of the lesson. Students were more enthusiastic and willing to contribute their ideas. In terms of data, most students reached or exceeded their end of year targets. This demonstrates that the use of a rewards based system can be a success. I ran a survey to see what impact using Class Dojo had on my students. It was clear that they valued receiving positive points, and felt more motivated in class based on its use.

To conclude, this is an example of how research can be used effectively in the classroom to resolve a problem. By researching an issue and trialling different strategies, teachers can become reflective practitioners that use evidence-informed ideas to develop their classroom practice. Teachers need to constantly evolve to meet their pupils needs, and research is fundamental in achieving this.

References

Becker, W.C., Madsen, C.H., Arnold, C.R. and Thomas, D.R. (1967) The Contingent Use of Teacher Attention and Praise in Reducing Classroom Behaviour Problems. The Journal of Special Education 1(3): pp 287-307.

Kaplan, A., Gheen, M. and Midgley, C. (2002) Classroom goals structure and student disruptive behaviour. British Journal of Educational Psychology 72(2): pp 191-211.

Maag, J.W. (2001) Rewarded by Punishment: Reflections on the Disuse of Positive Reinforcement in Schools. Exceptional Children 67(2): pp 173-186.

McLeod, S. (2015) Skinner – Operant Conditioning [online]. Available at: http://www.simplypsychology.org/operant-conditioning.html


January 08, 2018

Can’t do maths? Try Fermi problems instead! – Jeremy Burrows

I talk to Jean - an intelligent, articulate Glaswegian who left school with no qualifications - over the internet. I told her about my essay on re-engaging students who are “switched off” to maths.

“I can’t do maths.”

“Perhaps you could if you were taught using Fermi problems.” Being keen to try this approach, advocated by some of the literature, I told her how Enrico Fermi solved problems such as “how many piano tuners are there in Chicago?” without any data, using his knowledge to supply defensible estimates.

“I don’t care about piano tuners in Chicago.”

“Fermi problems can be about anything,” I said. “The teacher should choose a problem which is meaningful to their students.”

“How?”

“You’re interested in cycling, so … how long would the averagely fit person take to cycle from Land’s End to John o’ Groats?”

“I don’t know. Two weeks? Three weeks?” Jean was engaging with the problem, but she was guessing. She needed some scaffolding.

“Don’t guess: use your knowledge. How many hours a day will they spend in the saddle?”

“Eight.” This sounded too high but I didn’t want to discourage her, so I said nothing.

“What will their average speed be?”

“40 mph.”

No way! That’s the speed of a world champion, not the averagely fit person. I challenged it, and after discussion Jean settled for 15mph.

“How many miles will they cover each day, riding at 15 mph for 8 hours?”

“120” was Jean’s instant response: she was “doing maths” without even realising it!

“What’s the distance from Land’s End to John o’ Groats?”

“I don’t know. About 1,000 miles?”

The actual answer is 874. I would have accepted 1,000 as an estimate, but she had guessed. You mustn’t guess when solving Fermi problems.

“Don’t guess. How can you estimate it?”

“I don’t know.” Jean was slipping into “maths lethargy”, but I was not going to let her give up.

“Suppose I tell you there’s a sign outside King’s Cross saying Edinburgh 401 miles? So London to Edinburgh is about 400 miles.”

“1,000 miles is two and a half times that.” Jean was re-engaging, and we were back in the hunt!

“Think about the map of Britain. Is Land’s End to John o’ Groats two and a half times London to Edinburgh?”

A pause, then: “Yes, it’s about that.”

“Good. So you can defend your figure. How many days will it take to cycle 1,000 miles at 120 miles a day?”

“Eight.”

“What’s 8 times 120?”

“960. Oh! So nine.”

“Is that your answer? Nine days?”

“Yes,” said Jean. Then, “No! Some days they might not do 120 because of punctures, or hills. So, ten.”

“Is that your final answer?”

“Yes.”

“Are all your numbers defensible?”

“Yes.”

“OK. Let’s check it.”

I consulted Wikipedia. Land’s End to John o’ Groats cyclists normally take 10 - 14 days. Jean’s sense of accomplishment when I shared the link was palpable: she had just solved a Fermi problem and absolutely nailed it! In doing so she had multiplied 8 by 15 and 120 by 8; divided 1,000 by 400; estimated comparative distances; and identified and applied an appropriate rule of rounding. She had “done maths”; and I intend to incorporate Fermi problems into my teaching practice.


Mind the Gap! (between what is taught and what is learned) – Jeremy Burrows

I had three Latin teachers. Between them they taught me everything I know about Latin … and a whole lot more besides. It is this “whole lot more” which concerns me right now. We have taught something to a class, but that doesn’t necessarily mean that all of them (or even any of them) have actually learned it. In my previous career with HMRC I was concerned with closing the “tax gap”: the difference between the amount of tax which was owed and the amount of tax which was actually collected. In my new career as a teacher I am concerned with closing the “learning gap”: the difference between the things we teach and the things our pupils actually learn.

In mathematics, this problem is particularly acute. Children do not like learning mathematics. Boaler (1996, 1997, 1998) and Nardi & Steward (2003) have conducted studies which offer some very keen insights as to why this is: it’s all down to the way in which we are teaching them. When I learned woodwork at school, they didn’t just show me how to use a drill, tell me to drill 16 holes in a piece of wood, and then move on to the next skill as soon as they judged that I had mastered drilling holes (or move on even if they didn’t judge that I had mastered drilling holes). They taught me woodworking skills in context, and I actually used them for a purpose. I made a box, with dovetailed corners and a hinged lid. I veneered a chess board on the top and a backgammon table on the inside. I never finished it, but that doesn’t matter: I learned the skills and what they were for. I used the skills in order to make something. I have not forgotten those skills.

In mathematics, we just seem to teach the skills, without any context, and then move on. We cannot take time to explore how those skills are used in practice, to set them in context, because then we wouldn’t have time to get through the whole syllabus. And we must teach the whole syllabus, mustn’t we?

Must we?

In Boaler’s comparative study, the pupils who were taught the traditional way covered the whole syllabus. The pupils whose teaching consisted of open-ended mathematical investigations did not. There were gaps in their teaching. But … they performed better in their examinations, because the “learning gap” was smaller. They were taught maths with a purpose. They “made boxes”, rather than just “drilling holes”. At the end of the day there was a closer identity between the maths they had been taught and the maths they had learned, and they understood how to use what they had learned.

Maybe we need to spend more time in the mathematics classroom “making boxes”, and not be afraid if this results in a “teaching gap”. It is, after all, the “learning gap” that matters.

References

Boaler, J. (1996) Learning to lose in the mathematics classroom: a critique of traditional schooling practices in the UK. International Journal of Qualitative Studies in Education 9 (1), 17 – 33

Boaler, J (1997) Experiencing School Mathematics: Teaching styles, sex and setting. Maidenhead (Open University Press)

Boaler, J. (1998) Open and Closed Mathematics: Student Experiences and Understandings. Journal for Research in Mathematics Education 29 (1), 41 – 62

Nardi, E. and Steward, S. (2003) Is Mathematics T.I.R.E.D? A Profile of Quiet Disaffection in the Secondary Mathematics Classroom. British Educational Research Journal 29 (3) 345 - 367


April 18, 2017

Stepping Backwards to Move Forwards: A very honest reflection – By Lauren Atkins

The end of term was fast approaching and I was, like most, in need of a break. I was so pleased with my progress this term and was very much looking forward to being that one step closer to finishing the course. Then the morning of 22nd March came, my formal observation with my Head of Department. I had avoided having a formal observation with my Head of Department for the past couple of weeks because I wanted to focus on my areas of development and show some improvement.


The lesson came and pretty much everything went wrong. I was settling the class when I realised I was in the wrong classroom and another teacher was lining her class up outside. The starter task took 20 minutes instead of the designated 10, not good when you have decided to include a whole host of activities within the lesson. The students did not seem their usual, engaged selves and I was faced with 30 distant looking faces staring at me. Let me confirm here, these faces were not that of students who were gripped and mesmerized by my teaching, more disengaged and most likely thinking about what they were having for lunch that day from the school canteen. The activities were unappealing and you could see that the students were not impressed as they dismissively wafted the worksheets I gave them and looked at me as if to say “Miss, why are we doing this?” At this point, I received several echoes of “Miss, what do we have to do again?” It is fair to say at this point, I knew things were not going great and I wanted to run out of the classroom; I have never wanted a fire alarm to have go off, anything to leave the lesson. I could picture my Head of Department highlighting the boxes on my observation form, and I just knew that this was not going to be the result I had hoped for. After delivering my verbal feedback she slid the form across the desk; I felt embarrassed and disappointed. I folded the form up and placed it in my bag with the plan to shred it as soon as I got home.


That evening, I was sorting my planner out and I found the observation sheet inside it. I was thinking about the lesson and the bemused faces of my students throughout. I was frustrated that a lesson on Civil Rights with a class usually so involved was so flat. Then I thought about the planning process. Usually, I plan my lessons with the focus in mind and then decide on tasks I know my students will respond to. I didn’t do that on this occasion, I planned to please my observer and ultimately, I planned with ‘outstanding’ in mind, not my students; I had taken a step backwards. Recently, I had changed how I planned which meant that my lessons were more engaging for my students and they were central to the planning process, unfortunately the observer did not see the students at their best because I had prevented that from happening. If I had thought about the tasks properly, I would have known that they would not have bought the best out of my students. However, despite taking a step backwards here, I decided to use this lesson to move forwards. Yes, you could argue I was making the same mistakes as I was in September, however, I was reflecting on them differently and able to identify the problems. I made a promise to myself after this lesson that I would resume my usual planning process and focus on having the foresight to know what tasks would get the best out of my students. This observation highlighted to me the importance of everything I had learnt, sometimes you do need to step backwards to move forwards.


Increasing student voice in class discussions – By Lauren Atkins

When facilitating class discussions, I was asking the same questions, ‘what do you think of this?’ or ‘how is this historical event important?’ I wanted a strategy that allowed students to identify where an answer could be challenged or developed without me asking the questions. The card technique was recommended to me by a colleague and I decided to try it out. I gave students cards with ‘challenge’ written on one side and ‘develop’ on the other. Students were invited to hold up the cards when they wanted to challenge or develop their peer’s answer. Students could use these throughout the lesson. Additionally, I would begin a discussion with a basic question for example, ‘why was the Gunpowder plot important?’ Immediately, I found myself facilitating discussions and my students were leading them. My role changed from asking various questions to simply select students by name; the student voice increased greatly! Instantly, students were looking for ways to challenge or develop one another’s answers. The quality of response improved as they were explaining their points in greater detail. On occasions, I would find myself gesturing to students to keep talking so they developed their response. From a teaching perspective, I was able to observe my students debating with each other rather than thinking of questions to encourage discussion. The challenge and develop cards help to improve students written work too because when I mark their books and write ‘how can you develop this answer further?’ or ‘how could your argument be challenged?’ students have a better idea of what I am referring too. If on occasions students found this difficult, I would direct them to the discussions we had in lessons to prompt their thinking. Particularly for higher attaining students it provides an opportunity for them to access higher order thinking skills. By challenging, they are analysing and evaluating arguments. I have since used this strategy with my other classes and it has been a success too.


March 08, 2017

Tasty Teaching


Tasty Teaching


Chemistry is an abstract subject riddled with possible misconceptions and areas for confusion. One of the educationalists who made great contributions to tackling this was a Scotsman, Alex Johnstone. He approached chemical education from an information processing perspective, which views the mind in a similar way to a computer. The best way to deliver chemistry to young people, he argued, was to introduce challenging ideas in a concrete way first of all. There is perhaps no more concrete of examples to students than food and drink, and these have worked wonders for engagement and understanding.


To demonstrate the concept of conservation of mass in chemical reactions, it is common to carry out reactions on scales to show that mass is not created or destroyed. Inspired by Johnstone, I instead bought a pack of microwave popcorn and asked my Year 10 pupils to predict whether the mass of the pack would go up or down, or stay the same. To my surprise, the pack lost mass as well as whetting the appetite of the class before lunch. Students explained that this was caused by the pack not being air tight, allowing steam to escape. When it came to chemical reactions, they had little difficulty then applying their knowledge to explain mass changes in open and closed systems.


Popcorn typically goes down well with a drink however, and it was a 2L bottle of Pepsi Max which served me in demonstrating trends in the Periodic Table to both Year 8 and Year 10 classes. Using the bottle as an electron, I asked one student to hold onto it closely while another tried to take it off them. Of course, the ‘electron’ was held. I then asked the student to hold the bottle at full arm’s length, and repeated the exercise. The bottle was easily taken, and each class managed to use this to explain why elements lose their electrons more easily as their atoms get bigger.


Last but not least, chocolate. When tasked with teaching bottom set Year 10 classes about chemical formulations, I looked to the ‘concrete first’ approach for help. Chocolate is a complex formulation of cocoa, sugar, milk, and other ingredients, and the composition affects how it looks, tastes, and feels. My technicians were able to find the best white, milk and dark chocolate money could buy at Asda, and the students did the rest. Initially in disbelief at being allowed to eat chocolate in a science lesson, the students made excellent observations about how the different chocolates tasted, snapped, and melted. Students with usually very weak literacy skills used a wide range of good words to describe what they saw and relate these to the formulation of the chocolate.


The research literature shows that understanding is stronger if the learner actively engages with new information. In turn, this is more likely if that information is presented in relevant and relatable contexts. For this approach, Dr Johnstone, both my students and I have you to thank.

Further reading: The biggest contributors to 'meaningful learning' and its relation to engagement were Ausubel and Novak and a nice research paper, looking at students doing compulsory chemistry at American universities available freely, is: Grove, N.P. and Bretz S.L. 2012, A continuum of learning: from rote memorization to meaningful learning in organic chemistry Chemistry Education Reseasrch and practice, 13, 201-208 Accessed via: http://pubs.rsc.org/en/Content/ArticleLanding/2012/RP/C1RP90069B#!divAbstract (you may need to cut and paste this into your browser)


December 19, 2016

Reflecting – “…through a mirror darkly…” Keith Pugsley

So, term starts, and there you are in the classroom, pen in hand, notebook at the ready, senses sharpened, dutifully primed (Christmas pun intended) by the well-oiled operation of the Warwick CPE induction team (leave that one with you!) and ready for applying yourself to observation. Observing, do it all the time, have done pretty much since birth, should be good at it. Off we go. An hour later and that’s one down. Much as I thought. Kids lined up, came in, sat down, slapped down a bit for being noisy, reminded that underlining is done with a ruler and, according to my notes, did some exercises. Oh yes, I recognised a strategy or two going on: countdowns; gentle rebuke to the disengaged; reminder of expectations. There we are job-done.

A week or two passes, more notes are taken when the sneaking feeling that these notes are all much the same and, dare I say, somewhat dry and moribund. I’m even writing down the topics and annotating the exercise questions? There are now bits of scaffolding jottings in my pad where I have broken away from observing to get involved in the doing (not that there is anything wrong with that per say). But is writing about whether the ladder leaning against the wall is safe, really going to help my classroom practice (short of the classroom’s openable windows being elevated to a significantly lofty location.)? I need to re-focus, and probably even take-a-look at the session we had on ‘observation’ at uni., which, I am sure, would have almost certainly been useful. Ah yes, focus on one aspect, study all the techniques used for BfL or AFL or differentiation. Makes sense. Right, I’m ready to go. I’m focussed. A few lessons pass. A quick look at my notes. What! Is that all I’ve written? Even some of my least diligent pupils would have recorded more than that! Needs re-thinking, but for now I need to concentrate on delivering my first full lessons.

What went well? I emerged, relatively unscathed. Excellent level of heat generated, possibly accompanied by a flicker of light. What, ‘could be better’? I’m left reflecting, but the next lesson is imminent, so I’m back to a bit more ‘observing’.

The Epiphany. Ah! so that’s what’s been happening. The Teacher ensures the students are admitted in good time, they are settled quickly, they know the routine, they have stuff to do immediately. The teacher glides effortlessly and with minimum instruction to the main focus of the lesson. The students are all, according to their respective needs, and with a relaxed freedom, on task. A flicker of disengagement is smoothly quelled and students are transitioned easily through effortless orchestration from the steady to appropriate, more challenging, tasks. Students are acting as autonomous agents, doing work, at consummative ease in an environment of unspoken, yet understood, boundaries. There is peer to peer support. The teacher is almost subliminally aware of the proceedings. There is a sense of safety and mutual respect, which seems to underpin the whole operation. Assessment of learning leads to a careful transition of tasks achieved effortlessly due to prior preparation. A brief round-up and the class ends. Students are reminded firmly but respectfully of the exit procedure. Staff and students are relaxed and smiling as they depart.

Funny, for all those previous notes and years of experience of ‘observing’, I somehow seemed to have missed all that, until I’d had a go myself.


December 06, 2016

Bacc–ing the Arts in Education

Bacc-ing the Arts in Education

Arts Council England stated that “Drama communicates through the language and connections of theatre. This results in all pupils… gaining access to one of the great forms of human expression.”. As a Drama trainee, I can only agree.

Since the 1980’s, we can see how Drama has grown in education as its own subject, and how it can be a method of delivery in other subjects. However, the current situation surrounding the National Curriculum suggests that history may be repeating itself; the Arts once again are at risk, and Drama in particular is being threatened as a subject that has little academic value due to the recently introduced EBacc system. Drama was the most commonly withdrawn subject as the EBacc made its way into the curriculum; in 2011, the Department for Education conducted studies amongst ten schools in preparation for the 2012/13 academic year, and found that 23% had already withdrawn Drama, with Art, Design/DT and Textiles following behind at 17%, 14% and 11% respectively.

But why is this case? Any teacher of Drama can tell you of the importance Drama can play on a child’s development; it builds both interpersonal and intrapersonal skills, boosts confidence, and can turn the shyest of children into one of the most confident within their school. Any teacher of Drama can tell you how having a creative outlet like Drama can engage even the naughtiest of pupils. And any teacher of Drama can also tell you that it is rare for students to spend lessons pretending to be trees!

Has this research into the impact of the EBacc benefitted my teaching? In a sense, yes. It has made me realise that, as Drama seems to be making its way back into the English Department in many schools, I may have to continue to ‘fight’ for my subject’s recognition. Although Drama is more focussed on social and cognitive learning, with a focus on development overall as opposed to purely academic value, it does not seem to be enough to give Drama a place within the EBacc.

With this in mind, I wonder if perhaps it is the potential lack of written work that has caused problems for the subject. From experience, KS3 rarely engage in written work in Drama, meaning that when they begin to study it at GCSE, problems can arise when it comes to written exams as students are having to learn a different method of writing alongside everything else. Perhaps written work needs to be implemented into Drama lessons considerably more than it is, and Drama will be seen as a more academically viable subject than it currently is. Perhaps then it may not suffer at the hands of the EBacc as much.

Do I still think Drama should be available within the EBacc? Certainly. Already I have mentioned the benefits it can offer socially and cognitively, but the simple fact is that students need creativity. They need an outlet that breaks away from the academic rigour of school, and for those who struggle academically, Drama can be a fantastic tool. As Ken Robinson stated, “Creativity now is as important in education as literacy, and we should treat it with the same status.”.

Abigail Byrne


December 01, 2016

Staff room epistemological highlights

Sitting next to me at one of the computers in the staff room was a science teacher of no little experience and maturity. He was busy preparing a hand-out sheet when with a deep sigh, he mentioned he would need to find some Tippex (other brands are available). Surprised, I glanced at what he was doing, "I could do without all these symbols", he remarked staring at the picture image on his powerpoint presentation. Eager to offer support (and naturally bearing in mind teaching standards part two) I was happy to suggest he insert a box, do a bit of formatting and, as if by magic, the result he was looking for was achieved. Such was his joy that his mood immediately lightened and after at least two high-fives later, this newly acquired knowledge was already rippling, wave-like to his fellow colleague the other side. "Look what you can learn by talking" he exclaimed." Bingo! "All learning is social, according to Vygotsky, I proudly announced, keen to ensure good academic deference, whilst happily condensing too many journal articles into a crudely 'constructed' and grossly oversimplified sound bite (hey, I’m team maths, we like abstraction). A short discussion ensued to the point where our respective zones of development were appropriately proximal, and we returned to our respective tasks. The Plenary. So, what happened here? Well, while the radical constructivists tussle over the epistemological nature of objective truth, or otherwise, we seem to have at least some evidence that learning took place through social interaction, go Lev, and don’t forget to put it in your PDP. People were made happy through the learning experience (smiley face), and I managed to deliver, albeit of a largely procedural nature, one of my best lessons of the week!

November 30, 2016

Bloomin’ Marvellous: Taking my hat off to Bloom by Lauren Atkins

Questioning a student prompts thought, it allows them to pick apart elements of History in order for them to investigate why events happened, what their impact was and also what would the world look like if these events did not take place.

After six weeks of teaching, it became apparent that my lessons were not as challenging for higher achievers as I had hoped; back to the drawing board it was. From writing about Bloom’s taxonomy in two of my assignments, I thought this would be a good place to start. Bloom’s theory follows a linear format, ideal for students studying History. I found that, in theory, if the taxonomy was incorporated within my lessons that I would be able to challenge my higher achieving students. Bloom stipulates that students need to start by recalling information and through questioning they are guided to the evaluation stage. In my lessons, I found that some students arrived with prior-knowledge and so, beginning with the ‘knowledge’ and ‘comprehension’ stages hindered their progress. I then looked at activities that would help to challenge the higher attaining students in the class. After research, I found De Bono’s ‘Thinking Hats’ as this activity allows for students to begin at various levels. However, as Bloom’s theory applies to History so well I thought it was important that this form of questioning was incorporated. I combined the ‘Thinking Hats’ activity with Bloom’s questioning. Students were then given a colour, representative of the stage they should begin at, in their book, they then had to complete three sections. This task immediately challenged higher ability students whilst differentiating for those who need additional support. Students utilised their historical skill set and analysed the information they were given before synthesising and evaluation. I found that because I was researching the theory at the same time as applying it, I could tailor it to meet the needs of my higher attaining students within lessons.

There is one potential problem here though, in History it is important for students to empathise with a source to evaluate it. This is a skill that I am currently developing with my Year 7 groups through questioning, for example, ‘why do you think the Black Death was portrayed in this way?’ ‘How does it reflect people’s fears at the time?’ Through this ‘high-order’ questioning students can empathise with the source which inevitably aids their ability to evaluate it. By understanding why a source has been published, students are able to then evaluate why it is representative of the time. To combat this, I placed great emphasis on ‘empathy’ within the ‘synthesis’ stage. Bloom instructs that this stage is reserved for inference and imagination; both concepts which link to empathy. Students, through questioning are asked what can they infer from the source? From this we can then ask them to imagine they are living during that period, ‘what might their key concerns about the Black Death be?’ ‘What were people’s fears about the Black Death?’ This allows higher attaining students to reach the top stages of Bloom’s taxonomy thus extending their knowledge and challenging them appropriately in lessons.


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