The proof behind one of the most famous theorems in mathematics

Vishaali, Year 10, looks behind the proof of one of the most famous mathematical theorems – that of Pythagoras’ theorem.

 

What is the difference between a theorem and a theory?

A theorem is a mathematical statement that has been proven on the basis of previously established statements. For example, Pythagoras’ theorem uses previously established statements such as all the sides of a square are equal, or that all angles in a square are 90°. The proof of a theorem is often interpreted as justification of the statement that the theorem makes.

On the other hand, a theory is more of an abstract, generalised way of thinking and is not based on absolute facts. Examples of theories include the theory of relativity, theory of evolution and the quantum theory. Take the theory of evolution; this is about the process by which organisms change over time as a result of heritable behavioural or physical traits. This is based on undeniable true facts, but more from experience and from an abstract way of thinking.

It is also important not to confuse mathematical theorems with scientific laws as they are scientific statements based on repeated experiments or observations.

The proof behind Pythagoras’ theorem

You have probably all heard of Pythagoras’ theorem, one of the simplest theorems there is in mathematics, that is relatively easy to remember. Given that it’s so easy to remember and to learn, wouldn’t it be an added bonus to know exactly how this theorem came to be?

The theorem, a²+b²=c², relates the sides of any right-angled triangle enabling you to find the lengths of any side, given you have the lengths of the other two.

This whole theorem is based on a triangle like this:

These four right-angled triangles are exactly the same just rotated slightly differently to create this shape:

Two shapes have been made by putting these triangles in this order. A big square on the outside, and another slightly smaller square in the middle. As all these triangles are the exact same you can label them A, B and C.

You can tell from the labels the triangles have been given, that the bigger square would have the sides (a+b), and the smaller triangle in the middle will have sides of c. Therefore we know the area of the smaller square is c² :

Using the exact same four triangles, we can rotate and translate them to create a slightly different shape:

Now two more squares have been added to this shape. We can call them  a² and b².

Thinking back to the shape we made before, we can also see that the length of this shape is also (a+b). As we know we used the same four right-angled triangles for the shape before and now, we can infer that the two squares  a² and b² are exactly the same as the square from the first shape, c². Hence we get Pythagoras’ theorem, a²+b²=c²:


References:

https://www.livescience.com/474-controversy-evolution-works.html
https://www.askdifference.com/theorem-vs-theory/

Does the Harkness Method improve our understanding of Maths?

Elena and Amelia, Y12 Further Mathematicians, explore how the Harkness Method has opened up a new way of thinking about Pure Maths and how it allows them to enhance their mathematical abilities.

For Further Maths A Level, the Maths department has picked a new style of teaching: the Harkness Method. It involves learning by working through problem sets. The problems give clues as to how to get to the answer and this is better than stating the rules and giving examples; we have to work them out ourselves. These problem sets are given for homework, and then we discuss them together during the next lesson by writing the answers on the board and comparing our results with each other.

Elena:

At the beginning of term, I found it quite challenging to complete exercises without knowing what rules I was expected to apply to the problems, as each question seemed to be completely different to the one preceding it. The tasks also require us to use our previous GCSE knowledge and try to extend it ourselves through trial and error and by applying it to different situations and problems. I found it difficult to understand how to apply a method to solve different problems as previously each problem came with a defined method.

Maths diagrams As the lessons progressed, I started enjoying this method of teaching as it allowed me to understand not only how each formula and rule had come to be, but also how to derive them and prove them myself – something which I find incredibly satisfying. I also particularly like the fact that a specific problem set will test me on many topics. This means that I am constantly practising every topic and so am less likely to forget it. Also, if I get stuck, I can easily move on to the next question.

Furthermore, not only do I improve my problem-solving skills with every problem sheet I complete, I also see how the other girls in my class think about each problem and so see how each question can be approached in more than one way to get the same answer – there is no set way of thinking for a problem.

This is what I love about maths: that there are many ways of solving a problem. Overall, I have grown to like and understand how the Harkness Method aims to challenge and extend my maths skills, and how it has made me improve the way I think of maths problems.

Amelia:

When I first started the Harkness approach for Pure Maths in September, I remember feeling rather sceptical about it as it was unlike any method of learning I had encountered before. To begin with, I found it slightly challenging to answer the questions without knowing what topic they were leading to and found confusing how each sheet contained a mixture of topics.

However, I gradually began to like this as it meant I could easily move on and still complete most of the homework, something which you cannot do with the normal method of teaching. Moreover, I found it extremely beneficial to learn the different topics gradually over many lessons as I think that this improved my understanding, for example for differentiation we learnt it from first principles which gave me the opportunity to comprehend how it actually works instead of merely just remembering how to do it.

Furthermore, I think that the best part of the Harkness Method is that you are learning many topics at a time which means that you cannot forget them as compared to in the normal method which I remember finding difficult when it came to revision for GCSEs as I had forgotten the topics I learnt at the beginning of Year 10. I also began to enjoy the sheets more and more because the majority of the questions are more like problem-solving which I have always found very enjoyable and helpful as it means you have to think of what you need to use instead of the question just simply telling you.

Moreover, I very much enjoyed seeing how other people completed the questions as they would often have other methods, which I found far easier than the way I had used. The other benefit of the lesson being in more like a discussion is that it has often felt like having multiple teachers as my fellow class member have all been able to explain the topics to me. I have found this very useful as I am in a small class of only five however, I certainly think that the method would not work as well in larger classes.

Although I have found the Harkness method very good for Pure Maths, I definitely think that it would work far less well for other parts of maths such as statistics. This is because I think that statistics is more about learning rules many of which you cannot learn gradually.

What are the links between romance languages and music?

Matilda, Year 13, investigates the links between romance languages and music to discover whether the learning of one can help in the understanding of the other.

Music and language

It is often said that music is the ‘universal language of mankind’, due to its great expressive powers which have the ability to convey sentiments and emotions.

But what are the connections between music and languages?

A romance language is a language derived from Latin and this group of languages has many similarities in both grammar and vocabulary. The 5 most widely spoken romance languages are Spanish (with 470 million speakers), Portuguese, French, Italian and Romanian.

There are 3 main connections between languages and music:

 

The first of these is the role of melody in recall:

There is a link between languages and music in remembering words. This is shown in a study where words were better recalled when learned as a song rather than a speech. This is because melody and rhythm give the memory cues to help recall information.[1]

Language, music, and emotion:

The British anthropologist and evolutionary psychologist who specialises in primate behaviour, Robin Dunbar, says that music and language help to knit people together in social groups. This is because musicians process music as a language in their heads. Studies have shown the planum temporal in the brain is active in all people whilst listening to music.

However, in non-musicians, the right-hand side was the most active, meanwhile, in musicians, the left side dominated, this is the side believed to control language processing. This shows that musicians understand music as a language in their brain.

In another study, scientists analysed the Broca’s area, which is crucial in language and music comprehension. It is also responsible for our ability to use syntax. Research has shown the in the Broca’s area of the brain, musicians have a greater volume of grey matter, suggesting that it is responsible for both speech and music comprehension.

The relationship between music and languages:

Brain and Languages Both music and languages share the same building blocks as they are compositional. By this, I mean that they are both made of small parts that are meaningless alone but when combined can create something larger and meaningful.

For example, the words ‘I’, ‘love’ and ‘you,’ do not mean much individually, however, when they are constructed in a sentence, carry a deep sentimental value. This goes the same for music notes, which when combined can create a beautiful, purposeful meaning.

Musical training has been shown to improve language skills.[2] In a study carried out in 2011, developmental psychologists in Germany conducted a study to examine the relationship between development of music and language skills. In the experiment, they separated children aged 4 into 2 groups, 1 of these groups receiving musical training, and one did not.

Later on, they measured their phonological ability (the ability to use and manipulate language) and they discovered the children who had received music lessons were better at this. Therefore, this shows that learning and understanding language can go hand in hand with musical learning and ability.

References: 

[1] See https://www.theguardian.com/teacher-network/2018/mar/14/sound-how-listening-music-hinders-learning-lessons-research
[2] See https://www.psychologytoday.com/intl/blog/the-athletes-way/201806/how-does-musical-training-improve-language-skills

Rehearsal, Rehearsal, Rehearsal – how repetition helps us learn

Anna, Year 13, discusses not only how rehearsal is the key to a good performance but also how the repetitive nature of rehearsing can aid studying.

For those who favour the more ‘academic’ subjects, drama may seem like a discipline which requires substantially less work than the sciences due to the propagated belief that a student does not need to revise as much, as well as the active nature which makes it more of a practical subject than academic. However, while there is certainly more action involved than with other subjects (with ‘acting’ being the most vital part of theatre for an audience), the claim that revision is not necessary is entirely false.

When speaking of acting, an audience member often reviews what they can see in front of them in one moment as, more often than not, they are not privy to the behind-the-scenes rehearsal process. While it is true that the audience impact is a vital part of theatre performance and theory, it is the rehearsal process itself which allows the final finished product to flourish; without it, the actor would not know how to act the line in order to achieve the greatest impact for the audience. Having studied drama myself for the entirety of my Wimbledon High attendance, as well as gotten involved in various plays and musicals over the years, I have come to think of this rehearsal process as high-intensity interval training (without the exercise, thankfully) which results in muscle memory and allows an actor to create the intended effect.

Rehearsing is primarily an active, practical activity; the repeated action over time enhances memory, which then lets an actor read off book (without a script) without any doubt of what they are going to do next or what their line is. For my fellow kinaesthetic learners – who Professors Dunn and Dunn describe as ‘students who require whole-body movement to process new and difficult information’ – this is already a behaviour that we are familiar with; when I am trying to memorise tricky English quotes or mathematic formulae, it is not uncommon to see me pacing back and forth or jumping up and down in order to enhance my learning. Viewing rehearsal as a study form automatically demonstrates academic benefits, as this subconscious form of learning that is routine for a drama student or actor can be employed elsewhere as a studying technique where ‘spaced repetition’ (that is, learning the same thing over a long time with regular intervals) where repetition over a month will result in 90% memorisation. This allows for more consolidation of information, and so ultimately the person will remember more than if they simply crammed the night before. Not only this, but it allows for muscle memory (a form of memory where there isn’t conscious awareness of the actions) to be developed; with resultant feedback received in rehearsal from the director, it means that a person not only develops skills and learning but allows more information to be absorbed as a result.

Therefore, when considering the long-term repetitive nature of rehearsal, it seems logical that it can be labelled a form of active revision; the act of rehearsal instills both useful studying tools in a person without them even realising, as well as a fun way to showcase messages to audiences with the eventual performance.

The importance of collaborative learning

How can we encourage collaborative learning? Alex Farrer, STEAM Co-ordinator at Wimbledon High, looks at strategies to encourage creative collaboration in the classroom.

Pupils’ ability to work collaboratively in the classroom cannot just be assumed. Pupils develop high levels of teamwork skills in many areas of school life such as being part of a rowing squad or playing in an ensemble. These strengths are also being harnessed in a variety of subject areas but need to be taught and developed within a coherent framework.  Last week we were very pleased to learn that Wimbledon High was shortlisted for the TES Independent Schools Creativity Award 2019. This recognises the development of STEAM skills such as teamwork, problem solving, creativity and curiosity across the curriculum. Wimbledon High pupils are enjoying tackling intriguing STEAM activities in a variety of subject areas. One important question to ask is what sort of progression should we expect as pupils develop these skills?

The Science National Curriculum for England (D of E gov.uk 2015) outlines the “working scientifically” skills expected of pupils from year 1 upwards. Pupils are expected to answer scientific questions in a range of different ways such as in an investigation where variables can be identified and controlled and a fair test type of enquiry is possible.

However, this is not the only way of “working scientifically”. Pupils also need to use different approaches such as identifying and classifying, pattern seeking, researching and observing over time to answer scientific questions. In the excellent resource “It’s not Fair -or is it?” (Turner, Keogh, Naylor and Lawrence) useful progression grids are provided to help teachers identify the progression that might be expected as pupils develop these skills. For example, when using research skills younger pupils use books and electronic media to find things out and talk about whether an information source is useful. Older pupils can use relevant information from a range of secondary sources and evaluate how well their research has answered their questions.

The skills that are used in our STEAM lessons at Wimbledon High in both the Senior and Junior Schools utilise many of these “working scientifically” skills and skill progression grids can be very useful when planning and pitching lessons. However, our STEAM lessons happen in all subject areas and develop a range of other skills including:

  • problem solving
  • teamwork
  • creativity
  • curiosity

Carefully planned cross-curricular links allow subjects that might at first glance be considered to be very different from each other to complement each other. An example of this is a recent year 10 art lesson where STEAM was injected into the lesson in the form of chemistry knowledge and skills. Pupils greatly benefited from the opportunity to put some chemistry into art and some art into chemistry as they studied the colour blue. Curiosity was piqued and many links were made. Many questions were asked and answered as pupils worked together to learn about Egyptian Blue through the ages and recent developments in the use of the pigment for biomedical imaging.

There are many other examples of how subjects are being combined to enhance both. The physiological responses to listening to different types of music made for an interesting investigation with groups of year 7. In this STEAM Music lesson pupils with emerging teamwork skills simply shared tasks between members of the group. Pupils with more developed teamwork skills organised and negotiated different roles in the group depending on identified skills. They also checked progress and adjusted how the group was working in a supportive manner. A skill that often takes considerable practise for many of us!

Professor Roger Kneebone from Imperial College promotes the benefits of collaborating outside of your own discipline. He recently made the headlines when he discussed the dexterity skills of medical students. He talks about the ways students taking part in an artistic pursuit, playing a musical instrument or a sport develop these skills. He believes that surgeons are better at their job if they have learned those skills that being in an orchestra or a team demand.  High levels of teamwork and communication are essential to success in all of those fields, including surgery!

Ensuring that we give pupils many opportunities to develop these collaborative skills both inside and outside of lessons is key. We must have high expectations of progression in the way that pupils are developing these skills. Regular opportunities to extend and consolidate these important skills is also important. It is essential to make it clear to pupils at the start of the activity what the skill objective is and what the skill success criteria is. It is hard to develop a skill if it is not taught explicitly, so modelling key steps is helpful as is highlighting the following to pupils:

  • Why are we doing this activity?
  • Why is it important?
  • How does it link to the subject area?
  • How does it link to the real life applications?
  • What skills are we building?
  • Why are these skills important?
  • What sort of problems might be encountered?
  • How might we deal with these problems?

Teacher support during the lesson is formative and needs to turn a spotlight on successes, hitches, failures, resilience, problems and solutions. For example, the teacher might interrupt learning briefly to point out that some groups have had a problem but after some frustrations, one pupil’s bright idea changed their fortunes. The other groups are then encouraged to refocus and to try to also find a good way to solve a specific problem. There might be a reason why problems are happening. Some groups may need some scaffolding or targeted questioning to help them think their way through hitches.

STEAM lessons at Wimbledon High are providing extra opportunities for pupils to build their confidence, and to be flexible, creative and collaborative when faced with novel contexts. These skills need to be modelled and developed and progression needs to be planned carefully. STEAM is great fun, but serious fun, as the concentration seen on faces in the STEAM space show!

Twitter: @STEAM_WHS
Blog: http://www.whs-blogs.co.uk/steam-blog/

Kagan structures: creating an engaging environment to promote effective learning

Beth Ashton, teacher of Year 5 and 6 English in WHS Junior School, investigates Kagan structures and how this methodology helps to create an engaging classroom atmosphere focused on promoting effective learning.

“When teachers use Kagan structures they dramatically increase both the amount of active engagement and the equality of active engagement among students.”

Kagan, S. Structures Optimize Engagement. San Clemente, CA: Kagan Publishing. Kagan Online Magazine, Spring/Summer 2005

There is no doubt that creating a climate of active learning in the classroom contributes directly to the success and lasting impact on children’s development educationally.

As children progress through the key stages, the curriculum shifts in balance from skills to a more content-based approach. This can result in diminishing opportunities for lessons to be delivered with practical content. As a result, ensuring an active learning climate can be challenging.

Passive learning places focus on the teacher to dictate the learning environment, acting as the locus of control and knowledge within the classroom. Research has demonstrated that this approach results in poor knowledge retention and lasting issues for students in terms of taking ownership over their learning.

In terms of personal growth and the development of a lasting relationship with learning, this can result in pupils lacking the autonomy and independence to sustain their own studies.

With a whole-class ‘hands-up’ approach, pupils’ perception of their own ability can also be damaged.

“If the teacher has students raise their hands and calls on the students one at a time, students learn to compete for teacher’s attention. They are happy if a classmate misses, because it increases their own opportunity to receive recognition and approval”

Kagan, S. Kagan Structures for Emotional Intelligence

However, when time is of the essence and teachers are required to deliver a dense and complex curriculum, finding practical solutions to avoiding passive learning and ensuring active engagement in lessons can be difficult.

“The first critical question we ask is if the task we have set before our students results in a positive correlation among outcomes. Does the success of one benefit others?”

Kagan, S. Structures Optimize Engagement. San Clemente, CA: Kagan Publishing. Kagan Online Magazine, Spring/Summer 2005

In order to combat passive learning in the classroom, Years 5 and 6 in WHS Juniors have been using Kagan interactive learning structures in English lessons to promote inclusive and engaged dialogue when engaging with texts. Over the course of the year, girls have demonstrated an improved ability to move between social groups easily within lessons. Focussing on social awareness and the ability to converse with their peer group effectively has meant that teachers have been able to reward a multitude of different skills, rather than just praising those girls who put their hand up.

Kagan is a system of cooperative learning structures, based on using peer support to engage pupils. Using a series of variety of different interactive structures, pupils are placed in mixed ability groups of four. Constructing these groups with an awareness of social dynamics and learning styles is vitally important.

Kagan structures require every student to participate frequently and approximately equally https://www.kaganonline.com/about_us.php

By encouraging students to work as a team, teachers are able to remove the elements of competition and insecurity within the classroom, replacing them with a culture of collaboration and mutual support. The ‘hands-up’, whole-class approach to lessons is removed and replaced with pupils learning and discussing questions as a group, and feeding back to other groups around the classroom. This is achieved by swapping different numbers and using strategies such as ‘round robin’ and ‘numbered heads together’.

For example, when analysing a poem in English, girls would work in mixed ability groups, trying to identify the use of symbolism and looking at its effect. After thinking time, each number would be given an allocated time to share their thinking. This could be organised with the most able student sharing last, so that they don’t automatically lead the conversation. In order to ensure the lower ability pupil remains engaged, they could be pre-warned that their number would be responsible for reporting the outcome of the group discussion to the rest of the class.

The round robin structure described above ensures that each pupil:

  • has a role
  • is given allocated and structured time to share their views
  • is listened to by their peers

Importantly, the conversation is not dominated by one particular student. The option to opt out is also managed effectively by the teacher, by ensuring that pupils are aware of the high expectations around their engagement and contribution to class discussion.

“Group work usually produces very unequal participation and often does not include individual accountability, a dimension proven to be essential for producing consistent achievement gains for all students.”

Kagan, S. Structures Optimize Engagement. San Clemente, CA: Kagan Publishing. Kagan Online Magazine, Spring/Summer 2005

By using the Kagan interactive models, unstructured group discussions are removed from the classroom environment. Strategies such as ‘Timed Pair Share’ give discussion a scaffold. This means that pupils who usually demonstrate a dominant approach and tend to speak first, are able to develop the capacity to listen. Equally, students who tend to take a back-seat are guided through the process of sharing their thinking more readily.

The teacher is also able to allocate roles within groups with ease and adaptability according to the pupil’s number within the group. This ensures that dominant pupils are not able to control team discussions and feedback time, and less engaged pupils are drawn into participation through interaction with peers.

“If students in small groups discuss a topic with no ‘interaction rules’, in an unstructured way, often one or two students dominate the interaction. If, however, students are told they must take turns as they speak, more equal participation is ensured”

Kagan, S. A Brief History of Kagan structures.

As well as academic participation, Kagan can be a vital tool in improving social awareness and skills. The format of structured discussion time within class, results in clear social strategies being delivered to pupils through lesson content. Providing discussion in class with a framework also increases confidence and promotes risk-taking. These skills translate to the playground and, ultimately, the students’ life outside school and into the world of work.

Research shows that there is a strong correlation between social interaction and exchange of information. Generally, higher achieving students tend to form sub-groups within a cohort, creating enclaves where information is rapidly exchanged, and excluding those students they perceive as ‘lower ability’. This can result in those students who struggle feeling isolated and excluded, and ultimately disengaging from their studies. By using Kagan to scaffold and structure the sharing of information between children of different abilities, we can ensure that pupils of all abilities are gaining access to the social interactions which will ensure they make excellent progress.

A whole-class approach to questioning is proven to disengage a significant proportion of the class, whilst placing strain on the teacher. By passing ownership of the lesson to the students, through posing questions and allowing them to answer collaboratively, the teacher is able to take a step back and observe the learning process, taking feedback from each child through listening to their discussion.

By providing the teacher with the time and mental space to observe the lesson as it progresses, changes are able to be made over the course of the lesson, adapting to pupils needs. By using Kagan structures when tackling new learning, students are guided through the stages of learning through peer support. In the first stage of learning, pupils are able to work as a larger group, obtaining a significant amount of team support. Following this, pupils are then able to take on the problem in pairs, and finally, individually.

Using this format provides the more able pupils with the challenge of articulating their thinking to support their peers and provides those with barriers to learning with support of multiple different kinds within a lesson. Using established interactive structures means that the structures themselves are transferable across subjects, allowing them to be applied to all lessons. Having a readily available, student-led body of cooperative learning strategies embedded in the curriculum means that differentiation through discussion and peer support avoids a system of creating worksheets and allows pupils to ensure they are constantly being challenged, stretched and supported.

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Should standardised exams be exchanged for another form of assessment?

wimbledon logo

Jasmine (Year 11) explores the merits and weaknesses of exams as the formal assessment of intelligence, discussing whether an alternative should be introduced that suits all students.

Exams – the bane of existence for some but an excellent opportunity to excel for others. Thought to have been founded in China, with the use of the standardised “imperial exam” in 605 AD, they are the education system’s way of assessing the mental ability and knowledge of students whilst also creating a practical method of comparison to others in the country. They are therefore an important factor and indicator for employers. But does this strict, tight method really work for assessing intelligence or is it just a memory game that is only achievable for a select few?

I asked 80 students in a survey if they think that exams should be exchanged for another form of assessment and the results concluded that 78% agree that they should. However, when asked about their reasoning, it was mostly due to stereotypical dislike for the stressful period. Some who agreed with the statement also mentioned the unrealistic exam conditions that would not occur in daily life. An example was set forth that during a language oral exam a great amount of pressure is put on the students causing them to become nervous and not perform to their best ability. However, in a real-life conversational situation they would not have to recite pre-prepared answers and the pressure would be taken off so the conversation would flow more naturally. This shows that although someone may have real fluency and talent for the language, their expertise will not be notified and rewarded accordingly

Among many students, examinations are accused of being memory tests that only suit a certain learning style; and the slow abolishment of coursework at GCSE level is contributing to this. This could be shown by the fact that many people in the country have learning difficulties such as dyslexia. These students may be particularly bright and diligent workers however, their brains do not function in the way exams rely on them to. Nonetheless, if they are put in front of a practical task that they have learned to do through experience, they are deemed to be far more knowledgeable and perceptive. Studies show that by learning something consistently for a long period of time it stays in our memory but though it is important to ingrain essential facts into our brains, especially at GCSE level, GCSEs are mostly comprised of learning facts over a period of around 2-3 years and then a final exam at the end; which does not particularly show consistent learning and is more just an overflow of information.

Stress levels caused by the lead-up, doing, and waiting period for results that subsequently follows are also a major factor in the argument that traditional standardised tests should be augmented. According to the NSPCC, from 2015-2016 there was a 21% increase in the likelihood of counselling sessions being for 15-18 year olds affected by exam stress many of whom would be doing GCSEs and A Levels. Some say that the stress these tests cause is necessary for success and mimics the stresses of the real world; but how essential are some of these exams like non-calculator Maths papers when nowadays most people of have calculators on their phones? Exams are also said to create healthy competition that prepares people for the struggles and competitive nature of the modern working world and also motivates students, but can’t this be done with another form of assessment that is more suited to the individual student?

However, the use of different approaches to examination may, in fact, lead to the risk of the test being corrupted. This would mean that grading would be mainly subjective and there would be more scope for unfair advantage for some rather than others. The restrictive nature of our exams today with a set time, set paper and set rules does ensure that fairness is a priority but is the actual exam really the most equal way to test so many different students?

Standardised exams are not the best way of determining the knowledge and intelligence of students around the world. This is due to the stress and pressure they cause, the fact that they are only appropriate for certain learning styles and their ill comparison to real life events in the working world. Changing the form of these assessments may, however, cause grades to be unreliable. My suggestion would be smaller and more practical examinations throughout the course that all contribute to the final grade as this puts less pressure on the students and helps those who rely on different learning strategies to excel and demonstrate their full potential.

Using images to inspire and engage our future scientists.

Alex Farrer, one of our Scientists in Residence, looks at ways images can be used both inside and outside the classroom.

The Wellcome Trust is a global charitable foundation that supports scientists and researchers to work on challenges such as the development of Ebola vaccines and training health workers in ways to reduce the risk of infection when working on the front line. What you might not realise about the Wellcome Trust is that they also invest over £5million each year in education research, professional development opportunities and resources and activities for teachers and students. A key part of their science education priority area is primary science and they have a commitment to improving the teaching of science in primary schools through compiling research and evidence for decision making, campaigning for policy change and making recommendations for teachers and governors. Their aim is to transform primary science through increasing teaching time, sharing expertise and high quality resources, and supporting professional development opportunities such as the National STEM Learning Centre.

One of the excellent resources that the Wellcome Trust provides is Explorify, a free digital resource, developed with help from teachers and partners such as BBC Learning and the Institution of Engineering and Technology that is “focused on inquiry and curiosity, designed to appeal to children but also ignite or reinvigorate teachers’ passion for science”.

The resource can be found here https://explorify.wellcome.ac.uk

It consists of fun and simple science activities that utilise teaching and learning techniques that give pupils and teachers rich opportunities to question, think, talk and explore STEAM subjects inside and outside the classroom. Confidence and passion is harnessed as links are made and pupils and teachers can see that STEAM knowledge and skills connect us all. They say that a picture is worth a thousand words and Explorify uses images to great effect with videos, photographs and close ups, as well as hands on activities and what if discussion questions.

Explorify is an excellent tool to use in science lessons, especially in primary settings, but many outstanding lessons use different images in a variety of ways to promote talking and thinking in all subject areas, with all age groups. When images are used higher order questioning can be developed and there are also many opportunities to

  • use subject specific vocabulary
  • explain and justify
  • work together
  • ask questions
  • think about different possible answers
  • identify misconceptions
  • look for connections
  • generate further lesson ideas
  • model thinking
  • listen to each other

Common examples of questions to ask when using images might include

  • odd one outs
  • true/falses
  • similarities and differences
  • sequencing
  • what happened next…

All of which involve reflection and asking pupils to justify their answers and persuade others using evidence and examples.

Some less usual examples for you to ponder on include the following:

What is this?

 

 

Come up with a question that can only be answered yes or no to help work out what it is. Once 8 questions have been answered it is time to decide your answer using the evidence you have gathered. Which question was most useful in finding out the answer?

 

 

 

What is this?

 

 

Be specific! Are you sure of your answer? Come up with a 5 convincing bullet points to persuade everyone you are correct. Do you change your mind when you hear the ideas of others?

 

 

 

This is the answer:

 

 

What is the question? What do you already know about what is happening here?

 

 

 

 

Scientific words?

 

 

Which 5 keys words would you choose inspired by this image? Have you chosen the same words as others have? Where was this photograph taken?

 

 

 

 

What should the title be for this lesson?

 

 

Return at the end of the lesson to your title. Was it the correct title? Do you now need to alter it?

 

 

 

 

Are polar bears good swimmers?

 

 

Are polar bears good enough swimmers for 2018? What time of year was this photograph taken?

As well as in lessons images and questions can be used around the school to promote talking and thinking with all members of the school community.

 

 

How many metres per minute does a fly move?

 

 

Is it possible to check your estimate?

 

 

 

 

For more details and examples please see a copy of the presentation entitled Using images to inspire and engage our future scientists that I delivered at the Primary Science Teaching Trust Conference in Belfast.

https://pstt.org.uk/what-we-do/international-primary-science-conference

We are now working on exciting new resource for PSTT utilising images to inspire and engage pupils in conjunction with schools in SW London and with Paul Tyler @glazgow and schools in Scotland. If you have any inspiring images and questions please do send them in!

We look forward to continuing to inspire and engage the scientists of the future as our STEAM journey at Wimbledon High continues.

Follow us on @STEAM_WHS    

Where academic and pastoral meet: why we should value what we remember and will remember what we value.

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Fionnuala Kennedy, Deputy Head (Pastoral), looks at research in to memory and how this can be used to aid revision for examinations.

As with most of my thoughts about education, this one was provoked by a conversation over supper and a glass of wine with someone not involved in the educational field. Unlike most of my thoughts about education, it is based on the work of a Dutch psychologist and Chess Master born in 1914, whose initial thesis, “Het denken van den schaker”, was published in 1946 (the English translation, “Thought and Choice in Chess”, appeared in 1965).
During the 40s, 50s and 60s, Adriaan de Groot conducted a series of cognitive chess experiments which ultimately formed the basis for ‘chunking’ theory and allowed for the development of chess computers. Testing all levels of chess player, from rank beginners through to Grand Masters, de Groot’s goal was to explain how the very best chess players could visually absorb a full chess board, assess the positions of pieces, process the different numbers of moves they could make next and rank them in order of preference, and all within seconds. This process was divided into four key phases, occurring rapidly in sequence:

  1. The orientation phase – assessing the position and coming up with general ideas of what to do
  2. The exploration phase – analysing concrete variations
  3. The investigation phase – deciding on the best move
  4. The proof phase –confirming the validity of the choice reached in phase three.

This in itself is an incredibly useful model of thought and study, particularly for the examination student under pressure of time. It is, however, not this which really piqued my interest in de Groot’s study, but rather the next phases of his thinking which have since been built upon by psychologists in the US.

Having determined the role of visual perception and thought processes of Grand Masters that lead to their success, de Groot went on to consider how they would memorise and what it was about that method of memory which made them so particularly successful. And the findings were – and are – fascinating.

In de Groot’s most famous demonstration, he showed several players images of chess positions for a few seconds and asked the players to reconstruct the positions from memory.  The experts – as we might predict – made relatively few mistakes even though they had seen the position only briefly.  So far, so impressive. But, years later, Chase and Simon replicated de Groot’s finding with another expert (a master-level player) as well as an amateur and a novice.  They also added a critical control: the players viewed both real chess positions and scrambled chess positions (that included pieces not only in random positions, but also in implausible and even impossible locations). The expert excelled with the real positions – again, as might have been predicted – but performed no better than the amateur and even the novice for the scrambled positions. In essence, then, the expert advantage seems only to come from familiarity with actual chess positions, something that allows more efficient encoding or retrieval of the positions. The grand master’s memory, the test suggests, will only have absorbed the positions on the board which matter to them, which have meaning and purpose; it is not that their memories are simply ‘better’, or better-trained, but that they have become more efficient in storing meaningful patterns. Without that meaning, the expert and the novice will both struggle equally.

And this amazed me, and got me thinking. As educators, we know that theories about the ways in which we think and remember come and go, that pupils may learn in different ways, at different ages, in varying degrees of success and failure, and thus we shouldn’t jump on too many bandwagons pedagogically. I know for example that I am almost certainly more reliant on audio and visual modes of learning than kinesthetic, but then I suspect that’s because the latter didn’t really exist when I was at school; and I also tend to believe that I remember letters and words better than numbers, but this I now recognise to be because I grew up with parents who listened to music and read literature. It is not that our brains can or cannot remember aspects of learning; it is not necessarily that we have different ways of thinking and remembering and learning, or indeed brains which ‘absorb’ certain information better or worse than others. Rather:

We will remember that to which we ascribe value; we will memorise where there is pattern and meaning.

Which only goes to add more grist to the mill to Mrs Lunnon’s message delivered in our opening assembly this term: ‘What I do is me: for that I came’ (Manley-Hopkins). If we approach learning as a task which must be achieved simply to obtain an end-goal, we simply will not learn as well. Rather, if each task is ascribed a meaning and value for and within itself, it will become much easier to remember and store away. Thinking ‘I want to get 10/10 in my Spanish vocab test because I want to be top of the class’ will only make your task more difficult. Looking at each word you are learning and putting it into a context where you might use it one day, or including it in a joke in Spanish, or making a connection between the words, will save you time and maximise the chances of your brain storing that information away for you for longer.

What’s more – and this is where the pastoral side really kicks in – such an approach takes away the slog and grind of learning. Instead, meaning will surround us and be ascribed in all we do. And, of course, more excitingly than that: if we are on the look-out for meaning, it will help us to find the area which feels the most meaningful for us, in which we can readily spot and identify patterns of meaning and which fills us with joy and satisfaction. And it is this, and not simply a desire to do well or know more, which will lead to true mastery as we negotiate the chess board of our own learning and lives.

Follow @DHPastoralWHS and @Head_WHS on Twitter.

A trip to הארץ (the land)

By Keith Cawsey, Head of RS.

Having been at Wimbledon High School for a whopping twelve years (how did that happen?), I was due a sabbatical. My first stop was Israel. 

I first visited Jerusalem in the January of 2000 and was keen to see what had changed and what had stayed the same. I was also interested in visiting a few places and museums that I have taught about since qualifying as a teacher, but never actually visited.

My first stop was to the Western Wall. Often called the ‘Wailing Wall’, it is best known by the Jewish community as ‘the Kotel’ (literally, The Wall). This is the only part of the original temple that was destroyed by the Romans in 70 AD. Indeed, it is part of a supporting wall of that temple and is the most sacred place visited by the Jewish community today. To the left of the wall itself, is an arch – Wilson’s Arch – where the faithful were praying and a discussion on the Talmud was taking place.

At school, I lead the annual trip for students in Year 10 – Year 13 to Poland, where we visit Auschwitz concentration camp and Oskar Schindler’s factory. When he died, Oskar Schindler asked to be buried in Jerusalem, facing the Mount of Olives and his grave is visited by millions each year. On my second day, I searched for his grave. In a way, it was closing a circle. I had visited his factory in Poland, listened to many Schindler survivor testimonies and, of course, watched the film. Here was my opportunity to pay tribute to that awe-inspiring man, who saved so many. His grave had stones placed on top of it, a Jewish tradition to honour the dead. Later in the week, I visited Yad Vashem, the Israeli memorial to the Shoah (Holocaust) and saw his tree planted in the ‘Avenue of the Righteous’ – a row of trees placed in memory of all the non–Jews who helped save the lives of Jewish people during the Shoah.

Starting in the Muslim quarter on the third day, I walked down the ‘Via Dolorosa’ – a road that traditionally Jesus walked down on his way from being sentenced by Pontius Pilate, to his crucifixion. Each of the fourteen stations is marked by a number and many have churches or chapels where you can pause and reflect on the Passion of Christ. The last four stations are to be found in the Church of the Holy Sepulchre – a church traditionally built on Golgotha, where Jesus was crucified. You can also see the place where Jesus was laid out after his crucifixion and the tomb where, according to tradition, Jesus was placed after his death and subsequently rose from the dead. Rudolf Otto used the word ‘numinous’ to explain that feeling of holiness and of the almighty and in this church. It was all around me.

Later that week, I queued very early in the morning to climb up to the area of the Temple Mount (Har Habayit in Hebrew). This is the place where the Jewish Temple once stood and is traditionally is the site where Abraham demonstrated his devotion to God by almost sacrificing his son Isaac. Today, the Al-Aqsa Mosque stands on the site as the rock that the mosque is built around is traditionally the place of Muhammad’s ascent to heaven during his night journey in the 7th Century CE. The view of Jerusalem and the vastness of the site itself was remarkable. The site of the Al-Aqsa Mosque, some say, was once the ‘Holy of Holies’ of the Jewish temple and, as a result, praying by Jews on this site today is not allowed as they may be treading on sacred ground; only Muslims are allowed into the mosque itself to protect the sanctity of the building.

In Jerusalem, my final visit was to Yad Vashem, the Israeli memorial to the Shoah. The building itself cuts dramatically through the countryside as visitors are led past the Avenue of the Righteous through to the main museum. Here, there is a chronological display of how the Shoah unfolded between 1933 – 1945 as well as focussing on what happened to the Jewish community afterwards. The Hall of Remembrance has an eternal light and a list of all the concentration camps written into the floor – a fitting memorial to the six million Jews murdered in Nazi Germany. A time to reflect on the past, but also a time to pray that we all have a responsibility to ensure that such an event must never happen again.

The last couple of days of my trip were in Jaffa – a port just outside Tel Aviv. It is connected to a great character of the Old Testament – Jonah – sent by God to deliver bad news to the people of Nineveh. He tried to hide from God, but God had other ideas and taught him, and us, a valuable lesson.

I leave you with a Jewish toast – ‘L’Chaim’, which is Hebrew for ‘To life’.