Category Archives: 2 Prof. Knowledge & Understanding

Concept Cartoons

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Concept Cartoons

  • Investigate & research concept cartoons
  • What are they?
  • How do they help you teach science?
  • Make links between these and the constructivist theory of teaching

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Concept cartoons are pictorial aids to help with learning, in this case the learning of science. They allow children to consider different scientific concepts and make informed hypotheses and choices. This should lead to greater understanding, as children are able to think for themselves without as  much teacher input to over-guide their thinking. It will stimulate them to make mistakes and then be able to investigate why they thought they were right, and why they might be wrong, which should lead to greater understanding of the concepts as opposed to simply knowing the answer.

Constructivism in the classroom calls for children to learn through active problem- solving, and the use of a concept cartoon could fit perfectly into this model. If I were to use one in through a constructivist approach, I would show the cartoon to start with and ask the children to hypothesise the answer, and then have them conduct an experiment to find out the correct answer. I believe this would help them to understand the science behind the experiment.

For example, one could use the concept cartoon on the left to test the stated hypotheses. When suitable weather conditions became available one could ask the children what they thing, or which of the children the agree with, and then go outside and build two snowmen and put a coat on one and have them monitor which melts faster or if they melt at similar speeds, which would allow children to learn about insulation and the melting process in an active way which should consolidate their understanding. With older children, one could do a similar experiment and allow them to make their own concept cartoon. Or give them some resources and allow them to create their own experiment and a concept cartoon to be completed by peers.

http://www.pstt.org.uk/ext/cpd/dips/concept-cartoons.htm

http://www.thirteen.org/edonline/concept2class/constructivism/

Do Schools Kill Creativity

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Before watching the above clip, I would have said that I could understand the arguments that schools do stifle creativity, through making them wear uniforms, and learn uncreative subjects like mathematics and providing them with a structured day. But I would also have said that many schools do provide what I would deem adequate facilities for children to express their creativity, through the compulsory inclusion of the expressive arts.

Having listened to the ideas of Sir Ken Robinson, I find the concept of ‘compulsory expressive arts’. This seems ironic now, as we are attempting to structure our children’s creativity. I now agree that we probably do educate children out of their creative capacities, as we move through the education system, less and less emphasis is placed upon the expressive arts subjects, unless one has a specific talent in it, at which point we again attempt to structure their work, while we have the other children learn ‘more useful’ subjects.

I also accept his point that children begin to lose the ability to have a go and make mistakes, I see it all the time at university. I myself do not volunteer to answer questions or otherwise contribute incase I am wrong or look daft in front of other students. I think that children are almost conditioned to think that mistakes are bad as they go through school, and I hate to think that the children I will work with will have this worry.

I remember sayings like “Don’t do music, you won’t be an musician” and “Don’t do art, you won’t be an artist”. And while I did not have a specific interest myself, I have friends who did and I am sure would have done well, but they had parents who did not think that there was a lot of value in it, though on the other hand, I also had friends who received scholarships to school in music and have now left school and gone on to pursue their talent.

I think that there are some children who have to ‘move to think’, though I was not one myself, preferring to sit and listen. I think that there is probably more that schools could do to help these children to learn effectively, though I would have to do some more research to give any examples. I think that an increase in the amount of time spent on the expressive arts may be a good place to start.

Productive Failure: A Recipe for Success!

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Productive Failure, it sounds strange, basically it is a teaching strategy by which children are set up to fail. They are set a mathematics task that they have not learned yet: standard deviation; parabolas; algebra, and they have to try to do the problem by working through it. The method was first coined by Dr Manu Kapur, who is the head of the Learning Sciences Lab at the National Institute of Education of Singapore. His website – see above – is well worth a read of to see more of his work.

I have been thinking a lot about this method of teaching. Essentially children are being asked to complete problems that they do not know how to complete, it is completely beyond their abilities at this point. Initially I wondered how this could possibly be helpful, we all know the dangers of setting work at a level that is too difficult for the child to complete, with their self-esteem and confidence especially in a subject such as mathematics as it is the cause of much anxiety in and of itself.

But then I though more about it and it struck me that there were strong links with Productive Failure and Vygotski’s Zone of Proximal Development.

zpd-graphic

Essentially, Productive Failure asks children to work within the red section of the Zone of Proximal Development, as they are asked to complete problems that they cannot do. Now that I can see this, I realise that Productive Failure could be a highly useful classroom tool if used in the right way. I think that the method would have to be talked through first, so that children understand fully that it is not to catch them out, it’s not a test, and that it is a chance for them to see what they will be learning and look for possible links to topics they have done before. I also think that it would have to be a collaborative activity where children could work in small groups or pairs to work on a problem to bits of it work out. It would very much be about scaffolding and building up knowledge.

I think that this is a concept that I would like to use, possibly on my 3rd or 4th year placement to see if it works well in practice, and whether it is easily adapted to different ages and stages and even subjects, perhaps for beginning new topics or learning spelling words.

 

https://getyourheadaroundit.files.wordpress.com/2013/11/zpd-graphic.gif

http://qz.com/535443/the-best-way-to-understand-math-is-learning-how-to-fail-productively/

Why Floundering Is Good

French Workshop 23 /10/15

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Workshop 2

 

Today in the French Workshop we were looking at numbers. Immediately I was significantly more relaxed than last week, I believe it was because I am more confident with numbers than with greetings.

The most memorable part of the workshop was the ‘Kings and Queens’ game, we sat in a circle and all had a number associated with the chair we were sitting on, and had to say a number and if someone made a mistake then they had to go to the end of the circle. I found this to be quite stressful, in that I was really very nervous about being in the hot-seat and really did not like everyone looking at me when I spoke. Though I had to think about how I would feel if I was a primary school child. On one hand, if I was a nervous type of person I would be thinking that I wanted to not lose and may feel quite stressed about being the only one to get things wrong. If I was more of a confident person, I would be concerned with winning, possibly beating my friends.

I think that the activity was good, but I think that I would have to be aware of the different personalities in the class, I may split the class into smaller groups so that they will be more confident that they are not speaking in front of the whole class. Another option would be to play the game in English for a few week so that they could become really confident in the game so that it would not be too stressful in French.

I left feeling less panicked and stressed than last week, but I am not feeling very confident and would like to have done a lot better. Next week I am going to try to participate a little more and boost my confidence levels.

Out of 5, I would give my anxiety levels a 3.

The Fearful French Workshop

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Before I start, I feel I should point out that this post is about me, not the tutor leading the workshop or the other students that are part of it.

I went up to the room feeling normal, walked into the room and the tutor greeted us by saying “bonjour!” and I could feel myself begin to panic. I am not ‘bad’ at French, I got an A at Int 2, and I still remember quite a lot of what I was taught. The second that the tutor started speaking French, however, I was transported back to sitting in French class in high school feeling awkward, uncomfortable, and wanting to hide under a desk the whole time. It may sound dramatic but that’s how I’ve always felt about French. I hated speaking it in front of anyone or doing anything in a french class to draw attention to myself!

This workshop was particularly stressful. The tutor had us doing actions to go with some of the vocab, I avoided joining in as long as possible, then when I had to I put in as little energy as possible. When she was asking unto say things out loud I found myself pretending not to know things, or pretending to write just to avoid making eye contact and being asked to participate by speaking out loud.

Looking at the workshop objectively, I thought what we were learning was very good, I thought that all the games and speaking out loud would be fun to most people. I think it is probably a very effective way to learn a language. I wonder if my reaction to French could be similar to ‘Maths Anxiety’ (explored in another post), do I have some kind of a phobia of French? If so, then it will need to be sorted. As a teacher I cannot pass my own feelings about the subject on to the children that I work with. If I do not come across confident in teaching a language, then the children will not be confident in my ability to teach them, which would significantly impact on their education.

I decided to look up my feelings and came back with ‘Foreign Language Anxiety’. It is described as  “a distinct complex of self-perceptions, beliefs, feelings, and behaviours related to classroom language learning arising from the uniqueness of the (foreign) language learning process” which makes a lot of sense to me. I also found the Foreign Language Classroom Anxiety Scale (FLACAS). It is a questionnaire which asks participants to read statements and rate how much they agree. Questions include “I start to panic when I have to speak without preparation in language class.” and “It embarrasses me to volunteer answers in my language class.” Looking at the questions, almost all of them apply to me!

So what should I do now? Realistically I think that languages are always going to be the cause of some anxiety for me. Now that I am aware of it, I have to deal with it. I think that I should start participating more often in class, there are only 20 people, and realistically they are not there to pounce on me if I speak and make mistakes! For all I know, many of them may be feeling the same way that I do. I think knowing this will make it easier for me to teach languages to children who feel nervous or anxious too. I will be able to differentiate better as I will be able to recognise children who feel this way and perhaps allow them to do slightly different tasks, for example working with a partner as opposed to a large group.

I feel that this small amount of research and reflection has been very useful to me. I now know that I am not alone in panicking over learning a language and I am confident that I can overcome the worst of such feelings to be an effective teacher in the future.

Out of 5, I would give my anxiety levels a 1.

Al-Saraj, Taghreed M. (No Date) FOREIGN LANGUAGE ANXIETY: WHAT IS THIS? Available at: https://www.soas.ac.uk/lmei/events/ssemme/file67903.pdf (Accessed: 16 October 2015)

Horwitz, Elaine K., Horwitz, Michael B., and Cope, J (1986) Foreign Language Classroom Anxiety Scale. Available at: http://www.studyabroad.purdue.edu/Resource/InterculturalLearning/ForeignLanguageAnxietyScale.pdf (Accessed: 16 October 2015)

Maths Anxiety: What is it and how can we deal with it?

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Maths Anxiety

Maths anxiety is about the way we feel when faced with everyday mathematical problems, for example adding up shopping; splitting the bill in a restaurant; or working out how much flour to put in a cake recipe. It’s not about ability in mathematics, one could be highly competent but struggle with the most basic mathematics. David Robson, writing for bbc Future is a good example of this, he says:

“I have a university degree … in mathematics. Yet somehow, advanced calculus in the privacy of my own room was a breeze compared to simple arithmetic under the gaze of others – or even remembering my building’s security code.”

You could not possible claim that he is ‘bad’ at maths, but he struggles with very basic mathematics, why? Maths anxiety was researched in Stanford University, where was shown that then people with maths anxiety are exposed to mathematics, their brains react in the same way as a person who had a phobia would react to seeing their phobia. We should take from this that maths anxiety is not about ability, it’s not a label for people who struggle academically. It goes deeper than that, just as you would not chase an arachnophobic person with a spider to cure them, you cannot throw mathematics in a high-pressure situation at a person with maths anxiety as it will not help.

Something that we should also be aware of is that girls may be more likely to occur in girls, especially if their teacher is also female. Even in my own experience, women are more likely to shy away from mathematics, however the Department of Empirical Educational Research, University of Konstanz found in a study that girls did have more maths anxiety than the boys, but that both had similar abilities when tested.

What can we do about maths anxiety? One suggested method is to have pupils with maths anxiety write about their fears, the idea being that they can see their feelings about it written down and not see them as insurmountable. It is also thought that pupils should be taught to approach mathematics in a completely different way. David Robson suggests looking at maths more as a challenge than a problem, to try to do it and not be put off because its maths.

As a teacher, we should remember that children will pick up on the way that we feel about maths. If we act as if we are nervous or scared by maths, then children will think that there is something to be scared of, which there is not. They also may not fully trust us to teach them properly and they may not get as much out of the lesson as they should. I think that teaching style may be important here, making sure to spot any pupils who may have maths anxiety and giving them the necessary support, allowing them to work through mathematics, without any need to be anxious.

I decided that I would find out for myself if I have maths anxiety, the test I used gave 10 questions and I had to rate how much I agreed on a scale of 1-5. The results suggested that I am ‘fearful’ about maths but not that I have maths anxiety. This is useful to be aware of, as I would hate to pass such fear on, and it is part of the reason I am taking this module. I think that

Goetz T, Bieg M, Lüdtke O, Pekrun R, Hall NC(2013) Do girls really experience more anxiety in mathematics?. Available at: http://www.ncbi.nlm.nih.gov/pubmed/23985576 (Accessed: 14 October 2015)

Robson, D (2015) Do you have ‘maths anxiety’?. Available at: http://www.bbc.com/future/story/20150619-do-you-have-maths-anxiety (Accessed: 14 October 2015)

Freedman, E (2006) Do You Have Math Anxiety? A Self Test. Available at: http://www.pearsoncustom.com/mdc_algebra/math_anxiety_material.pdf (Accessed: 14 October 2015)

www.theguardian.com/education/2012/apr/30/maths-anxiety-school-supportBrian, K (2012) Maths anxiety: the numbers are mounting. Available at: http://www.theguardian.com/education/2012/apr/30/maths-anxiety-school-support (Accessed: 14 October 2015)

Tessellation

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Following the lecture on 28/9/15 on creative mathematics, I had some idea of what tessellation meant, but had never considered it in any great detail. I decided to look it up and see what I could find out about it. I decided to investigate what shapes would and would not tessellate…

I started by choosing some random shapes to see if I could tessellate them myself. I chose an isosceles triangle (orange) [photo 1], a pentagon [photo 2], an equilateral triangle (purple) [photo 3], a hexagon [photo 4], a star [photo 5], and a right-angle triangle (pink) [photo 6]. I made copies of the shapes, cut them out and attempted to tessellate them. Now my cutting and sticking skills are not up to scratch, but think it’s still clear that some definitely tessellate while others do not.

Following what was said about the angles at the meeting points on the tessellation, I decided to check that this was true. I found that that I could measure that point and it did add up to 360°. The equilateral triangle [photo 8] and the hexagon [photo 9] had angles which were exactly the same, whereas the isosceles triangle [photo 7] and right angle triangle [photo 10] had two different angles which helped to add up to the full 360°

The star and the pentagon did not tesselate at all, so I decided to look into this a little more, and came up with this website. {https://plus.maths.org/content/five-fits}. It explains that we get convex and non-convex pentagons. Non-convex pentagons have points which are bent into the shape, see example [photo 11], and these are not included. In the example, it can be seen that the bottom ends in to the shape, which is why it is non-convex. They set out to find an irregular convex pentagon which would be able to tesselate. It appears that there are 15 pentagons which will tessellate, the most recent of which has been published this year by Casey Mann, Jennifer McLoud and David Von Derau at the University of Washington Bothell, which looks like this [I will make it clear at this point, that this is not my own work, simply a summary of research conducted by Marianne Freiberger and those she has cited]:

My conclusion from this research is that clearly mathematics is not as rigid as I previously believed. If this new ‘tessellateable’ pentagon was only discovered this year, then clearly mathematics is still  continually evolving and updating, meaning that mathematics really is all around us and there will always be new discoveries to be made. From a teaching perspective, I think that this is an important message to impart to children, that mathematics should not be done to them, but they should be doing it and trying things out and perhaps one day they will be discovering new shapes or theories, and they should be able to use the basic skills learned at school to do so.

 

Freiberger, M. (2015) A five that fits. Available at https://plus.maths.org/content/five-fits (Accessed 29 September 2015).

Math-Salamanders (2015) Shapes Clip Art Triangles & Quadrilaterals. Available at:http://www.math-salamanders.com/shapes-clip-art.html (Accessed 29 September 2015)

Wikimedia Commons (2006) File:Isosceles-right-triangle.jpg. Available at: https://commons.wikimedia.org/wiki/File:Isosceles-right-triangle.jpg (Accessed 29 September 2015)

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