Category: 3.1 Teaching & Learning

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Why do we use a base 10 number system?

Easy peasy question many people might think. We have ten fingers so it can be a tool to help us count. However, how many teachers told you as a child to not use your fingers to count? I remember hiding my fingers under the table from around primary five upwards to count.

What about topics that we use in maths that don’t use a base ten system? Time. Time uses a base 60 for minutes and seconds. Time uses a base twelve system for the hours. Why don’t we count in any of these base systems? This is why time can be very difficult for a child to learn. When counting they have only ever used a base ten system and then when we introduce time anything familiar goes out the window. They are now introduced to counting in 60’s for each minute, for each hour. Another student on this elective discussed whether or not we should still be teaching time because of this (Dunne, 2015) – her opinion gives for an interesting read.

So apart from having our fingers as a tool I thought I would have a look into other base systems and the advantages of using a base ten system in this post.

As already discussed briefly in a previous post (“Our Number System”) there have been numerous different number systems which count in different base systems. The Sumerians “developed the earliest known number system” which had a base 60 system. The base 60 numeral system came from two tribes merging together as one used a base 12 numeral system and the other used a base 5 system and the lowest common multiple of both systems would be 60. Their symbols for their number system are below:

Number system

A base 60 system would perhaps make teaching time a lot simpler than a base 10 system. It would make sense for the minutes and the seconds but would also be very confusing still for the hours. On the other hand, this system has a lot of symbols which could be quite challenging for children to learn.

However, a base ten system does have a number of benefits. The base 10 system allows for simple explanations of hundred tens and units etc. Using a base two system such as the Arara tribe in the Amazon would get very repetitive and confusing rather quickly but on the other hand using a base 60 system it would take a long time until you exchange it for another to start again. A base 10 system has the benefit that it is big enough to not be repetitive but small enough that you are not continuously counting before exchanging.

This has given me a profound understanding of why our base system has come about. The benefits of the base ten system and why this is simple, as well as complicated when it comes to things like time or angles, for children to learn to count. Although there are many different types of number systems that are not just out normal base ten system or the roman numeral system that we teach children which I could use to broaden children’s knowledge, in my future career, on the different types of number systems such as showing them the yan, tan, tethera… video below as a different type of number system (a base 20 system) used for counting sheep more commonly used in the early 20th century but still used by farmers now.

 

References:

Dunne, J. (2015) Is it time to scrap time? Available at: https://blogs.glowscotland.org.uk/glowblogs/jennysjourney/2015/10/25/is-it-time-to-scrap-time/ (Accessed: 4/11/15)

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Learning to Unlearn

When I first heard the phrase “learning to unlearn” I was immediately thinking what on earth. Why would we want to unlearn? Where can the benefit on unlearning things? However, it turns out there are lots of benefits. Driving is an easy one – we learn bad habits, become lazy, stop checking mirrors not long after passing our tests and it only takes one accident to make people think I need to go back to my standard of driving when I passed my test. This is unlearning. It is unlearning bad habits.

Something crucial that I took away from one of our lectures from Professor John Baldacchino on “Learning, Education and schooling” today was that we constantly drill many things into children that they are losing their individual personality and their ability to interpret things differently or as Professor John put it – we are teaching children to think to a standardised model. I began to question why we teach children to be this way. Professor John compare this to art and when we go into an art gallery as a child we are told what to see in a painting. We are told what the painting must be. Why can’t we allow children to use their imagination of what a picture may be?

My former flat mate and fantastic artist drew a picture for one of her briefing which I have included underneath. I will not immediately include the briefing or title of the picture and allow you to imagine what this picture might represent.

hair

I am sure there are many ideas of what this picture could mean or represent. This picture is a self- portrait. Although when I think of the word self-portrait I assume it means a picture of the artists face and what they look like. To me (and I also assume many other people would think this as well), that is also standardised thinking, it is what I have been taught or told the word self-portrait means. On the other hand, Claire has done exactly what we spoke about in our lecture today. Claire has unlearnt what she has been told a self-portrait is. She has not gone away and spent hours perfecting a drawing of her face. She has taken a new meaning to self-portrait. The drawing itself and Claire’s thought process behind the drawing has inspired me to stop being so conformist and thinking everything for face value.

Claire has taken her briefing to do a self-portrait and instead taking into account the factor in her life that make Claire, Claire as an individual. Claire (who I am not going to attach a picture of yet – I will let you imagine and take as much as you can from her drawing just now) believes that the thing that make her an individual and what she has convey in the drawing is her ginger hair and her love of tea. She has incorporated two big things her life and used this to show herself in a self-portrait. This to me shows Claire as a person and not just by the way she looks.

On my first year professional practice I had done an art lesson on portraits. The art lesson wasn’t just to get the children to draw pictures of their peers. There was a message behind the lesson after getting to know my class. When I was planning for my lesson – I shared it on facebook for others on the course which I captioned “In an attempt to inspire my class that art can be for everyone and there is no wrong answer in art, my wonderful flat mates” (yes one being Claire) “and I (one art student, one English student and one teaching student) have drawn portraits… to show them there is always a range in abilities in art like any subject so we shouldn’t be disheartened. I have a range of abilities in my portraits to show them… and a range of abilities in acrostics… to try and show them we all have our own talents but we should always at least give it a shot, like my very willing flat mates have” who have also agreed to let me put them into my blog!

portrait 1 portrait 2 portrait 3

All of the portraits that were drawn by my flat mates, my class and myself were of course from the standardisation of thinking a portrait had to be of another person’s looks. In fact so standardised that the portrait only included their face not even a portrait of what the person looks like from head to toe.

If I were to do this lesson again, after reflecting on what I have learnt about standardised thinking and learning to unlearn. I would more than likely do a series of lessons: firstly getting them to do the same exercise again with the “standard portrait”; then have a brain storm of what else we think portrait could mean; and then have them create a portrait without anything to do with the person or their own face/look and see how differently we can show a portrait of someone.

 

(Big thank you once again to my willing flat mates for letting me including their personal art into my blog and lessons!)

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My French Phobia

As a teacher I probably shouldn’t be as worried about as many subjects as I am. Maths, French, English… However, in French I have always had a big phobia. I remember missing my first few lessons of French in primary six and forever feeling permanently behind since then. I have never really known the French alphabet or the basic numbers confidently. French has always been one of the few subjects whilst studying that I haven’t enjoyed. A subject I have had to force myself to do any work for. At the same time being one of two subjects that I had to study for almost daily to even attempt to pass my standard grade credit exam for.

All of this fear and anxiety was transported back into my body the second I walked through the door of my first French workshop at university. I was immediately greeted by a cheerful Carrie saying “Bonjour!” as I entered the room and there I was fear struck and transported back to second year at academy. I wanted to turn round and run straight back out of that room.

Carrie had set out the room to be in small groups. I had managed to sit in a group with someone confident in French. I began to slouch in my chair and try to avoid eye contact with anyone. I felt although I did not belong. I hadn’t spoke, read, written or even thought about French since passing my standard grade and I was no longer obligated to do it.

However, even though there were a few things I did not know in the lesson, I felt the workshop went quite well. At first I was very reluctant to join in with saying things or doing the actions that Carrie had prepared for the words. I would sit quietly saying the words I knew and avoid saying anything I didn’t until it came to the point Carrie would watch to make sure we were all joining in. I began getting more and more involved in the workshop when we were all one big group.

The minute we were spilt into five and more eyes were on me, I felt uncomfortable and anxious again. I felt people were actually listening to me and probably judging how bad I was. However, listening to people saying they were uncomfortable and also had the same experiences as me again made me relax a tiny bit more. Then once again, Carrie then changed it to focus more and more on the individual – in a group of twenty five. I was panicked. This was the worst. However, once I had over exaggerated this. No one told me I was wrong. No one embarrassed me. Carrie handle the class perfectly.

Even if I was completely rubbish at the French, I came out of the workshop feeling more comfortable, confident and ready to go back next time. Carrie had not only taught me some French, she taught me how to teach French in a fantastic way without even saying it. I compared the workshop to my primary and secondary education: I automatically knew what kind of teacher I wanted and did not want to be when it comes to my turn to teach French which is always a successful outcome in a education degree.

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Cross-Curricular Maths

After the Tessellation and Islamic Art maths lecture with Tara, I thought I would reach to the blog again.

Before starting this lecture, I thought shape in general for maths was quite boring. There was nothing interesting or mesmerising about shape when I was learning about it in primary school. However, tessellation was taking shape and doing something completely different.

Tessellation dIMG_6575oes not only involve shape but angles as well. I never realised that only shapes that when the points touch the external angles make 360 degrees would tile. For example four square edges would join together, each square internal angle is 90 degrees so four touching square angles equal 360 degree and they fit together perfectly therefore they have the ability to tile/tessellate. This also works for triangles (shown to the left), hexagons (shown below) and any quadrilateral shapes. However, it does not work for octagons and pentagons.

This is mathematics that is used by any tiler probably subconsciously. If I ever need to tile a room, I now know which shapes to use and which shapes to avoid! Although I do doubt if I will ever been tiling anything…

Using shape to make Islamic Art was fascinating. I have never thought of usiIMG_6586ng shape to create art before in this way and it will definitely be a cross curricular activity I use when I go back into the class room. The nipple and paste idea to create new picture of tessellation is also another maths and art activity I will definitely consider using within the classroom.

This is the kind of art that inspire myself to get the children involved in rather than just another drawing or painting, it is something different for maths, art and religion that I would hope I engage children in all curriculum areas.

These are a few more examples of a shape that tessellate and a shape that doesn’t tessellate.IMG_6576IMG_6579

 

 

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My Maths Mindset

Just after starting thMathAnxiety (2)e Discovering Mathematics elections, we were asked to do a maths anxiety questionnaire and reflect upon our maths anxiety. Therefore, this is my blog post on my maths mindset.

I feel my maths anxiety is overall quite low just now. I am fine, and actually quite enjoy, to listen to maths lectures and tutorials. I do not mind doing maths assessments that I am prepared for and aren’t graded such as the OMA. However, I feel more anxious doing examinations that are graded – this isn’t just maths related. The last time I felt like this was in standard grade maths. I quite enjoy the relaxed yet challenging atmosphere my standard grade maths teacher created. This is the way I wish to portray maths in my own classroom.maths

However, I dropped out of higher maths after two weeks because of the anxiety that I would not be able to cope with the level of mathematics and the stress of higher maths. After two weeks, I was feeling extremely anxious that the mathematics was too difficult and I would not get the support I needed to pass the exam.

I feel that maths is approached with a lot less anxiety and stress in university – it is a lot more relaxed atmosphere which is how I hope to convey it within my classroom as a teacher. I remember in primary 7 having a teacher on their probationary year and being very scared to answer any maths question in his class in case I got the answer wrong and was told so in front of the entire class. I feel that show me boards like we used in the lecture today is a good way for only me, as the teacher, to see how everyone is getting on with the topic without shaming them in front of their peers.

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The “Running Revolution” in Stirling.

For this blog post, I am going to look at Outdoor Education in particular comparing Sweden and the UK (in particular St Ninians, Stirling).

After our lecture inputs Brenda, I found myself in awe at Sweden and their approach to learning. I am very keen to learn more about outdoor education and this is what I intend to do with my learning from life placement this year hopefully as well as just getting a part time job with links to outdoor learning.

I found myself eager to complete the TDT tasks for the comparative education with Sweden yesterday and realised how far behind the UK actually are in terms of outdoor education. I remember being in primary seven and the class asking to go and learn outside about a topic and being told we couldn’t as it hadn’t been risk assessed. However, Sweden on the other hand, totally trust their system, pupils and most importantly the teachers to not do anything that would cause huge amounts of risk.

Today however, I just read an article (The Running Revolution) about a school in Stirling, Scotland which prompted this blog post. St Ninians School have recently made the news around Scotland for the fact they now have no children with childhood obesity and they have also managed to increase concentration in class. Their secret. The great outdoors. As cringey as that sounds – it works in Sweden and it is clearly working in Stirling. In Sweden, the teachers state that getting outdoors for at least half of the school day in preschool Runningbuilds good health in children. Whilst at St Ninians this has proved that even getting outdoor for a small part of the day has improved the health of children by reducing the amount of children with childhood obesity to zero. St Ninians have spent the last three years having a daily mile – this is where they get their children outside to walk or run a mile every day. The teachers choose when in the day they do it, whenever fits best with their timetable for the day.  The only thing that stops the classes doing their daily mile is heavy rain or ice.

The teachers and the children both clearly benefit from this scheme – the teachers have commented on how much the children enjoy going out for the daily mile or it would not be maintainable with their enjoyment. The teachers and children both benefit from the increased focus and concentration in the classroom as well. Therefore it shows that taking 15 minutes away from teaching time can clearly impact positively on the learning time in the class. In Sweden, the teachers cannot believe that the children especially in early years education are not getting outdoors to play and enjoy childhood. St Ninians, Stirling clearly are edging towards this aspect of outdoor education and enjoyment with the children at their school with even just a very small proportion of the day.

In my opinion, I believe that this shows that outdoor education clearly positively impacts on the learning, health and concentration of children at school. Both Sweden and Stirling have been able to prove this statement. Sweden tops European League tables in literacy by the age of 10 and Stirling have been able to banish childhood obesity from their schools. Other schools in the UK are beginning to take notice to Outdoor Learning, more now due to the success at St Ninians which is a positive but slow start compared to Sweden.

I have left a link to the Guardian newspaper in a hyperlink above in case anyone wishes to find up a little bit more about St Ninians and their daily mile.

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Discovering Mathematics: An Introduction

As we are just finished week three of the Discovering Mathematics but we have just started our new ePortfolio on glow blogs: this introduction is a bit overdue so it is not one hundred percent an introduction precisely.

Before starting the elective on mathematics I was a mixture of nervous and excited. I haven’t studied maths since fourth year in academy which meant this could test my maths skills a bit. However, after the email (from Richard) and hearing how enthusiastic Richard was about the maths elective made me think how great this elective could be. I knew that I had enjoyed teaching maths on my first year placement and I was looking forward to finding out new and exciting ways to bring maths into the classroom.

So far, this is possibly the most engaged I have been with any module. I am really enjoying all of the lectures and the lecturers excitement about maths. There is so much about maths that I did not know about and it has so far totally changed the way I look at maths and the way I feel about maths all together. I have been eager to blog and share my discovering mathematics experiences so far.

I am looking forward to the rest of the module, blogging about my experiences and taking the maths anxiety quiz again at the end to see how my feelings towards maths has changed over the elective.

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Blackboard to Glow Transition

After our ICT lecture with Derek on the ePortfolio transition to the VLE Blackboard to Glow Blogs, I have decided to blog the changes. Last year in MA1 we had a bit of a disastrous time using blackboard for our ePortfolio, the lack of engagement with the ePortfolio showed because of this.

The blackboard ePortfolio was a long list of pages with no interconnectivity between them, this meant that the students  had to write and copy and paste anything they wanted to feature in more than one page. However, on the Glow blogs, students can categorise  one blog post onto as many pages as they wish as well as linking each blog post to the professional standards.

The Glow blogs allows easier sifting through posts. In the ePortfolio on blackboard, there was endless pages and posts getting lost throughout the pages which I can only believe made life difficult for the advisor of studies and markers to look through and find the relevance of each post. However, on the glow blogs ePortfolio, the blog posts can be tagged and categorised into different pages and professional standards which means that the posts can be found with a lot more ease in my opinion.

I personally think that adding links, different blogs/ePortfolio’s, media I think is a lot easier on the glow blogs than the ePortfolio from blackboard. I think adding links, videos, pictures is more straight forward on glow blogs than it was on the ePortfolio, I never once added a video or picture to my old ePortfolio but I will not hesitate to add to my new ePortfolio.

Overall, in my own opinion, I definitely prefer the new glow blog ePortfolio over the blackboard ePortfolio and I think this will show especially with the MA2 engagement in the ePortfolio.

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