Category Archives: 3.1 Teaching & Learning

Vita Brevis – Exploring the usage of Artefacts and Sources within Social Studies

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Pickford, Garner and Jackson (2013, p.62) define artefacts as being valuable man-made or man-influenced objects that can encapsulate particular locations or sections of time within the world, which explains why they can serve as being strong backbones to particular contexts for establishing social studies learning. They can also vary greatly  in their appearance and purpose. Within Social studies, they can be extremely useful for teachers to be able to paint a picture of a particular era in history that they may be exploring or even be able to showcase a particular culture of a different part of the world (Fines & Nichol, 1997) or even both together, as the social studies subjects are interwoven; a particular place is essential to the event as it is the location in which an event has transpired.

Within our elective inputs we have continually had time to be able to utilise and explore artefacts, thus inspiring this piece within the portfolio as I wanted to delve deeper into the pedagogical core that lies within the teachings of social studies through the usage of artefacts and sources.

A prime example of the usage of artefacts during our inputs was during our Tay Rail Bridge Disaster session where we were able to work with various types of sources relating to the disaster in Dundee. A staff member from the University of Dundee’s Archives came in to provide us with these artefacts and gave us some background knowledge and also emphasised to us as future practitioners the importance of using links like the University of Dundee’s Archive, where real-life sources from particular eras can capture student’s attention towards history and geography. The archiver made some great points in terms of justifying the usage of artefacts with a class, mainly as it allows a great basis for telescoping the past with the present and vice versa. For example, one of the artefacts was a newspaper from the 1880s (a few years after the Tay Rail Disaster, which occurred in 1879) which could be used for the basis of various points for inquiry. We explored how the formats of newspapers will have developed over history and how they compared to the newspapers of today, giving us a greater insight on how the demand for media has adapted as time has progressed, showing that an artefact can take many different approaches when deconstructed. Nicole Brown (2015), a lecturer within education, has also emphasised this point of importance towards the usage of artefacts being capable of exploring multiple faucets of learning, as practitioners can show production processes within enterprise (an area of great importance within Social Studies for Curriculum for Excellence), or a significant event within History, or an artefact can also serve as a contextualised link to a particular culture and language of another country.

Other sources within the input from the time included images that were taken during the aftermath of the collapse of the rail bridge and then of the construction of the rail bridge that stands today, a poem that was found inside one of the victim’s coat pockets that washed up on the shore, and a compensation form that was assumed to be submitted by a family affected by the disaster. In regards to the photographs, we found it quite difficult to pinpoint what the photos were at first due to the omission of captions detailing what the images are. This then brought about an interesting point for criticality in terms of the usage of artefacts. It is all well and good to have real-life artefacts and sources from a particular age, however, if one does not have the story and historical context surrounding the source itself, then a practitioner is left in a difficult position to facilitate correct learning surrounding it.

Artefacts can also be explored through a more imaginative approach if a particular context wants to be explored. Hughes et al. (2000, p.32) believes that the strategy of creating an Evidence Bag can serve as an excellent hook for students to really hone in on criticality towards a particular topic that a practitioner wants to explore. For example, the usage of an old worn suitcase can spark a great discussion surrounding who it might have belonged to, how old it might be and what kind of contents may be inside. This can be the basis for many areas in the curriculum: WWII evacuation, Victorian era and even modern-day evacuations just being a few. Linking back with the example we explored in lectures, even a bag from the Tay Rail Disaster could be employed and items of local significance could be used to get the children to pinpoint where the case/bag was from and what time period it may be. This process allows children to make interpretations with there being no one right answer during the questioning and investigation process, which can aid in self-esteem of students who feel that they are pressured to be right when they provide an answer.

Identity and Context Meet – the usage of an evidence bag approach can really serve as a great basis for getting students to unravel and explore people from the past.

I feel that the biggest impact surrounding artefacts was when we got to see the original version of the poem that was recovered from a body from the waters after the Tay Rail Disaster. Tattered and torn, minute in size and yet it had an instant impact for what it could have meant for whomever had kept it within their possession during their journey on the train. Instantly I felt myself trying to draw conclusions towards this peculiar artefact before us in terms of its backstory… maybe it was written by a close friend or relative to the person… perhaps it was written by the unfortunate soul themselves… or maybe it was written by a loved one and that was why it was packed away safely within their coat pocket…

No matter the true backstory towards this artefact, it showed the power of using real-life sources for exploring the Social Studies. It also brought about a deeper appreciation for Historians as they were able to preserve this piece of history in order for people like us to see a snapshot into the lives of people in the past. The person may have lost their life in the disaster, but the live in through this artefact that they held dearly with them.

We also listened to a piece of fictional prose surrounding the night of the disaster and it really encapsulated the raw emotion that is evident within history.

Vita Brevis – Life is Short: This is the piece of prose that we listened to in the input. It showed the power that fiction can bring towards artefacts surrounding a topic. Click the image to be re-directed to the prose at the BBC.

The prose, created for the BBC School Radio (2017) also emphasised the importance of language and how effectively literacy activities can be used in Social Studies. It was great to be able to explore the artefacts that were from the time of the event, however, a piece of writing that was narrated in such an emotive manner allowed for us as listeners to be able to connect the present with the past, just as the archiver said was the key purpose in teaching social studies. We could relate real human emotions towards something that could feel somewhat abstract in the grand scheme of things; this event happened many years before us and we probably would find it challenging to contextualise it as efficiently without something to captivate our emotions. Using something like this would be beneficial as well for students to hone their listening skills as they need to really be actively listening and engaged to be able to gain the depth of emotion and empathy (Busch and Oakley, 2017) relating towards the topic that was such a sad disaster.

Overall, after the inputs and further reading towards the importance of artefacts and sources within practice whilst teaching the social studies, I feel more capable that I could be adventurous and daring with my teaching of historical topics. This is because I have seen the difference it can make to deep understanding for not only a particular event in history, but also for human reactions to disasters and chaos as a whole. Using a wide breadth of artefacts can also really make a difference in the understanding that is picked up by students. Furthermore, I also understand the issues that can come about with using artefacts that have little story behind them. I also realise the great importance of sourcing artefacts from the likes of the University of Dundee’s Archives, as they can have valuable sources and artefacts that would be otherwise hard to come by within practice.

Reference:

BBC (2017) School Radio: Victorian railways: 3. The Tay Bridge disaster [Online] Available at: https://www.bbc.co.uk/programmes/p05903hw (Accessed: 18 October 2018)

Brown, N. (2015) Teaching with artefacts [Online] Available from: http://www.nicole-brown.co.uk/teaching-with-artefacts/ (Accessed: 15 October 2018)

Busch, B. and Oakley, B. (2017) Emotional intelligence: why it matters and how to teach it [Online] The Guardian Available at: https://www.theguardian.com/teacher-network/2017/nov/03/emotional-intelligence-why-it-matters-and-how-to-teach-it (Accessed: 18 October 2018)

Fines, J. & Nichol, J. (1997) Teaching Primary History. Oxford: Heinemann Educational Publishers.

Hughes, P. Cox, K. & Goddard, G. (2000) Primary History Curriculum Guide London: David Fulton Publishers

Pickford, T., Garner, W. & Jackson, E. (2013) Primary Humanities: Learning through Enquiry. London: SAGE Publications Ltd.

Grade 5 Exhibition – Examining the PYP

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I have successfully worked my way through all of the grade levels during my first month at ISS and have been able to teach and assist in all of the levels of progression that are offered at the Lower School… except for Grade 5.

This was done purposely during planning because it is now the time for the students in grade 5 to be focusing in on preparing for the exhibition where they will need to have investigated a topic independently and organised a presentation centred around the issue.

My job for the next month of my placement is to assist in the teaching of the grade 5 students in their exhibition, which are all unique to the child. So, my dynamic as a teacher will need to adjust to fit the PYP once again.

Within the Primary Years Programme Exhibition guidelines (2008), it outlines the exhibition as being a key event that displays all of the skills a student has built up during their time in the international education system and it allows students to showcase their findings and actions that they have done to work through a real-life problem in the world.

More Documentation – The guideline reading has been really beneficial for me to get a better understanding of what the overall framework looks like and must feel like in order for a school to be truly considered an IB school.

Purpose:

The purpose of the exhibition is for the children in their last year before moving into the middle school to really go in a large amount of detail during their inquiries that they predominately do in a collaborative manner with their peers. It also allows students to really show their own learning on both an individual and group level basis. This is because, in the run up to the exhibition, the students are continually reflecting on their learning journeys with their teachers, their mentors and their peers.

The Basic Outline:

  • Students work towards the exhibition during (normally) the last term and it culminates towards a big event day where students can showcase their learning through a specific topic of their choice that interlinks with the central idea.
  • The exhibition itself must enable all the attributes of the learner profile to be showcased, whilst also incorporating the key concepts and also making sure that the transdisciplinary themes and skills are being utilised. Overall it is the grand finale of the PYP before students move onto the next phase into the middle school/secondary education.
  • The students need to also cover all of the “subject areas” with the exhibition incorporating an artistic component (which could be art, writing, music or a drama piece; it must relate to the expressive arts subject areas), a usage of mathematics (data handling in our case), writing (speech, interviews, research) and technology (using technology to create websites or to research information). Another other area can also be tapped into with their action – some are doing experiments to collect results (science) and others are looking into the background of a particular event (history). The pathways are really open to interpretation so long as they interlink with the central idea and the key concepts of the PYP.

The Central Ideas & Key Concepts – these are core to the PYP programme and the exhibition as a whole, as the exhibition is showcasing all of the skills students have culminated up to this point in their time in education.

Now, seeing this in practice, I have really found that the exhibition really holds a strong place in the eyes of the children that are actually part of the process within grade 5. This is because they are choosing a topic that both interests them but also a topic that is an issue in society that they can bring awareness to and even bring about change towards. For being aged 10-11, the topics are really hard-hitting: racism, anorexia, warfares in home countries, air pollution and many more topics have been chosen by the children. What I’ve found is that the issue really is of a great passion for the children. In the words of the Exhibition guidelines, it should “offer the students the opportunity to explore knowledge that is significant and relevant” (International Baccalaureate, 2008, P.2)

Within these topics then, is where teaching can be worked within the frameworks that we are used to. Data handling and graphs are the centred topic within mathematics so many students are creating surveys and then analysing the data they have collected centred around their topic, thus creating a duality product of inquiry-based knowledge interlinking with the advancement of skills within a particular “subject area” (however, the subjects are not so regimented in comparison to other curriculums).

This then all allows for more freedoms for teaching, but also places more constraints on it as well. It is much harder to do a whole class lesson with this approach to learning because the children are very individual in their specific areas of inquiry. However, what can be done instead is the introduction and advancement of specific skills – how to analyse sources, how to construct grafts, how to write a speech and other useful approaches needed to conduct the exhibition.

The children are continually reminded by their environment of what they are capable of when they work towards being the best versions of themselves. Not only this, but also focusing on reflecting across the journey of learning.

Looking beyond this stage of learning, I can see how it is really preparing the students for the futures ahead. They are required to maintain a log of their references (something that rings true at university level) through NoodleTool. This way, the students are not just plagiarising from their sources and are seeing the relevance of crediting where they have found their information. Then the topics themselves and the process of finding action to try and make a difference towards the problem really emphasises the internationalism within the learner profile that the school strives to achieve. It shows students from an early age that, through drive and determination, they can truly make a difference once they have established a strong ground of research behind a topic.

What I also find is that because there is no standardised testing in the system (or not as heavily as other systems) the students are really being able to explore as much as they want to with their topic. It is establishing an environment where students continually want to be doing their best because it is those that reap the best benefits. There’s no need for extrinsic motivation because the children realise that the learning is for themselves. This also interconnects with another area of the exhibition and that is the reflective journal. I knew straight away what this meant for the students being that for this very module I have to maintain reflection around my learning. The students are required to document their progress in their exhibition weekly in the run up to the event and create goals. These goals are then self-assessed – “was I too ambitious?”, “do I need to work harder next time?” and “where do I go next?”. Regulation and self-awareness are then also advanced because students are checking in with themselves on what they’ve done. It is not a focus on what someone else believes upon their progress, because at the end of the day the learning is for them.

Taking this outlook on the concept of the Grade 5 Exhibition has been very helpful for my practice because it allows me to go in with my time with the grade 5s with a greater understanding of what is both required of them and what is required of me as a teacher that is directing them and aiding them in their learning.

Reference:

International Baccalaureate (2008) Primary Years Programme: Exhibition guidelines. International Baccalaureate Organization: Cardiff.

Taten sagen mehr als Worte – Week 3 in Stuttgart Reflection

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Third week in and it is that time again to sit down and critically reflect on what has transpired this week. Already I am feeling really at home working at ISS.

I started my work with the grade 1 classes on Monday (26th of March 2018), as I have already worked with the grade 4s, 3s, and 2s, so I continued working my way down the grades right up until the beginning of the Easter holiday break (which is approaching very quickly!). Then, I will work with the Early Years team at ISS for the first week back and then I will work more in-depth for the rest of my placement with Grade 5s as they prepare for their Exhibitions (which I will no doubt blog more about nearer the time).

What is most insightful from working between grades is that I get to not only see the overall progression within an educational institution, but I also get to become a recognisable face to many more people around the school! This is one area that I’ve found has expanded a great deal as the weeks have progressed: my confidence to work with people at ISS, as I am becoming well acquainted with more staff members and children with every passing moment. This will stead me well in other educational settings (particularly the placements in MA3 and MA4) because I realise that as a teacher, you need to be both approachable and open for everyone that comes into contact with you, this shouldn’t be exclusive for just the kids in your practice. You should also go out of your way to welcome others in the school community; something that the staff members at ISS have done with me, which has greatly aided my confidence.

Now, although the school week was a little shorter this week for the Easter break, so much was packed into my time with the grade 1s.

From the get-go, I was working hands-on with practical work with the young children that are in their first year of primary school at ISS (I have found it was a lot more practical-based in comparison to the other grades). I first had to act out different scenario poses to help the students come up with “dialogue” for me as a character. This would feed into their work towards their writing activities that centred on introducing speech marks into text. Albeit giggly and giddy, this approach got the children really focused on really thinking about what their characters would be saying in their own stories and it also served as a great icebreaker for the kids to get introduced to me as one of their teachers for the week.

The dialogue options that the children came up for me as a character

Straight away I could see clear areas of progression that are crucial in getting children engaged with any form of writing. The classroom environment was surrounded by language in the format of posters, books and signs. The children also illustrated the stories that they were writing in order to fully experience their writing in a multi-sensory manner. These skills and knowledge in language through multi-platforms of media will serve them very well once they progress through their time in education. I can vouch for that from seeing that skills in writing only expand as we work up the grades (however, this can only happen effectively when children are within an enriched environment like the one established in the grade 1 classrooms).

Two of the examples of the different processes that can be used by the children when working with numbers – drawing pictures and writing number sentences are key skills needed in having fundamental knowledge within the skills of mathematics

Mathematics followed a similar theme as the grade 1s were working with numbers and number sense. Just like in grade 4 and 3, the students were tasked with looking at their mathematics problems in a deeper way than just as problems that simply need correct solutions. Instead, the practitioners made it clear to the children that they had to emphasise the methods they could use in solving problems. Number lines, tally marks, pictures and number sentences were some of the examples on the board that the children had to show in their working out for problems, which further emphasised my understanding that was established in both the Discovering Mathematics module and the STEM module which showed us that students need to be able to get a real fundamental understanding of the core areas of mathematics and be made aware of the interconnections between concepts (Ma, 2010) (which the International Baccalaureate heralds as a key area that teachers need to do across all areas of learning).

I also, on Monday, got to witness the children’s specialist music lesson, which was also very helpful to see areas of progression, as the older students are very capable in playing instruments. This is evidently because the grade 1s are, like in all the other inquiry-led learning situations, set off to investigate into their knowledge in music to expand on it and to form it into something new. A particular group I saw that really engaged with the inquiry-based approach within music were trying to play the full song of “twinkle twinkle little star” together with boomwhackers that were different sizes to correlate with the different pitches of noise they made when played. The children had already explored the notes that they could use in playing instruments prior with the teacher, however, they had to figure out the correct sequence to produce the song together. Through lots of practising and determination, they were able to achieve the full song together and I got to see the importance that it brings to the children to figure something out for themselves. The music teacher could have easily stepped in to show them how to play it correctly, however, the process into achieving the song was the core essence of the learning experience as a whole. They were working with interdisciplinary skills of sequencing (a skill evident in mathematics and science), knowledge of music notation, and their listening skills, to name a few, in order to problem solve their way to success! It really showed me that too much involvement from a practitioner could really spoil the overall learning experience for the children in certain circumstances. Time should be allowed for the children to come to their own conclusions in learning – something I think we can take for granted sometimes as practitioners.

Tuesday was a very busy day for me as there were a few staff members off due to sickness. I started my morning with interviewing the children in grade 1 individually or in pairs depending on their projects that they were working towards for the Erasmus visitors. Just like the grade 3s had their school of fish on their doors and the grade 2s had their movement in play artwork on theirs, the grade 1s were tasked with creating their dream playground that used many different forces with 3D shapes. Forces in the world is the main area of inquiry for the grade 1s and it, much like all the other aspects of learning in grade 1, is evident across the whole learning environment.

Examples of some of the books evident in the grade 1 class – emphasising the importance of research through different medias, particularly for their UOI topic in forces.

I had to make sure that the children could justify their creations, which interlinked with the core area of post-reflection that is a critical stage in the learning process for the International Baccalaureate – “Reflection can happen at any time in the lesson, and it is vital that it is given time, whether through the teacher, individuals or groups, written or verbal” (Bunting, 2015). Forces such as pushing, pulling, going forward and backwards, moving up and down and stretching and bouncing were evident across most of the designs that were so outlandish in the imaginations. It was great to see such a creative outlet being used for exploring a really scientific topic.

Science, however, was not missed out from the learning. To end the day on Monday, I read a book that was about the different types of forces and the concept of friction to the children. An interesting idea that I found in the book was the concept that friction can slow objects down – particularly if you roll a ball down a ramp that has a carpet on it. So, the teacher came to me and gave me the task of establishing a science experiment that could test out this discovery. During the UOI time this week, the teachers all set up their own station that the children would go around to see different: magnets, Lego, creating dances with force movements and so on. My station was centred around what we learned in the book on Monday: what happens when you roll a ball down a ramp with and without a carpet? I also added different factors like changing the type of ball used, increasing the slope of the ramp etc. The children were really engaged in this station, however, for some their youthfulness meant that they got a little carried away with building their ramps. This was beneficial for me, however, to see the difference in approaches needed with younger children. Upon reflection, I can see that I maybe should have had more tasks to keep the children focused on what it was I asked them to do – maybe included different types of carpets or limited the amount of blocks they were allowed to use when building their ramps or given them examples of what they could make. An area that I thought I tackled well was the big factor that many of the grade 1 children were on a vast spectrum of English communication. The sheet that they had to complete about what they had learned at my station could be completed either by writing or by illustrating the equipment that they used. Some even had a mixture of labelled diagrams, However, the overall learning was still there and the same children that could not write out their learning could easily explain the forces behind the experiments that we had conducted, which emphasised to me that the language barrier should not be the main hindrance for children to progress in their learning. Overall, it was great to lead groups of younger children through learning, as it has better prepared me for my Early Years placement and already started areas within me that I know I need to delve into deeper to understand the importance of early years teaching as a whole.

It was great to be back with the grade 2s to see how they were progressing with their models and overall understanding of castles! It was particularly interesting to see the kids painting the brickwork onto their castles.

Tuesday afternoon was a prime example of the changes that can happen within a school on a daily basis. One of the grade 2 teachers explained at lunchtime that day that her support assistant was sick and she could not complete an as in-depth lesson as she hoped. It luckily worked in time when the grade 1s had a specialist lesson so I thought it was best for me to return to grade 2 to assist in the lesson. The children were excited to see me again as they had enjoyed my lesson about Scottish castles the week before. I remained with the main class to assist and guide them through their writing activity that was around a castle book that they had read as the teacher took groups out to start the painting of their model castles. It was a great feeling to be in charge of a class again and the techniques of management that I had learned last year served me well for maintaining order in a lively afternoon class (especially when they so desperately wanted to go out and paint their castles). The lesson was a success and the children were then all brought out to paint the rest of their castles.

Thursday saw the day ending early for teachers to embark on another professional development day. I got to continue my science experiment station for the kids that did not get around to trying it out the other day and I also got to witness the children’s specialist art time. The day ended with a circle time talk about the children’s plans for their Easter break and it was extraordinary to hear the all the different places that the children would be visiting in the world!

Overall, this week has been a shorter week in the school however it has been packed with so many learning points. I have made great progress in my professional development and have been using the information I have gained from my investigations into the International Baccalaureate system when working with the different grade levels. I have also worked more heavily in teaching points this week and hope to continue this when I come back after the Easter break, particularly when I work more intensively with the grade 5s. However, now I hope to truly experience the Easter celebrations of my host family and come back refreshed and ready for more learning!

Reference:

Buting, N. (2015) Approaches to Reflection [Online] Available at: http://blogs.ibo.org/blog/2015/10/31/approaches-to-reflection/ (Accessed: 30 March 2018)

Ma, L. (2010) Knowing and Teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States Anniversary Edition. New York: Routledge.

 

99p – Maths Behind Consumerism

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During my first year placement, a key topic that I was regularly given the responsibility of planning lessons for within mathematics was budgeting. Now, within the Experiences and Outcomes documents there are various outcomes that cover this topic:

MNU 2-09a – “I can manage money, compare costs from different retailers, and determine what I can afford to buy.” (Scottish Government, 2009, pg.6)

MNU 2-09c – “I can use the terms profit and loss in buying and selling activities and can make simple calculations for this.” (Scottish Government, 2009, pg.6)

I write this blog post in the prospect of gaining a deeper reflection upon the experiences in relation to what we have been exploring during the Discovering Mathematics module.

Having an upper stages class allowed for more creative freedom in terms of setting up lessons that could be relevant to the learners within the class. More contextual and relevant aspects could be explored, with their existing knowledge of mathematics, in comparison to just establishing rules and procedures when calculating problems.

The community around the school had a large shopping centre where there were various shops that had large catalogues full of products for people to buy.

Using relevant resources, such as catalogues, allows for children to understand the connection between the ‘real world’ and the mathematical skills they learn

I used these catalogues in order to establish a lesson centred on the concept of working within a budget. I divided the class into varied ability groups, so that less confident students could be aided by those more confident in their calculations.

Their task was simple in its expectations: as a group, you have to decorate a living room whilst staying within budget. There was a list of required items they had to get and then there was space for free choice once they had got the basics (Sofas, TV, coffee table etc.) What the groups didn’t know was that I gave each group their own individual budget so that the types of furniture and the amount of furniture bought would be very different across the groups.

Once the groups had finished up with their purchases and calculation I brought them back as a whole class in order to gain some feedback on how successful they were with staying within budget. What I expected occurred: the students with the smaller budget struggled to stay in budget at first and had to adapt and change their expenditure. Also, the groups with larger budgets were able to buy more free choice products once they had worked out what money they had left over once getting the living room decorated.

“Why is it important to do calculations like this when buying things?” I asked the class.

The responses hit the nail on the head with the entire purpose of the lesson – so you know what money you actually have and so you know what you can afford. As much as the kids found it entertaining and different going catalogue shopping, it had a real underlying purpose that went beyond just reinforcing their mental math skills. The core purpose was to bring importance to skills they had learned, through the four operations, and bring a context that was familiar to them in order for them to see the relevance of learning mathematics in school. This lesson will no doubt occur for them once they reach adulthood and have to decorate their own homes.

Beyond this lesson, I also got the groups to use IT in order to explore other shopping websites to compare the prices of similar products (which taught them the importance of searching around when being restricted to a budget, as one price isn’t final) and I also wanted to delve into the marketing side of things when exploring the catalogues.

A key point made by a few of the students was that the majority of the products were not simply £15 or £50; they were £14.99 or £49.99. I knew that I couldn’t lose the opportunity to explore this topic further.

The whole consumerism psychology behind pricing of products has been thoroughly explored by these huge companies that we shop from. Psychological pricing is a phenomenon that is literally inescapable across the vast amounts of aisles within supermarkets and shopping centres. It is everywhere

ONLY 99P! SALE! ALBUMS UNDER £5! REDUCTIONS!

These bold, bright and in-your-face slogans are all there to get us to cave into buying something, to put it bluntly. These strategies are also there so that, when we buy something, we feel as though we have gained some form of saving in our spending. There are various theories and concepts of why .99 is so effectively used, however, a core reason that a price ending in .99 or .95 is chosen is because we read prices from left to right, so we associate the first number as being the overall price (Melina, 2011). Another example is that it is harder for us to calculate the total cost by the time we have amassed a large quantity of shopping in our carts by the time we arrive at the checkouts (in real life or online) and this can be another example of maths anxiety plaguing adults who fear working with numbers. We psychologically believe that £4.99 is cheaper than seeing £5 because our brains first see the 4. The ‘under £5’ slogan is one that is used regularly to heighten this idea of saving being gained, when in actual fact the product is probably £4.99 or £4.95. Factually it is under £5 but, is there really a massive saving here?

“[Consumers] have become conditioned to believe that they are getting a good deal when they buy something with a price ending in .99 even if the markdown is minimal” (Melina, 2011)

The children in my class were very aware of this aspect when we decided to explore the topic of shopping and budgeting further as a whole class. Links to buying their favourite sweets at the shop outside the school were made when exploring the fact that businesses are, economically, looking to make as much money from us as positively possible. Another important point that one of the kids brought up was that, when buying things, they mainly received back change after they had bought something.

Change is another tool utilised by businesses. When we purchase something, it is normally unlikely that we have the exact change outright, so we pay with something over the price and, in return, we receive the change in difference. Doesn’t seem complicated, does it? However, with fractional totals come more lucrative gains from vendors because studies have shown that we like receiving money back once we have spent, what was most likely a lot of money. It doesn’t make the blow of handing over cash so hard to take, continuing our spending because we aren’t going away completely empty-handed. (Bizer and Schindler, 2005)

Teaching children to be critical of pricing strategies used by big companies widens the importance of Mathematics

Overall, the various lessons that I planned on budgeting explored topics that go far beyond the realm of perceived primary school mathematics. Skills such as addition, subtraction, rounding, place value and more were utilised on top of a contextual learning space of consumerism, marketing awareness and psychological studies of how we shop! This ties in well with Ma’s theory on connectedness, which I wasn’t made aware of until studying this module.

Reflecting on placement now, in the midst of studying the Discovering Mathematics module, I can now see how my first experience with teaching mathematics was quite successful. Beforehand, I had to brush up on my mental arithmetic, explore the psychology of marketing and then construct lessons that fit towards the E’s and O’s. This shows that I was making myself aware of the ‘simple but powerful basic concepts of mathematics’ (Ma, 2010, pg. 122) in order to make my lessons more effective. This links well with Ma’s Basic Ideas in terms of the PUFM (profound understanding of fundamental mathematics) an educator must know in order to be successful in their teaching.

Progressing through the module, I am very glad that I chose it because it not only benefits my conceptualisation of mathematics for the future, but it is also reshaping my understanding of my previous experiences and sparking points of professional reflection (and reflection upon what money I’ve spent in the sales!).

Reference:

Bizer, George Y. and Schindler, Robert M. (2005) Direct evidence of ending-digit-drop-off in price information processing [Article] Available at: http://onlinelibrary.wiley.com/doi/10.1002/mar.20084/full (Accessed 25th of October 2017)

Ma, Liping (2010) Knowing and Teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States New York: Routledge.

Melina, Remy (2011) Why Do Prices End in .99? [Article] Available at: https://www.livescience.com/33045-why-do-most-prices-end-in-99-cents-.html (Accessed 25th of October 2017)

Scottish Government (2009) Numeracy and mathematics: experiences and outcomes document [pdf] available at: https://www.education.gov.scot/Documents/numeracy-maths-eo.pdf 

Interesting Link:

http://news.bbc.co.uk/1/hi/magazine/7522426.stm Why is a 99p price tag so attractive?

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Maths Anxiety: What We Should All Fear…

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The subject of Maths is divisive, even beyond the system of education, and it has the potential to greatly impact people’s everyday life (both for good and for bad, depending on someone’s experience with it during their school years) (Bellos, 2010). It has been argued that it has the potential to separate humans into two distinctive categories; there are those who just “get Mathematics” and then there are people in society who think that it is an impossibility for them to ever understand the fundamental concepts of mathematics, so avoid maths for the rest of their lives (Foss, cited in Skemp, 1986). Today, we can understand this as a person being anxious about mathematics: Maths Anxiety.

Having a fear of anything related to mathematics has plagued society for generations and it continues to affect our young learners of today. An even scarier reality is that it even affects our educators.

Us.

It has been said that teachers that feel insecure within their knowledge of mathematics will pass on their worries to their students and they will instil negative connotations towards the subject because of the anxiety, resulting in their students not reaching their full potential (Haylock, 2014). Thus, resulting in a class-full worth of people being incapable or intolerant to working with maths (something that is essential to being successful in life i.e. being able to work with your finances). Therefore, it must be paramount that a teacher who feels jittery about mathematics seeks help for their fears. The only way to do that is through diving headfirst into the world of mathematical thinking.

I myself can relate to the fact that teachers pass on their woes to their students as I have had many teachers tell me that mathematics is really tricky, which from the get-go, put boundaries between the subject of mathematics and I. However, to contrast this, I have had some amazing math teachers in high school when I was sitting my exams and their profound understanding of the subject allowed me to fully enjoy the subject and get the grade that I needed. The best teacher I had during my higher exams worked through topics with feedback from us, as students, to gauge what needed to be revised and revisited in the run up to the exam time.

However, once I did get the grade in higher Mathematics that was it for me with the subject. At least, that’s what I thought. Until it became clear that I myself was going to be teaching the subject.

I decided to choose the discovering mathematics module as an elective because I wanted to know the behind-the-scenes of what makes a successful teacher in mathematics and I felt that it would be in my best interest to study Mathematics in order to iron out any queries before teaching the subject myself. As I saw on placement, it isn’t enough just to know how to work out a problem. You also need to investigate the complexities of incorrect answers, alternative methods and the varying opinions and abilities of the subject within the classroom.

The main text of the module, Liping Ma’s “Knowing and Teaching Elementary Mathematics” is a great example of an academic text that picks apart the realities faced by teachers on practice. Not only that but, Ma (2010), contrasts and compares the teachings of practitioners from the United States and China, as it has been seen in the likes of the Programme for International Student Assessment (PISA tests) that the Chinese excel within mathematics and the sciences in terms of academic scores, whilst American students have stumbled (Serino, 2017). The investigations and research conducted by Ma found that, although the training wasn’t as extensive or as long as the USA, teachers in China were better equipped with a breadth of knowledge within the fundamental principles of elementary mathematics (Ma, 2010).

How could this be?

Before education is even taken into consideration, one aspect that came to my mind was the cultural differences between the countries. Firstly, it is regarded as being intellectual to understand mathematics within school within the United States (the same can also be said about societal beliefs here in the UK about those who can ‘get maths’) as students are increasingly only seeing it in isolation as a single subject (Green, 2014). So, many students feel that it is normal just to be bad at mathematics, as it has become the cultural norm. It is a bigger fear to fail at the subject than to just dismiss it completely. Those same students become the workforce that hold this opinion of the subject throughout their pathways through life; impacting their children, peers, students, colleagues, partners… you name it. This continues the cycle of fear.

Worldwide tests, such as PISA, have made education more competitive, which highlights what aspects of teaching mathematics needs to be taken into consideration when assessing the success of teaching the subject.

China, however, enthuses students and teachers alike to never give up and that anyone is possible of intellectual understanding through a hard work ethic. So much so, that “The Chinese teachers think that it is very important for a teacher to know the entire field of elementary mathematics as well as the whole process of learning it.” (Ma, 2010, pg.115) which highlights the severity the teachers in China place on their subject knowledge. They know how crucial they are to a child’s everlasting opinion on anything they come across when being taught.So, understanding this societal issue, we can then see how it translates in an educational setting when Chinese students are seeing a practitioner that knows the entire textbook by memory where as American (or in our case Scottish) students are taught topic-by-topic and their experience of mathematics is, traditionally, very linear.

Returning to the issue of Maths anxiety, I believe we need to change our societal opinions on education instead of just how we can tackle mathematics in isolation. In this way, we change the worries themselves. To do so, we need to encourage a you-can-do-it attitude, not only in school, but also for everyday life. Whilst on placement, my teacher was very adamant on being open with making errors within mathematics and heralded the students to call these ‘marvelous mistakes’. This worked effectively as it allowed for open dialogue, as a class, about how an error came about when working through problems. There was no shaming of who made the error because, in the end, we are all capable of failure. It was more about what we do with the failure that was important. I believe this scenario that I experienced is a fine example of a growth mindset approach (which the school utilised as a whole-school initiative). This is another aspect that needs to be at the forefront of any teaching: coherence. Green (2014), explains that many great ideas in teaching fail purely because teachers have not been sufficiently prepared collectively to tackle any given issue.

In conclusion, having fear and anxieties about mathematics is very common and many of us suffer from it, however, we need to make it our mission to break away the years of instilled fear. To do so, we need to use the studies of scholars within our schools effectively and we also need to make sure we are open and honest about how we feel about the subject. Furthermore, we need ensure that we are consistently and constantly seeking various ways to tackle mathematical thinking through problems, which will enable our students to have a richer understanding in computing numbers and formulae.

Reference:

Bello, Alex (2010) Alex’s Adventures in Numberland London: Bloomsbury

Green, Elizabeth (2014) Why do Americans Stink at Maths? [Article] Available at: https://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html (Accessed 20th of October 2017)

Ma, Liping (2010) Knowing and Teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States New York: Routledge.

Skemp, Richard R. (1986) The Psychology of Learning Mathematics, 2nd edn. London: Penguin Books

Serino, Louis (2017) What International Test Scores Reveal about American Education [Blog] Available at: https://www.brookings.edu/blog/brown-center-chalkboard/2017/04/07/what-international-test-scores-reveal-about-american-education (Accessed: 20th of October 2017)

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Binary, Counting Horses, Indigenous Tribes… Oh my!

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Richard’s last two inputs about number systems and place value have left me perplexed to say the very least.

Binary, a counting horse and indigenous tribes…

All these aspects were covered in two inputs and they definitely broke down my structured beliefs on what mathematics really is. A key point that I took away from the lessons was to think beyond the confinements of what we know about the subject of mathematics and our 10-based numeral system.

It really is Discovering Mathematics all over again in a much deeper-rooted manner.

Rather than getting bogged down in the complexities of the possibilities of differing number systems and giving up, I embarked on reading Alex’s Adventures in Numberland in order to find an everyday answer:

“Without a sensible base, numbers are unmanageable” (Bellos, 2010, pg. 44).

Base systems of five, ten and twenty have been the most commonly used through the various cultures of mankind (Bellos, 2010) and it’s a pretty straightforward answer of why:

What is the most common tool a child (or anyone for that matter) would use in order to count? They use their fingers! In Early Years, “fingers are used in a range of ways and with varying levels of sophistication.” (Wright et al. 2006, pg. 13) Well, this instinctive notion towards mathematics has a rich meaning in terms of how we represent our numbers because, in reality, that is all a numeral system is: a way in which we express numbers and quantities of those numbers.

However, Richard introduced us to different variations on number systems that go beyond our commonly known systems. Not only that, but we were also shown the other number systems that were influenced by the culture that they were used within.

Number systems, in reality, are ways in which we give identity to a quantity. 1,2,3,4,5 are all just the symbols we have given to a quantity. Delving deeper into this concept of a numeral system, we need to first realise, how did we create such a vast amount of numbers?

Lets take an indigenous tribe like the Arara tribe in the Amazon for example; they only have base 2 number system, where they only have 2 words for 1 and 2, and anything after that is a combination of the two (anane =1, adake = 2, adake anan = 3, adake adake = 4 etc.) (Bellos, 2010).

Why? They have no real use for numbers beyond that. Their lives revolve around survival. A reserved community in the amazon are never going to need thousands or even hundreds of something, so they just don’t have it.

Farmers have also been shown to have their own number system where Base 20 is used. Farmers would count up (yan, tan, tethera) until they got up to 20 and then they would either pick up a stone or make a mark on the ground in order to indicate that he had got up to one set of 20 sheep and then he would begin again.

Yan. Tan. Tethera.

Could you imagine trying to quantify, say, a population of a whole country using these formats of number systems? The representations would be very time consuming! Once again, the tribes and farmers would not have a population that could equal the populations we have across the modern nations.

The fact that we have so many numbers is down to the fact that we have advanced to the point that we need a huge amount of numbers. We are beyond just surviving as a species, like the indigenous tribes or the independent farmers of the past. Similar to my post about the advancement in agricultural, we’ve adapted in order to advance and, in doing so, adopted a number system that allows us to easily distinguish between place value when putting a quantity on something (particularly large quantities). As we have multiplied, so have our quantities of population, food, cars, houses and so many more factors. An indigenous tribe does not need a number system that goes up to a million because that number has no right to exist. When are they ever going to need a million things of anything?

Here is an interesting video by TED about the history of our numeral systems:

Binary, another spanner thrown into the math-works, was also something difficult to understand at first, due to it using the original place holder symbols of 1 and 0… and that’s it. Similar to the Arara’s, binary only uses two symbols to define various quantities. I vaguely remember aspects of binary being used way back in high school IT lessons; however, I didn’t really know the whole purpose behind it. Computers do not work the same way our brains do. Binary is used because a computer can only work through programming with a state of on or off. This is where the 2-based number system of binary comes into practice well:

The circuits in a computer’s processor consist of billions and billions of transistors. A transistor is basically a tiny switch that is initiated by signals of electricity passed through the computer. The digits 1 and 0 used in binary can reflect the on and off states of a transistor (BBC, 2017). So, computer-literate people can program commands into a computer using binary and the computer will be able to translate these codes (much quicker than the human brain could) into processes.

James May explains binary numbers within this video:

Now, if indigenous tribes, binary and abstract number systems weren’t enough to comprehend across two inputs, then this question that we were faced with will surely perplex you:

Can animals count?

Many opinions and theories circulated the room but the main thinking was… not really. An animal can maybe understand a form of quantity but they probably don’t know why they understand this.

An interesting video Richard showed us was about the enigmatic counting horse called Clever Hans. In the 1900s in Germany, Hans was taken around the country to demonstrate to people his great ability to work out arithmetic that his owner asked him to calculate… Could this possibly be true?!

Unfortunately, it was too good to be true. What Hans was actually doing was reacting to the positive praise through body language of his owner when given a sum. He would learn from cues when to facilitate an answer through tapping his hoof. Psychologist Oskar Pfungst investigated this and even discovered that the owner of the horse didn’t even know he was giving these positive cues, which revealed another theory years later known as observer-expectancy effect. This means that Han’s owner subconsciously gave the answer that he wanted through visual hints like a nod of the head.

Animal cognition is not the same as human cognition. Milius (2016) wrote an article about the topic of animals and mathematics and stated that “some nonhuman animals — a lot of them, actually — manage almost-math without a need for true numbers” and she explores how the argument has varying perspectives from psychologists and scientists alike. One theory is that animals just so happened to gain aspects of mathematical thinking through convergent evolution from similar ancestors as us. This evolution is similar to how bats and birds can fly however, are from completely different families and their wings derived in different pathways of evolution (Milius, 2016). It is also similar to sharks and dolphins both having to gain the best possible traits and abilities to survive in the ocean, yet neither are related in any format. Animals have gained the ability to understand some form of quantity in order to judge if there is 1 or many predators in front of them, however, they don’t have a numeral system to define this understanding.

In reality, much like the tribe, animals have no real use in knowing numbers because they do not think conceptually, like we do as a modern society.

Returning to the concept of place value within numeral systems, teachers need to be able to comprehend what the underlying meaning behind what place value really is. As Ma (2010) found in her studies, the students that excelled the most in mathematics in terms of comprehending number systems were the ones that were taught the appropriate measures when dealing with higher digit numbers when it comes to differing place value with subtraction and addition, for example.

Therefore, as educationalists, we need to know what the best methods for students to tackle number systems are. The answer? Preference is really down to the student. However, we need to be there to facilitate the various learning styles, challenges and boundaries that come our way in terms of learning mathematics – in a positive manner. This correlates well with Ma’s basis of multiple perspectives: teachers should be “…able to provide mathematical explanations of these various facets and approaches. In this way, teachers can lead their students to a flexible understanding of the discipline.” (Ma, 2010, pg.122). Giving children multiple avenues to explore problem solving, in terms of arithmetic, will only benefit their independent evaluation in terms of dealing with mathematical problems. It will benefit them far greater than giving them a formula.

In conclusion, Mathematics has various avenues when it comes the representing quantities and exploring huge amounts of quantities. Knowing the basics of 1,2,3 as teachers will only get us so far. It will also hinder our children greatly… Even discussing the great horse Clever Hans would be an interesting lesson to explore how different mathematics is between them and their pet peers. Being open to mathematics as a vast subject can only bring about great things within the classroom.

Reference:

BBC (2017) Bitesize: Binary [Website] Available at: https://www.bbc.co.uk/education/guides/z26rcdm/revision (Accessed 19th of October 2017)

Bello, Alex (2010) Alex’s Adventures in Numberland London: Bloomsbury

Milius, Susan (2016) Animals can do ‘almost maths’ [Article] Available at: https://www.sciencenewsforstudents.org/article/animals-can-do-almost-math (Accessed 17th of October 2017)

Wright Martland Stafford Stranger (2006) Teaching Numbers: Advancing children’s skills and strategies 2nd edn. London: Sage Publishing Ltd.

Ma, Liping (2010) Knowing and Teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States New York: Routledge.

Scientific Literacy – Group 1

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AC1:

“Scientific literacy is the knowledge and understanding of scientific concepts and processes required for personal decision making, participation in civic and cultural affairs, and economic productivity.”(National Science Education Standards, 1996, pg.22)

In order for someone to be capable of understanding and fully comprehending the depth and importance of science in our society as a whole, one must be ‘scientifically literate’. “Science and literacy are interwoven. In order to take part in a science activity children need to be able to communicate both by spoken and written word” (Hollins and Whitby, 2001, Pg.3). This, however, applies to aspects beyond the curricular subject of science itself, as enabling children to experience scientific concepts within the classroom will prepare them for life beyond school. The art of science itself is very much about delving into the world in which we live in and having the ability and confidence to pick apart theories and concepts, much like in other subject areas within the curriculum. Being teachers, we need to have a strong grasp on this concept of being literate in science in the same manner we would as being literate in language itself. Giving children the correct tools to comprehend, analyse and reflect upon scientific experiments and reactions will allow them to build a safe and healthy relationship with science as a whole. Progression through education sees the scaffolding approach to teaching science being a perfect way in enabling pupils to be scientifically literate because learning is built upon through the stages, which coincides with one of the principles of the curriculum, progression – “opportunities to develop skills for learning, skills for life and skills for work for all young people at every stage” (Scottish Government, 2008, pg. 7).

AC2:

Problems arise when individuals have not been taught the correct methods and practices when being investigative with science, particularly within the wider media. Today, the media is littered with varying claims, news reports and beliefs on just about anything scientific. Controversial headlines are used in journalism to attract readers into the stories being reported and a lot of the time the degree of severity in the headlines are normally heightened in order to gain attention. Reports can of course be flawed and in many instances cause a media frenzy with the ‘scientifically illiterate’ claims being unavoidable for the public. A big example of this is the MMR vaccine scare that plagued the media with the claim that the vaccine caused the development of autism in children. This false claim was made by a now disproven doctor called Andrew Wakefield. Wakefield made the claim in 1998 during his investigations into autism and his status of being a doctor led to his findings being taken as complete fact by many in the media. This then led to avoidable deaths of many children due to them not getting the vaccine, due to the fears held by the parents that their child would develop autism. A report made in 2004 found that Wakefield’s claims were indeed flawed. This is a clear example of where lack of science literacy within society caused many to create conclusions without core facts and thorough evidence. This is a huge problem in science that can have disastrous consequences. This is why, as educators we need to prepare children with the skills to be able to analyse the claims that will be thrown at them, both true and false.

AC3:

This, almost imposing, effect the media has on our society can be beneficial to teachers to some degree as research associate, Caren Cooper, insists that “studies have shown that educators would be more effective if they expanded their modes of communication beyond science centers and museums to radio, television, movies and blogs” (Ramanujan, 2011). Going beyond the traditional teaching methods of science will, in turn, remove the traditional errors made in the long run. Embracing the media for what it is has a better impact than refuting it completely and having a head in the sand approach to it. Unfair testing, making a test deliberately flawed in its amount of variables, is a great way of flipping the idea of result finding on its head within the classroom. Experiments are meant to be controlled, with only a few variables changed in order to collect accurate date, however, making a test extremely unfair makes a great talking point for the kids to identify where an experiment was flawed and could be amended to be fairer. Teaching kids about these types of claims within the media and showing them unfair tests will put them in the right direction of being scientifically literate as they can see what is real and what needs to be challenged and changed. These are valuable skills that, not only consolidate the learning of science, but also enable pupils to be critical when coming to conclusions in everyday life.

Group 1 – Alan Macdonald, Emily Gunn, Lauren Farquhar and Rachel Adamson

Reference:

Greenslade, Roy (2013) The Story Behind the MMR Scare Available at: https://www.theguardian.com/society/2013/apr/25/mmr-scare-analysis (Accessed 4th of February 2017)

Hollins, Martin and Whitby, Virginia (2001) Progression in Primary Science: A Guide to the Nature and Practice of Science in Key Stages 1 and 2, Second Edition, London.

National Science Education Standards (1996) Scientific Literacy Available at: http://www.literacynet.org/science/scientificliteracy.html (Accessed 26th of January 2017)

Ramanujan, Krishna (2011) Public Distrusts Climate Science Partly Due to Lack of Media Literacy, Available at: http://www.news.cornell.edu/stories/2011/03/distrust-climate-science-due-lack-media-literacy (Accessed 27th of January 2017)

Scottish Government (2008) Curriculum for Excellence: Building the Curriculum 3 – a framework for learning and teaching Available at: http://www.gov.scot/resource/doc/226155/0061245.pdf (Accessed 6th of February 2017)