Category Archives: 2.1 Curriculum

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.

Die Zeit ist so schnell – Week 8 in Stuttgart Reflection

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The end of placement is nearing and the weeks are rolling by at an alarming rate.

The Grade 2 teacher surprised me this week with pictures she had taken during my time teaching the class about Castles in Scotland – this was a particularly enjoyable time for me because I really got to be heavily involved in a topic that was very close to home. The students also really enjoyed to get an insight about castles from a different country than their own or even from Germany.

This week was a shorter school week because of the bank holidays on Monday and Tuesday in Germany, therefore, we only had a 3-day school week.

However the days were packed with lots of work due to the grade 5s’ exhibition date coming closer and closer, as the students now only have until Wednesday (9th of May) to prepare for their grand display of the research they have conducted this term around a global issue that they have felt passionate about.

This meant that lots of handwork has been continued around lots of different projects that culminate towards the entirety of the exhibition: artistic components, speeches, display boards, mathematics sections and many more nitty gritty parts have been worked on to get finished and it has been somewhat tricky as a practitioner to keep on top of the different stages of all the different students and how each student is progressing individually.

This is where the journal entries have been a great aspect of the assessment because it allows for us teachers to gain an insight on the feelings of the students on how they are progressing and it also means that students are getting continual feedback on their progress. Students can ask questions in the journal, can highlight issues they wish to address but also it allows them to keep on track of the things they’ve accomplished so far. I know that once the exhibition is concluded, the students will reflect on the entirety of the learning they have done in preparation for this project and the journal will be the best source of information for them. They have documented their progress every week and each entry will be a snapshot of what they did at any given time during their learning process. This all demonstrates that the IB really considers learning as a process that requires reflection to give it real purpose to the students and for the students to find that purpose for themselves, as it is them that have enquired through the topics (International Baccalaureate, 2009).

This has been the common sight in the Grade 5 Classrooms – lots of preparation is going into this event from the students and it is really starting to take shape.

Now, my big responsibility this week was to begin preparing the exhibition reflection video that will be played at the beginning of the evening to all the guests. I had to touch base with the students that were ahead enough in their work to take time out to be a part of this additional responsibility of the exhibition. I first got them all together and we brainstormed some of the skills they had gained from this exhibition experience. I then got them to interlink this with some of the attributes of the learner profile within the IB, which demonstrated a greater understanding of the curricular framework that is in international baccalaureate schools. We then divided responsibilities and I allowed for free choice amongst the kids if they wanted to record a section individually or to do parts in twos or threes. Normally, in my usual setting, I probably would have assigned the groups myself however working at ISS I have realised that organisation skills should be enthused within the children and it also shows a real sense of trust when a teacher says to students that they are responsible for who they work with and that if it doesn’t work out sensibly, then the consequences are on them.

So, we got down to recording and it was great to see the kids take ownership of what they wanted to say and how they were providing feedback for one another on their presentation skills on screen; something that will be beneficial for them later next week when they will be presenting for their exhibition.

We successfully got all the parts recorded and we now just need to piece it all together and add in transitions and the video will be good to go! Its been good to take charge of a technology-component whilst here at ISS because I have luckily had experience using iMovie before and I know that it can be tricky sometimes when trying to perfect the transitions of a video.

On Thursday, I had my end-of-placement review meeting with the head teacher of the lower school and we discussed all the learning that I had gained over my two months of being here. He even said himself that he couldn’t believe how quickly the placement has went. It was great to have a finalisation of my work at ISS as it is drawing to a close. I still have next week at the school, however, we will have our Vivas beginning next week (mine specifically will be on the Thursday the 10th of May via Skype interview). Many of the staff members at ISS have said they will miss my presence at the school and it is such a great feeling knowing that my determination has been seen by other staff members and they can see that I always strive to work my best towards my professional development. Teachers have told me that I will just have to stay here because I have made myself too useful!

Then of course Friday saw the Multi-Cultural Evening which was an extravaganza of cultures and heritages all under one roof at ISS. It was the perfect way to end the 8th week of my time in Stuttgart, particularly as, although this week has been short, it has been very heavy going with work for all of the students and teachers at the school.

Time really does fly by when you are having fun – even more so when that fun is interlinked with hard work and determination!

Reference:

International Baccalaureate (2009) Making the PYP happen at ISS: A curriculum framework for international primary education. Cardiff: International Baccalaureate Organization.

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.

The Primary Years Programme at ISS (Section 2)

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I believe it is necessary to delve deeper and to unpick the framework of the Primary Years Programme at the International School of Stuttgart in order for a better understanding of the International Baccalaureate curriculum and the school of ISS. Therefore, I think it is best to create a blog post that centres around this exploration of the curriculum that is taught at ISS and to unravel the history behind the IB pathway in education. Not only this, but I hope to examine the underlying school ethos that is established at ISS through the PYP.

“Aims and aspirations are translated into a curriculum that is structured from the earliest years around a Programme of Inquiry that contains formal ‘units of inquiry’ in each year. In the early years (aged 3–5 years) the children are required to engage in at least three units of inquiry a year. After this they must engage in six units of inquiry under each of six broad transdisciplinary themes namely: Who we are; Where we are in place and time; How we express ourselves; How the world works; How we organise ourselves; and Sharing the planet.” (Bacon and Matthews, 2014, p.356) – an interesting take on the International Baccalaureate’s system of inquiry-based learning, something that I have also unpicked in another blog post that examined this phenomenon of inquiry-based learning.

The concept of “units of Inquiry” was very alien to me at the beginning of my placement. However, even from the first week, I soon realised the massive importance they have for learning – not just for the teachers teaching the curriculum but for the children that are experiencing and doing the learning. I particularly found that most of the kids at ISS love it when it is UOI time, no matter the grade level. Within the timetable, UOI is a prominent feature amongst the homeroom times, specialist lessons and recesses and break times that the children have on any given day. Across the entire year, students will explore various topics in a great amount of depth, whilst also tapping into other areas of the curriculum in order to establish a cross-curricular model that fully encompasses all areas of learning that can occur. Whilst talking with the grade 3s, I found they had already completed inquiry topics this year on ancient civilisations, how the brain works, space and living things. They are now moving on to preparing for a show where they will all have a role in acting or production. I couldn’t believe the breadth of knowledge that the children were given in terms of exploration for knowledge. However, this is very normal for international schools that follow the PYP.

Using Atlas Rubicon, we can see the Grade 3s progression of UOI Topics as they work through the year.

The Scottish Curriculum for Excellence (CfE) is far more rigid in the sense that set times are normally the case for most primary teachers. They know they are doing maths at a specific time on specific days every week, with only minor changes to the routine. Lots of initiatives however are pushing for CfE to be a flagship for the similar practices found in the IB methods – transdisciplinary skills, cross-curricular and interdisciplinary learning links and having mindfulness of the wider world in everything we do. We can see this with the four key purposes in the Scottish education system CfE – successful learners, confident individuals, responsible citizens and effective contributors.

Now, the International Baccalaureate offers more than just the Primary Years Programme, it covers education from 3 all the way up to 19, with Middle Years, Diploma and Career-related programmes also being offered to students.

The different programmes offered by the International Baccalaureate within international schools – sourced from http://www.ibo.org/en/programmes/

Although it is handy to know where students will progress to, my main focus will be on the Primary Years Programme, as this is the level that I will be working with as a future primary school teacher.

It was first offered in 1997 after much deliberation was conducted in the early 1990s around the offering of a curriculum that was suited for students aged 3 – 12. Today, we can see that the curriculum itself is centred around the connection of 6 transdisciplinary themes: 1. who we are 2. where we are in place and time 3. how we express ourselves 4. how the world works 5. how we organise ourselves 6. sharing the planet (International Baccalaureate, 2017). These themes are interwoven and correlate towards creating “knowledgeable and caring young people who help to create a better and more peaceful world through intercultural understanding and respect” (International Baccalaureate, 2017, p.2). But what does this mean in a literal context? From what I’ve witnessed at ISS, I can say that it is children, adults, staff members and students alike being open amongst one another – it is going beyond the idea that education is the transmission of knowledge. There is a real connection amongst the people that call ISS their home for however long that they are there for – and even beyond this with alumni students being welcomed with open arms at the school during my time here. Staff members interacted with particular former students as if they were nieces and nephews, showing that real connections are formed between student and teacher.

My take on the dynamics that are clear in the Primary Years Programme at the International School of Stuttgart (and I assume many of the other international schools that offer the IB PYP) is that, because everyone is predominately from different backgrounds from one another, they feel united through their differences. These differences come together to create a learning space that cares a lot about achieving individual goals whilst also establishing a space that people can come together in unity to be there for one another in a wider sense, which is emphasised in Attitudes and Action in the PYP that are there to empower students within their experiences of learning. Within these experiences is a wide array of topics that can be covered through units of inquiry and other topics in the curriculum with their homeroom teacher or specialist teachers.

Something that I really liked that emphasised this entire school ethos was during another assembly where students that were leaving to start school abroad received a farewell song from the staff and students. It was an emotional day for many because there were students that were moving to far away countries to start a whole new life.

Overall, there is a big difference in the curriculums between international schools and the curriculum used by many schools across Scotland. However, we can see that a lot of the ideologies are stemmed from the same roots. Furthermore, much of the same pedagogical understanding was used to form both curriculums. Looking at both systems with a critical lens that has been able to experience both in practice has allowed me to really look internally and question my personal and professionals beliefs on education as a whole. A lot of the practices that I’ve seen at ISS have been very different and others have been very similar to ones that I have used myself. However, the biggest thing I will be taking away from the framework of the Primary Years Programme is the Units of Inquiry, as these core subject areas allow for a lot of independence and development of a child as a whole, and it also indicates to me that learning MUST come from the children themselves.

Reference:

Bacon, K. & Matthews, P. (2014) Inquiry-based learning with young learners: a Peirce-based model employed to critique a unit of inquiry on maps and mapping, Irish Educational Studies, 33:4, 351-365, DOI: 10.1080/03323315.2014.983303

International Baccalaureate (2017) The History of the IB. [Pdf] Available at: http://www.ibo.org/globalassets/digital-tookit/presentations/1711-presentation-history-of-the-ib-en.pdf (Accessed: 1 April 2018)

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)

Image sourced from – Flikr

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.

Time – The Underlying Mathematics and Science

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As a species, we form our daily lives around clocks, calendars and alarms. It would be extremely difficult for us to cope if we didn’t know what time it was or what day it might be because the concept of time is at the core of our society and our civilisation. From what I gathered before investigating into the concept further, it is the manmade vehicle that traverses us through our entire existence on our planet and beyond. I always believed that time was something that we just made up ourselves… My discoveries proved me wrong.

Firstly, let’s take an example: what does a normal morning begin with for many?

An alarm blares at 8:00am to sound that it is time for us to get up and start the day. However, the snooze button delays the awakening to 8:12am (12 more minutes still leaves us a sufficient amount of time). Washed, dressed and ready; our phone reads 8:54am. We’ve wasted too much time because we need to be at our destination by 9:00am and we know 6 minutes is not long enough for a journey that takes 10 minutes. We’re going to be late. We need to be more organised next time.

You may or may not know it but this little scenario – that may be all too familiar – is oozing with mathematics.

It may seem like common sense to the average person, but planning towards time is all linked with having skill and knowledge within the fundamental principles of mathematics: estimation, planning, problem solving, sequencing events, organisation and so much more. They’re all how
we go about our days. Without being competent in these various fundamental skills, we’d be at a huge loss. Ma (2010) categorised 4 aspects of mathematics that teachers need to tap into in order for their students to have a rich understanding in their learning in maths during her investigations in teaching in China and the United States. They are: interconnectedness, multiple perspectives, basic ideas and longitudinal coherence.

A day would not be a day without a reference to what the digits on a digital clock read or where the hands were pointing on the analogue equivalent. But what really is a ‘day’? How have we measured 24 hours as a full day? I asked this question to the Internet and even myself multiple times. This led me to the discovery of the Circadian Rhythm:

The number 24 was not chosen out of sheer randomness, it is a crucial number that correlates to various living beings on the planet.

(Latin) Circa – about

(Latin) Diem – day

The phrase Circadian rhythm, broken down, literally means about-a-day rhythm.

In short, the circadian rhythm, a phrase coined by scientist Franz Halberg (2003), is an organisms’ body clock that indicates what they need to be doing at any given time across a 24-hour cycle. Sleeping, waking up and eating are examples of where the circadian rhythm is at work. It is heavily influenced by environmental factors. The sun and the moon indicate to our bodies when to rise and when to sleep (phone and computer screens being great deceivers to our body clock’s perception of night and day). Similarly, plants’ leaves adapt to the environment by moving in order to attract pollinators depending on the time of day.

Maths is natural to us.

Plants have a body clock too

Discovering the underlying biology to how we’ve conjured up time has led me to really appreciate why we need the manmade structure of clocks to keep us on track through our natural daily lives. This has shown me the real importance of mathematics having a relationship with the earth and it’s creatures. Its context is so core to every little thing we do, that we don’t even realise the underlying principles behind it. The mathematical ideas we are using to problem solve, estimate, decide and sequence events are intertwined with our bodies.

The clocks, calendars, phones and timers are all mathematical tools made from our innate ability and urge to define time and to quantify our instinctive movements. Furthermore, this further exemplifies Liping Ma’s theory of [inter]connectedness, as the various tools and formulae of mathematics are linked with, not only with each other but also with the real world (Ma, 2010). Tapping into this, as professionals, will be the difference between a student who can answer questions and a student who fully comprehends the work that they are doing. Knowledge in time is a topic that is heavily linked with the real world and children need to be competent with working with numbers. “Understanding relationships between numbers, and progressively developing methods of computation, has become the focus for learning, replacing the traditional ‘four rules of arithmetic’” (Skemp, 1986, Pg. 7).

Relating this further towards education, children, even from a very early age, have a great understanding of the concept of time. Toddlers “become familiar with the routine of their day” (Early Years, no date, pg. 2) and know, logically, what they’re doing and when they’re doing it. They may not know how to read what time it is when they have a snack or go for a nap, but they know instinctively when they are actually going through with consistent tasks (their circadian rhythm are already keeping them on track from the get-go). This, although it may seem minimal, is a child’s early access to problem solving mathematics.

Overall, my investigations into the concept of time have only scratched the surface of what is to come within the Discovering Mathematics module, and in my professional development as a student teacher.

Circadian Rhythm

Looking ahead, I know now why we must teach time to children, as it is part of their being. Furthermore, having the underlying knowledge of the basic ideas, coined by Ma (2010), will improve how deep a teacher’s teaching roots can grow in a child’s ability to truly grasp mathematics and go beyond just the academic mathematics that we throw onto a child.

I finish this post with a pop song that explores our fascination with what is possible in 24 hours:

“I wish these 24 hours

would never end,

oh in these 24 hours,

 wish the clock had no hands”

(Ferreira, 2013)

Reference:

Early Years (no date) Maths through Play [brochure] Available at: http://www.early-years.org/parents/docs/maths-through-play.pdf (accessed 22nd of September 2017)

Ferreira, Sky (2013) 24 Hours In: Night Time, My Time [CD] 0602537712793 Capitol Records.

Halberg, Franz. (2003) Journal of Circadian Rhythm: Transdisciplinary unifying implications of circadian findings in the 1950s [article] Available at: https://www.jcircadianrhythms.com/articles/10.1186/1740-3391-1-2/ (Accessed 20th of September 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, Second Edition, London: Penguin Books.

Useful Link:

https://sleepfoundation.org/sleep-topics/what-circadian-rhythm

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)