Category Archives: 3.1 Teaching & Learning

Teaching New Phrases – French

French was never my strong point at school. I felt that I didn’t have the underlining and basic skills to forward my development and therefore the subject broke down for me. In Scotland, we are now introducing a second language in Primary 1. This is a positive means of having the underlining basis of a language such as French or German and therefore moving forward and learning another, for example Spanish, will become easier in accessing the grammar and speech.

Children learn a modern language through receptive skills and productive skills. Receptive is similar to our language – learning through listening and reading. It is important that children have the opportunity to listen to a language before attempting to read it. This is because in many European languages they use accents. These can change the way the words are pronounced. Therefore, if a child were to read a new word first, they would have an interpreted pronunciation and continue to say the word wrong. It is important that productive skills are brought forward also. These are talking and writing. Talking is important feature that can run alongside listening. Teachers can get involved with this also, as demonstrated by Carrie on Tuesday. Carrie used a lesson with us where the teacher used associated actions with a word, such as a left-hand wave with “bonjour” and right-hand wave with “au revoir”. This repeated back and forward from the teachers and pupils can reinforce specific phrases and therefore they have a sound understanding of new vocabulary. This makes it easier in future to receive the words through recognition of sounds and phrases.

These new phrases can then be brought forward through the introduction of the words being written and read. As a teacher, it can be difficult to bring forward a second language when a child’s first language is continuing to develop. Therefore, as mentioned previously, it is important that they are not bombarded with phrases and lessons are focussed on a maximum of 8 new words in a lesson. This provides opportunity for new vocabulary to become embedded in a child and talking and listening activities can progress through writing and reading lessons.

When Carrie was carrying out the lesson she solely focussed on some individuals. This was a reflection task for us all as we were required to think like a class of primary school pupils would. As a teacher, we have to understand that not everyone will be confident in accessing a different language or confident enough to say phrases in front of their peers (Jones, J and Coffey, S 2006). It is therefore important to make activities group tasks to get everyone involved and if feedback is required this is done on a collective basis. We must also keep the work engaging for pupils, whilst progressing at the same time. Keeping activities relevant to the language by having lessons based around a song, a game or an art lesson, provides pupils with fun activities whereby the language is not their sole focus. However, we must develop progression. In Primary 1-3 talking and listening is emphasised, so the pupils have a key understanding of basic language. But older pupils will engage more with reading and writing lesson so therefore they are expanding their skills (Jones and McLachlan 2009). This however may require for teachers to recap pre-taught language to gage the level of the pupils’ understanding and reinforce the words. Therefore, by checking for understanding, use of progression and the use of the four main language skills, children CAN have a sound understanding of a foreign language and maintain this language throughout primary school, with progression in upper stages.

References:

Jones, J. and Coffey, S. (2006) Modern Foreign Languages 5-11: Issues for Teachers. David Fulton. London

Jones, J. and McLachlan, A. (2009) Primary Languages in Practice: A Guide to Teaching and Learning. McGraw-Hill Education

 

 

 

What is a Number?

We come into contact with numbers every day. Time, working out how many portions of dinner we’ll need to make or simply “hey what’s your number?”. But have we ever taken the time to think, what is a number and why do we even use them?

My first question is, why does the number three collectively represent other items in threes? Surely three dinosaurs would be more than three peas, even though they represent the same amount collectively. But it’s not due to weight, height or mass, its due to the value of the number three. Numbers are a language. For value, comparison and equivalence. They help us understand how many there is of something (value), help us compare that five dinosaurs are two more than three peas and that three peas and three dinosaurs are equal.

Numerals play a significant part in this. A numeral is the symbol or collection of symbols used to represent a number. A child’s first experience of a number is most likely going to be an adjective that would collectively describe a set of something e.g. five cats or two arms, this is more commonly known as the ‘cardinal aspect of a number’ (Haylock, 2014). This highlights that children can recognise an equivalence between two sets of objects and is why we understand that three dinosaurs are equal to three peas. At this stage numerals are the link to numbers. Therefore, children can look at numerals such as pictures of shapes or objects and count how many are there of one thing. This will therefore help them connect to real life situations and when shown beside numbers, they can begin to connect numerals and numbers together. By beginning to connect the two, children will have a deepened understanding of numbers and therefore their longitudinal coherence will develop. Starting their journey with numbers and maths simply and positively to prevent future maths anxiety (MA, 2010).

Numerals have been shown throughout our history and teach us a lot about the development of mathematics. One of the oldest is hieroglyphics, used by the Egyptians, dated as far back as 3000 BC. Their numerals were shown through drawings and symbols such as a bird and an Egyptian man (O’Connor and Robertson, 2000). Maths was commonly used by Egyptians if they were dividing food, solving problems for trade and market and most importantly for the pyramids (Mastin, 2010). This highlights the first use of maths for economy and trade. Wealth played a significant part in Egyptian life and social class was divided by money but more than anything, maths. Through looking at our history, we can see the similarities in the importance of economy then and now. We live in a world that’s economy changes daily and has the power to change and impact upon people’s lives. If we looked more in depth at historical economy such as Egyptian trade and social classes, we could learn and reflect on our economy nowadays and therefore maths is a historical aspect of economy that involves counting and numbers.

All factors of numbers have a place in fundamental maths, but most importantly teach us a lesson for now. We can apply what we have seen previously in history and the importance of numerals and numbers to aid our development with maths and see that it is essential for our wider society and not just basic classroom use. Relevance is a fundamental principle of Curriculum for Excellence (Scottish Government, 2010) and therefore it is important that teachers bring this forward from historical findings into our everyday maths lessons and make children think about their future with maths in society.

Number Patterns and Sequences

Another way of teaching maths can be through number patterns and sequences. This can be another way of making maths interesting for children whilst developing their relationship with numbers. Vale and Barbose (2009, p9), stated that the use of patterns in maths can challenge students to use “higher order thinking skills and emphasise exploration, investigation, conjecture and generalisation.” Therefore, basic skills in maths are used within problem solving to develop not only longitudinal coherence but also multiple perspectives as they can use different methods to find the solution to a problem.

An interesting number pattern is Pascal’s Triangle, named after Blaise Pascal, a French mathematician. This is a triangle that starts with the number ‘1’ and then below are the sum of the addition from the numbers above. For example, if 1 is beside 2 in the triangle the sum (number written below) would be 3. An example of this can be seen below.

Pascal’s Triangle makes maths fun for children whilst learning about addition and number patterns. Addition is a fundamental aspect of maths that it taught as early as ages 4-5 and can be continued to be taught throughout primary school through ways such as Pascal’s Triangle. The introduction of colours can also produce other findings within the triangle. For example, pupils can colour odd and even numbers or work out the horizontal sums of the triangle (Maths is Fun, 2017). This therefore keeps maths relevant and allows for differentiation in a classroom, as some can complete the main body of the triangle (addition) and some can move forward looking at other aspects of the triangle. Therefore old maths techniques and problem solving continue to find a relevance in our everyday maths and classroom.

References:

Haylock, D. (2014) Mathematics Explained for Primary Teachers. 5th edition: SAGE.

L, Mastin. (2010) Egyptian Mathematics https://www.storyofmathematics.com/egyptian.html (Accessed: 5th October)

J, O’Connor and E, Robertson. (2000) Egyptian Numerals. http://www-history.mcs.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html (Accessed: 5th October)

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. (Anniversary Ed.) New York: Routledge.

N/A (2017) Pascal’s Triangle.  https://www.mathsisfun.com/pascals-triangle.html (Accessed: 6th October 2018).

Scottish Government. (2010) Curriculum for Excellence Building the Curriculum 3 A Framework for Learning and Teaching: Key ideas and Priorities. Available at: http://dera.ioe.ac.uk/1240/7/0099598_Redacted.pdf  (Accessed: 5th October 2018).

Vale, I. and Barbosa, A. (2009) Multiple Perspectives and Contexts in Mathematics Education. Available at: https://www.academia.edu/1485703/Patterns_multiple_perspectives_and_contexts_in_mathematics_education  (Accessed: 5th October 2018).

The Art of Tessellation

When Jonathan first said the word “tessellation”, I immediately thought what on earth is he on about?! Yet, following this lecture I now understand that tessellation is something that surrounds us.

Tessellation is the arrangement of identical shapes that fit together perfectly to create a pattern. These shapes have to fit precisely beside one another, meaning they’ll leave no gaps. If we look closer at items that we come into contact with on a regular basis, such as chocolate, footballs and kitchen tiles, we can see that there are shapes such as hexagons, squares and triangles that are joined together to form tessellation.

But how does tessellation link into a classroom setting?

Tessellation can occur through two different types of shapes. The first are regular. These include squares, hexagons and equilateral triangles and therefore form a more simplistic tessellation, for example, in the form of chocolate squares. Regular shapes, unlike irregular, have the ability to interconnect as all the vertices meet one another and therefore create the sum of 360 degrees. The second are irregular shapes, these are shapes such as pentagons, octagons and isosceles and scalene triangles (Maths is Fun, 2018). These work similarly to regular shapes, however, the shapes must be cut and pasted to a different part of the shape to be able to interlock with the other identical shapes. An example of this is shown below in the creation of a horse.

A form of tessellation can particularly be seen in Islamic religion through mosaics and geometric patterns (Hames, 2017). Islamic art focus on the creation of stars through tessellation. For example, they particularly use equilateral triangles to create 6 to 12 points of stars. These represent and symbolise harmony and hum consciousness. These features can be introduced into a classroom. Using maths (tessellation) and interconnecting it with art is a great way of introducing a calm and settled environment to the classroom. Boaler (2009), states that completing tasks in different ways therefore allows children to see that there are different methods to learning maths and therefore maths can be enjoyable for everyone.

Liping MA’s idea of inter-connectedness is highlighted through the use of maths and art. By using a mixture of the two, children who feel anxious about maths will therefore find a task such as creating Islamic art, as a more relaxed approach to maths. For example, if they enjoy art they believe it is more about art than the maths. Furthermore, this will lead to their longitudinal coherence. This is because they will have the basic understandings of shapes and therefore children have a sound enough understanding to bring this information forward to more complex areas such as tesselation.

An example of a lesson that could be used for tessellation is multiplication to create stars. By finding the different digital roots e.g. 4 times 6 = 24 which therefore this simplifies to 2 + 4 = 6, you can start at a point in the circle and continue to connect to the following dots (answer). When completed the pupils can colour these in and therefore maths and art have been interconnected in a lesson, helping those who have a passion in art have a profound understanding of maths.

 

Example of tesselaltion star from the digital root of the 4 times tables.

 

 

Overall, tessellation is a great lesson to introduce differentiation within a classroom. It allows for both art and maths to be taught at the same time, making maths fun and achieveable for those suffering from maths anxiety. Tesslation links into our classroom setting through a number of different lessons and has a major link to pupils’ understanding of shapes. A basic concept of maths that is learnt thoroughly to bring forward. This lecture in particular is one that I will continue to revisit when teaching, as I have not only learnt how maths can be fun, but have learnt about a different culture in the process. Therefore, I think this topic could be integrated into the classroom in a number of ways such as a class topic or investigation task.

References:

Boaler, J. (2010). The Elephant in the Classroom: Helping Children Learn and Love Maths. London: Souvenir Press.

Giganti, P. (2010) Anatomy of an Escher Flying Horse. Available at:  https://www.youtube.com/watch?v=NYGIhZ_HWfg (Accessed on: 25th September 2018).

Hames, S. (2017). Tessellations in Islamic Art. Available at: https://classroom.synonym.com/tessellations-in-islamic-art-12085299.html. (Accessed on: 12th November 2018).

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. (Anniversary Ed.) New York: Routledge.

Maths is Fun. (2018). Tesselation. Available at: https://www.mathsisfun.com/geometry/tessellation.html (Accessed on: 24th September).

Warner, M. (no date) Digital Root Patterns Available at: https://www.teachingideas.co.uk/number-patterns/digital-root-patterns (Accessed on: 26th September 2018).

 

 

Discovering Maths in Me

When choosing my elective, I had to think rationally about what would have the most influence on my future career. Maths was the one subject that leapt out at me on the elective list. But not in a good way. I, like many other people, associate the word ‘maths’ with fear, horror, failure and disappoint. I eventually chose this elective, as I wanted to change this thinking and my feelings about maths.

Teachers can be placed in a difficult position. If they don’t understand or like a subject they cannot pass this on to their pupils. As many lecturers said during placement “faking it, till you make it” is vital. If we don’t fake our confidence within a subject and our teaching, then the children will see through this and adopt the same attitudes. Kelly and Tomhave (1985) found that primary school teachers have the ability to transmit their own anxiety about maths to their pupils. This, multiplied by 20-33 pupils, has the ability to influence children from age 5 to adulthood, which could have a detrimental effect on their future careers and their own children.

Maths plays a prominent part in our everyday activities, from reading bus timetables, to working out when to set an alarm. If children begin to believe that they can’t do maths, then easy everyday activities can become a difficulty. I remember telling two of my high school maths teachers that maths was impossible and I didn’t understand anything. The first, told me that maths wasn’t for everyone and maybe more English based subjects were my forte. The second, broke it down for me. He asked me if I could read a clock, count money, organise my day. All of which I agreed to. He then told me that maths is not just ‘find the equation’ or Pythagoras, but it was simple concepts that we take for granted. As teachers, we have to break maths into different components, to show children the everyday uses of maths to highlight to them that they CAN do maths.

A study carried out by the university of Cambridge shows that anxiety in any subject can prevent progression in learning. Having your mind tell you that you cannot do something can be one of the most detrimental things. Children need to know that they can improve and they can do maths. One factor that may knock a child’s confidence is always being told they’re wrong. Adults have a responsibility to tell children that it’s fine to get things wrong and it is just a learning curve that they can overcome. Teachers in particular need to be careful about constantly using a cross beside wrong answers or using the dreaded red pen. Instead, helping a child understand step by step where they went wrong and reassuring them that they can do maths, will hopefully prevent maths anxiety. Therefore, their confidence will maths can flourish in everyday uses and in the classroom.

Overall, my main goal with discovering maths is to develop a positive relationship with the subject and finally believe that I can do maths to develop my skills as a teacher.

References:

Cne.psychol.cam.ac.uk. (2018). The Relationship Between Maths Anxiety and Maths Performance — Centre for Neuroscience in Education. [online] Available at: https://www.cne.psychol.cam.ac.uk/the-relationship-between-maths-anxiety-and-maths-performance [Accessed 15th September].

Schwarzer, D., Bloom, M. and Shono, S. (2006). Research As A Tool for Empowerment. Greenwich, Conn.: Information Age Pub., p.4.

 

 

The Science Behind the Experiment

When entering 1F06 before our first science lesson I was nervous. The prospect of having to teach a science lesson is an area of learning I felt I couldn’t do. However, instantly the lesson grabbed my attention and showed me that science can be engaging.

We were all given the task of demonstrating an experiment and explaining how it works. I chose to show how to create ‘cornflour slime’. For this you only need cornflour and water. Once the consistency is right the liquid becomes hard when force is applied and returns to a liquid when there is none. It becomes a solid when force is applied as the particles of the cornflour lock together and then a liquid when there is no force, as the particles are suspended within the water. I believe that this experiment can intrigue children of all ages and is extremely simple to conduct. However, the science behind it is more focused towards those in upper level and this can be broken into the concepts behind the experiment.

Richard made us aware of the importance ‘P-O-E’ (predict, observe, explain). Firstly, you can get the children to predict what they think will occur in the experiment and the outcome. This could be formally written in a report as a hypothesis or just verbally. Secondly, they observe the experiment, this means they can repeat the experiment in groups or later at home. Lastly, explaining why the experiment occurred and what it means, will get them thinking about a variety of science concepts and thinking about real life scenarios that an experiment would apply to.

Science is extremely important to teach within primary schools as children will engage with active learning, whilst learning new concepts. There are many possibilities for future lessons from experiments such as; report writing, presenting, measuring distances and calculating time. Furthermore, I am now less apprehensive with teaching a science experiment and have seen a variety of other experiments that I can now use for a class lesson. These science workshops have demonstrated the many possibilities that science can bring – something which excites me.