The language and skills of maths

During the past week, I spent some time reflecting on the specific language associated with maths, and the skills to be learned as part of the 1999 curriculum.

Language
It is so important to bear in mind that the very vocabulary we use in maths might pose problems to pupils when they are learning new concepts.

In some cases, the words or phrases we use might not have been previously encountered by the children - for instance, 'prime number', 'multiply', etc.

In other cases words might be used in different ways than pupils have previously seen. For example, consider the word 'table'. From a young age, this word will be familiar to children as representing a concrete item that they can see in their homes - a piece of furniture. In maths, however, suddenly it means something new. The word 'table' may be used in the context of multiplication, or perhaps in the representation of data in columns and rows.

The teacher must be mindful of potential misunderstandings or confusion. This may be overcome by repeatedly using this new vocabulary in context, having presented it during the Introduction phase of a lesson. Activities and tasks which require pupils to communicate with one another using the language of maths are ideal. The teacher should observe such work and scaffold or model correct language use as required to aid pupils' development.

Skills
During a recent on-site class for maths I was reminded by my tutor to heed the mathematical skills that the curriculum aims to develop in children. Learning in maths should be "practical and relevant" (Mathematics Curriculum, NCCA, 1999, p.15). It is important that skills learned in one area can be generalised and applied elsewhere, both within maths and across other subject areas. Maths permeates our lives in a plethora of contexts, and the role of the teacher is to prepare the children for this. Where good skills development occurs, the pupil will be enabled not simply to solve familiar problems, but to extend his/her learning to overcome new obstacles using good reasoning and logic.

The ability to think in such a fashion has many uses, not least in the field of computer science and programming. Pupils might apply their skills in activities such as using the computer programme Scrach, which requires some knowledge of co-ordinate geometry, and consideration and cause and effect. Teachers should endeavour to ground learning in the context of pupils' interests and hobbies outside of school, where possible, to engage and maintain their interests.

Yu Ming is Ainm Dom

An tseachtain seo, d'fhéach mé ar an ngearrscannán 'Yu Ming is Ainm Dom'. Chonaic mé an scannán seo cheana ach fós bhain mé taitneamh as.

Sa scéal, bhog fear óg ón tSín go hÉirinn mar theastaigh saol nua uaidh in áit éigin eile. Mar ullmhúchán, d'fhoghlaim sé an Ghaeilge, mar léigh sé gurbh í príomh-theanga na tíre. Nuair a shrioch sé Éire, áfach, thuig sé a bhotún nuair a bhuail sé le seanfhear i dteach tabhairne.

Léiríonn an scannán seo stádas íseasl na Gaeilge in Éirinn inniú. I rith an scannáin, déanann Yu Ming sár-iarracht cumarsáid a dhéanamh trí mhean na Gaeilge gan móran raith. I gCuraclam na Gaeilge (1999), cuirtear an bhéim ar úsáid na bheidhmeanna teanga i dteagasc agus foghlaim na Gaeilge - mar shampla, caidreamh sóisialta a dhéanamh, eolas a thabhairt agus a lorg, srl.

4 key steps in the measurement process

This week in the maths session I explored the Measures Strand. Among my key learning points was the 4-stage process involving in measuring.

1. Estimate - Pupils should be encouraged to make a reasonable attempt to estimate a quantity (e.g. length or weight) before they formally measure it.

2. Measure - Pupils can use a variety of tools for measurement. Pupils will initially use non-standard measures (e.g. finger lengths for distance) before progressing to standard measures (e,g. centimeters).

3. Compare - Pupils should then compare their initial estimate with their measurement.

4. Discuss - Pupils will then discuss the difference between these two figures.

The teacher must place the emphasis on the difference between an estimate and an answer; pupils sometimes have difficulties distinguishing between these two concepts.

Pupils must also be guided in considering the reasonableness of their answers.

Over time, pupils will learn how to select the most appropriate measure for a given situation; for example, centimeters might be appropriate for measuring the length of a side of a textbook but metres would be suitable for the length of the school yard.

Exploring curricular integration using Digital Storytelling

I enjoyed learning more this week about how digital storytelling offers an enjoyable, natural means of integrating learning across different curricular subjects. Such a lesson would appeal to pupils of different interests, as the production of a short film using a process such as stop motion would require very different skill sets.

Digital storytelling promotes literacy development both in English and Gaeilge. Pupils must consider aspects such as characters, plot and setting. Story outlines would need to be written, along with scripts and possibly captions. This would allow for drafting and re-drafting to be explored. For pupils drawn more to the Arts subjects in the curriculum, roles include creating sets, models for characters, and props. Appropriate music or background sounds would also have to be selected.

From this perspective, digital storytelling has a little of something for everybody. The challenge facing the teacher is to ensure effective group work is taking place where each child feels he/she has a meaningful role and is making a contribution. This process is more interactive that simply writing a composition in English as the children can see their ideas come to life before their eyes in the finished film, and it can be shared with other classes and parents/guardians as well.

Group work in Ped 2 subjects

My learning this week throughout several Teaching Pedagogy 2 subjects gave me greater insight into the importance of group work, and how it can be structured in these subjects. At out first maths on-site class, we were advised against group work involving groups larger than four pupils. This message was reinforced for me this week when I studied a session in a different module (Preparing for School Placement 2).

I have learned that it is vital to gradually build up to group work by having pupils first work independently. The next step is to introduce pair work and the Think-Pair-Share activity. It is only when pupils are reasonably capable of cooperating in this setting that larger group tasks should be attempted. Teachers should be mindful of the cognitive and social demands posed by group work. From my reading of Gardner's theory of multiple intelligences (M.I.), I can see the relevance of inter-personal and intra-personal intelligence here.

There is a real risk of off-task behaviour, or a diffusion of responsibility effect as no-one takes responsibility for a task. I saw this firsthand on School Placement 1 with a fifth class group, where I put pupils in groups of six to create a short dramatic pieces. In each case, the task was not successfully completed.

I can see the benefits of using group work in Pedagogy 2 subjects such as maths, where exploration and experimentation is key to understanding new concepts prior to rules being formally taught. For example, pupils should be enabled to discover for themselves that the area of a rectangle may be calculated by finding the product of its length and breadth. In the teaching of languages, children could be given opportunities to collaborate on group projects, such as creating a photo story project. This would require the skills of cooperation, communication, planning, division of labour and exercising patience.

As the children grow older they will be expected to work in groups more and more, for instance as they progress to secondary school and later college, and beyond. The skills that they acquire at primary level will stick with them as they mature, and will be built upon. It is crucial that teachers do not just give pupils opportunities to work in groups, but that they also equip them with the skills needed to do so.

Exploring 3-D shapes as a gateway to 2-D shapes

In my session in maths this week, I discovered why 3-D shapes are introduced to pupils before 2-D shapes. The session explored how maths must be relevant to pupils and must build upon their experiences with the world around them. It is for this reason that learning starts with 3-D shapes as these are the shapes which children observe in their environments.

Emphasis must be placed on the language of maths and specifically the language required to describe various shapes - vertices, angles, faces, edges, round. At first, descriptions can focus on whether or not an object can roll, whether it is solid, and whether it can be stacked with other shapes like it without any empty space between them.

Once more, maths trails were promoted as a popular and effective learning activity which help pupils to see the real-world applications of the maths they learn within the classroom.

Múineadh na Gaeilge - tréimhsí i ngach ceacht

Inniú, rinne mé staidéar ar Churaclam na Gaeilge. Is breá liom an Ghaeilge mar theanga ach bhí deacrachtaí agam ag múineadh an ábhair seo nuair a bhí mé ar chleachtadh múinteoireachta. Ag an am sin, níor thuig mé céard a bhí i gceist sna trí tréimhse cumarsáide (réamhchumarsáid, cumarsáid agus iarchumarsáid) toisc nach raibh staidéar déanta agam cheana ar an gcuraclam.

Anois, tá níos mó eolais agam faoi chiall na dtéarmaí seo. Bheinn níos muiníneach agus mé ag ullmhú ranganna Gaeilge sa todhchaí. Is é an rud is tábhachtaí deiseanna a thabhairt do na páistí an teanga a úsáid. Is gá dúinn, mar mhúinteoirí, an bhéim a chur ar chumarsáid.

Mastering the four basic operations in maths

During this week's sessions I learned, among other topics, about the teaching of subtraction and division in primary school maths. This built upon my learning last week about the teaching of addition and multiplication. Maths is among my favourite subjects on the primary school curriculum. In fact, I have enjoyed the subject since my own days in primary school.

The sessions this week and last week interested me for two main reasons. Firstly, I have been giving maths grinds to secondary school pupils for the past seven years and I have seen pupils displaying a range of difficulties with these four basic operations. In particular, I have encountered many pupils whose knowledge of multiplication tables is quite weak, with such pupils relying heavily on calculators. The second reason these sessions interested me is that I noticed that there are now some different approaches to the teaching and explanation of certain operations to when I learned them in primary school.

This made me appreciate the importance of consistency in a child's learning, and that this takes place in two key ways. Firstly, as pupils move up class levels and to a new teacher, it is imperative that the school has a uniform, agreed means of teaching the operations to prevent the children being confused by different methods. Secondly, the class teacher must communicate with parents/guardians to inform them that the method they themselves learned may not be the method their children are learning in class. It would be useful for this parent/guardian inform to contain worked examples with explanations to aid this process. This will allow parents/guardians to assist with homework and promote learning in line with what is taking place in the classroom.

My main learning point was that pupils' learning in these operations begins in a rudimentary manner in Junior Infants with their introduction to the concept of number and continues all the way throughout their eight years in primary school. Pupils need to be exposed to problems with real-life examples and relevance to their lives.

First steps

As I embark on my blogging adventure with this post, I am excited at the prospect of maintaining a journal of my learning in the Teaching Pedagogy 2 module. I previously blogged while volunteering in India, and later as a Student Ambassador at UCD, but in both of those cases I did not set out with clear goals as to what I hoped to achieve and I did not write consistently in the blog.

I decided to start my blog today as I just completed an on-site class in ICT. As a group, we discussed the learning possibilities that blogs offer pupils and teachers in the modern classroom. Our tutor recommended that if we started blogging we should aim to write regularly. My hope is to contribute posts to this blog twice weekly, ideally at the beginning and end of each week. I aim to reflect on the content of the module, comparing my preconceptions and prior experience with what I take from the online sessions, my additional readings and my interactions with my classmates.

I am passionate about the three curriculum subjects covered by this module (English, Mathematics and Gaeilge). I have enjoyed the learning I have done to date and I look forward to the coming sessions, particularly as we are embarking on our study of Curaclam na Gaeilge this week. Similarly, I have enjoyed exploring the range of technologies to which we have been introduced in this module, particularly Scratch.

Overall, my experiences so far have caused my to reflect on how these subjects might be taught, for example the use of pair/group work. I look forward to having the opportunity to put some of these ideas into practice on School Placement 2 in November/December.