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.