It is important for students to be introduced to the mathematics language in each of the strands of the mathematics curriculum. The mathematical language which underpins the focus of mathematics concepts in the classroom should be reinforced continually during the teaching and learning process.

Mathematics has its own set of vocabulary and terminology. In some cases the language is common everyday language, such as ‘that’s a large tree’; or it can be explicit mathematical terminology such as congruent, similarity and symmetrical.

Mathematics is a language within itself. We understand that 2 + 5 = 7. This is the symbolic language of mathematics. The mathematics symbolic language is underpinned by language such as ‘get’, ‘plus’, ‘add’, ‘collect’, ‘together’ and ‘altogether’. This type of mathematical addition language and numbers are represented in word problems that form the basis of NAPLAN testing. Students need to see what operation or strategy is involved in solving a word problem or mathematical situation that is presented to them.

Australian Curriculum Mathematics for Year 2 states that students should be able to ‘solve simple addition and subtraction problems using a range of efficient mental and written strategies’.

Look at this example: ‘There were 10 chickens in the yard; some were white and some were brown. If there were 6 white chickens, how many brown chickens were there?’ Notice in this problem a student needs to know whether this is an addition or a subtraction. There are no contextual clues to say what operations to use. There are, however, clues that students need to know and there is the part-part-whole strategy that students should be introduced to along with the mathematical language and symbolic language. Students need to see that the whole is represented by 10 chickens, one part is 6 white chickens and we need to find the other part which happens to be the brown chickens.

Part (brown chickens) + 6 (white chickens) = 10 chickens

In order to understand and use mathematics, students need to understand the everyday language and mathematical vocabulary/terminology. These understandings will enhance students’ ability to read, write, say, use and make connections within mathematics and across other learning areas.

Literacy is strongly linked to mathematics in that students need to be able to:

• listen to what is said
• process the information (thinking/reflecting)
• think of a strategy to do the mathematics
• communicate what they have done verbally (talk) or written (write) or drawn
• share ideas with others
• read the mathematics when it appears in word problems and other texts such as books, television, advertising, other learning area activities and games.

What does all this mean?

In the mathematics classroom we should have a process that looks at the mathematics language and the strategies that students need in order to understand the mathematics being taught and learned. One successful strategy is to develop a ‘mathematics word wall’ which gives students a visual of what is important to learn in the topic being studied in the classroom.

Click below to see the Word Walls product from R.I.C. Publications:

• Word Walls: Building mathematics vocabulary

Some more mathematical language resources from R.I.C. Publications:

• Lower Primary Maths Games
• Middle School Maths Games
• Maths Terms and Tables

Does knowing this mean teachers should ʻteach to the testʼ? In this instance, teaching specifically to ready students for the test might be appropriate. To perform well in the NAPLAN writing task, students need to be able to write a persuasive text effectively and efficiently on demand. This is a very useful skill for life outside of school and for the future, when students will need to produce texts for things such as an application for a job, written university exams and assignments, a presentation in front of a group, or a classified advertisement. In fact, persuasive writing is one of the most common forms of writing types.

What are persuasive texts?

According to the NAPLAN definition, persuasive writing is ʻwriting in which the writer needs to convince someone of his or her point of view or opinionʼ.

Even very young students can give opinions and their reasons for them, be they in oral or written form. Asked a question about his or her favourite animal, a student could answer, ʻI like dogs best because … ʼ. This is the beginning of persuasive speaking (and writing). An opinion is given and a reason for this opinion is stated. We encourage students to write narrative texts because they encompass the childʼs immediate, egocentric world. How much more difficult, from early childhood onwards, is it to have students write a simple persuasive text? If you think about it, they probably already do it without realising as it can simply involve someone giving his or her opinion. These examples could be considered as first steps in writing persuasive text: ʻI like this book because … ʼ, ʻMy favourite character is … because … ʼ, ʻMy favourite part of the story is … because … ʼ, ʻSarah is my best friend because … ʼ, ʻI love Mum because … ʼ.

Introducing persuasive writing

In the years preceding their first NAPLAN testing in Year Three, students should be encouraged to express opinions orally (while considering the feelings of others) and in a logical, concise manner. From there, it is not a great leap from presenting opinions orally to doing so in a written format.

Short daily writing exercises could include a sentence or two relating to news items, school issues (such as having to sit in the shade if a hat is not brought for playtime), or questions that arise in other learning areas, such as personal development education. Examples: ʻI donʼt think it is fair children canʼt play if they donʼt bring a hat because … ʼ, ʻThe best place to live is … because … ʼ.

Specific task-related topics could be: ʻIs it ever okay to lie?ʼ (related to personal development or values education); ʻWe should have more time to … because … ʼ; ʻI object to … because children should not have to do chores at homeʼ.

Read and analyse persuasive texts

Students should not be expected to write using a particular format of persuasive text without first reading and analysing examples. They need to be very familiar with the structural and language features before attempting to write a type of text.

You can do this during more formal lessons on the topic, discussing what persuasive text is and the reasons for it. Students could suggest examples, then view and discuss types of persuasive text. Find examples from newspapers, magazines, television advertisements, debates, book reviews, and letters to the editor.

Be sure to analyse some examples in regard to format. Students should identify the introduction, main body of the text and the conclusion and then look at the finer details of the text. Once the structure, language features and vocabulary have been discussed, students should use a persuasive writing checklist as a reference to ensure all important elements have been included.

Download examples of persuasive text:

• Primary Writing – Book A – Pocket money
• Primary Writing – Book C – Making beds
• Primary Writing – Book G – Real people

Other examples of persuasive texts to use are:

• fictional books, such as: I wanna iguana by Karen Kaufman Orloff and David Catrow, and Charlotte’s web by EB White
• advertisements from magazines, radio, television, websites, billboards
• letters to the editor
• persuasive songs, such as:ʻFrom little things big things growʼby Paul Kelly and Kev Carmody, ʻThe three Rs (Reduce, Reuse and Recycle)ʼ by Jack Johnson, and ʻKing verbʼ by Jim Thompson.

R.I.C. Publications have produced some excellent posters to help introduce and reinforce the features and elements of persuasive texts.

Modelling and writing persuasive texts

Following the analysis of persuasive texts, the teacher should model writing one or more of them with class assistance—referring to the posters as necessary. These should cover different types if possible.

How teachers start students writing their own persuasive texts will depend on teacher preference. They may ask students to write a basic structure and then have them change aspects of their first draft, to include the language features and vocabulary common to persuasive texts. They should, of course, use their checklist to ensure they have included all necessary elements.

Students should use a simple plan based on the ʻStructure of a persuasive textʼ poster. Additional aspects relating to language features should be added to relevant sections, in conjunction with the checklist.

A list of persuasive text vocabulary could be complied as a class and displayed for use during writing.

Skills needed

The skills a student will need for the NAPLAN persuasive writing task reflect those that students will require in real-life persuasive writing situations:

• an awareness of and an ability to manage time
• an ability to analyse the task given
• a knowledge of the structural components of persuasive text
• an ability to plan the writing
• an ability to write quickly and efficiently on the topic
• an ability to edit.

Tasks to help develop these skills could include:
(a) identifying what elements ʻgrabʼ an audience, what elements keep the audience involved and what elements persuade the audience to a certain point of view
(b) writing persuasive texts daily within a set time limit of approximately 10 minutes. This could include two minutes for planning and one to two minutes for editing and proofreading. A writing prompt could be provided, using images from magazines or an online image. This will closely model the NAPLAN test. Visit http://www.nap.edu.au/NAPLAN/About_each_domain/Writing/index.html to download a colour copy of the 2011 writing stimulus, if desired
(c) encouraging the students to use checklists to ensure they have included all the structural components and language features of a persuasive text
(d) providing opportunities for students to share their writing with others
(e) allowing students to choose their best piece of writing from the week, and then to edit and rewrite it
(f) practising on-the-spot informal debates. Divide the class into pairs and provide each group a topic. One student in each pair provides a view accompanied by a reason and an example. The partner then provides an opposing view, reason and example.

Assessing the writing task

The full 2012 NAPLAN persuasive writing marking guide is available at http://www.nap.edu.au/NAPLAN/About_each_domain/Writing/index.html. Also available on this site is the national minimum standards for writing for Years Three, Five, Seven and Nine, which teachers might find helpful. Perhaps the most useful piece of information provided is the description of the persuasive writing criteria, which forms the basis of the marking guide. Teachers could use this as a guide to teaching persuasive writing, which they could adapt to a more simplified form with more student- friendly language.

With careful planning and directed instruction, teachers will not only be able to assist students with becoming familiar with NAPLAN-style testing, but also be able to instruct students with a variety of writing forms for school and later use in life.

The following resources are available from R.I.C. Publications to help teach persuasive writing in your classroom:

• Persuasive text posters: Six A2-size fully laminated posters – persuasive text checklist, persuasive text vocabulary, language features of a persuasive text, structure of a persuasive text, types of persuasive text
• Primary writing: A set of seven photocopiable resource books for primary schools. The series provides sample texts, analysis pages, checklists, writing activities, language feature activities and comprehensive teachers notes.
• 60 writing topics and Another 60 writing topics: Each title consists of three photocopiable books for primary classes, containing writing tasks covering the six writing genres. It also contains an explanation of each writing genre, including definition, text structure and special language features, teacher and student checklist, blank proforma to allow teachers to add activities, reward certificates, teachers notes, outcome links and suggestions for multiple use.

‘The most important skill we take from the study of mathematics [is] a need to explore, describe and define the universe around us.’
—Richard Schaar, Professor of Mathematics, University of Southern California

‘The mathematician and the preschooler have much in common. They approach the study of mathematics in much the same way. Like mathematicians, young children are intrigued by the mathematics in their world. Consider the intensity and determination children bring to their investigations of the mathematics that surrounds them. This comes not from a need to complete an assignment or because it will be useful to them. It comes from a need to know.’
‘Guided only by their feeling for symmetry, simplicity and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.’
—Eric Temple Bell, mathematician

Many young children are naturally interested in numbers and in response to a situation, will ask: How many are there? How many do we need? Do we have enough? Who has the most? Are there any extras?

They are interested in geometry and explore to find out: How are these shapes alike? How are they different? Which fit together? Which ones leave spaces? What can we build with these? What other shapes can we make using these shapes?

They want to measure and compare, and they wonder: Which is … bigger? More? Heavier? Longer? Shorter? How can we find these out?

They experience the connections between maths and music when exploring rhythm and patterns, and between maths and art when working with symmetry and design.

The mathematics that engages the mathematician and the preschooler is the study of patterns and relationships, order and predictability. This is not mathematics the way most of us experienced it in school. Yet it is the mathematics that will serve our children most as they move through school, and, in time, that will await them as they enter the workforce. The mathematician and the preschooler need and want to experience the joy and excitement of the world of mathematics.

The learning of mathematics is an active endeavour. Children need to be involved in investigating, comparing, wondering and checking to see what happens. They need to think about what they are experiencing, to notice what happens and to begin to talk about what they notice. They need to listen and think about what other people have to say. They need to begin to make connections, to see relationships among mathematical ideas. They need to see how experiences can be recorded: with blocks, with pictures and sometimes with mathematical symbols. Important mathematical ideas will naturally arise through children’s play.

‘Children’s play and interests are the sources of their first mathematical experiences. These experiences becomemathematical as the children represent and reflect on them … The most powerful mathematics for a preschooler is usually not acquired while sitting down in a group lesson but is brought forth by the teacher from the child’s own selfdirected, intrinsically motivated activity.’
—Douglas H Clements, Mathematics for young children

Number

Children’s mathematics includes number experiences that ask them to discover: How many … leaves did you pick up? How many pockets do you have? Can you put three horses in the stable? Can you put four fish in the ocean? Can you give me four of those?

There are a number of ways to explore number; for example, acting out counting songs. This helps children bring meaning to the counting sequence they are learning. They learn to count beyond what they already know by counting along with the teacher. A teacher can ask, ‘How many children are here today?’ and then model writing numerals when the children tell how many. Some children will label what they counted with a numeral and show how many horses they put in the stable, and a few will even try to write the numeral on their own.

Spatial experiences

Try to provide opportunities that allow children to see how shapes fit together through experiences with puzzles, blocks and boxes. Children who play with blocks will gradually build structures that begin to look more and more organised and stay balanced a bit longer. It is also good for the children to have them hear their teacher using language that describes where objects are located: Here it is—under the table.; Let’s look behind the cubbies.; We put the calendar over the bookshelf.

And they begin to use spatial language themselves, like: The baby is in the baby bed. She is under the covers.; The biscuits are inside our play oven.

Pattern experiences

Or you can model patterns based on colour. As an example, model patterning when making a long Unifix™ train with students, with blocks positioned as red, red, yellow, red, red, yellow. Ask children what colour they think comes next?

There are usually many opportunities to show children patterns that exist in everyday life. It can be as simple as pointing at a child’s shirt and studying the pattern on the clothing: Look, I see a pattern on your shirt—red, green, white, red, green, white.

Allow children opportunities to copy repeating patterns using a variety of materials; for example: block, button, block, button. If they have pattern cards available to copy, some will continue the pattern beyond the card.

Children can experience patterns through music and become aware of rhythm and repetition when they march around the room, tap their rhythm sticks or beat on their drums. They experience patterns through stories when a teacher reads predictable books and they delight in guessing what comes next.

Download free activity pages from Developing maths concepts in the early years

Click here for more information on Developing maths concepts in the early years

In my 11 years of teaching Years 3 and 4, I have noticed, and taken an interest in, how children learn basic maths facts. This includes having conducted an action research project in which I studied approaches to teaching maths facts and concluded that students learn and retain automaticity of facts when they are taught them by using strategies and looking for patterns, and are given opportunities for meaningful practice.

Afterwards, I shopped at teacher stores, bookstores and online for a book that teaches multiplication facts in this manner. I was unable to find it! What I found was ‘drill and kill’ (worksheets that present the facts repeatedly), or speed tests. I bought and tried many of these books … and they didn’t work!

As such, I began creating my own practice pages to make up for the lack of effective materials on the market. The strategies I developed for teaching the multiplication facts are the basis for Multiplication success with algebra. My intention is to share my successful strategies with other teachers who are also looking for more efficient, practical ways to teach their students these facts.

What’s different about this approach?

The approach used in my book provides students with meaningful practice as they learn multiplication. They are exposed to and practise algebraic concepts as they master the facts. In a time when the curriculum is overwhelming and difficult to fit into a school day, an approach that synthesises concepts provides an important advantage.

The following are examples of the strategies used in my book:

1. Students use the identity property to figure out that any number (n) multiplied by 1 is equal to that number (n • 1 = n); and the zero product property, which states that any number (n) multiplied by zero is always equal to zero (n • 0 = 0).
2. Students use the doubling–halving strategy to help them learn many of the multiplication facts. For example, if you multiply a number by 2 and then double it, you will get the answer to multiplying that number by 4. If you multiply a number by 4 and halve it, you will get the answer to multiplying that number by 2: (n • 2) x 2 = n • 4 or (n • 4) ÷ 2 = n • 2
3. Students are also prompted to look for patterns to help them figure out the products. For example, all numbers multiplied by 9 have a digit sum of 9; all numbers multiplied by 5 have a 0 or 5 in the ones place of the product.

While students are learning the facts using strategies and looking for patterns, they are also practising algebraic ideas like balance, variable and function.

Balance involves the idea that the equal sign shows the relationship between numbers. As such, while students are practising the 10 and 5 multiplication tables, they are also practising balance when they solve the equation: 4 x 5 = Δ • 10

Variables are the unknowns in an equation, and this book provides students with practice in determining the value of the variable in an equation. For example, in the equation Δ x 3 = 15, the student solves for Δ (the unknown).

Function is another idea that students practise. Students use the given rule to determine the output in a function table.

Download these free activity pages from Multiplication success with algebra by Jen Rubera

Click here for more information on Multiplication success with algebra by Jen Rubera

If you are reading this, then you are one of the first to access the R.I.C. eNews and Views section of our website.

Our hope is that R.I.C. eNews and Views will provide you with interesting and thought-provoking articles regarding education in Australian primary schools, along with regular updates on what’s happening at R.I.C. Publications. Think of it as R.I.C.’s blog.

We aim to make it an easy read and one that you’ll return to with each update. Indeed, we want you to keep returning month after month, so if you have any suggestions regarding ways to improve the page we want to hear from you. We want the content to be fresh, interesting and worthwhile to you … the busy classroom teacher. So here’s a quick snapshot of some of the things we intend to offer:

• Teaching tips: We will include a monthly article that targets a subject area of current interest to teachers. Hopefully, we will give you some ideas and tips you can apply to your classroom teaching.
• Educational news: This will be a rundown of what’s been making news education-wise in Australia and around the world over the past month.
• Product reviews: We will provide a monthly selection of product reviews of available primary texts and resources—written by teachers, so you can be sure that the products have been tried and tested.
• Free stuff: Yes, we will have some free activities, resources, blackline masters etc to win to help you in the classroom … or to give you a taste of something we think you will like.
• Special deals: Return to the webpage to keep a tab on any specials which we may have happening. This will allow you to keep up to date with the best resources at the best prices.

Reliable as a provider of easy-to-use reproducibles, recently R.I.C. Publications has widened our product offerings to include some great new products such as The comprehension box, Essential phonics, BrainSnack™, a large range of interactive whiteboard resources and much more. Of course, we will also continue to update our current teaching resources to keep them current with the Australian national curriculum.

And one final comment … 2012 is the year of the London Olympic Games and we are again the licensed educational publisher to the Australian Olympic Committee and will provide you with the best in educational resources to help you ride the wave of interest in this event with your classroom. Watch this space!

So, we hope this sounds as exciting to you as it is to us! And we want to hear from you. Our job is to make your life easier, so we need to know what types of problems teachers are encountering so we can help find a solution. Conversely, tell us what is working for you, so it can be shared with others.

Speak soon
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