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NZ mathematics in general

       Sometimes teachers talk about levels in maths and sometimes it’s stages. What’s the difference? (show answer)

The New Zealand Curriculum includes 4 levels of mathematical content which primary school students are taught. That’s one level of maths content for every two years at school. So Level 1 applies in particular to students in years 1 and 2 at school, Level 2 to students in years 3 and 4, and so on. The levels apply to all parts of maths: number, algebra, geometry, measurement and statistics.

The stages refer to stages of the Number Framework, and relate to number in particular. Over time, researchers observed that children tend to pass through different stages as they learn to solve number problems. These developmental stages are numbered consecutively. Each stage is a description of things students do, and they are quite different from the prescribed levels of content in the Curriculum. 

       I hear about numeracy and I hear about maths. What’s the difference? (show answer)

Essentially, there was not intended to be any difference. The word numeracy began to replace the word mathematics during the roll out of a teacher education initiative called The Numeracy Development Projects that was introduced to all NZ schools between 2001 and 2009.

Officially, being numerate was defined as “having the ability and inclination to use mathematics effectively – at home, at work and in the community.” Numeracy was meant to hold the same meaning as maths. However, during that time ‘numeracy’ tended to focus more on the number in mathematics rather than more broadly on algebra, geometry, measurement and statistics too.

Accordingly, so there is no ambiguity, mathematics is becoming the preferred word once again. 

       A student teacher is taking maths in my child’s class. Are they trained enough to do this? (show answer)

A student teacher is a teacher in training who has not completed their full teacher education programme. However, a student teacher is fully supported by programme tutors, by a visiting lecturer from their university and, most importantly, by the classroom teacher to ensure that the maths learning programme they plan and run in the classroom, best meets the immediate needs of those students. Often student teachers also bring additional resources and a fresh enthusiasm to mathematics learning, which students appreciate and benefit from. 

       Does the Ministry of Education control the mathematics that is taught in schools now? (show answer)

The Ministry of Education controls the maths taught in schools to the extent that the Ministry provides a New Zealand Curriculum document which defines the scope of the mathematics in which all students in NZ schools should receive instruction. Schools must, by law, teach the curriculum.

Schools do however have the autonomy to bring the curriculum alive for their students in relevant and creative ways. It is the job of the Education Review Office (ERO) to visits schools regularly, to ensure that all students, regardless of the school they are in, are receiving a quality (mathematics) education based on The New Zealand Curriculum.

Maths homework

       We’ve just changed schools. My child isn’t getting any maths homework now. What should I do? (show answer)

Firstly, check with your child’s teacher what maths homework, if any, is set and how regularly. If there is no set homework, indicate that you would like to work with your child on maths at home and seek their advice and some examples of what you could do. Secondly, find out what the homework policy is in the school. You are likely to find this on the school website, or, if not, ask for it at the school office. Finally, look further on this site, particularly in the Maths at our house section, for activities that you might do together. 

       What’s the purpose of maths homework? (show answer)

Doing homework should be a positive experience for a child. The purpose of time spent ‘doing maths’ at home, is for a child to share their learning with family and whānau, to practise maths skills that they have been introduced to at school, and to revise knowledge, such as addition, subtraction, multiplication and division facts. Often homework can involve practising maths while playing card, dice, or board games, using their learning to solve a practical problem or puzzle, and talking about ways to get to a solution. Doing maths homework should result in a child growing in maths confidence and competence. 

       Why are times tables written back to front now?
            I learned them: 2x1, 2x2, 2x3, 2x4 and so on.
            Now they’re written 1x2, 2x2, 3x2, 4x2... Why? (show answer)

Times tables can certainly be written in different ways. However, children need to be helped to see that 2 x 4 and 4 x 2 are both equal to 8. (This is known as the commutative law of multiplication).

However, the way we read each written, or symbolic form, is a little different. 2 x 1, 2 x 2, 2 x 3, 2 x 4 etc. can be read as ‘two made once’, ‘two made twice’, ‘two made three times’, ‘two made four times’ and so on. This is why these facts are known as times tables.

Today, most times tables are written and taught in NZ schools the other way. That is, 1 x 2, 2 x 2, 3 x 2, 4 x 2 etc. These are read as, “one group of two’, ‘two groups of two’, three groups of two’, ‘four groups of two”, and so on.

If you were using equipment, both ways should be represented with groups of two like this @@ @@ @@ @@ (2 x 4 ‘two made four times’ or 4 x 2 ‘four groups of two’) 

       I learned about Families of Facts when I was at school. Is it still okay to do these with my child? (show answer)

Yes it is okay. Exploring Families of Facts is a very good way for children to learn basic facts and, in particular, to come to understand that addition and subtraction are related, and that multiplication and division are related.

Whether a family is one like this: 2+4=6, 4+2=6, 6–2=4, 6–4=2 or this: 2x3=6, 3x2=6, 6÷2=3, 6÷3=2 it is helpful if your child can show how the four facts are related to each other, by using coloured counters, marbles, little stones, shells etc. to model what is happening in each equation.

By using objects, rather than just by writing them or by rote memorization, your child will see and better understand how the three numbers in the four facts really do work together to make their own special ‘family.’ It’s also probably worth telling your child’s teacher that you are working on Families of Facts at home. 

       We go over the times tables in my child’s notebook each night. Is there something else we should be doing? (show answer)

It would be helpful for you to register your child to join the free student e-ako learning pathways on this site. However, first ask your child if their teacher has already joined them. If so, they can use the same password at home.

Once you are into the site, click on Pathway on the left and choose Basic Facts. In particular, explore both Learning Tools by clicking on their green box. Your child will also enjoy and learn from the games listed below the green box. Also see the suggestions in the Families of Facts question above, and for the card and board games below. 

       My child gets a lot of maths homework which takes ages. What’s the best way to help with this? (show answer)

Doing homework should be a positive experience for your child.

The purpose of time spent ‘doing maths’ at home, is for a child to share their learning with family and whānau, to practise maths skills that they have been introduced to at school, and to revise knowledge, such as addition, subtraction, multiplication and division facts. Decide for yourself, or check with the class teacher, what is a reasonable amount of time for your child to spend on their maths homework. Encourage and support your child to complete what they can in this time. When there is a lot of maths homework to complete, remember it serves no purpose for you to do it for them. It is after all, the person who does the work who does the learning. It is better for the maths homework to go back to school incomplete, with a note explaining why, than for you to finish it for the sake of ‘getting it done.’

If maths homework is a struggle and is making doing maths an unpleasant experience for everyone at home, discuss this with your child’s teacher. 

       Can you suggest some good electronic maths games we can play at home? (show answer)

There are thousands of websites with games that your child can use. Many of these are useful for helping them to learn maths, but many are not. The sites listed on the Resources for students page are all good educational sites. There are also a collection of number facts games available in e-ako maths.

       I know that playing card and board games can help with maths. Can you give some examples? (show answer)

Consider first what maths your child might practise as they play games. This is most likely to be quick recall of addition, subtraction, multiplication and division basic facts, and finding the answer to number problems using these four number operations. It may also be that your child needs to practise putting numbers in order or understanding their place value. The nature of the games will depend on the year level of your child and the kind of learning you want them to practise.

A large selection of games is available in the Number Knowledge activities section, sorted according to year level and the maths learning focus.

       Maths seems different these days. Are there any things I shouldn’t do now with my child? (show answer)

It’s useful to remember that mathematics itself hasn’t changed. What was true about numbers and equations, measurements, shapes, maps and graphs when you were at school, is still true today.

What is different is that there is a lot more discussion in classrooms these days on understanding how and why things work they way they do in maths. Rather than only knowing and remembering rules, children are encouraged to see the patterns that make the rules true.

Therefore, one thing that is unhelpful, is to shut down discussion about maths. Do encourage your child to talk about how they solve a problem (get an answer) and importantly why. You can then show them your way and talk about why you do what you do. You might want to check out the section below, Talking about maths with my child.

One other thing you shouldn’t do, is think that knowing basic addition, subtraction, multiplication and division facts are unimportant now. Knowing basic facts will always be important, so don’t neglect these.

Maths in the classroom

       Is there somewhere I can find out the maths content my child should be learning? (show answer)

Yes there is. In the Supporting school maths section, you’ll find Maths tips by year level. Click (show links to files) and choose the year level appropriate for your child. 

       My child often says, “We didn’t do maths today.” Is this okay? (show answer)

It is not uncommon for children to say they haven’t ‘done maths’. Usually this is because the mathematics learning was part of a practical activity. For example, a child may, depending on their age, have been making and describing colourful patterns they have made, or following a recipe, or questioning claims made in an advertisement.

Our number system is made up of patterns so exploring and describing patterns develops foundational algebraic concepts and language. Cooking requires the precise measurement of liquid and solid ingredients. Measurement is an applied and important part of mathematics. Being able to critically examine the statistics behind a particular claim made an advertisement, is fundamental in a world full of media ‘spin’.

So maths may be ‘disguised’ but not absent. However, if you are concerned that maths really is being overlooked in a very busy classroom programme, approach the class teacher, and explain that you’d like to know about the maths learning in class, so that you can help at home. 

       I know my child’s group doesn't get a maths lesson each day. Why is this? (show answer)

In most classrooms, students demonstrate a wide range of abilities. One way that teachers cater for the diverse needs of their students, is to group students of like abilities. So in any one class, there may be several groups and each group may receive a different lesson.

In order to spend quality teaching and learning time with any one group, a teacher may have in place a group rotation system. Accordingly, a group may not work with the teacher every day.

However, most teachers are careful to set appropriate mathematical tasks for individual students or small groups to work on independently. These tasks, which are checked upon completion, are usually opportunities for a student to practice or apply new learning in a range of situations. 

       I see an abacus with coloured beads in my year 6 child’s class. Why? Are they still counting the beads to work out maths problems? (show answer)

An abacus with 100 coloured beads is a common teaching tool in many NZ classrooms. This (Slavonic) abacus is versatile, and is useful for students to manipulate quantities and to see relationships between quantities. For example, in a junior classroom, an abacus may be used for counting, exploring place value or for modeling addition and subtraction operations. In a senior classroom, the same abacus may be used to explore situations involving multiplication and division, fractions, decimals and percentages. 

       Do older children learn practical things about money in maths these days, like saving and budgets? (show answer)

Yes, many schools include ‘financial literacy’ as part of their mathematics programme, particularly with students who are in year 4 or beyond. A number of schools implement an enterprise programme that involves their students in creating, earning and managing a school currency. If this is in place in your child’s school, they are likely to have provided information about this in a newsletter.

Many schools use a financial literacy mathematics book resource that was created for the Ministry of Education and is supplied to all NZ primary schools. You may like to follow this link to the teachers’ notes that support this Figure It Out book resource for year 5 and 6 students.

It would be a good idea to ask your child’s teacher about this too. 

       Lately in maths time my child has been making patterns. How does this help them with sums? (show answer)

Our number system is made up of patterns: base ten patterns, odd and even numbers, patterns that multiplication tables make, and so on. In exploring patterns of their own, younger children come to understand the unit of repeat and the ‘rules’ that describe the pattern. For example, “The pattern goes red, blue, green, red, blue green, so the next one must be red. And I know the tenth one in the pattern will be red because it goes 3, 3, 3, and then 1”.

Important foundational algebraic concepts and language are developed through pattern exploration.

Talking about maths with my child 

       I often ask, “What did you do in maths today?” What other questions could I be asking? (show answer)

Perhaps when you ask your child, “What did you do in maths today?” their answer is, “Nothing.”

You could try other questions and approaches such as:
“Tell me about something….
…that you were proud of
…clever you that found out
…you found hard to understand
…you found was easy
…that you showed someone else how to do in maths today.”

“What kind of maths did you do today?”
“Try out on me something you learned in maths today. See if I can do it!”
“Who did you work with in maths today and what did you work on?”

Remember that maths is much more than arithmetic. Maths is often part of a practical activity such as measuring, baking or exploring shapes or patterns, or making and following maps! 

       If my child works out an answer differently from the way I do, what should I say? (show answer)

You could say:

  • “It’s good that there are often lots of ways to solve a problem (get an answer). Let’s look at your way and then look at my way and talk about what’s the same and what’s different.”
  • “I’m really interested to know how you did that and why you did it that way.”
  • “Gosh, that’s two ways we’ve got to solve this. Are there any other ways?”
  • “I wouldn’t have thought of doing it that way. Tell me why you did that.’ 

       Because I’m not good at maths myself, I feel awkward talking about maths with my child. Can you help? (show answer)

It’s helpful to think about why you say you’re not good at maths and why this is the case. It will help you to see that you don’t want your child to be saying this when they reach your age!

A very important way you can help is by not being negative about maths, despite your own feelings. Saying, “I was never any good at maths, so perhaps you won’t be either.” is unhelpful. Instead, be enthusiastic and be ready to learn with your child. Encourage them to talk about their learning in maths and be open to what they show and tell you. The answers to other questions in this section may help you with this.

You could also register an account for yourself on e-ako maths, and do some of the student e-ako learning pathways.  You might want to begin with the measurement and geometry pathway of modules, and have fun with them!

Like many parents, I have a complicated relationship with homework. One day I’m reminding my children to get to work – vocabulary doesn’t happen by osmosis – and the next I’m struggling to understand the work myself, let alone find the time to help.

I’ve had nearly two decades of helping my children (now aged 22, 19 and 12) with everything from simple addition to Spanish verb endings. Homework has covered the gamut of straightforward memorization or comprehension, to detailed research of family matters, complete with photographs and tales supplied by me.

There are some things I accept about homework: teachers can’t spend the entire lesson making sure all children keep up and most students need time for new topics to sink in. Unfortunately, however, there are a few items on my dislike list too.

Parental involvement

First there’s the dreaded instruction to “Ask a parent to help”. Many of us also work full-time, have other children needing homework help, dinner or a lift somewhere. While we love helping our children learn, we don’t always have the time to build a small scale ark at the end of a long day.

Top tips for teachers on engaging parents in learning

Inviting parental involvement can also be a slippery slope. My approach is usually to brainstorm ideas then see how much the child can do on their own. But I’m well aware of parents who roll their sleeves up and do 99% of it themselves. Therein lies the dilemma – I don’t want to do my child’s homework for them, but I also don’t want their lovingly created ark to get laughed off the playground just because it looks like a child made it.

An introductory email at the beginning of the school year, spelling out exactly how you’d like us to help our children, would be extremely useful. Do you want to see all their mistakes or should we go over homework, catch mistakes and have them try again? How much of their homework should we help with? Is it okay to write a note on the homework pointing out the exact place where the penny didn’t drop?

New information

My pet peeve is the extra questions or challenges thrown in at the end of a homework sheet. This can range from an extra set of brackets suddenly appearing in the order of operations maths homework, to a newer verb added to the “Use this verb in a sentence” assignment.

It may seem harmless – a good exercise in independent learning, even – but parents have a one in three chance of this ending well. Some children rise to the challenge and give it a go, others are frustrated they can’t do the work, and the last third simply say “Why do optional homework?” and resist all persuasion. Most of us aren’t teachers and simply don’t know how to introduce new concepts or topics without tears – theirs and ours. What’s more, while many children are quite happy to take instruction in the classroom, bristle when their parent tries it around the kitchen table. I get that sometimes it’s a race against the syllabus, but if parents are expected to cover new material, please give us tips on how to teach.

New methods

It appears I can no longer do long division and multiplication. Or at least, I can’t do it the way my children are taught. If I’m going over their homework, I can tell them whether their answers are right or wrong, but for the life of me I can’t tell them why in terms they understand. (The phrase “Carry the one” is like a foreign language to them.) For me to help them, they first have to teach me their method so that I can see where they’ve gone wrong. If they don’t fully understand that method, it all falls apart very quickly.

Secret Teacher: I'm astonished by what some parents complain about

Cheat sheets – where teachers share their method with parents – would be really useful. There are now excellent internet tutorials on many academic subjects; sending us links to these if they use the same methods would be extremely helpful. Last year, when my youngest was studying operations of arithmetic (Brackets, Operation, Divide, Multiply, Add, Subtract, or BODMAS to me), his terminology was so different to mine, I had to email his teacher to confirm that I had remembered the method correctly. Her availability to me was much appreciated – I know teachers have a life outside of school.

Too many subjects per night

The kids may have five or more lessons a day but problems arise when subject-specific teachers all give homework on the same night. Even if students don’t have after-school activities, life (in the form of a sibling trip to A&E or a panic shop for new gym shoes) can get in the way, making hours of homework a challenge.

Teachers can help by allowing students a day or two extra to hand the work in work so that they can plan when they’ll do each assignment. After all, time management is a life skill we all need. Alternatively, collaborate with colleagues to ensure that pupils aren’t being given every single subject for homework on the same night.

As I said, it’s complicated. Most parents want what’s best for their children; we want to help them do well, but we vacillate between tolerance and outright hatred of homework, depending on what else we have to juggle. Teachers can’t win either as there are usually complaints when there’s no homework at all. We need a middle ground, where teachers teach and parents support the learning at home, both parties respect each other’s’ roles and communicate regularly about the how best to help the individual child.

Toni Hargis is a British author and blogger, currently living in Chicago, US.

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