# More tips for teachers: Essential materials for every mathematics classroom

What hands-on materials and resources do you have in your mathematics classroom?  Concrete materials, coupled with good teaching practice and strong teacher content knowledge, provide opportunities for learners to construct rich understandings of mathematical concepts. In addition, allowing opportunities for children to physically engage with materials can be much more meaningful than working only with visual or even digital representations, particularly when learners are still in the concrete phase of their learning about specific concepts. For example, if you’re teaching concepts relating to 3-dimensional space, it makes sense that it is better for children to be able to manipulate real objects in order to explore their properties and relate their learning to real-life, as opposed to exploring objects through graphical representations only. Concrete materials also promote the use of mathematical language, reasoning, and problem solving.

I’m often asked about the essential resources required for primary mathematics classrooms. There are quite a few, but if you have a limited budget or storage space, there are some resources that are what I would consider to be essential, regardless of the year level that you are teaching. My advice would be to invest in materials that are flexible and able to be used in a variety of ways, perhaps in conjunction with other materials. Also consider collecting things that are not necessarily intended as educational resources but may have some mathematical value, such as collections of things (keys, lids, plastic containers, etc.) for activities that require sorting and classifying. Here is a list of basics that can be purchased from educational resources suppliers (some of the items can also be sources at normal retail and/or discount stores):

• Counters
• Dice (as well as the standard six sided dice, you could purchase many other variations including blank dice)
• Calculators (yes, these are great, even in the early years. Think about using them to investigate numbers rather than simply as , computational devices)
• Base 10 material (be careful how you ‘name’ these – using terms like ones, tens, hundreds and thousands limits their use. It is best to use the terms minis, longs, flats and blocks so they can be used flexibly to teach a range of whole number and measurement concepts)
• Measurement materials (you’ll need a range of things to cover all aspects of measurement, eg. scales, tape measures, rulers, )
• Pattern blocks (great for more than just exploring 2D shape – these can be used to teach fractions, place value, area, perimeter etc.)
• Dominoes (one of my truly favourite things!)
• Playing cards
• Unifix blocks
• Paper shapes (circles, squares, etc.) to promote a range of concepts including fractions, shape, and measurement

Of course, any resource is only as good as the teacher using it and the way it is integrated into teaching and learning. Prior to using any concrete material or resource, consider the purpose of the lesson and the mathematical concepts being covered. Also consider how you can make the most out of those resources – how will you differentiate the task, and how will you capture evidence of learning? This is where technology can play a useful role and allow teachers and students to capture evidence when working with concrete materials. Technology can also be used alongside concrete materials. For example, work with pattern blocks can be recorded using the Pattern Block App on an iPad. Or students could integrate their use of concrete materials with a verbal reflection or explanation using the Explain Everything app.

The best way to get the most out of concrete materials is to do some reading. There are many high quality resource books and there are also many great websites such as NCTM Illuminations that provide excellent teaching ideas. Once you see the potential of high quality, flexible concrete materials such as those listed above, your students will become much more engaged with mathematics and will develop deeper conceptual understandings.

And one last thing…students are never too old or too smart to benefit from hands-on materials so never keep them locked away in a cupboard or storeroom (the materials, not the students)! Students should feel they can use concrete materials when and if they need them. After all, we want our students to be critical, creative mathematicians, and hands-on materials assist learning, and promote flexibility in thinking and important problem solving skills.

# Beach Towels and Pencil Cases: Interesting, Inquiry-based Mathematical Investigations

In several of my previous posts I discussed the importance of promoting critical thinking in mathematics teaching and learning. I’ve also discussed at length various ways to contextualise mathematics to provide opportunities for students to apply prior learning, build on concepts, and recognise the relevance of mathematics in our world. In addition, investigations provide excellent assessment material – usually when we assess in mathematics we ask for specific answers. In investigations, students can show us a range of mathematics, often beyond our expectations. They are also a great way to integrate other subjects areas such as literacy and science.

In this blog post I am going to share some ideas for open ended and inquiry-based mathematical tasks based on two items that most students would be familiar with – beach towels and pencil cases!

### Pencil Cases

Let’s start with pencil cases. It’s the start of the 2018 school year next week and many children begin each school year with brand new stationery, in brand new pencil cases. Even if they’re not brand new, most children have a pencil case. I came across an interesting article relating to pencil cases a few days ago, and I think this could be used to spark interest and curiosity. The article can be found here:

https://honey.nine.com.au/2018/01/19/14/35/pencil-case-missing-letter

#### Short activities:

1. Who has the heaviest pencil case? Compare the mass of your pencil case with the pencil cases of your group members. Who has the lightest? Estimate the mass, then use scales to test your estimations. How close were the estimations?
2. Estimate, then calculate the surface area of your pencil case. What units are the most appropriate to use? Explain how you measured the surface area.
3. Faber Castell is a famous brand of pencils. Investigate the history of Faber Castell and illustrate this on a timeline.
4. According to the Faber Castell website, it takes one ‘pinus caribaea’ tree 14 years to be ready to be used to manufacture pencils. Each tree can produce 2500 pencils. If one tree was allocated to each school, how many pencils do you think each child in your school might receive? How did you work this out?
5. If each of the 2,500 pencils were sold for \$1.50, how much do you think the entire tree be worth in pencil sales?

#### Investigations:

1. At the beginning of each school year many children get brand new pens and pencils to take to school. Investigate how much it would cost to buy your stationary. Which shop offers the best value for money?
2. Some pencil cases like the one in the photo and in the Missing Letter article have small clear plastic pockets to put your name in. If a pencil case has only eight pockets, is this enough for your name? Investigate the length of names in your class. What would be the average length name in your class? What else could you explore about names?
3. The pencil case in the picture came with some pre-printed letters for the clear pockets. There are more of some letters than others. Investigate the most common letter occurring in students’ Christian names. Do you think it would be the same in all countries?
4. Design and make a pencil case to suit your individual stationery needs. Write about the mathematics you use to do this.

#### Extension Activities:

1. Design a new and improved pencil and explain the changes you have made.
2. Design, justify, and create a marketing campaign for a new, ‘miracle’ pen.
3. Research and discuss the following statement: “To save the environment, wooden pencils will no longer be manufactured”.

### Promoting Curiosity and Wonder

Mathematical investigations should promote curiosity and wonder. The pencil case questions and investigations are open, yet provide some structure and support. They give enough detail to communicate the type of mathematics required to complete the task or investigation. Students should eventually be able to feel confident enough to come up with their own questions and follow their own path in terms of the mathematics they access and apply, just like mathematicians do.

### Round Beach Towels?

In the last year or two a new beach towel has emerged onto the beach towel scene. It’s round. Now this idea immediately caused some concern for my mathematical brain. I had questions.

• Is there more fabric in a round beach towel than a regular, rectangular beach towel?
• Is there more fringe, and wouldn’t this make the towel more expensive?
• How does one fold a round beach towel?
• Could you wrap a round beach towel around you the way you wrap a rectangular beach towel?
• How much more area on the beach gets taken up by people spreading round beach towels?
• Does this mean less people get to lay on the sand?
• Could you design a round beach towel that has a tessellating pattern?

All of the questions above can be explored using a range of mathematics…I wonder how many more questions your students could come up with?

# Tips for Parents: Helping Your Child Succeed with Mathematics

As another new school year approaches, parents are once again busy preparing their children to ensure they have the things they need to be successful. School uniforms, books, pens and pencils are important, but what’s even more important is the preparation and support parents can provide to help their children learn and be happy at school.

We often see and hear media reports that lament Australia ‘falling behind’ other countries when it comes to mathematics.  Unfortunately, some people think it’s okay to be bad at maths and sadly, many children develop anxiety around mathematics from a young age. Maths seems to be a problem.

Is there something you, as a parent, can do to help? Relying on teachers alone can’t fix the problem.  There are many things parents can do to help their children learn, understand, and appreciate mathematics  before they begin school and during the  school years. The following is a list of tips for parents that will help them to help their children succeed:

May people openly claim they don’t like maths or they’re not good at it, unintentionally conveying the message that this is okay. Unfortunately, this can have a detrimental effect on the children who hear these messages. In my research on student engagement, children whose parents made similar comments often used the same comments as mathematics became more challenging during the high school years. These behaviours can lead to children opting to stop trying and drop out of mathematics as soon as they can, ultimately limiting their life choices.

As a parent, be conscious of displaying positive attitudes towards mathematics, even when it’s challenging. Adopting what is referred to as a ‘growth mindset’ allows children (and parents) to acknowledge that mathematics is challenging, but not impossible. Rather than saying “I can’t do it” or “it’s too hard”, encourage statements such as “I can’t do it yet” or “let’s work on this together”. If you’re struggling with the mathematics yourself, and finding it difficult to support your child, there are options such as free online courses like Jo Boaler’s YouCubed website (www.youcubed.org), apps such as Khan Academy, or you can seek help from their child’s teacher.

If you choose to use a tutor to help your child, make sure it’s a tutor who knows how to teach for understanding, rather than memorisation. Too often tutoring colleges use the traditional teaching method of drill and practice, which won’t help a struggling student to understand important mathematical concepts. Find a tutor who understands the curriculum and can tailor a program to work alongside what your child is learning at school.

1. Developing a positive working relationship with teachers

It’s important for parents to work with their child’s teacher to ensure they are able to support the learning of mathematics. This will help the teacher understand the child’s needs and be better able to support the child in the classroom, while at the same time helping the parents support the child at home. Often schools hold information evenings or maths workshops to help explain current teaching methods with few parents turning up. It’s important to attend these events as they are a good opportunity to learn ways to help children with mathematics at home.

1. Know what maths your child is learning

Mathematics teaching and learning has changed significantly over the last few decades. Unfortunately, many of the older generations still expect children to be learning the same maths in the same way, regardless of how much the world has changed! Access to the mathematics curriculum is free to everyone. Parents have the opportunity to find out what their child should be learning simply by accessing the curriculum online, or talking to their child’s teacher. This can help parents who may have unrealistic expectations of what their child should know and be able to do, and will also help them understand that mathematics is not just about numbers or learning the multiplication tables.

One of the most common complaints when it comes to school mathematics is that children don’t ‘know’ their multiplication tables. Is this important? Yes, it’s still important that children gain fluency when dealing with numbers. However, it’s also important that we don’t just rely on rote learning, or repetition. Children need to understand how the numbers work. In other words, they need to be numerate, and have a flexibility with numbers. Once they understand, then fluency can be built. Using maths games is a good way of getting children to build up speed with number facts.

1. Make maths part of everyday activities

Bring maths into daily conversations and activities with your child. After all, there’s maths in everything we do. For example, if you’re cooking you might ask your child to help you measure out ingredients. If you’re shopping, you could have a little competition to see who can make the best estimation of the total grocery bill or perhaps ask your child to work out the amount of change (this may be challenging given that we use credit cards most of the time).

If your child likes to play digital games, download some maths apps so they can use their screen time to learn while having fun at the same time. Alternatively, traditional games can provide opportunities to talk about maths and help your child. Games that use dominoes and playing cards are great for young children as are board games such as Snakes and Ladders or Monopoly. Even non-numerical games such as Guess Who have benefits for mathematics because the promote problem solving and strategic thinking, important mathematical skills.

Parents who can work with their child’s teacher, be proactive in their child’s education, and demonstrate positive attitudes towards mathematics can make a big difference to their child’s success at school. It’s an investment worth making.

# Educational activities for the summer break to beat boredom and learning loss

Christmas is over, the novelty of new toys has worn off, and the holiday chorus of “I’m bored” is echoing in households everywhere. What can you do to stop the boredom?

First, it’s important to understand why children feel bored. According to the literature, boredom signals a person’s need for physical or mental activity to keep him or her occupied and to vent energy, just like needing food to satisfy feelings of hunger. Apart from the constant nagging, having bored children can lead to negative behaviour, and that’s the last thing parents want during the long summer holidays.

## What’s wrong with kids being bored?

Apart from maintaining the peace, there are other important reasons to keep your children from being bored. The long summer holiday period can result in what’s called learning loss. That is, children who aren’t kept mentally and physically active during the long school holidays can lose some of the skills they learned during the school year.

The phenomenon of learning loss is well documented in research, and studies have shown that often schools have to spend several weeks bringing students back to their pre-holiday learning levels.

Read more: Should Aussie kids go on US-style summer camps?

At best, children learn little or nothing during the summer holidays, and at worst, they can lose weeks of learning. The greatest losses occurring in the area of mathematics, and then spelling. The children most at risk of learning loss are those from low-income families, because of the differences in holiday experiences and activities of children from high-income families.

Regardless of income, there are many ways to stop children being bored, maintain their learning and keep them busy and happy during the holidays.

## Activities at home

Home is where you can get back to basics with your children.

Encourage your child to read a book. Research has proven that reading for pleasure improves reading attainment and writing as well as general knowledge, and community participation. Reading also provides insight into human nature and decision-making. If you don’t have books at home your child is interested in, take a trip to the local library and let them choose.

Play games with your children. If you want to help maintain your child’s mathematical learning and keep them having fun, there are lots of simple games you can play. All you need is a deck of cards, a set of dominoes or some traditional board games such as Monopoly, Guess Who or Yahtzee.

If you want to help with spelling, try playing Scrabble or teach your child to do simple crossword puzzles. For those who like a challenge, chess promotes important problem-solving skills.

Get messy with some creative art. If your child is feeling creative and you don’t mind a mess, let him or her paint, build, sculpt, design or invent. Creative art has been found to assist in children’s learning and promote well-being.

## Digital activities

Play fun and educational video games. If traditional activities don’t do the trick, there are always the digital alternatives. Research has found playing video games can have cognitive, emotional and social benefits. But it’s important to choose carefully.

Read more: Why digital apps can be good gifts for young family members

Rather than choosing games that promote mindless violence or require little or no thinking, there are many educational games and apps that can help your child continue learning over the holidays such as Minecraft, Pick-a-Path, or MathDoodles. Many good apps are free and even if they’re not designed to be educational, they often involve problem-solving skills important in developing critical and creative thinking.

## Outdoor activities

Take your children to the local park or playground. Recently, the NSW Department of Education announced over this year’s summer holidays it will trial having the playgrounds of 40 schools open to the public. This is aimed at providing access to outdoor spaces for families who don’t have backyards for children to play in.

The benefits of outdoor play during the summer holidays are significant. Science says holidays often result in weight gain among adults and children but there are also social benefits like improved self-confidence to be gained from interacting with other children.

Read more: Will you gain weight this Christmas?

If you want to add educational benefits to outdoor activities, play games that involve keeping score to help children maintain their mathematics skills. Younger children could go on “shape hunts” or “number hunts”, or you could play a game of I Spy to ensure there is mental and physical activity happening.

There are lots of other low-cost activities to support your children’s education. Going shopping can help your kids learn about financial literacy. Going to a museum or going hiking can teach children about history and nature.

Most importantly, all of these activities will keep your kids’ minds and bodies active, keep you sane and stress free, and stop the kids from saying “I’m bored”.

Catherine Attard, Associate Professor, Mathematics Education, Western Sydney University

# Teaching kids about maths using money can set them up for financial security

As the world of finance becomes more complex, most of us aren’t keeping up. In this series we’re exploring what it means to be financially literate.

One of the most common complaints children have about learning maths is its lack of relevance to their lives outside school. When they fail to see the importance of maths to their current and future lives, they often lose interest.

This results in opting out of mathematics study as soon as they can, and proclaiming they are “not good at maths”.

Financial literacy – learning about budgeting, saving, investing and basic financial decision making – taught by both parents and teachers can help keep them engaged.

## Three strategies for teachers

The Australian Association of Mathematics Teachers promote the teaching of financial literacy through maths with the help of contemporary teaching and learning resources that reflect students’ interests. These include lesson plans, units of work, children’s literature, and interactive digital resources such as games.

A wide range of resources are available from websites such as MoneySmart and Financial Literacy Australia. These are an excellent way to begin teaching financial literacy concepts, with some units of work specifically designed with a mathematics focus. However, these units can and should be adjusted to suit the specific needs of the students in your classroom.

Additionally, teachers should consider using resources that are familiar to students’ everyday lives. These could include items that are in the news media, shopping catalogues, television commercials etc. Keep watch for interesting photographs or misleading advertisements. They are great for starting discussions about maths. Questions such as “is this really a good deal?”, “what is the best deal?” or even “what mathematics do we need to know and understand to work out if this advertisement is offering a bargain?” could begin discussions.

There are also a range of apps that could be used alongside maths and financial literacy explorations, including budgeting apps and supermarket apps such as TrackMySpend, Smart Budget, or My Student Budget Planner . If you like using picture books to introduce and teach concepts, the Money & Stuff website has an extensive list of books relating to financial literacy.

## The money connection

One way to improve engagement with mathematics is for schools to teach it in ways that children are familiar with. Most children are familiar with money, and many are already consumers of financial services from a young age. Research has found that it’s not uncommon for children to have accounts with access to online payment facilities or to use mobile phones during the primary school years. It’s clear that financial literacy and mathematics skills would be beneficial when using such products.

Financial education programs for young people can be essential in nurturing sound financial knowledge and behaviour in students from a young age. Using real-life contexts involving financial literacy can help children learn a range of mathematical concepts and numeracy skills like lending and borrowing, budgeting, and interest rates. They are more likely to remember and understand what they have learned because they applied mathematics to something they’re interested in and something that they can use in their lives.

Research into the teaching of financial literacy combined with mathematics in primary schools shows how important it is for all children to understand the importance and value of money and recognise the maths that underpins consumer and financial literacy.

They also need to engage in real world projects and investigations relating to consumer and financial literacy to understand how mathematics is applied in everyday decisions that could influence life opportunities.

## Shopping is a teaching opportunity for parents

Many young children don’t understand where money comes from. It’s important that they begin to develop some understanding of how our economy works, even from a young age. Research has found a pattern emerging where children whose parents talk to them about money develop an earlier understanding of its importance. They are also provided with more opportunities to deal with making decisions about money.

If you have young children in primary school, it’s a great time to start their financial literacy and mathematics education. There are plenty of opportunities when you are out shopping to include your child in discussions and decisions where appropriate, or explain the financial decisions you make on their behalf. Talk about the mathematics involved in financial decision-making. Where possible, encourage children to make their own financial decisions with things like pocket money or savings. If you feel you need to improve your own financial literacy first, there are many resources available for adults.

Teaching children about money through mathematics helps children learn. It helps them use mathematics in real-life scenarios and, more importantly, can help set them up for future financial security.

Catherine Attard, Associate Professor, Mathematics Education, Western Sydney University

# Mathematics and the transition from primary to secondary schooling

As the end of the year looms, many students are preparing to transition from primary to secondary school. Most children look forward to going to high school and adjust quickly to the transition, expressing a preference for secondary school above primary school (Akos & Galassi, 2004; Howard & Johnson, 2004). Unfortunately, despite these initial positive sentiments, as their first year of high school progresses many students begin to develop negative attitudes towards secondary schooling (Ashton, 2008; Bicknell, 2009), and often, towards mathematics.

Students about to transition from primary to secondary schooling often have pre-conceived ideas and high expectations of the academic challenges presented by secondary schools. Often students’ perceptions of what is involved at secondary school are distorted and are promoted by parents, older siblings and often primary school teachers. Despite their best intentions, parents and primary teachers are generally unfamiliar with the secondary school environment and curriculum and attempts to prepare primary students for secondary schooling may result in preparing them for an environment that does not exist (Akos & Galassi, 2004). This is particularly relevant to the study of mathematics, where students are often prepared for work they perceive to be ‘much harder’ than primary school mathematics (Howard & Johnson, 2004).

In an Australian study of students’ perceptions of the transition to secondary school, students found the academic work during their first year of secondary school was no harder, or was easier than their final primary year, yet they still had difficulty adjusting to the academic environment of the secondary school (Kirkpatrick, 1992). Although there may be a lack of challenge, the transition to secondary school often results in some level of achievement loss (Athanasiou & Philippou, 2009; Bicknell, 2009). This is sometimes due to secondary students being focused on performance rather than being task-orientated in order to improve competencies (Alspaugh, 1998; Zanobini & Usai, 2002). Academic challenge seems to be an ongoing and contentious issue in the middle years of schooling.

Difficult transitions to high school can lead to disengagement, negative attitudes towards school, reduced self-confidence, and reduced levels of motivation, particularly in the area of mathematics education (Athanasiou & Philippou, 2009). Some of the transition difficulties that impact negatively on students are the disruptions within friendship networks, reducing relatedness to school and classroom, the different structure of the secondary school (larger number of teachers), and a more competitive and norm-referenced environment, resulting in lower engagement. A study of motivation and engagement levels of 1019 Australian primary and secondary school teachers conducted by Martin (2006) found that, reflecting the teachers’ levels of motivation and engagement, the primary school students’ motivation and engagement levels were rated higher than that of high school students. Martin’s study found that some of the transition difficulties that impact negatively on students’ motivation and engagement are:

• disruptions within friendship networks reduces relatedness to school and classroom;
• some students experience difficulty adapting to a larger environment, reducing the feeling of community;
• the structure of some high schools involves students having a significantly larger number of teachers, resulting in difficulty establishing supportive relationships;
• more authority-based teacher-student relationships within the high school result in less intrinsic motivation; and
• a more competitive and norm-referenced environment in high school often results in lower engagement levels.

Such transition issues are not limited to students in Australian schools. McGee et al., (2003) found substantial agreement in international literature that an effect of transition is often a decline in achievement. Eccles and Wigfield (1993) attribute the decline in students’ attitudes and performance in subjects such as mathematics to changes in students’ concepts of themselves as learners as they get older. In contrast to this belief, Whitley et al., (2007) claim secondary teachers often have higher expectations of students when compared to primary school teachers, thus explaining the decline in achievement as a mismatch between teacher expectations and students’ abilities. Related to high expectations of students, one of the issues facing secondary teachers is how much they want to know about their students coming from primary school. Some teachers favour a ‘fresh start’ approach as they are often faced with students from a variety of schools, perhaps to the detriment of some students. Research has found this to be particularly the case with mathematics, causing a lack of continuity across the curriculum (Bicknell, 2009).

Another long-term issue of transition identified by McGee et al., (2003), is curriculum continuity and coherence across primary and secondary schools. It was found there are gaps in subject content, differences in teaching and learning practices and inconsistencies in the expectations of students. Current curriculum documents aim to address this and minimise gaps in curriculum by presenting content as a continuum across the grades, with all teachers having access to the content requirements for learners at all stages (Australian Curriculum Assessment and Reporting Authority (ACARA), 2010).

Lowered achievement levels could also be explained by the use of more formal, competitive assessment practices that students experience in secondary school. A move away from intrinsic methods of assessment towards a more impersonal, more evaluative, more formal and more competitive environment is another significant factor effecting transition to secondary school.

So what can teachers and schools do to ensure students maintain their engagement with mathematics and with school as they enter secondary education? Here are some suggestions:

• Build transition programs that promote collaboration between primary and secondary schools
• Invite secondary mathematics teachers to visit and observe (and perhaps teach) primary mathematics lessons and vice versa
• Hold joint parent and student information sessions that explain pedagogy and the mathematics curriculum expectations
• Attend professional learning aimed at middle years mathematics pedagogy and content
• Be familiar with mathematics curriculum requirements at both primary and secondary levels.

References:

Akos, P., & Galassi, J. P. (2004). Middle and high school transitions as viewed by students, parents, and teachers. ASCA Professional School Counseling, 7(4), 212-221.

Alspaugh, J. W. (1998). Achievement loss associated with the transition to middle school and high school. The Journal of Educational Research, 92(1), 20-23.

Ashton, R. (2008). Improving the transfer to secondary school: How every child’s voice can matter. Support for Learning, 23(4), 176-182.

Athanasiou, C., & Philippou, G. N. (2009). Students’ views of their motivation in mathematics across the transition from primary to secondary school. Paper presented at the 33rd Conference of the International Group for the Psychology of Mathematics Education., Thessaloniki, Greece.

Australian Curriculum Assessment and Reporting Authority (ACARA). (2010). The Australian curriculum: Mathematics Retrieved 8th August, 2010, from http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10

Bicknell, B. (2009). Continuity in mathematics learning across a school transfer. Paper presented at the 33rd Conference of the International Group for the Psychology of Mathematics Education, Thessaloniki, Greece.

Eccles, J. S., & Wigfield, A. (1993). Negative effects of traditional middle schools on student motivation. . Elementary School Journal, 93(5), 553-574.

Howard, S., & Johnson, B. (2004, 28 November – 2 December). Transition from primary to secondary school: Possibilities and paradoxes. Paper presented at the Conference of the Australian Association for Research in Education, Melbourne.

Kirkpatrick, D. (1992, November). Students’ perceptions of the transition from primary to secondary school. Paper presented at the Australian Association for Research in Education/New Zealand Association for Educational Research joint conference, Deakin University, Geelong. http://www.aare.edu.au/92pap/kirkd92003.txt

Martin, A. J. (2006). The relationship between teachers’ perceptions of student motivation and engagement and teachers’ enjoyment of and confidence in teaching. Asia-Pacific Journal of Teacher Education, 34(1), 73-93.

McGee, C., Ward, R., Gibbons, J., & Harlow, A. (2003). Transition to secondary school: A literature review. Ministry of Education, New Zealand.

Whitley, J., Lupart, J. L., & Beran, T. (2007). Differences in achievement between adolescents who remain in a K-8 school and those who transition to a junior high school. Canadian Journal of Education, 30(3), 649-669.

Zanobini, M., & Usai, M. C. (2002). Domain-specific self-concept and achievement motivation in the transition from primary to low middle school. Educational Psychology, 22(2), 203-217.

# Technology in the classroom can improve primary mathematics

Many parents are beginning to demand less technology use in the primary classroom due to the amount of screen time children have at home. This raises questions about whether technology in the classroom helps or hinders learning, and whether it should be used to teach maths.

## Blaming the calculator for poor results

We often hear complaints that children have lost the ability to carry out simple computations because of the reliance on calculators in primary schools. This is not the case. In fact, there has been very little research conducted on the use of calculators in classrooms since the 80’s and 90’s because they are not a significant feature of primary school maths lessons. When calculators are used in primary classrooms, it’s usually to help children develop number sense, to investigate number patterns and relationships, or to check the accuracy of mental or written computation.

There is also evidence that children become more flexible in the way they compute through the use of calculators. It allows them to apply their knowledge of place value and other number related concepts rather than using a traditional algorithm.

The Australian Curriculum promotes a strong focus on the development of numeracy, including the development of estimation and mental computation. These are skills that children need in order to use calculators and other technologies efficiently.

The curriculum also promotes the thinking and doing of mathematics (referred to as “proficiencies”) rather than just the mechanics. There’s much more to mathematics than computation. That’s where more contemporary technologies can improve primary mathematics.

## The importance of technology in learning maths

The use of digital technologies in the primary mathematics classroom is not an option. The Australian Curriculum and Reporting Authority (ACARA) has made it mandatory for teachers to incorporate technologies in all subject areas. Fortunately, schools have access to more powerful, affordable devices than ever before. Importantly, these are the same devices that many children already have access to at home, providing an opportunity to bridge the gap between the mathematics at school and their lives outside the classroom.

Literature around digital technologies and mathematics suggest new technologies have potentially changed teaching and learning, providing opportunities for a shift of focus from a traditional view to a more problem-solving approach. This notion is supported by research that claims the traditional view of mathematics that was focused on memorisation and rote learning is now replaced with one that has purpose and application.

When used well, technology can improve student engagement with mathematics and assists in improving their understanding of mathematical concepts.

In a recent research evaluation of the Matific digital resources, the findings were positive. The students found that they enjoyed using the digital resource on iPads and computers, and went from thinking about mathematics as something to be tolerated or endured to something that is fun to learn. An added bonus was that the children voluntarily started to use their screen time at home to do maths. Pre- and post-test data also indicated that the use of the technology contributed to improved mathematics results.

## How technology is used in the classroom

Many would consider that the use of mobile devices in maths would consist of simple game playing. A search of the App Store reveals tens of thousands of supposedly educational maths games, creating a potential app trap for teachers who might spend hours searching through many low- quality apps. Although playing games can have benefits in terms of building fluency, they don’t usually help children learn new concepts. Luckily, there’s much that teachers can and are doing with technology.

The following are some of the different ways teachers are using technology:

Show and tell apps, such as Explain Everything, EduCreations or ShowMe, allow students to show and explain the solution to a mathematical problem using voice and images

– Flipped learning, where teachers use the technology to replace traditional classroom instruction. YouTube videos or apps that provide an explanation of mathematical concepts are accessed by students anywhere and anytime

– Subscription based resource packages such as Matific which provide interactive, game-based learning activities, allow the teacher to set activities for individual students and keep track of student achievement

– Generic apps (camera, Google Earth, Google Maps, Geocaching) that allow students to explore mathematics outside the classroom.

Just as the world has changed, the mathematics classroom has also changed. Although technology is an integral part of our lives, it shouldn’t be the only resource used to teach maths. When it comes to technology in the classroom, it’s all about balance.

Catherine Attard, Associate Professor, Mathematics Education, Western Sydney University