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Technology in the classroom can improve primary mathematics

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There’s much more to mathematics than computation, and that’s where more contemporary technologies can improve primary mathematics.
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Catherine Attard, Western Sydney University

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.

The ConversationJust 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

This article was originally published on The Conversation. Read the original article.

For a list of maths apps, click here:

iPad apps and Mathematics 2015

Education, mathematics, parents, teachers

Setting Your Child up for Success with Maths: Tips for Parents

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As a new school year approaches, many parents are 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 children succeed academically.

Late in 2016 there were reports from international testing that Australia continues to slip further behind in mathematics when compared to other countries.  So, what can you do about this? Relying on teachers alone won’t fix the problem. There are many things parents can and should do to help their children learn mathematics, particularly before they begin school and during the primary school years. The following is a list of tips for parents that will help them to help their children succeed:

  1. Be positive about maths!

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 (there are lots of apps that help with this) 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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Assessment, Education, mathematics, parents, Problem Solving, Professional development, teachers

Australia’s Declining Maths Results: Who’s Responsible?

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Once again, mathematics education is in the spotlight. The most recent TIMMS  and PISA results highlight a decline in Australia’s mathematics achievement when compared to other countries, which will no doubt perpetuate the typical knee jerk reactions of panic and blame. So, what are we doing about this decline? Who’s responsible? Typically, the first to get the blame for anything related to a decline in mathematics are teachers, because they work at the coal face, they spend significant amounts of time with students, and they’re an easy target. But shouldn’t we, as a society that considers it acceptable to proudly claim “I’m not good at maths” (Attard, 2013), take some portion of the blame?

Numeracy and Mathematics education is everyone’s business

As a society, we all need to take some responsibility for the decline in mathematics achievement and more importantly, we all need to collaborate on a plan to change the decline into an incline. From my perspective, there are three groups of stakeholders who need to work together: the general community, the policy makers and school systems that influence and implement the policies, and the teachers.

Let’s start with the general community. It seems everybody’s an expert when it comes to mathematics education because we all experienced schooling in some form. Many say: “I survived rote learning – it didn’t hurt me”. The world has changed, access to information and technology has improved dramatically, and the traditional ‘chalk and talk’ practices are no longer appropriate in today’s classrooms. Many hold a limited view of school mathematics as drill and practice of number facts and computation. Although it’s important that children build fluency, it’s simply not enough. We must promote problem solving and critical thinking within relevant contexts – making the purpose of learning mathematics visible to students. It is, after all, problem solving that forms the core of NAPLAN, TIMSS and PISA tests.

The community pressure for teachers to use text books and teach using outdated methods, along with a crowded curriculum and an implied requirement for teachers to ‘tick curriculum boxes’ causes significant tensions for teachers, particularly in the primary school where they are required to be experts at every subject. If we consider the limited number of hours allocated to mathematics education in teacher education degrees compared with the expectations that all primary teachers suddenly become experts on graduation, then we should understand that teachers need continued support beyond their tertiary education to develop their skills. In addition, rather than focusing on students’ learning, the crowded curriculum  leads them to focus on getting through the curriculum (http://v7-5.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=2#page=1) and this often leads to a ‘back to basics’ approach of text books, work sheets and lots of testing that does not create students who can problem solve, problem pose and problem find.

This is where the policy makers and school systems must come into play by providing support for high quality and sustained professional learning and encouraging primary teachers to gain expertise as specialist mathematics teachers. We already have a strong curriculum that promotes problem solving and critical thinking both through the Proficiencies and through the General Capabilities. The General Capabilities provide teachers with the opportunity to embed mathematics in contextual, relevant and purposeful mathematics. However, teachers need to be supported by all stakeholders, the community and the policy makers, to use these tools and focus less on the teaching of mathematics as a series of isolated topics that make little sense to students.

What can we do?

There are no easy solutions, but one thing is clear. We need to disrupt the stereotypical perceptions of what school mathematics is and how it should be taught. We need to support our teachers and work with them rather than against them. Let’s band together and make some changes that will ultimately benefit the most important stakeholders of all, the children of Australia.

 

 

Attard, C. (2013). “If I had to pick any subject, it wouldn’t be maths”: Foundations for engagement with mathematics during the middle years. Mathematics Education Research Journal, 25(4), 569-587.

 

Education, mathematics, parents, Problem Solving, teachers

Christmas Maths: Open ended investigations for Grades 4-6

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In this final Christmas themed post, I am including a range of open-ended investigations that are suitable for upper primary and lower secondary students (from the book Engaging Maths: Everyday Investigations Years 3 to 6). You will notice that some of the investigations extend beyond the mathematics curriculum and integrate quite easily into other key learning areas. This is intentional. If we want to engage students in mathematics, then making it contextual often requires it to either be embedded within another subject area or at least have some connections to other areas. Another consideration is the General Capabilities of the Australian Curriculum: Mathematics. When we incorporate contextual mathematics and investigation-based tasks, we are more likely to include the General Capabilities and this is evidenced in the activities below.

Short activities:

  1. If you have a Christmas tree in your house or school, how tall is it? Can you reach the top of the tree by reaching up? How much taller than you is the Christmas tree? What fraction of the height of the tree is your height?
  2. Draw a picture of a Christmas tree. Use your drawing as a plan to show where you will place the decorations.
  3. Tie a piece of tinsel to the very top of the Christmas Tree. Wind the tinsel around the tree until you reach the lowest branch. What is the length of the tinsel?
  4. If the individual lights of a string of Christmas lights are 30 cm apart, how many lights would you need so decorate the perimeter of the classroom?
  5. How would you work out how much wrapping paper needed to wrap 10 presents that were each the size of a shoe box? Record all of your working out. What mathematics did you use?

Investigations:

  1. Plan a Christmas party for some of your friends. Show all the mathematics that you need to use for your planning.
  2. Many families start to budget for Christmas presents several months before Christmas day. Design a budget for the Christmas presents that you would like to give to your family members, relatives and friends. Perhaps you might like to include your teachers.
  3. Survey the other students in your class using the question, “Do you have a Christmas tree in your home?” “Is it a real tree or an artificial tree?” “Which type of tree do you prefer and why?” Present the data that you have collected and present a report to your class.

Extension Activities:

  1. Investigate and research the tradition of decorating a tree for Christmas. Answer questions such as “When did the tradition start?”
  2. Plan menus for the meals for family for Christmas Day and Boxing Day and include a budget.
  3. Make a list of the things you would like for Christmas. Sort your items into needs and wants. How would your list compare to the list of a child in a different country? Investigate.

I hope you have enjoyed this series of posts that have included many rich activities to keep students engaged with mathematics until the very last day of the school year. If you do implement any of the tasks, I would love to hear from you and see your students’ work samples!

Education, mathematics, parents, Problem Solving, teachers

More Christmas Maths: Open-ended tasks and Investigations for the Early Years Classroom

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The use of open-ended tasks and mathematical investigations provides opportunities for students to demonstrate their abilities in a creative, non-threatening and meaningful way while promoting high levels of engagement and providing rich assessment data. Although the end of the year is near, the use of Christmas as a context for meaningful mathematics is an opportunity that is too good to miss. Providing students with a context that is exciting and relevant will ensure they maintain their engagement with mathematics until the end of the school year.

This week I am sharing a set of tasks that are taken from a book written by John Pattison and myself: Engaging Maths: Everyday Investigations for Early Years (2014). The tasks are separated into short activities, investigations, and extension activities. The short activities are intended as a warm up for the more complex investigations.

Short activities:

  1. This year how many days holiday will you have before Christmas Day? How many days will there be between the beginning of the school holidays and the last day of the year?
  2. Do you have a Christmas tree? How tall is the tree? Can you touch the top of the tree if you stand on tip toe? Is the tree taller than your dad or mum? How many lights are there on the tree?
  3. Does your family put presents under the Christmas tree? How many presents did each member of your family receive? How many of the presents were yours?
  4. How much tinsel would you need to decorate the Christmas tree?
  5. Your grandmothers, grandfathers, uncles, aunts and cousins are coming to your house for Christmas. If each person has a Santa bag full of presents under the Christmas tree, how many bags would there be?
  6. If each person is given a knife, fork and spoon with which to eat their Christmas dinner, how many pieces of cutlery would you need altogether?

Investigations:

  1. Make a list of the ten presents you would like Santa Claus to bring you for Christmas. Put the presents in order starting with one (1) for your first choice. Write a letter to Santa giving reasons for your choice of presents.
  2. Use store catalogues to help you to find the cost of your list of presents. Santa has said that he can only supply one hundred dollars worth of presents. Which presents will he choose to give you?
  3. Make a list of all the food items that Mum and Dad have to buy for the Christmas dinner. How many shopping bags will they need to take to the shops to carry all the food?

Extension Activities:

  1. Christmas Day always takes place on the 25th of December. Christmas Eve is the day before Christmas Day and Boxing Day is the day after Christmas Day. In 2013 Christmas Day was a Wednesday. What day was Christmas Eve and what day was Boxing Day in 2013? On which days of the week will Christmas Eve, Christmas Day and Boxing Day take place in the next five years? What did you discover?
  2. Christmas celebrations are very different in other countries. Use the Internet and the books in your library to investigate how people in other countries celebrate Christmas. Share the information you discovered with your classmates and teacher.
  3. There are many books with stories about Christmas in Australia. Find some of these books in the school library or on the Internet. Read your favourite story to the rest of your class.
Education, mathematics, parents, Professional development, teachers

Engaging students with mathematics: Back to school tips

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In Australia teachers are preparing to return to a new school year, and many would already be planning those first ‘getting to know you activities’ for the first few days of class. I remember when students used to spend the first few days of the school year colouring in title pages in all of their new workbooks. Rather than using this precious time on activities that have no real educational purpose, consider ways that you can begin to understand the needs of your learners – particularly in mathematics and numeracy.

It’s critical to take the time to understand your learners’ needs and establish what I call a ‘positive pedagogical relationship’ with students, where your familiarity with individual and group learning needs will form the foundations for engagement with mathematics (FRAMEWORK FOR ENGAGEMENT WITH MATHEMATICS). So how do you move away from the title page scenario and engage students early in the school year? Instead of colouring in, ask students to reflect on how they see themselves as users of mathematics. The following four prompts might be useful:

Draw or write a response to each of the following questions:

  • What does mathematics mean to you?
  • What do people you know think about mathematics?
  • What is something in mathematics that you find easy?
  • What is something you find challenging?
  • What it something in mathematics you would like help with this year?
  • How do you learn mathematics best?

Gaining insight into students’ identities as mathematics learners is critical in helping you plan your mathematics lessons at the start of the year. For example, if you find that the majority of your class have a fear of mathematics or are anxious, find out why, and work out a way to address this. Sometimes this will require working with parents to ensure a positive attitude is demonstrated in the home (see my article in The Conversation). If you are lucky and have a group of enthusiastic and confident young mathematicians, you have the perfect opportunity to get straight into exciting problem solving and mathematical investigations – great ways to determine where students are situated within the mathematics curriculum and where they need to move to next.

Have some rich mathematical conversations from day one! A great mathematical ice-breaker and discussion promoting activity that I have used extensively is a little like a mathematical treasure hunt – Getting To Know You Mathematically. You can adjust the criteria according to the age and stage of the students in your class. It runs like this (using my example). Give each child an attribute block (this could be a domino, a playing card or anything else you can think of, but you will need to adapt the proforma). Instruct the students to find a different person to match each criteria on the page. Encourage the students to move around the room and talk to different people. When the task is complete, have a discussion about the mathematics underpinning each of the criteria, for example, if you use attribute blocks and the criteria is “find someone with the same shape but in a different size”, you could have a discussion about how we know the shape is the same, and what are the mathematical properties of that shape.

Finally, think about how you are going to plan and teach this year. Perhaps you have the opportunity to do something different. For example, if you previously used textbooks to teach, you might use more open-ended, problem-solving based tasks and more concrete materials or games. Think about planning collaboratively rather than working in isolation (if that’s what you would usually do). You might decide to place more emphasis on student reflection, allowing time during each lesson for students to contemplate and discuss what they have learned and what they need to learn. You might consider changing the way you teach mathematics and take on a ‘big idea’ approach.

Whatever you decide to do, changing your practice is a great way to continue your professional learning. Have a great start to the school year and don’t forget to let your students know that maths is fun, and it’s something that everyone can do!

Education, mathematics, parents, teachers

Christmas Maths Part 3: More open-ended tasks for Grades 3 – 6

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In this final Christmas themed post, I am including a range of open-ended investigations that are suitable for upper primary and lower secondary students (from the book Engaging Maths: Everyday Investigations Years 3 to 6). You will notice that some of the investigations extend beyond the mathematics curriculum and integrate quite easily into other key learning areas. This is intentional. If we want to engage students in mathematics, then making it contextual often requires it to either be embedded within another subject area or at least have some connections to other areas. Another consideration is the General Capabilities of the Australian Curriculum: Mathematics. When we incorporate contextual mathematics and investigation-based tasks, we are more likely to include the General Capabilities and this is evidenced in the activities below.

Short activities:

  1. If you have a Christmas tree in your house or school, how tall is it? Can you reach the top of the tree by reaching up? How much taller than you is the Christmas tree? What fraction of the height of the tree is your height?
  2. Draw a picture of a Christmas tree. Use your drawing as a plan to show where you will place the decorations.
  3. Tie a piece of tinsel to the very top of the Christmas Tree. Wind the tinsel around the tree until you reach the lowest branch. What is the length of the tinsel?
  4. If the individual lights of a string of Christmas lights are 30 cm apart, how many lights would you need so decorate the perimeter of the classroom?
  5. How would you work out how much wrapping paper needed to wrap 10 presents that were each the size of a shoe box? Record all of your working out. What mathematics did you use?

Investigations:

  1. Plan a Christmas party for some of your friends. Show all the mathematics that you need to use for your planning.
  2. Many families start to budget for Christmas presents several months before Christmas day. Design a budget for the Christmas presents that you would like to give to your family members, relatives and friends. Perhaps you might like to include your teachers.
  3. Survey the other students in your class using the question, “Do you have a Christmas tree in your home?” “Is it a real tree or an artificial tree?” “Which type of tree do you prefer and why?” Present the data that you have collected and present a report to your class.

Extension Activities:

  1. Investigate and research the tradition of decorating a tree for Christmas. Answer questions such as “When did the tradition start?”
  2. Plan menus for the meals for family for Christmas Day and Boxing Day and include a budget.
  3. Make a list of the things you would like for Christmas. Sort your items into needs and wants. How would your list compare to the list of a child in a different country? Investigate.

I hope you have enjoyed this series of posts that have included many rich activities to keep students engaged with mathematics until the very last day of the school year. If you do implement any of the tasks, I would love to hear from you and see your students’ work samples!