Category Archives: Mathematics lessons

Assessment, Education, Home Schooling, mathematics, Mathematics lessons, parents, Problem Solving, Professional development, teachers

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

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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

Screen Shot 2018-01-25 at 5.20.40 pm

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?IMG_4837

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?

Education, Home Schooling, Learning, mathematics, Mathematics lessons, Professional development, teachers, teaching

Tips for Teachers: Setting up Your Students for Mathematical Success

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Many children begin the new school year with feelings of fear and anxiety. Will they like their new teacher or teachers? Will the work be difficult? What will the homework be like? As you prepare programming and planning for a new teaching year and new students, give some thought to the strategies and activities you and your students can do in the first few weeks of term to ensure everyone gets the most out of their mathematics lessons for the entire school year. Think about what you can do differently this year to make your work more engaging for both you and your students. The following are some ideas to consider.

  1. Be a positive mathematical role model

I’m sure this won’t come as a surprise, but there are teachers in our schools who actually don’t like maths and don’t like teaching it. Why is this a problem? Student know! This knowledge perpetuates the common misconception that it’s okay to dislike mathematics, and worse still, it’s okay to be considered ‘bad’ at maths.  Unless the teacher is an award-winning actor or actress, it’s really difficult to hide how you feel about a subject – it’s obvious in body language, tone of voice and of course, the way you teach the subject and the resources you use. If you know someone like this, suggest they seek some support from a colleague or colleagues. Often the reason a person dislikes mathematics is related to a lack of confidence.

  1. Get to know your students as learners of mathematics

The foundation of student engagement requires an understanding of students as learners, in other words, the development of positive pedagogical relationships (Attard, 2014). Positive relationships require teachers to understand how their students learn, and where and when they need assistance. It’s also important to provide opportunities for ongoing interactions between you and your students as well as amongst your students.

Another way to get to know your students as learners is to use existing data. For example, if your school takes part in external testing such as PAT, you can use this data as a guide. However, keep in mind that things change quickly when children are young – what they knew or understood three months ago may be very different after a long summer holiday.

A great activity to do in the very first few maths classes of the year is to ask your students to write or create a ‘Maths Autobiography’. If required, provide the students with some sentence starters such as “I think maths is…” “The thing I like best about maths is…” “The thing or things that worry me about maths is…” They could do this in different formats:

  • In a maths journal
  • Making a video
  • Using drawings (great for young children – a drawing can provide lots of information)
  1. Start off on a positive note

Have some fun with your maths lessons. I would strongly recommend that you don’t start the year with a maths test! If you want to do some early assessment, consider using open-ended tasks or some rich mathematical investigations. Often these types of assessments will provide much deeper insights into the abilities of your students. You can even use some maths games (either concrete or digital) to assess the abilities of your students.

A great maths activity for the first lesson of the year is getting-to-know-you-mathematically, where students use a pattern block and then need to go on a hunt to find other students who have specific mathematical attributes. Encourage your students to find someone different for every attribute on the list, and change the list to suit the age and ability of your students. For example, in the younger years you could use illustrations and not words. In the older years, you could make the mathematics more abstract.

  1. Take a fresh look at the curriculum

Even if you’ve been teaching for many years, it’s always good to take a fresh new look at the curriculum at the start of each year. Consider how the Proficiencies or Working Mathematically processes can be the foundation of the content that you’re teaching. For example, how can you make problem solving a central part of your lessons?
Take a close look at the General Capabilities. They provide a perfect foundation for contextual, relevant tasks that allow you to teach mathematics and integrate with other content areas.

  1. Consider the resources you use: Get rid of the worksheets!

Think about using a range of resources in your mathematics teaching. Regardless of their age or ability, children benefit from using concrete manipulatives. Have materials available for students to use when and if they need them. This includes calculators in early primary classrooms, where students can explore patterns in numbers, place value and lots of other powerful concepts using calculators.

Children’s literature is also a great resource. A wonderful book to start off the year is Math Curse by Jon Scieska and Lane Smith. Read the book to your students either in one sitting or bit by bit. There are lots of lesson ideas within the pages. Ask your students to write their own maths curse. It’s a great way to illustrate that mathematics underpins everything we do! It’s also a great way to gain insight into how your students view mathematics and what they understand about mathematics.

  1. How will you use technology in the classroom?

If you don’t already integrate technology into your mathematics lessons, then it’s time to start. Not only is it a curriculum requirement, it is part of students’ everyday lives – we need to make efforts to link students’ lives to what happens in the classroom and one way to do that is by using technology. Whether it’s websites, apps, YouTube videos, screencasting, just make sure that you have a clear purpose for using the technology. What mathematics will your students be learning or practicing, and how will you assess their learning?

  1. Reach out to parents

As challenging as it may be, it’s vital that parents play an active role in your students’ mathematical education. They too may suffer from anxiety around mathematics so it’s helpful to invite them into the classroom or hold mathematics workshops where parents can experience contemporary teaching practices that their students are experiencing at school. Most importantly, you need to communicate to parents that they must try really hard to be positive about mathematics!

These are just a few tips to begin the year with…my next blog post will discuss lesson structure. In the meantime, enjoy the beginning of the school year and:

Be engaged in your teaching.

Engaged teachers = engaged students.

Attard, C. (2014). “I don’t like it, I don’t love it, but I do it and I don’t mind”: Introducing a framework for engagement with mathematics. Curriculum Perspectives, 34(3), 1-14.

Education, mathematics, Mathematics lessons, Problem Solving, teachers

Critical Thinking, Mathematics, and McDonald’s

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You might be wondering what McDonald’s has to do with mathematics and critical thinking. Recently I found a copy of the original McDonald’s price list dating back to the 1940s when McDonald’s was owned by the original founders, Dick and Mac McDonald. Since that time, the fast food franchise has become a global fast food brand recognised by most. It is because of this recognition that the 1940s menu makes a perfect stimulus for mathematical investigation and critical thinking. The links between mathematics and children’s lives are not always obvious for students, so opportunities such as this are important to ensure our students understand how mathematics can help to make important decisions that affect our finances, health and general well-being. Although you might consider rejecting this idea so as not to promote a fast food culture, consider this an opportunity for students to think critically about food choices.

The Maths and McDonald’s graphic below contains some suggestions for mathematical investigations and would best be suited to students in upper primary or lower secondary classrooms. However, they can be adapted quite easily for younger students.

Maths & McDonald_s (3)

Below, the prompts are listed in a table that details some of the potential mathematical content that students would be expected to apply, and the processes they would use in the application of the mathematics. Although not included in the table, the tasks also address several of the General Capabilities from the Australian Curriculum: Mathematics. In addition, the tasks lend themselves well to integration with other curriculum areas.

Investigation

Use Mathematics to:

 Mathematical Content

 

 

 Processes
(Working Mathematically components/Proficiencies)		 Notes

 

 
Investigate how prices have changed over time (comparing similar items) · Addition

· Subtraction

· Fractions (percentages)

 · Problem Solving

· Reasoning

· Communicating

· Fluency

· Understanding

 · Provide access to Internet where possible to allow students to compare current prices

· Students could access census information to explore changes in cost of living
Explore the popularity of McDonald’s food compared to other fast food options · Statistics · Reasoning

·Communicating

·Fluency

·Understanding

 · Students will need to spend time considering appropriate questions to ask

· Encourage students to analyse data and formulate conclusions resulting from the data
Analyse the nutritional value of a McDonald’s meal compared to a typical home cooked meal · Addition· Subtraction

· Multiplication· Division· Fractions

 ·    Problem Solving·    Reasoning·    Communicating·    Fluency·    Understanding · The beauty of this investigation is that it is personalised. If students are working in groups, they will need to negotiate what a ‘typical’ home cooked meal is.

· Grocery store apps would be handy for this investigation if students have access to mobile devices

· There are multiple ways this task could be completed
Consider the cost of a McDonald’s meal for your family, compared to your favourite home cooked meal · Addition

· Subtraction

· Multiplication

. Division

· Fractions

 ·    Reasoning·    Communicating·    Fluency·    Understanding · The beauty of this investigation is that it is personalised. If students are working in groups, they will need to negotiate what a ‘typical’ home cooked meal is.

·Grocery store apps would be handy for this investigation if students have access to mobile devices· There are multiple ways this task could be completed
Analyse the financial cost of eating takeaway compared to cooking the same food at home · Addition

· Subtraction

· Multiplication

·Division

.Fractions

 ·    Problem Solving

·    Reasoning

·    Communicating

·    Fluency

·    Understanding

 . The takeaway food considered in this task may not necessarily be McDonald’s.

. It is important to allow students to draw from personal experience to ensure they are engaged with the mathematics and the task.

Using the Investigations in the Classroom

Once you have given students time to look at and discuss the original McDonald’s menu, you can choose to allow students to choose one or more of the investigations to explore. Better still, once they have completed an investigation they may be able to come up with one of their own – this is a great way to promote mathematical curiosity and wonder. Allow students to choose how they present their work, and encourage them to document all of the mathematics they do. It is also critical to build reflection into the investigation, so make sure you have some reflection prompts prepared for either verbal or written reflection.

The Maths and McDonald’s investigation provide opportunities for students to learn and apply mathematics in context. This improves student engagement, allows them to see the relevance of mathematics, promotes critical thinking and provides important and authentic assessment data.

The McDonald’s menu: https://www.thesun.co.uk/fabulous/food/3564107/mcdonalds-original-menu-1940-first-ever/

Education, financial literacy, mathematics, Mathematics lessons, parents, Professional development, teachers

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

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File 20171020 1082 atxtty.jpg?ixlib=rb 1.1Shutterstock

Catherine Attard, Western Sydney University

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.

The ConversationTeaching 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

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

 

Education, mathematics, Mathematics lessons, parents, Professional development, teachers, technology

Technology in the classroom can improve primary mathematics

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File 20170905 28074 1wx7i8h
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

Assessment, Education, mathematics, Mathematics lessons, Professional development, teachers

Promoting Student Reflection to Improve Mathematics Learning

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Critical reflection is a skill that doesn’t come naturally for many students, yet it is one of the most important elements of the learning process. As teachers, not only should we practice what we preach by engaging in critical reflection of our practice, we also need to be modelling critical reflection skills to our students so they know what it looks like, sounds like, and feels like (in fact, a Y chart is a great reflection tool).

How often do you provide opportunities for your students to engage in deep reflection of their learning? Consider Carol Dweck’s research on growth mindset. If we want to convince our students that our brains have the capability of growing from making mistakes and learning from those mistakes, then critical reflection must be part of the learning process and must be included in every mathematics lesson.

What does reflection look like within a mathematics lesson, and when should it happen?Reflection can take many forms, and is often dependent on the age and abilities of your students. For example, young students may not be able to write fluently, so verbal reflection is more appropriate and can save time. Verbal reflections, regardless of the age of the student, can be captured on video and used as evidence of learning. Video reflections can also be used to demonstrate learning during parent/teacher conferences. Another reflection strategy for young students could be through the use of drawings. Older students could keep a mathematics journal, which is a great way of promoting non-threatening, teacher and student dialogue. Reflection can also occur amongst pairs or small groups of students.

How do you promote quality reflection? The use of reflection prompts is important. This has two benefits: first, they focus students’ thinking and encourage depth of reflection; and second, they provide information about student misconceptions that can be used to determine the content of the following lessons. Sometimes teachers fall into the trap of having a set of generic reflection prompts. For example, prompts such as “What did you learn today?”, “What was challenging?” and “What did you do well?” do have some value, however if they are over-used, students will tend to provide generic responses. Consider asking prompts that relate directly to the task or mathematical content.

An example of powerful reflection prompts is the REAL Framework, from Munns and Woodward (2006). Although not specifically written for mathematics, these reflection prompts can be adapted. One great benefit of the prompts is that they fit into the three dimensions of engagement: operative, affective, and cognitive. The following table represents reflection prompts from one of four dimensions identified by Munns and Woodward: conceptual, relational, multidimensional and unidimensional.

Picture1(Munns & Woodward, 2006)

Finally, student reflection can be used to promote and assess the proficiencies (Working Mathematically in NSW) from the Australian Curriculum: Mathematics as well as mathematical concepts. It can be an opportunity for students to communicate mathematically, use reasoning, and show evidence of understanding. It can also help students make generalisations and consider how the mathematics can be applied elsewhere.

How will you incorporate reflection into your mathematics lessons? Reflection can occur at any time throughout the lesson, and can occur more than once per lesson. For example, when students are involved in a task and you notice they are struggling or perhaps not providing appropriate responses, a short, sharp verbal reflection would provide opportunity to change direction and address misconceptions. Reflection at the conclusion of a lesson consolidates learning, and also assists students in recognising the learning that has occurred. They are more likely to remember their learning when they’ve had to articulate it either verbally or in writing.

And to conclude, some reflection prompts for teachers (adapted from the REAL Framework):

  • How have you encouraged your students to think differently about their learning of mathematics?
  • What changes to your pedagogy are you considering to enhance the way you teach mathematics?
  • Explain how your thinking about mathematics teaching and learning is different today from yesterday, and from what it could be tomorrow?

 

References

Munns, G., & Woodward, H. (2006). Student engagement and student self-assessment: the REAL framework. Assessment in Education, 13(2), 193-213.

 

 

 

 

Education, mathematics, Mathematics lessons, Problem Solving, Professional development, teachers

Promoting Creative and Critical thinking in Mathematics and Numeracy

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What is critical and creative thinking, and why is it so important in mathematics and numeracy education?

Numeracy is often defined as the ability to apply mathematics in the context of day to day life. However, the term ‘critical numeracy’ implies much more. One of the most basic reasons for learning mathematics is to be able to apply mathematical skills and knowledge to solve both simple and complex problems, and, more than just allowing us to navigate our lives through a mathematical lens, being numerate allows us to make our world a better place.

The mathematics curriculum in Australia provides teachers with the perfect opportunity to teach mathematics through critical and creative thinking. In fact, it’s mandated. Consider the core processes of the curriculum. The Australian Curriculum (ACARA, 2017), requires teachers to address four proficiencies: Problem Solving, Reasoning, Fluency, and Understanding. Problem solving and reasoning require critical and creative thinking (). This requirement is emphasised more heavily in New South wales, through the graphical representation of the mathematics syllabus content , which strategically places Working Mathematically (the proficiencies in NSW) and problem solving, at its core. Alongside the mathematics curriculum, we also have the General Capabilities, one of which is Critical and Creative Thinking – there’s no excuse!

Critical and creative thinking need to be embedded in every mathematics lesson. Why? When we embed critical and creative thinking, we transform learning from disjointed, memorisation of facts, to sense-making mathematics. Learning becomes more meaningful and purposeful for students.

How and when do we embed critical and creative thinking?

There are many tools and many methods of promoting thinking. Using a range of problem solving activities is a good place to start, but you might want to also use some shorter activities and some extended activities. Open-ended tasks are easy to implement, allow all learners the opportunity to achieve success, and allow for critical thinking and creativity. Tools such as Bloom’s Taxonomy and Thinkers Keys  are also very worthwhile tasks. For good mathematical problems go to the nrich website. For more extended mathematical investigations and a wonderful array of rich tasks, my favourite resource is Maths300  (this is subscription based, but well worth the money). All of the above activities can be used in class and/or for homework, as lesson starters or within the body of a lesson.

Screen Shot 2017-06-25 at 5.40.37 pm

Will critical and creative thinking take time away from teaching basic concepts?

No, we need to teach mathematics in a way that has meaning and relevance, rather than through isolated topics. Therefore, teaching through problem-solving rather than for problem-solving. A classroom that promotes and critical and creative thinking provides opportunities for:

  • higher-level thinking within authentic and meaningful contexts;
  • complex problem solving;
  • open-ended responses; and
  • substantive dialogue and interaction.

Who should be engaging in critical and creative thinking?

Is it just for students? No! There are lots of reasons that teachers should be engaged with critical and creative thinking. First, it’s important that we model this type of thinking for our students. Often students see mathematics as black or white, right or wrong. They need to learn to question, to be critical, and to be creative. They need to feel they have permission to engage in exploration and investigation. They need to move from consumers to producers of mathematics.

Secondly, teachers need to think critically and creatively about their practice as teachers of mathematics. We need to be reflective practitioners who constantly evaluate our work, questioning curriculum and practice, including assessment, student grouping, the use of technology, and our beliefs of how children best learn mathematics.

Critical and creative thinking is something we cannot ignore if we want our students to be prepared for a workforce and world that is constantly changing. Not only does it equip then for the future, it promotes higher levels of student engagement, and makes mathematics more relevant and meaningful.

How will you and your students engage in critical and creative thinking?