Tag Archives: middle years

Critical Thinking, Mathematics, and McDonald’s

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/

Beyond Monday’s Maths Class: Making the Most of Teacher PD

Last weekend I travelled interstate to attend a professional development day for teachers of mathematics. It was a good day, with lots of ideas shared and great enthusiasm from the 500+ audience. The presenter was well informed and, in fact, created quite a lot of hype due to her international reputation. Everyone went home happy and the word on Twitter was that Monday’s maths lessons were going to be different. Fantastic! But what about Tuesday’s lesson, and what about next week’s, next month’s, and next year’s lessons? What about the lessons of other teachers in the school?

How do you make the most of professional development?

Too often teachers attend PD sessions, get enthusiastic, try a few new things, but quickly get bogged down in the day-to-day challenges of life in a busy school and the demands of administration and curriculum authorities. How can you translate the underlying philosophy being promoted in the professional development sessions into sustainable change that can be shared amongst colleagues to improve and transform mathematics teaching and learning?

PD is expensive, and it’s important that opportunities aren’t wasted. I’ve been talking and writing a lot recently about promoting critical thinking in the mathematics classroom. It’s equally as important for teachers to engage critically with professional development. The following list contains a few thoughts that might help teachers get the most out of PD opportunities.

  1. Choose the right PD

Do a little research on the person presenting the PD. What are their credentials? Are they a self-proclaimed expert or do they have an established reputation? A simple Google search should reveal some insights, and, if the presenter is an academic, you could search Google Scholar for some of their academic publications. Spending time researching the presenter’s background can save you from attending a PD session that may not be right for you, and can provide some good research background should you choose to go ahead with the session. You also need to consider what you want out of a PD session. If you want a ‘bag of tricks’ in the form of a handful of ready to go activities, then you probably shouldn’t be wasting your school’s money. Rather, think about PD that is going to cause you to think deeply about your practice, and have a long-term effect on students’ educational outcomes.

  1. Does the presenter understand the Australian school context and curriculum?

When you attend PD, you expect that the presenter is aware of the Australian school context, and more importantly, the Australian Curriculum. This assists you, the teacher, in applying the learning to your practice, and also makes the content of the PD more relevant to you and your students.

  1. Understand the structure of the PD session

Before you commit to attending a PD session, ensure you understand what is going to happen in that session. Nobody likes sitting down and being lectured to for hours on end, nor do you want to listen to a presenter talk about themselves for an entire day! Look for presentations that are interactive and allow participants to apply theory to practical activities. If we are going to ask our students to do something differently, we need to experience it ourselves first. It’s also a better way of retaining information.

  1. Active Participation

When you’re at the PD session, don’t be afraid to ask questions. It’s also important to think critically about the information you are receiving. Presenters are usually very happy to answer questions that spark discussion – this often results in deeper learning, and better value for your school’s money! If the presenter doesn’t welcome questions, this is a sign that they may not have expert knowledge.  During the PD session it’s important that you participate in any activities – there’s usually a good reason a presenter has asked you to engage in a task. Active participation gives insight into the student experience and possible challenges, and it’s a great way to make links between theory and practice.

  1. Use the session as a networking opportunity

Often one of the most valuable aspects of professional development sessions is the opportunity to connect with teachers from other schools. It’s a great opportunity to discuss practice, students and school procedures. Networks developed at PD sessions can be maintained easily using tools such as LinkedIn, Twitter, and Facebook.

  1. Reflection

Before you leave your PD session, pause and consider what you have learned (a good presenter will actually give you opportunity to reflect). Think about how you might apply what you have learned (not just the activities, but the educational philosophy underpinning them) to your classroom, and don’t limit yourself to just replicating the activities. What are the underlying messages? How can you use those messages to adapt your practice? What will be different in the way that you plan and implement lessons? It doesn’t have to be a big change. Often subtle differences have huge effects.

  1. Sustainability: Sharing the Learning

Finally, it’s important to share the learning. It’s difficult to sustain any kind of change that will have ongoing benefit for students if it’s not supported by others in your school. This may not be easy, but small changes are better than no changes. Sometimes it’s a good idea to try out new things in your own class first, then use evidence of your success to convince others.

When it comes to PD, one of the most important things to remember is the reason we do what we do. We want our students to be the best they can, and when it comes to mathematics, we want to give them confidence, skill, passion and excitement that will ensure they continue to study and use mathematics beyond their school education.

Promoting Student Reflection to Improve Mathematics Learning

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.

 

 

 

 

Promoting Creative and Critical thinking in Mathematics and Numeracy

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?

 

 

 

 

Are you an engaged teacher?

“The first job of a teacher is to make the student fall in love with the subject. That doesn’t have to be done by waving your arms and prancing around the classroom; there’s all sorts of ways to go at it, but no matter what, you are a symbol of the subject in the students’ minds” (Teller, 2016).

Teller (2016), makes a powerful point about teaching and engagement, and how important it is that we, as teachers, portray positive attitudes towards our subject and towards teaching it. Do you consider yourself an engaged teacher? Are your students deeply engaged with mathematics, and how do you know? In education we talk about student engagement every day, but what do we actually mean when we use the term ‘engagement’? When does real engagement occur, and how do we, as teachers, influence that engagement? In this post, I will define the construct of engagement and pose some questions that will prompt you to reflect on how your teaching practices and the way you interpret the curriculum, influences your own engagement with the teaching of mathematics and, as a result, the engagement of your students.

Student Engagement: On Task vs. In Task

In education, engagement is a term used to describe students’ levels of involvement with teaching and learning. Engagement can be defined as a multidimensional construct, consisting of operative, cognitive, and affective domains. Operative engagement encompasses the idea of active participation and involvement in academic and social activities, and is considered crucial for the achievement of positive academic outcomes. Affective engagement includes students’ reactions to school, teachers, peers and academics, influencing willingness to become involved in school work. Cognitive engagement involves the idea of investment, recognition of the value of learning and a willingness to go beyond the minimum requirements

It’s easy to fall into the trap of thinking that students are engaged when they appear to be busy working and are on task.  True engagement is much deeper – it is ‘in task’ behaviour, where all three dimensions of engagement; cognitive, operative, and affective, come together (see figure 1).  This leads to students valuing and enjoying school mathematics and seeing connections between the mathematics they do at school and the mathematics they use in their lives outside school. Put simply, engagement occurs when students are thinking hard, working hard, and feeling good about learning mathematics.

Screen Shot 2017-05-23 at 1.35.49 pm

There are a range of influences on student engagement. Family, peers, and societal stereotypes have some degree of influence. Curriculum and school culture also play a role. Arguably, it is teachers who have a powerful influence on students’ engagement with mathematics (Anthony & Walshaw, 2009; Hattie, 2003). Classroom pedagogy, the actions involved in teaching, is one aspect of a broader perspective of the knowledge a teacher requires in order to be effective. The knowledge of what to teach, how to teach it and how students learn is referred to as pedagogical content knowledge (PCK). The construct of PCK was originally introduced by Schulman (1986), and substantial research building on this work has seen a strong focus on PCK in terms of mathematics teaching and learning (Delaney, Ball, Hill, Schilling, & Zopf, 2008; Hill, Ball, & Schilling, 2008; Neubrand, Seago, Agudelo-Valderrama, DeBlois, & Leikin, 2009). Although this research provides insight into the complex knowledge required to effectively teach mathematics, little attention is paid to how teachers themselves are engaged with teachers.

Engaged Teachers = Engaged Students

It makes sense that teachers need to be engaged with the act of teaching in order to effectively engage their students. If we take the definition of student engagement and translate it to a teaching perspective, perhaps it would look something like Figure 2, where teachers are fully invested in teaching mathematics, work collaboratively with colleagues to design meaningful and relevant tasks, go beyond the minimum requirements of delivering curriculum, and genuinely enjoy teaching mathematics in a way that makes a difference to students. In other words, thinking hard, working hard, and feeling good about teaching mathematics.

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Are you an engaged teacher?

Teaching is a complex practice with many challenges. Teaching mathematics has the additional challenge of breaking down many stereotypical beliefs about mathematics as being difficult and only for ‘smart’ people, mathematics viewed as black and white/right or wrong, and mathematics as a simply focused on arithmetic, to name a few. However, there are elements of our day to day work that we can actively engage with to disrupt those stereotypes, make teaching more enjoyable, and promote deeper student engagement. The following section provides some thoughts and questions for reflection.

Curriculum

How do you interpret the curriculum? Do you view it has a series of isolated topics to be taught/learned in a particular order, or do you see it has a collection of big ideas with conceptual relationships within and amongst the strands? How do you incorporate the General Capabilities and Cross-curriculum priorities in your teaching? Do you make the Working Mathematically components a central part of your teaching?

Planning

How do you plan for the teaching of mathematics? Does your school have a scope and sequence document that allows you to cater to emerging student needs? Does the scope and sequence document acknowledge the big ideas of mathematics or does it unintentionally steer teachers into treating topics/concepts in isolation?

Assessment

How often do you assess? Are you students suffering from assessment fatigue and anxiety? Do you offer a range of assessment tasks beyond the traditional pen and paper test? Do your questions/tasks provide opportunities for students to apply the Working Mathematically components?

Tasks

What gets you excited about teaching mathematics? Do you implement the types of tasks that you would get you engaged as a mathematician? Do your tasks have relevance and purpose?  Do you include variety and choice within your task design? Do you take into account the interests of your students when you plan tasks? Do you incorporate student reflection into your tasks?

Grouping

How do you group your students? There are many arguments that support mixed ability grouping, yet there are also times when ability grouping is required. Is the way you group your students giving them unintended messages about ability and limiting their potential?

Technology

How do you use digital technology to enhance teaching and learning in your classroom? Do you take advantage of emerging technologies and applications? Do you use digital technology in ways that require students to create rather than simply consume?

Professional Learning

How do you incorporate professional learning into your role as an educator? Do you actively pursue professional learning opportunities, and do you apply what you have learned to your practice? Do you share what you have learned with your colleagues, promoting a community of practice within your teaching context?

There are many other aspects of teaching mathematics that influence our engagement as teachers, and of course, the engagement of our students. Many factors, such as other non-academic school-related responsibilities, are bound to have some influence over our engagement with teaching. However, every now and then it is useful to stop and reflect on how our levels of engagement, our enthusiasm and passion for the teaching of mathematics, can make a difference to the engagement, and ultimately the academic outcomes, of our students.

References:

Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics (Vol. 19). Belley, France.

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.

Delaney, S., Ball, D. L., Hill, H. C., Schilling, S. G., & Zopf, D. (2008). “Mathematical knowledge for teaching”: Adapting U.S. measures for use in Ireland. Journal for Mathematics Teacher Education, 11(3), 171-197.

Hattie, J. (2003). Teachers make a difference: What is the research evidence? Paper presented at the Building Teacher Quality: The ACER Annual Conference, Melbourne, Australia.

Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualising and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.

Neubrand, M., Seago, N., Agudelo-Valderrama, C., DeBlois, L., & Leikin, R. (2009). The balance of teacher knowledge: Mathematics and pedagogy. In T. Wood (Ed.), The professional education and development of teachers of mathematics: The 15th ICMI study (pp. 211-225). New York: Springer.

Teller, R.  (2016) Teaching: Just like performing magic. Retrieved from http://www.theatlantic.com/education/archive/2016/01/what-classrooms-can-learn-from-magic/425100/?utm_source=SFTwitter

 

Setting up Your Students for Mathematical Success : Tips for Teachers

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 in 2017 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.

Christmas and Mathematics: Maximising student engagement until the last day of the year!

As the end of the school year approaches, report writing is in full swing and Christmas is on the horizon. It’s easy to lose focus, get distracted, and keep students occupied with ‘busy work’. However, it’s critical that we don’t waste a minute of students’ learning time, particularly when we know that over the long Christmas break some students may regress in relation to mathematical fluency and understanding.

So how can you keep mathematics engaging until the last day of school? Consider the elements required for sustained engagement to occur. Three factors are critical: cognitive, operative, and affective engagement. In terms of mathematics, true, sustained engagement occurs when students are procedurally engaged and interacting with the mathematics and with each other; when there is an element of cognitive challenge within the task; and when they understand that learning mathematics is worthwhile, valuable, and useful both within and beyond the classroom. It is easy to mistakenly think that students are engaged when they appear to be busy working, or ‘on task’. True engagement is much deeper than ‘on task’ behavior, rather, it can be viewed as ‘in task’ behavior, where all three elements; cognitive, operative and affective, come together. This leads to students valuing and enjoying school mathematics and seeing connections between the maths they do at school and the maths they use in their lives outside school (for more information see my FRAMEWORK FOR ENGAGEMENT WITH MATHEMATICS).

As this time of year it is easy to design mathematics tasks that promote high engagement and have the potential to stimulate learning. The following is a set of problem solving activities based on the famous Christmas Carol, The Twelve Days of Christmas. The activities are suitable for children in the middle years (grades 5 to 8), however can be easily adapted to suit younger or older learners.

Resources Required:

A copy of the lyrics of “The Twelve Days of Christmas”

The book “The Twelve Days of Christmas” (There are several versions available)

Price Lists

Other resources as required, eg. shopping catalogues

Possible Investigations starters/Task cards

Teaching/Learning Activities:

  • Read the book/lyrics or listen to the song “The Twelve Days of Christmas”
  • Discuss how the gift giver has to increase the number of gifts to his true love each day.
  • Provide students with a price list (this can be adapted according to the ability of the group)
  • At this point students can be asked to investigate the cost of the gifts, turning the activity into an open-ended investigation, or, specific questions can be posed to the students.

Examples of possible problems to explore are:

  1. What is the total number of gifts given?
  2. Is there an easy way to work this out?
  3. What is the total cost of the gifts?
  4. If the department store was holding a pre-Christmas sale and offered a 15% discount for all purchases, what would the new cost be? (This does not include performers, maids, lords etc)
  5. What if the discount offered only applied to live animals?
  6. The maids give a 10% when booked for more than two consecutive days. What would their new fee be?
  7. The musicians charge a 10% Goods and Service tax and this must be added to the total cost.
  8. How many people arrive at the true love’s house on the twelfth day?
  9. What would it cost to feed all the people and the animals? (Internet would come in handy here!)
  10. Use some Christmas shopping catalogues to replace the gifts with something more appropriate for a modern true love and calculate the cost.
  11. Re-write the lyrics to fit your new list of gifts.

The full list of activities and hypothetical price list are available on PDF here: The Twelve Days of Christmas

Other engaging end-of-year mathematics tasks are:

All of the above activities have the potential to promote high levels of engagement at a time of year when it is difficult for students and teachers to remain focussed. However, it is important to remember that any activity is only as good as the teacher implementing it. To enhance students’ engagement and learning, ensure there is regular student reflection, and rich discussion about the mathematics embedded with the tasks.