Tag Archives: primary mathematics

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

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The community pressure for teachers to use text books and teach using outdated methods, along with a crowded curriculum and an implied requirement for teachers to ‘tick curriculum boxes’ causes significant tensions for teachers,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.

 

Christmas Maths: Open ended investigations for Grades 4-6

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!

Primary Mathematics: Making the Most of Technology to Assess Student Learning

As the school year rapidly draws to a close, many teachers are beginning the task of reporting student achievement. For some, there may be a scramble to collect assessment data, and often, due to a sense of panic, teachers revert to pen and paper testing to gain a snapshot of their students’ ability measured against syllabus outcomes…one of the main reasons students develop a dislike of mathematics in the first place. The purpose of this blog post is to ask you to consider using alternative assessment evidence, and in particular, consider taking advantage of some of the educational software tools you may already be using in your classroom.

Regardless of what technological devices you use, if you do use technology in your mathematics lessons, chances are you already have some good assessment data that you can use in your reporting. Take, for example, the use of apps on an iPad or other mobile device. If your students are engaging in different apps to either build on their mathematical fluency (typically game-type apps) or to express mathematical reasoning and communication (with apps such as Explain Everything, Educreations or ShowMe), then it’s rather easy to collect evidence of learning. Some apps offer the affordance of being able to save student progress, and others simply require students to take a screen shot of their results.

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Educreations allows you to save files that record audio and written mathematics, allowing assessment of content and process outcomes.

I recently conducted a research evaluation of the Matific suite of resources (access the research report here). One of Matific’s affordances is that it allows teachers to track student progress.

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The Matific website allows teachers to view assessment data in a number of ways

Interestingly, out of the 16 teachers involved in the study, only nine teachers used the ability to track student achievement and even fewer considered using it as assessment data. However, those who did use this affordance, considered it a valuable tool that allowed them to differentiate future tasks, tailoring the learning for individual student needs:

It was perfect in a sense that we made it a point that we started at the middle and we went down for those who needed extra support, which was fabulous because they were still doing it visually, they were doing the exact same thing, and then we also gave the option that they could go up if they felt confident enough but at the same time visually, it was exactly the same for those kids that don’t want to be different, that maybe do need that little bit of extra support (Year 6 teacher). 

Data from students’ interactions with educational apps such as Matific, game apps and productivity apps can provide valuable formative and summative assessment data that can remove the anxiety associated with formal pen and paper testing, particularly during the primary years when it’s critical that we foster high levels of student engagement. Consider the apps you currently use – how can you collect evidence and use it to your advantage and the students’ advantage…and also save you time? Isn’t it better to spend class time on learning rather than testing?

Problem solving and mathematics: Promoting cognitive dissonance

A couple of weeks ago I came across the term ‘cognitive dissonance’ in relation to teaching and learning mathematics and I have been thinking about it ever since. It reminded me of something a colleague of mine talks about with his primary class – the idea of getting a ‘sweaty brain’ when something is challenging or difficult during maths lessons. It’s that uncomfortable feeling you get, that feeling of disequilibrium, when you’re grappling to learn something new – something that is slightly out of reach.

Do you celebrate cognitive dissonance or ‘sweaty brains’ in your classroom? I think this is something that we have to promote – we need our students to value the struggle that takes place as part of the learning process and particularly when we engage in the problem solving process. Problem solving is a central part of the mathematics curriculum, and explicitly listed as one of the four Proficiencies of the Australian Curriculum: Mathematics and as a Working Mathematically component in New South Wales schools.

Another important aspect of the problem solving process and one that is closely related to the idea of cognitive dissonance is the development of perseverance in our students – when tasks are challenging it’s important not to give up – what some might refer to as having ‘grit’. So how do students develop perseverance when it comes to problem solving? There are things we can do as part of our pedagogical repertoires that promote perseverance and help celebrate having a ‘sweaty brain’. First, we need to understand the struggle that students are experiencing. By knowing your students well and developing a positive pedagogical relationship where you have a strong understanding of the learning needs of each individual student, you can set tasks and problems that are at an appropriate level of cognitive challenge for each child – not too difficult, but not too easy!

Set up opportunities for your class to work collaboratively on challenging problems – this gives students a chance to share their thinking and hear you model the thinking processes that occur when tasks are challenging. Use a growth mindset approach and focus on the language of ‘yet’. Often in mathematics classes we expect to begin and end a task within one mathematics lesson – giving students a very limited amount of time to work on what could be a complex problem. Why not allow students to walk away from the problem and think about it overnight before continuing to work on it the following day?

Use reflection as a natural part of the learning process, and model reflection for your students – very often we assume students can ‘do’ reflection, yet often they don’t really engage in metacognition because they haven’t practiced it or seen someone else engage in the process of reflection.

Finally, consider where problem solving fits into your classroom routines – is it part of your daily routine, and do you use problem solving as an opportunity to provide purpose for learning mathematical concepts and processes? Do you promote a classroom culture where mistakes are regarded as learning opportunities and cognitive dissonance is celebrated?

Programming & planning dilemmas in primary mathematics

Often when I work with teachers I am asked for advice regarding the design of a scope and sequence for mathematics. The programming and planning of mathematics seems to cause much concern, and often the reason is that there is no ‘magic fix’ or one-size-fits-all solution.

Traditionally, schools have planned their mathematics teaching using a topic-by-topic or strand-by-strand approach. Sometimes there is a formula for teaching the Number and Algebra strand for a certain number of days per week, with the other days dedicated to the remaining syllabus strands. Often, the strands are split into single, stand-alone topics. Unfortunately, there are issues with this approach. Teaching individual topics in mathematics hinders students in gaining a deep understanding of mathematics and the connections that exist between and amongst the strands. Teaching in this way can promote a traditional, rote learning approach where the opportunities for mathematical thinking are limited. Our curriculum places the proficiencies (Working Mathematically in New South Wales) at the forefront of teaching and learning mathematics – teaching topics in isolation does not promote the proficiencies.

So what’s the solution? Consider planning and programming using a ‘big idea’ approach. What’s a big idea? Big ideas are hard to define and different people have differing ideas on what the big ideas in mathematics actually are. However, all the definitions in literature have one thing in common – they all refer to big ideas as the key to making connections between mathematical content and mathematical actions, and they all link mathematical concepts. Take, for example, the big idea of equivalence. This relates to number and numeration, measurement, number theory and fractions, and algebraic expressions and equations. Connections can be made across the strands and these links should be made explicit to students.

Charles (2005) presents a total of 21 big ideas across the mathematics curriculum, however he states that these are not fixed – they can be adapted. He also states that a big ideas approach has implications for curriculum and assessment and professional development – teachers need to develop their pedagogical content knowledge to ensure they have a deep understanding of the connections within the curriculum if they are to teach mathematics successfully.

Of course, there are challenges to teaching using a big ideas approach. Teachers often feel under pressure to address all curriculum outcomes, and often this is the reason that the topic-by-topic approach is adopted. Using a big ideas approach can feel messy – it is not linear and in some ways feels as though it is conflicting with the organisation of our curriculum. However, we must remember that although our curriculum is separated into strands and sub-strands, this is simply an organisational tool and does not mean that mathematics should be taught in this same way.

My advice would be to take our curriculum, pull it apart and try seeing it differently – what areas of the curriculum have obvious links? How can you link aspects of measurement to the number strand? Where does measurement and geometry link? And how can you use the statistic and probability strand to teach number concepts? Making connections will make your teaching easier in the long run, and more importantly, will result in deeper learning and deeper engagement with mathematics.

 

Randall, C. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. NCSM Journal, 7(3), 9-24.