Mathematics and the transition from primary to secondary schooling

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

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

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

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

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

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

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

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

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

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

References:

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

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

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

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

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

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

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

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

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

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

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

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

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

Technology in the classroom can improve primary mathematics

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

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

Blaming the calculator for poor results

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

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

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

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

The importance of technology in learning maths

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

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

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

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

How technology is used in the classroom

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

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

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

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

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

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

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

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

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

For a list of maths apps, click here:

iPad apps and Mathematics 2015

Games for teaching and learning Mathematics

Engaging Maths

We all know children love playing games, but how can we turn this love of games into rich mathematical learning experiences? What are the qualities of a good maths game, and should we be incorporating games into regular lessons and homework rather than a Friday afternoon filler activity?

Why use games in the mathematics classroom? First and foremost, they’re fun! Of course, that alone isn’t a good enough reason to use them. However, when children talk about fun and school, they often perceive fun lessons to be those where they felt challenged and learnt something new. In my research on student engagement, many students talked about fun maths lessons they had experienced, and these are some of their quotes:

“Maths is kind of fun when you get to play some maths games” (Year 6 )

“…if you sit on the carpet and the teacher goes on and on about what…

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Problem solving and mathematics: Promoting cognitive dissonance

Engaging Maths

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…

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“I wonder…..”: Promoting curiosity in the mathematics classroom

Engaging Maths

I recently came across an article published in the neuroscience journal, Neuron that caught my attention. The article, by Gruber, Gelman and Ranganath (2014), describes a scientific investigation that explored how curiosity influences memory. The authors found a “link between the mechanisms supporting extrinsic reward motivation and intrinsic curiosity and highlight the importance of stimulating curiosity to create more effective learning experiences” (p. 486). In other words, students will learn more about topics they are interested in – something we’ve known along in the education world, but now we have scientific evidence!

Gruber et al. (2014) claim high curiosity results not only in the learning of interesting information but also incidental material. They also discuss how most of the events a person experiences in a day will be forgotten. If we translate this to children and their classroom experiences, can we expect that they won’t remember much of what happens…

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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.