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Learning, mathematics, Mathematics lessons, teachers, teaching, technology

Flipped learning in primary and secondary mathematics: Some lessons

July 28, 2019 cattard2017 Leave a comment

Flipped classrooms and flipped learning approaches are fast becoming a popular practice in mathematics classrooms, providing opportunities for students to learn anywhere, at any time. A flipped pedagogical approach may go some way in addressing the continuing issue of student disengagement with mathematics, yet how do we know if it really works? And what are the advantages and disadvantages to flipped approaches? In this blog post I provide a brief explanation of flipped learning before sharing some of the lessons I’ve learned about the flipped approach from my research into the effective use of technology in mathematics classrooms.

First, let’s consider how flipped learning works. There are various approaches that range from the provision of direct instruction via the use of video recorded lectures, to those that allow teachers to individualise learning according to student needs. The fundamental reason flipped learning approaches evolved was to take advantage of new technologies that allow for the introduction of new knowledge via multi-media and shift passive learning (via direct instruction) to allow teachers and students to make better use of classroom time. Pre-lesson materials can take the form of prescribed readings, teacher-produced videos, screencasts that may incorporate resources created on software such as GeoGebra, videos sourced from Youtube, or resources created by others such as Khan Academy. Face to face lessons can then be freed up for more teacher/student and student/student interaction, collaboration, application of learning through problem solving and investigation, and opportunities to provide intervention where necessary (Bhagat, Chang, & Chang, 2016; Lo & Hew, 2017; Weinhandl, Lavicza, & Süss-Stepancik, 2018).

Lessons from research

Through my various technology-related research projects I have seen a variety of models of flipped approaches from primary through to senior secondary classrooms. The most important lesson I’ve learned is, just like any other teaching resource, a flipped learning approach is only as good as the person driving it: the teacher. It’s the teacher and his or her understanding of student needs, along with the ability to address those needs, that can determine the effectiveness of any flipped approach. For example, in research I conducted approximately five years ago, a Year 3 teacher tried a flipped approach. Unfortunately, not all of the students understood the content that was covered in the pre-lesson videos, and the flipped approach failed. This leads me to lesson two: A one-size-fits-all approach very rarely works in the classroom and is even more precarious in a flipped approach where young students don’t have access to the teacher to seek clarification.

In the five years since that research project, the emergence of new technologies and software has meant that flipped learning in the mathematics classroom has evolved and become much more sophisticated. Apps such as SeeSaw provide different flipped learning opportunities that allow multi-directional communication between home and school, as well as the sharing of work samples. Productivity packages such as OneNote and learning management systems such as Canvas or Echo allow for multimedia to be used rather than the simple use of video. Programs such as Matific and Prodigy allow teachers to allocate different levels of activity to different students and track student achievement.These applications have made it easier than ever to differentiate learning, view student progress, and collate assessment data, which leads me to lesson three: flipped learning is hard work for the teacher.

A successful flipped learning approach requires the teacher to be vigilant beyond the timetabled mathematics lesson. If students are accessing and responding to resources anywhere and anytime, this requires a substantial commitment on the part of the teacher. Similarly, if students are not accessing the set tasks in preparation for their lessons, the teacher must also be aware and adjust lessons accordingly. The issue of students failing to access material prior to lessons is a common one and was observed in my most recent research. It is important to carefully consider the students and their contexts beyond the mathematics classroom. The fourth lesson, therefore, is to beware of assumptions about access. Not all students will have access to devices or internet. Sometimes a flipped approach may result in exclusion, depending on socioeconomic circumstances or location. For example, in one of the schools involved in my research, there were connectivity issues due to the location.

The final lesson I’d like to share about flipped learning is perhaps the most important. It can help students, particularly those who are disengaged with mathematics. The teachers who use flipped learning effectively in my most recent research were able redefine mathematics learning spaces for their students. The flipped approach promoted self-confidence, built strong connections between teachers and students, and provided ‘just in time’ learning and support, and self-paced learning without the stigma usually associated with students who feel they just can’t do mathematics.

There is emerging evidence that a flipped learning approach in mathematics is achieving success in relation to increasing student engagement due to the increased autonomy that allows students more access to learning resources. However, the majority of research on flipped learning focuses on tertiary and secondary education, with little attention paid to the primary classroom. There is also a need to explore more deeply how and why flipped learning approaches improve student engagement, if we are to take advantage of the affordances of emerging technologies to enhance students’ learning experiences and ultimately improve outcomes and attrition in higher level mathematics. In my upcoming blog posts I will provide further detail about the different models of flipped learning I observed, and how they influenced student engagement and learning.

References

Bhagat, K. K., Chang, C.-N., & Chang, C.-Y. (2016). The Impact of the Flipped Classroom on Mathematics Concept Learning in High School. Journal of Educational Technology & Society, 19(3), 134–142.

Lo, C. K., & Hew, K. F. (2017). A critical review of flipped classroom challenges in K-12 education: possible solutions and recommendations for future research. Research and Practice in Technology Enhanced Learning, 12(1), 4. https://doi.org/10.1186/s41039-016-0044-2

Weinhandl, R., Lavicza, Z., & Süss-Stepancik, E. (2018). Technology-enhanced Flipped Mathematics Education in Secondary Schools: A Synopsis of Theory and Practice. K-12 STEM Education, 4(3), 377–389. https://doi.org/10.14456/k12stemed.2018.9

Education, financial literacy, Learning, mathematics, Mathematics lessons, parents, teachers, teaching

Don’t bank on Dollarmites to teach financial literacy: here are our alternatives

February 25, 2019 cattard2017 Leave a comment

File 20190222 195870 17bnfyg.jpg?ixlib=rb 1.1 — Research shows combining maths education and financial literacy concepts is a better way to teach children good financial habits and boost numeracy. http://www.shutterstock.com

Catherine Attard, Western Sydney University

The recent royal commission into banking has revealed rampant wrongdoing by the big banks. As a result, there is renewed public interest in school banking schemes. The Commonwealth Bank’s Dollarmites program has once again come into the spotlight.

Dollarmites was awarded a 2018 Choice Magazine Shonky award. The program has over 300,000 active participants, and although it’s not the only school banking program, it’s the largest by far.

According to the Commonwealth Bank, the motive behind the Dollarmites program is to teach good savings habits and develop financial literacy. But I could find little independent research evidence it actually does.

On the surface, the Commonwealth Bank’s intentions are good. But research has found 40% of people develop loyalty to their banks and continue banking with them into adulthood.

We need to consider other options. Here are some research-backed alternatives.

Alternatives to school banking

Financial literacy can be taught both at home and at school, in practical and meaningful ways. If we consider the core business of schools to be learning, then our classrooms are not an appropriate place for the distractions of corporate marketing. There is definitely no time to be wasted on the logistics of organising school banking.

In fact, schools have several options when it comes to teaching financial literacy. There are a number of free resources already aligned to the curriculum.

In my research, using ASIC’s MoneySmart resources, financial literacy was combined with maths. Students did activities that allowed them to deal with real money while applying maths skills.

For example, some students borrowed money from the school principal to set up small businesses. They then ran their business at a school market day, and used their profits to buy Christmas gifts for underprivileged children.

Simple activities such as setting up classroom economies or allowing children to help plan events (such as class excursions) are also excellent at engaging children in financial literacy in a fun, realistic and interactive way.

Findings from my study showed learning about money and maths improved engagement, understanding of mathematical concepts and knowledge of financial concepts such as budgeting, profit and loss, lending and interest.

There are also resources such as Banqer, a free subscription-based app that allows students to manage fictitious money to budget and cover expenses (such as “renting” a desk). In my professional opinion, apps such as this are high quality. They may have corporate sponsorships, but are offered brand-free, which is preferable.

Parents can teach financial literacy too

Parents are one of the biggest influences on the financial habits of children. Parents have a responsibility to model good financial behaviours.

Involving children in shopping, having discussions about family budgeting and encouraging children to save some of their pocket money using a bank account of their choice all contribute to the development of financial literacy. These are really simple, everyday things parents can do to help their children learn financial literacy.

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

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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

Engaging children with mathematics: Are you an engaged teacher?

July 29, 2018 cattard2017 Leave a comment

“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.

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.

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

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

Tips for Teachers: Setting up Your Students for Mathematical Success

January 22, 2018 cattard2017 5 Comments

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.

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.

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)

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.

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.

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.

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?

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.

Engaging Maths