Primary Mathematics: Engaged Teachers = Engaged Students June 29, 2016Posted by Editor21C in Primary Education, Teacher, Adult and Higher Education.
Tags: curriculum, mathematics education
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“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).
A few months ago I published a post about the issue of teacher engagement and mathematics. The following is an updated version of that post. The issue of student engagement with mathematics is a constant topic of discussion and concern within and beyond the classroom and the school, yet how much attention is given to the engagement of teachers? I am a firm believer that one of the foundational requirements for engaging our students with mathematics is a teacher who is enthusiastic, knowledgeable, confident, and passionate about mathematics teaching and learning – that is, a teacher who is engaged with mathematics. Research has proven that the biggest influence on student engagement with mathematics is the teacher, and the pedagogical relationships and practices that are developed and implemented in day to day teaching (Attard, 2013).
A regular challenge for me as a pre-service and in-service teacher educator is to re-engage teachers who have ‘switched off’ mathematics, or worse still, never had a passion for teaching mathematics to begin with. Now, more than ever, we need teachers who are highly competent in teaching primary mathematics and numeracy. The release of the Teacher Education Ministerial Advisory Group (TMAG) (2014) report, Action Now: Classroom Ready Teachers, included a recommendation that pre-service primary teachers graduate with a subject specialisation prioritising science, mathematics, or a language (Recommendation 18). In the government’s response (Australian Government: Department of Education and Training, 2015), they agree “greater emphasis must be given to core subjects of literacy and numeracy” and will be instructing AITSL to “require universities to make sure that every new primary teacher graduates with a subject specialisation” (p.8). While this is very welcome news, we need to keep in mind that we have a substantial existing teaching workforce, many of whom should consider becoming subject specialists. It is now time for providers of professional development, including tertiary institutions, to provide more opportunities for all teachers, regardless of experience, to improve their knowledge and skills in mathematics teaching and learning, and re-engage with the subject.
So what professional learning can practicing teachers access in order to become ‘specialists’, and what models of professional learning/development are the most effective? Literature on professional learning (PL) describes two common models: the traditional type of activities that involve workshops, seminars and conferences, and reform type activities that incorporate study groups, networking, mentoring and meetings that occur in-situ during the process of classroom instruction or planning time (Lee, 2007). Although it is suggested that the reform types of PL are more likely to make connections to classroom teaching and may be easier to sustain over time, Lee (2007) argues there is a place for traditional PL or a combination of both, which may work well for teachers at various stages in their careers. An integrated approach to PD is supported by the NSW Institute of Teachers (2012).
Many teachers I meet are considering further study but lack the confidence to attempt a Masters degree or PhD. I am currently teaching a new, cutting edge on-line course at Western Sydney University, the Graduate Certificate of Primary Mathematics Education, aimed at producing specialist primary mathematics educators – a graduate certificate is definitely less intimidating than a Masters, and can be used as credit towards a higher degree. The fully online course is available to pre-service and in-service teachers. Graduates of the course develop deep mathematics pedagogical content knowledge, a strong understanding of the importance of research-based enquiry to inform teaching and skills in mentoring and coaching other teachers of mathematics.
In addition to continuing formal studies, I would encourage teachers to join a professional association. In New South Wales, the Mathematical Association of NSW (MANSW) (http://www.mansw.nsw.edu.au) provides many opportunities for the more traditional types of professional learning, casual TeachMeets, as well as networking through the many conferences offered. An additional source of PL provided by professional associations are their journals, which usually offer high quality, research-based teaching ideas. The national association, Australian Association of Mathematics Teachers (AAMT) has a free, high quality resource, Top Drawer Teachers (http://topdrawer.aamt.edu.au), that all teachers have access to, regardless of whether you are a member of the organisation or not. Many more informal avenues for professional learning are also available through social media such as Facebook, Twitter, and LinkedIn, as well as blogs such as this (engagingmaths.co).
Given that teachers have so much influence on the engagement of students, it makes sense to assume that when teachers themselves are disengaged and lack confidence or the appropriate pedagogical content knowledge for teaching mathematics, the likelihood of students becoming and remaining engaged is significantly decreased, in turn effecting academic achievement. The opportunities that are now emerging for pre-service and in-service teachers to increase their skills and become specialist mathematics teachers is an important and timely development in teacher education and will hopefully result in improved student engagement and academic achievement.
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.
Australian Government: Department of Education and Training (2015). Teacher education ministerial advisory group. Action now: Classroom ready teachers. Australian Government Response.
Lee, H. (2007). Developing an effective professional development model to enhance teachers’ conceptual understanding and pedagogical strategies in mathematics. Journal of Educational Thought, 41(2), 125.
NSW Institute of Teachers. (2012). Continuing professional development policy – supporting the maintenance of accreditation at proficient teacher/professional competence. . Retrieved from file:///Users/Downloads/Continuing%20Professional%20Development%20Policy.pdf.
Teacher Education Ministerial Advisory Group (2014). Action now: Classroom ready Teachers.
Teller. (2016) Teaching: Just like performing magic. http://www.theatlantic.com/education/archive/2016/01/what-classrooms-can-learn-from-magic/425100/?utm_source=SFTwitter
Dr Catherine Attard is an Associate Professor in the School of Education and a senior researcher in the Centre for Educational Research at Western Sydney University, Australia. This article was first published in May 2016 by Catherine on her own blog site, Engaging Maths.
Tags: learning communities, learning theories, teacher beliefs, technology and education
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If we could equate teaching to learning, how would we account for the gaps in students’ achievements even though the students were taught by the same teacher and learnt in the same environment? If students could learn deeply by listening quietly to a teacher, would the traditional way of schooling be viable for our digital generation? Few people will deny the need to reconceptualise the notion of learning when digital media is shaping how learning is taking place in the classroom and beyond the confines of its walls. Learning sciences research is offering us lenses to understand the science of learning, knowledge construction, digital media, and principles of effective learning environments and the role of instruction.
What is Learning Sciences?
By learning sciences, we are not referring to how science is learnt. Rather, we are referring to an interdisciplinary field that investigates teaching and learning in various settings using theories and models from different fields such as cognitive science, educational psychology, instructional science, computer science and literacy studies. We are particularly interested in deep learning which is one of the scholarly inquiries in learning sciences. Like other learning scientists, we are interested in findings ways to understand and design innovative approaches to develop deep learning. By way of introducing learning sciences, we will present brief descriptions of some research areas in this field in the remaining parts of this blog.
What should Educators Know about Cognitive Architecture and Instructional Design?
A key research focus in the learning sciences is the design of learning environments that align with human cognitive architecture. Two key components of this architecture are working memory and long-term memory. Working memory can only process 2-4 elements of new information at one time (Cowan, 2001). Long term memory consists of schemas and has no known limitations.
Research on human cognition has generated a range of practical take-home messages for educators:
- In general, teachers should employ direct-guided instruction when introducing students to new learning materials. Guided instruction includes the heavy use of worked examples, particularly with well-structured problems, whereas unguided instruction requires students to adopt general problem-solving approaches such as trial and error and means-ends analyses which are heavily taxing on working memory.
- When students have developed a sufficient level of knowledge in a learning domain, teachers should not provide guided instruction. High knowledge learners have schemas in long term-memory to guide them when solving problems. However, when presented with external guidance by the teacher, these high knowledge learners are forced to mentally integrate the information provided by the teacher and cross-reference this with their own knowledge. This results in cognitive overload of working memory.
- Teachers should avoid situations which result in the redundancy effect. A common example is when a teacher uses a Powerpoint presentation and reads the text, word-for-word, from the slide. Such an approach causes cognitive overload because learners must attend to two streams of data which are conveying the same information.
- The spatial presentation of multiple sources of mutually-referring information can also lead to cognitive overload. For example, graphics and associated explanatory text are often placed separately from each other. Learners have to attend to both sources of information, because in isolation, neither source conveys the full information needed for the learner to problem solve. The cognitive resources required by learners to mentally integrate the separate sources of information are highly taxing on working memory. The solution is to physically integrate the two sources, thus reducing the search and match processes required by learners to understand the information presented.
Are Positive Learning Environments All about Developing ‘Feel Good’ Schools?
In our inquiry about the design of learning environments, we are also keen to examine the association between school environments and student’s wellbeing. Debates in this focus may conjure up outdated notions of teachers minimising scolding of students to preserve their self-esteem or schools saturated with posters reminding students that they are unique. There are educators who are incredulous of new curricula which invite both students and staff in schools to look at their emotional development. They most probably see it as far removed from the core business of schools and only contributing to ‘feel good schools’ which have little impact on important things in life.
Positive Learning Environments (PLE) are places of learning where the whole of person is engaged in an effort to contribute to the overall development of an individual and in turn his or her communities. The ‘positive’ is both an indication of the more traditional sense of pleasantness and safe, but also a mathematical concept of ‘addition’. It involves adding, contributing to an individual’s development. In PLE, knowledge of the factual traditional curricula of schools is intertwined with knowledge and development of the whole of self. This invariably includes an incorporation of affect in the everyday practice of schools. Affect, in this instance refers to not just the experience of feeling or emotion but also the physiological and cognitive (thinking) components of such experience. Although affect and knowledge acquisition have always been part of learning anything by anyone, it is fair to say that systematically talking about, intervening in and considering affect regulation, quality and development as part of schooling is a relatively new phenomena for schools to take on.
The detrimental impact of aversive affective states (e.g., anxiety) and school environments with components related to high affective dysregulation for students and staff (such as racism, bullying and violence) on learning and wellbeing are now well documented. However, the need for research and development of positive learning environments is not just about the removal of unpleasantness in schools. It is also about the gains which are made when affect regulation and development are also seen as the core business of schools alongside academic development. This research is exemplified by current efforts looking at social and emotional learning (SEL) in schools. SEL is defined as a process engaged in schools where all members of their communities apply themselves to the development and understanding of emotions with an understanding that “learning emerges in the context of supportive relationships that make learning challenging, engaging and meaningful” (CASEL, n.d.).
The economic and lifetime benefits of social emotional skills and schools’ unique position to develop them have also been acknowledged in a recent OECD report (see OECD, 2015). The report highlights and acknowledges the increases in access to education but recognises that social emotional skills are needed alongside academic/cognitive skills to foster lifetime success. It is through affect regulation (directly or as a mediator of other skills) that greater cooperation, task perseverance, and problem solving can be achieved by communities and individuals. Although current available evidence in relation to social emotional learning is growing and promising, there is still much to be discovered. What are the key skills our teachers need to engage in SEL? Are the effects of SEL universal? How do we best develop social emotional skills? For that matter, which skills do we develop? What are the best pedagogies that engage the whole of the child and how do we assist our school system to evolve from a system whose origins gave little credence to emotion to ones where knowledge and affect are treated as one.
Positive learning environments are more than just ‘feel good’ schools. They are active learning communities engaged in the education of the whole child for their and their communities benefit. They are complex communities with relationships, processes, and pedagogies directed at affect regulation and cognitive development practices. They are truly the 21st century schools.
Why Should We Study Teacher Beliefs?
In our inquiries into designing learning environments, we are not forgetting the importance of understanding teacher development and beliefs. Teachers develop a sophisticated amalgam of knowledge, beliefs, and skills to be effective in the classroom. In particular, teachers’ beliefs about teaching and learning can provide useful insights into their practice. Beliefs are “psychologically held understandings, premises, or propositions about the world that are felt to be true” (Richardson, 1996, p. 103). Teachers’ beliefs can be classified into views of the teacher’s role in the classroom, the students’ role in the classroom, how the students learn their subject area best, and how to make the subject matter comprehensible to others (Friedrichsen, van Driel, & Abell, 2011). These types of beliefs are often derived from prior K-12 school experiences. They are extremely robust and do not change easily (Jones & Carter, 2007).
Often, teachers are asked to implement new pedagogies in their classrooms that align with current reform efforts (e.g. inquiry-based approaches). Yet, teachers often experience considerable difficulty when implementing new pedagogies as they develop practical knowledge and perceptions of their school contexts. Practical knowledge and perceptions of context are then filtered through core beliefs about teaching and learning which can impact classroom practice. For example, consider a teacher who has just implemented an inquiry-based approach to instruction. After implementation, constraints may develop in the form of practical knowledge suggesting that students have considerable difficulty with the task. The teacher may also develop perceptions of his or her school being unsupportive of reform-based strategies. If the teacher also believes his or her role is to only transmit information to the students, this will likely cause him or her to abandon the strategies. Conversely, in the face of practical and contextual constraints, if the teacher believes it is his or her role to facilitate guided inquiry experiences so that students have some opportunity to wrestle with the concepts, he or she is likely to make modifications to his or her teaching and attempt the pedagogical strategies again (Sickel & Friedrichsen, 2015).
With the example above, we see that helping teachers elucidate and often confront their existing beliefs about teaching and learning is an important part of the teacher development process. A teacher with core beliefs that misalign with a teaching approach is a significant barrier to large-scale implementation. Understanding teacher learning provides important implications for designing teacher education and professional development programs which in turn help teachers enhance their students’ learning outcomes.
How has Digital Media Revolutionised the Way Students Learn?
Increasingly, learning sciences calls for an inquiry into students’ perspectives and the ways in which their literacies are accessed, used and lived in everyday practices, both inside and outside of school (Kim, Tan, & Bielaczyc, 2015). Existing learning sciences research shows an increasing interest in the emerging culture of learning in the virtual spaces. We sum up how students are self-directing themselves online using 5Cs of what they do in this emerging culture of participating online:
- Students are staying connected to their peers and interest-based groups to pursue passion-based learning.
- Often, these students are learning about a specific content or skill from mentors who may not necessarily be adults but have enough experience to share their knowledge with them.
- Students are displaying more ownership of their creative works or digital artefacts Using social media, they communicate their thoughts and “pass on” their works to solicit feedback and appreciation.
- They create networks to stay connected and communicate with people who share their interests and are keen on what they do.
- Learning becomes more distributive and social. Nonetheless, with the diverse backgrounds of people whom they interact with online, learning has evolved from simply group learning to collaborative learning where multiple perspectives of a focused issue are exchanged before a shared perspective is established.
- Conversations no doubt can include playful talks but have become more dialogic to facilitate deeper thinking in online interactions.
- Digital artefacts provide strong evidence of learning. When students interact with others online, learning has become more participatory. To learn from one another means there must be learning by doing.
- There are more bodies of research that show students are developing dispositions of experts as they learn by doing and intentionally cultivating thinking skills which classroom teachers are trying to develop in key content areas in the formal learning spaces.
- With learning becoming more distributive, collaborative and participatory, students are developing ways of managing their works and feedback online. Curation becomes part and parcel of what they do such as creating tags to organize their online artefacts.
- Students are looking for ways to exhibit and curate their current and past works using social media using Google Plus, Facebook or using apps to create their own websites.
In order to pursue our work in learning sciences, we have formed the LƩARN (Learning Sciences Affect Research Network) HDR cohort group. This is a group uniquely created for HDR students within the School of Education to embark on research related to the field of learning sciences. To build our student’s research capacity, we are conducting a series of workshops and forums in the second half of 2016. You are welcome to contact anyone of us for further information about this group and the research we do. We also welcome any comment and feedback from you regarding our research interests or activities in LEARN.
Researchers in LΣARN
|Dr Lee Chwee Beng
|Dr Aaron Sickel
|Dr Lynde Tan
|Dr Jose Hanham|
|Dr Roberto Parada
CASEL. (n.d.). Collaborative for academic, social and emotional learning. Retrieved from http://www.casel.org/social-and-emotional-learning/
Cowan, N. (2001). The magical number 4 in short-term memory: a reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87–114.
Friedrichsen, P., van Driel, J. H., & Abell, S. K. (2011). Taking a closer look at science teaching orientations. Science Education, 95(2), 358-376.
Kim, B., Tan, L. & Bielaczyc, K. (2015), Learner-generated designs in participatory culture: what they are and how they are shaping learning. Interactive Learning Environments, 23(5), 545 – 555.
OECD. (2015). Skills for Social Progress: The power of social and emotional skills. Retrieved from http://www.oecd-ilibrary.org/docserver/download/9615011e.pdf?expires=1461906844&id=id&accname=guest&checksum=B24ED59A273470F52724E55D6AA51152
Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula (Ed.), Handbook of Research on Teacher Education (pp. 102-119). New York, NY: Simon & Schuster Macmillan.
Sickel, A. J., & Friedrichsen, P. J. (2015). Beliefs, practical knowledge, and context: A longitudinal study of a beginning biology teacher’s 5E unit. School Science and Mathematics, 115(2), 75-87.