Teaching With Technology: Up, Up and Away With Parachutes in Primary Mathematics

In a teacher education institution just north of Sydney, a lecturer asked her students about their most vivid memories of learning about mathematics in their primary school years. By far, the most easily recalled positive experiences of mathematics involved some form of physical activity or the use of hands-on resources: One day the teacher organised for us to have a pizza party. The pizzas were divided into even pieces and we learned about fractions. I loved the way my teacher got us to use the things she found around her house in the classroom - . She\u27d bring them into our class and we\u27d use them in maths activities. We did cooking in our primary school class. I\u27m not sure if it was meant to be a maths lesson or not but we learned how to measure, how to cut up food into parts and how to estimate amounts. We did maths activities with parachutes. I really enjoyed that. We were all running around, laughing, counting and just doing maths

The Sound of _: The Role of Pedagogical Silence in Higher Education Learning

The value of interaction, discussion and dialogue in the online classroom is a common theme of literature about online education, especially because the discourse that typically takes place in on-campus classes does not naturally occur in online contexts. The noise associated with an interactive class is often viewed as an indicator that learning is taking place. So, can periods of silence also signpost learning or promote an environment conducive to learning? Some theorists believe silence is regarded negatively – this paper is proposed in antithesis to this dark side of silence. Activities such as quiet guided reflection, thoughtful exploration of how to apply learning to practice and silent reading are possible ways in which silence offers pedagogical benefit. This paper proposes that pedagogical silence can be employed to set up quiet moments before, during or after learning takes place; they may be teacher-initiated or student-led, structured or unstructured, formal or informal, planned or unplanned. This paper is not an attempt to define silence in a pedagogical sense, nor is it a defence of the pedagogical affordances of silence; it is a set of ideas put forth about how silence may be strategically embedded into teaching and learning spaces in higher education

Threshold Concepts and Attitudes in Mathematics Education: Listening to Students\u27 Past, Present and Projected Stories

The process of becoming a skilled and confident mathematics teacher can be strongly influenced by the teacher\u27s attitudes to both mathematics and mathematics teaching. Investigations into the attitudes of pre-service teachers have shown that teachers\u27 attitudes directly influence their teaching practices and, subsequently, their students\u27 learning experiences. Teachers\u27 understanding of mathematical content and concepts also impact on the quality of teaching. Hence, the identification of threshold concepts and attitudes associated with teaching mathematics can be beneficial to pre-service teachers and their students. By understanding the concepts associated with teaching mathematics to young children, pre-service teachers come to transcend their lack of confidence about mathematics and grow to realise the value of purposefully applying mathematics to everyday life. Their perceived lack of competence in their own mathematical abilities can be transformed into an appreciation of how mathematics can be taught in an enjoyable and meaningful manner. In the study reported in this paper, the researcher examined the threshold concepts and attitudes about mathematics and mathematics teaching held by two groups of pre-service teachers who were enrolled in a first year mathematics education course as part of an undergraduate teaching degree. The course in which they were enrolled aimed to enable the pre-service teachers to develop an understanding of the mathematical learning, understanding and attitudes normally experienced by young children aged from four to eight years of age. During the course, the preservice teachers were also expected to develop and demonstrate knowledge of the mathematical concepts relevant to teaching children of this age group

Acknowledging the Affirmative: Evidence of Supervision Learning Thresholds in Thesis Acknowledgements

Mantai and Dowling (2015) refer to the Acknowledgements pages of higher degree research (HDR) theses as “an under-utilised yet rich data source” (p. 106) and Hyland (2004) recognises the way in which thesis Acknowledgements have the potential to “reveal academic preferences” and “point to the processes of its [the thesis’] creation” (p. 305). Using a matrix analysis technique (Miles & Huberman, 2013; Patton, 2015), this study mines the Acknowledgements section of a sample of 120 Masters and Doctoral theses to investigate HDR graduates’ views of their postgraduate supervisors to augment our current understanding of the learning thresholds of HDR supervisors. Based on the conference sub-theme of “Troublesome not tricky: not all that challenges is a threshold”, this paper considers the more constructive nuances of threshold concept theory in relation to the learning thresholds of postgraduate supervisors. Instead of furthering the discussion that threshold concepts have become synonymous with learner difficulty, the question posed is: What do the affirmative and joyous experiences of postgraduate supervision have to offer threshold concept theory associated with the pedagogy of supervision? This study layers the viewpoints of HDR graduates’ positive experiences about supervision alongside some of the more negative experiences of supervisors that typically incorporate “darker themes”, “threats”, “ordeals” and “disorientation” (Carter, 2016, pp. 1139, 1145) as well as “barriers”, “power conflicts” and “tensions” (Ismail, Majid, & Ismail, 2013, pp. 165, 168). This study’s findings do not discount the challenging aspects of HDR supervision, as represented in earlier research. Instead, an intertwined representation is offered of the challenging “living through” experiences of the HDR supervisor with the rosier “looking back” views from HDR candidates at the completion stage of their studies. A collection of light and dark learning thresholds, acquired by HDR supervisors while developing a pedagogy of supervision, is offered for consideration. References Carter, S. (2016). Supervision learning as conceptual threshold crossing: When supervision gets ‘medieval’. Higher Education Research & Development, 35(6), 1139-1152. doi:https://doi.org/10.1080/07294360.2016.1160875 Carter, S., & Sterm, S. (2014). The hardest step is over the threshold: Supervision learning as threshold crossing. Paper presented at the 11th Biennial Quality in Postgraduate Research Conference, The National Wine Centre, Adelaide. http://www.qpr.edu.au/Proceedings/QPR_Proceedings_2014.pdf Hyland, K. (2004). Graduates’ gratitude: the generic structure of dissertation acknowledgements. English for Specific Purposes, 23(3), 303-324. doi:doi.org/10.1016/S0889-4906(03)00051-6 Ismail, H. M., Majid, F. A., & Ismail, I. S. (2013). “It\u27s complicated” relationship: Research students’ perspective on doctoral supervision. Procedia-Social and Behavioral Sciences, 90, 165-170. doi:https://doi.org/10.1016/j.sbspro.2013.07.078 Mantai, L., & Dowling, R. (2015). Supporting the PhD journey: Insights from acknowledgements. International Journal for Researcher Development, 6(2), 106-121. Miles, M. B., & Huberman, A. M. (2013). Qualitative data analysis (3rd ed.). Thousand Oaks, CA: Sage. Patton, M. Q. (2015). Qualitative research and evaluation methods (4th ed.). Thousand Oaks, California: SAGE Publications, Inc

Heutagogy and Researcher Education: Unleashing the Power of the Novice Researcher’s Agency

Novice researchers become experienced researchers by developing their skills in varied contexts, typically within higher education institutions as part of their university degrees. This chapter focuses on the novice researcher who progressively develops their research capacities during the process of completing a PhD (Doctor of Philosophy degree) within a higher education institution or university. Four established areas of research about the education of novice researchers, also known as research training, are examined: 1) the pedagogy of supervision; 2) threshold concepts of PhD candidates; 3) the Researcher Skill Development Framework; and 4) research metaphors. From these fields of research, practical recommendations are extricated to articulate how higher education institutions can promote learner agency, according to heutagogical principles, within the candidate’s doctoral journey. During this chapter, researchers are viewed as learners and the purpose of the chapter is to explore how the agency of these learner-researchers can be recognised and promoted, in practical terms, within the tertiary education sector

Selecting Criteria to Evaluate Qualitative Research

While the evaluation of quantitative research frequently depends on judgements based on the “holy trinity” of objectivity, reliability and validity (Spencer, Ritchie, Lewis, & Dillon, 2003, p. 59), applying these traditional criteria to qualitative research is not always a “good fit” (Schofield, 2002). Instead, educational researchers who engage in qualitative research have suggested various sets of alternative criteria including: transferability, generalisability, ontological authenticity, reciprocity, dependability, confirmability, reflexivity, fittingness, vitality and, even, sacredness and goodness (Creswell, 2002; Garman, 1996; Guba & Lincoln, 1989; Patton, 2002; Spencer et al., 2003; Stige, Malterud, & Midtgarden, 2009). While over one hundred sets of qualitative research criteria have been identified (Stige et al., 2009), some researchers warn against the absolute application of any criteria to qualitative research which is, by its nature, wide‐ranging and varied, and does not necessarily lend itself to the straightforward application of any evaluation criteria. Nevertheless, whether or not criteria are applied at all in the research evaluation process, postgraduate students face a number of decisions associated with the process of evaluating qualitative research: 1) whether or not to adopt a set of appraisal criteria; 2) which criteria to select, if criteria are used; and 3) how to apply alternative approaches to criteria‐focused evaluation. These decisions often require a paradigm shift (Khun, 1962) in the way postgraduate students perceive and approach their research. The messiness and complexity associated with such decisions can be confronting. This paper examines a number of approaches used by researchers to evaluate qualitative investigations in educational research

Lighting Up and Transforming Online Courses: Letting the Teacher’s Personality Shine

Affective aspects of learning have been shown to influence cognitive aspects of learning (Russo & Benson, 2005; Salmon, 2004) and online educators are increasingly aware of the role played by emotions in online learning. To encourage a well-rounded online learning experience for students, online course designers have long been encouraged to provide students with opportunities to express their own personality and identity (Palloff & Pratt, 1999). Such design features have been linked with improved learning outcomes and decreased attrition rates (McInnerney & Roberts, 2004). However, a comparable discussion about the value of teacher personality in online courses has yet to be comprehensively considered beyond definitions and discussions of teacher presence. Although the development of teacher presence in online learning contexts can contribute in some way to the development of an online atmosphere where the teacher’s role extends beyond the cognitive coach or resource provider, the role of teacher personality is yet to be fully acknowledged as an aspect of the virtual classroom that could further enhance and transform students’ learning experiences. Rather than suggesting which offline personality type would best suit an online teaching role, this paper suggests that teachers should have the opportunity to express their personality in online learning contexts. By acknowledging this nexus between online and offline identities, the paper provides the grounding from which to frame and launch future investigations into how diverse teacher personalities can be allowed to shine in the online environment and, consequently, transform and enhance online experiences for future students and online teachers

The educational beliefs of a group of university teachers and their students: Identification, exploration and comparison

The quality of teaching and learning in tertiary education contexts is influenced by many factors including the educational beliefs of the university teachers and students who teach and learn in such contexts. Most belief research in the tertiary education sector has, to date, reported on the teaching or learning beliefs of just teachers or the teaching or learning beliefs of just students. Much less research has explored the connections between the educational beliefs of these two groups. This research has aimed to extend the parameters of previous research by investigating the point of intersection between the educational beliefs of a group of university teachers and their students. To attain this objective, the study adopted a mixed method approach which employed predominantly interpretivistic data gathering, data analysis and reporting methods. These methods incorporated elements of inductive and comparative analysis, and were augmented by other qualitative methods. Combined, these methods facilitated the identification, exploration and comparison of the educational beliefs of the participants in the study

For the Technologically Challenged: Four Free Online Tools to Liven up a Mathematics Classroom

This article focuses on the use of a handful of free online tools that can be used to liven up and support mathematics learning in lessons and activities that take place inside or outside the primary mathematics classroom. While some of these tools have been purposefully developed for use in mathematics learning contexts, others have been developed for different purposes, quite apart from mathematics. Tools such as the interactive number board (http://www.abcya.com/interactive_100_number_chart.htm) and virtual chance tools such as virtual dice (http://www.curriculumbits.com/mathematics/virtual-dice/) and virtual spinners (http://www.mathsisfun.com/data/spinner.php) are examples of online tools that have been purposefully designed for use in mathematics learning activities. The online stopwatch (http://www.online-stopwatch.com/) can be used when students are learning about many aspects of the Australian Curriculum, especially the Content Descriptions focused on using units of measurement and explaining time durations . However, language-based tools such as Wordle (http://www.wordle.net/), a word cloud creator, and the online game-creation tool, Quizlet (http://quizlet.com/), have not necessarily been created with mathematics in mind. Despite the original intention of their design, this article outlines methods in which these two language-based online tools can be used in mathematics learning and teaching contexts. As well as recognising the functional uses of the five online tools presented in this article, they have also been evaluated in terms of their capacity to engage and motivate students in primary mathematics classrooms. Attard\u27s framework for engagement with mathematics in the primary classroom acknowledges the powerful role of motivation in engagement as well as the value of acknowledging students\u27 views about engagement in mathematics lessons (Attard, 2012a, 2012b). In their discussion of the value of hands-on and virtual manipulatives, Swan and Marshall (2010) reviewed Perry and Howard\u27s research on mathematics manipulative materials (Perry & Howard, 1997). Their work extends our understanding of hands-on mathematics manipulative materials to incorporate the use of virtual mathematics manipulatives. Together, these researchers and educators provide a contextual backdrop in which the theme of engagement in the mathematics classroom informs an evaluative guide that can be used to determine the quality of an online tool for mathematics learning in primary schools. This article presents a review of five technological tools that primary mathematics teachers and students can use in mathematics activities inside and outside their primary school classrooms. Each of the five tools outlined in this article have been classified and evaluated according to the Enhanced Engagement Evaluation Guide above

The Researcher\u27s Little Helper: The Design of an Enabling Online Resource for Postgraduate Students and their Supervisors

The question of how to support postgraduate students and their supervisors, especially neophyte supervisors, is a challenge faced by many higher education institutions. This paper outlines the early stages of a research study which incorporated a design-based research methodology to inform the planning and development of an online, self-paced resource for postgraduate students and their supervisors. Once the needs of these two groups were identified through regular focus groups, the findings from these collaborations, along with literature review findings, informed the structural framework of an online resource known as The Researcher\u27s Little Helper