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Schmude, Martin
- PublicationRedesigning a mixed-method research study during a pandemic: A case study from Nigeria and Australia(Western Australian Institute for Educational Research Inc, 2023-03-23)
; ; One major challenge researchers have faced during the disruptions resulting from the Covid-19 pandemic is how to adapt to the global virus and, at the same time, make good progress in their research pursuits. Also, many international researchers have suspended ongoing research in developing countries due to inadequate online facilities in these countries. This article identifies innovative methodologies that can be employed to carry out mixed-method research in a non-technologically advanced country and reflects on the benefits and limitations of carrying out such rigorous research during difficult times. The mixed-method research design reported here combines tests and open-ended reasons for procedures to explore the impacts of two pedagogical practices on students' mathematical understanding. In particular, the methodological framework leverages the aims of the research, the theoretical background, standard ethical practice, and Covid-19 safety precautions. This article contributes to the methodological approaches for carrying out mixed-method research during unprecedented times.
- PublicationStructure of the Observed Learning Outcomes (SOLO) model: A mixed-method systematic review of research in mathematics educationThe review followed the preferred reporting items for systematic review and meta-analysis (PRISMA) standard to search and report relevant articles on the use of SOLO model in mathematics. A systematic search was conducted in Education Source, ERIC, JSTOR, and PsycINFO databases and yielded 198 studies. After screening and appraisal, 62 papers (37 qualitative, 17 quantitative, and eight mixed-method studies) published in English between 1990 and 2020 were reported using a narrative synthesis. The findings indicated that SOLO model appropriately reflects students' learning outcomes; there is a direct relationship between students' performances and their SOLO levels; and SOLO model could explain several other developmental theories and contribute to the development of mathematics curricula. These findings highlight the gaps between theory and practice of this model in mathematics education, and informs education professionals about the diverse applications of the SOLO model for improving mathematics teaching and learning, fair assessment, and curriculum development.
- PublicationCritical Moments in Learning Mathematics: First Year Pre-service Primary Teachers' Perspectives(Mathematics Education Research Group of Australasia (MERGA), 2010)
; ; Pre-service primary teachers have been identified in several research studies as having poor self-conceptions of themselves as mathematics teachers. Many express feelings of anxiety when faced with mathematics tasks resulting in poor dispositions and understandings. This paper reports on beginning pre-service primary teachers' (N=106) recollections of critical moments in their mathematics education at school. Interestingly, their graphical ratings of their dispositions suggest a slightly positive recollection of their mathematical experiences. In contrast their justifications and recount was generally negative. - PublicationARTefacts: Managing children's art portfolios(International Association of Art in Early Childhood, 2018)
; ; Increased access to tablet and mobile technology within the early childhood classroom can allow for new approaches for creating, capturing and presenting children’s art. Not only can the use of iPads in the early childhood classroom allow young children in the pre-literacy stage of development to engage with the devices, it can also offer a robust and flexible ‘ePortfolio’ option of children’s learning. A digital collection of children’s work − including examples of literacy, numeracy and visual art works − can be collated in clearly navigable and shareable folders which can be added to over the teaching period. In this paper, we present one example of a syncing service, Evernote, and how it can become an easy-to-manage repository for various types of learning artefacts. These artefacts can be gathered during children’s participation in less formal, exploratory free play, intentional teaching moments, or more structured lessons. Artefacts can be created directly by the child from other interactive iPad apps or through using the iPad to record images, audio or video, of more traditional forms of art and creative play. An ePortfolio of children’s work can show progress throughout the year, and be an opportunity for reflection by the children, parents and educators. It can also be added to during future years while the child remains at the service. In this example, technology can help create a sense of belonging and community within the classroom and a sense of ownership by the children over their own work and the way in which their progress is captured and presented. - PublicationImproving self-confidence and abilities: A problem-based learning approach for beginning mathematics teachers(Mathematics Education Research Group of Australasia (MERGA), 2011)
; ; This paper draws from a pilot study about a teacher education program that focused on building preservice primary teachers' confidence and abilities in teaching and learning mathematics. The cohort involved on-campus [n=82] and off-campus [n=420] participants. The qualitative study was based on developing three aspects of mathematics teacher education: (1) Content knowledge; (2) Pedagogical knowledge; and (3) Knowledge of the learner. A problem-based learning environment was created to build students' self-efficacy and to encourage the beginning teachers' willingness to engage in the unit content by providing authentic teaching contexts, and to develop a richer conceptual and procedural understanding of mathematics. - PublicationAn Exploration of Effective Pedagogical Practices for Mathematics Learning in the Nigerian Context(University of New England, 2023-05-05)
; ; In recent years, mathematics teachers and educators in Nigeria and other countries have expressed concerns about the superficial teaching and low student achievements in mathematics, which hinder students from transferring mathematical knowledge to solve practical, real-life problems. One major cause of these problems is the pedagogical practices embraced by teachers in mathematics classrooms. Numerous studies have highlighted the importance of pedagogies connected to the van Hiele theory and the cognitive load in enhancing students' mathematical learning and, subsequently, their achievements. The pedagogies associated with the van Hiele theory and the cognitive load theory which this study focused on are the van Hiele teaching phases and the worked examples instruction respectively. The researcher explored and compared these two pedagogical approaches (the worked examples and the van Hiele teaching phases) to enhance students' learning and achievements in mathematics at the secondary education level. The exploration further considered how the pedagogical approaches contributed to students' retention of mathematical concepts, procedural understanding and conceptual mathematical understanding.
The research included 157 first-year senior school students, aged 14 to 15, and two mathematics teachers from Nigeria. Data collected in the experimental phases (pre-testing, intervention, post-testing and delay testing) of this study were analysed utilising a qualitative approach based on the Structure of Observed Learning Outcomes (SOLO) model and quantitative statistics in accordance with the Rasch model and Statistical Package for Social Sciences (SPSS). The results of the investigation showed that there was a significant difference between the effectiveness of the van Hiele teaching phases and that of the worked examples strategy, in favour of the van Hiele teaching phases. The van Hiele teaching phases significantly enhanced students' mathematical knowledge acquisition and retention, and had significant positive effects on students of low and high mathematics abilities, and on both male and female students. Conversely, the worked examples significantly aided students' acquisition of mathematical understanding" however, the acquired understanding is not retained beyond three weeks. Furthermore, the worked examples instruction favours only the low-ability students, and students' gender has no influence on the main instructional effect.
In terms of the procedural and conceptual understanding demonstrated by the students, the van Hiele teaching phases helped students to acquire more conceptual understanding than procedural understanding, whereas the worked examples strategy facilitated greater procedural understanding than conceptual understanding. Overall, the procedural and conceptual understanding acquired and retained by the van Hiele group is significantly greater than its worked examples strategy equivalent. These findings indicated that the van Hiele theory, which was originally designed for geometry could be applied to a different mathematical area. Lastly, the use of van Hiele teaching phases and an emphasis on conceptual understanding as opposed to the explicit instruction of worked examples is likely to lead to better and more sustained learning outcomes. Therefore, mathematics teachers should focus more on building conceptual understanding if deeper understanding of mathematical concepts, improved retention and greater transfer of mathematical knowledge are desired.