Introducing the multi-faceted teaching experiment

A mathematics classroom is comprised of many mathematicians with varying understanding of mathematics knowledge, including the teacher, students and sometimes researchers. To align with this conceptualisation of knowledge and understanding, the multi-faceted teaching experiment will be introduced as an approach to study all classroom participants’ interactions with the shared knowledge of mathematics. Drawing on the experiences of a large curriculum project, it is claimed that, unlike a multi-tiered teaching experiment, the multi-faceted teaching experiment provides a research framework that allows for the study of mathematicians’ building of knowledge in a classroom without privileging the experience of any one participant.

Virtual versus classroom language teaching : A comparative study of the learning outcomes and student responses between two English reading comprehension groups

A 26-hour English reading comprehension course was taught to two groups of second year Finnish Pharmacy students: a virtual group (33 students) and a teacher-taught group (25 students). The aims of the teaching experiment were to find out: 1.What has to be taken into account when teaching English reading comprehension to students of pharmacy via the Internet and using TopClass? 2. How will the learning outcomes of the virtual group and the control group differ? 3. How will the students and the Department of Pharmacy respond to the different and new method, i.e. the virtual teaching method? 4. Will it be possible to test English reading comprehension learning material using the groupware tool TopClass? The virtual exercises were written within the Internet authoring environment, TopClass. The virtual group was given the reading material and grammar booklet on paper, but they did the reading comprehension tasks (written by the teacher), autonomously via the Internet. The control group was taught by the same teacher in 12 2-hour sessions, while the virtual group could work independently within the given six weeks. Both groups studied the same material: ten pharmaceutical articles with reading comprehension tasks as well as grammar and vocabulary exercises. Both groups took the same final test. Students in both groups were asked to evaluate the course using a 1 to 5 rating scale and they were also asked to assess their respective courses verbally. A detailed analysis of the different aspects of the student evaluation is given. Conclusions: 1.The virtual students learned pharmaceutical English relatively well but not significantly better than the classroom students 2. The overall student satisfaction in the virtual pharmacy English reading comprehension group was found to be higher than that in the teacher-taught control group. 3. Virtual learning is easier for linguistically more able students; less able students need more time with the teacher. 4. The sample in this study is rather small, but it is a pioneering study. 5. The Department of Pharmacy in the University of Helsinki wishes to incorporate virtual English reading comprehension teaching in its curriculum. 6. The sophisticated and versatile TopClass system is relatively easy for a traditional teacher and quite easy for the students to learn. It can be used e.g. for automatic checking of routine answers and document transfer, which both lighten the workloads of both parties. It is especially convenient for teaching reading comprehension. Key words: English reading comprehension, teacher-taught class, virtual class, attitudes of students, learning outcomes

The effects of using an alternative method for teaching badminton to post secondary level students in Taiwan

The effect of teaching method in physical education is an important issue and has been a concern of the expert teacher. Teachers are expected to create a model of teaching in their field; therefore, it is reasonable to question what is the effect of an alternative teaching method on student performance in physical education. This study explores whether teaching methods with advanced planning, behavior and belief in high enthusiasm, use of instructional strategies and evaluation, together termed a systematic teaching approach, used in a physical education activity would provide an effective environment for learning which supports student achievement in the psychomotor, cognitive, and affective domains. This study also investigated whether there was a difference in performance between students who were taught with a systematic teaching approach and students who were taught with the traditional teaching model. Information was collected using two performance skills, a written test, and one questionnaire. The 68 participants were randomly assigned into either an experimental group or a control group. Two teachers were assigned to either the experimental group or the control group. The teaching experiment took place at Tamsui Oxford University College in Taiwan and lasted eight weeks. ^ Research questions were analyzed using the t-test. Results indicated that a significant difference in students' performance was found between the experimental group and the control group on both the skill tests and the paper test. Analysis of student attitude toward their teacher and their course on the questionnaire indicated a significant difference between the experimental group and the control group. ^ The findings of this study imply that students who were taught with a systematic teaching style were significantly superior to students who were taught with the traditional model on these measures. This finding supports the contention that effective teaching in physical education is related to advanced planning, high enthusiasm, instructional strategy and evaluation and that all physical education teachers should implement these planning elements in the development of the teaching strategies. ^

Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.

A problem-posing intervention in the development of problem-solving competence of underachieving, middle-year students

This study reported on the issues surrounding the acquisition of problem-solving competence of middle-year students who had been ascertained as above average in intelligence, but underachieving in problem-solving competence. In particular, it looked at the possible links between problem-posing skills development and improvements in problem-solving competence. A cohort of Year 7 students at a private, non-denominational, co-educational school was chosen as participants for the study, as they undertook a series of problem-posing sessions each week throughout a school term. The lessons were facilitated by the researcher in the students’ school setting. Two criteria were chosen to identify participants for this study. Firstly, each participant scored above the 60th percentile in the standardized Middle Years Ability Test (MYAT) (Australian Council for Educational Research, 2005) and secondly, the participants all scored below the cohort average for Criterion B (Problem-solving Criterion) in their school mathematics tests during the first semester of Year 7. Two mutually exclusive groups of participants were investigated with one constituting the Comparison Group and the other constituting the Intervention Group. The Comparison Group was chosen from a Year 7 cohort for whom no problem-posing intervention had occurred, while the Intervention Group was chosen from the Year 7 cohort of the following year. This second group received the problem-posing intervention in the form of a teaching experiment. That is, the Comparison Group were only pre-tested and post-tested, while the Intervention Group was involved in the teaching experiment and received the pre-testing and post-testing at the same time of the year, but in the following year, when the Comparison Group have moved on to the secondary part of the school. The groups were chosen from consecutive Year 7 cohorts to avoid cross-contamination of the data. A constructionist framework was adopted for this study that allowed the researcher to gain an “authentic understanding” of the changes that occurred in the development of problem-solving competence of the participants in the context of a classroom setting (Richardson, 1999). Qualitative and quantitative data were collected through a combination of methods including researcher observation and journal writing, video taping, student workbooks, informal student interviews, student surveys, and pre-testing and post-testing. This combination of methods was required to increase the validity of the study’s findings through triangulation of the data. The study findings showed that participation in problem-posing activities can facilitate the re-engagement of disengaged, middle-year mathematics students. In addition, participation in these activities can result in improved problem-solving competence and associated developmental learning changes. Some of the changes that were evident as a result of this study included improvements in self-regulation, increased integration of prior knowledge with new knowledge and increased and contextualised socialisation.

Young children's understandings about "square" in 3D virtual reality microworlds

This paper reports an investigation of primary school children’s understandings about "square". 12 students participated in a small group teaching experiment session, where they were interviewed and guided to construct a square in a 3D virtual reality learning environment (VRLE). Main findings include mixed levels of "quasi" geometrical understandings, misconceptions about length and angles, and ambiguous uses of geometrical language for location, direction, and movement. These have implications for future teaching and learning about 2D shapes with particular reference to VRLE.

Re-imagining STEM : peer scaffolding ICT in initial teacher education

In this paper, we report on how peer scaffolding was used to effect change in tertiary teaching practice and academic disposition in the use of Information and Communication Technology (ICT) in Science teaching and learning. We present a small-scale case study investigating the practice of one of this paper’s authors. It is told through two salient episodes which narratively describe the scaffolding used to support a teaching experiment. This was made possible through the national Teaching Teachers for the Future Project (2011-2012) which aimed to enhance the technological pedagogical capability of pre-service teachers across Australia. The outcome was a demonstrable shift in the academic’s disposition towards the use and benefits of ICT in teaching science and an increase in skills and confidence for both the academic and his students. This study and its outcomes fit within the contemporary push to “re-imagine” the teaching of Science, and more broadly of STEM, in schools.

Re-imagining STEM : peer scaffolding ICT in Initial Teacher Education

In this paper, we report on how peer scaffolding was used to effect change in tertiary teaching practice and academic disposition in the use of Information and Communication Technology (ICT) in Science teaching and learning. We present a small-scale case study investigating the practice of one of this paper’s authors. It is told through two salient episodes which narratively describe the scaffolding used to support a teaching experiment. This was made possible through the national Teaching Teachers for the Future Project (2011-2012) which aimed to enhance the technological pedagogical capability of pre-service teachers across Australia. The outcome was a demonstrable shift in the academic’s disposition towards the use and benefits of ICT in teaching science and an increase in skills and confidence for both the academic and his students. This study and its outcomes fit within the contemporary push to “re-imagine” the teaching of Science, and more broadly of STEM, in schools.

Indigenous students transitioning to school : responses to pre-foundational mathematics

Australian Indigenous students' mathematics performance continues to be below that of non-Indigenous students. This occurs from the early years of school, due largely to knowledge and social differences on entry to formal schooling. This paper reports on a mathematics research project conducted in one Aboriginal community school in New South Wales, Australia. The project aimed to identify and explain the ways that young Australian Indigenous students (age 2-4 years) learn number language and processes, specifically attribute language, sorting, 1-1 correspondence and, counting. The project adopted a mixed methods approach. That is, the methodology was decolonising (Smith 1999) in that it collaborated with and gave benefit back to the Indigenous community and school being researched. It was qualitative and interpretative (Burns 2000) and incorporated an action-research teaching-experiment approach where and teachers collaborated with the researchers to try new teaching methods. This paper draws on data pertaining to students' response to diagnostic interview questions, the pre- and post-test results of the interview and photographic evidence as observations during mathematics learning time. Participants referred to in this paper include one female principal (N = 1), and the transition class of students' pre- (N = 6) and post-test (N = 3) results of the pre-foundational processes (also referred to as attributes). The results were encouraging with improvements in colour (34%), patterns (33%); capacity (38%). As a result of this project, our epistemology regarding the importance of finding out about students' pre-foundational knowledge and understandings and providing a culturally appropriate learning environment with resources has been built upon.

Structuring representations of continuous data through investigations in grade 1

The study of data modelling with elementary students involves the analysis of a developmental process beginning with children’s investigations of meaningful contexts: visualising, structuring, and representing data and displaying data in simple graphs (English, 2012; Lehrer & Schauble, 2005; Makar, Bakker, & Ben-Zvi, 2011). A 3-year longitudinal study investigated young children’s data modelling, integrating mathematical and scientific investigations. One aspect of this study involved a researcher-led teaching experiment with 21 mathematically able Grade 1 students. The study aimed to describe explicit developmental features of students’ representations of continuous data...

Mathematics, programming, and STEM

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10-week teaching experiment, mathematical meaning-making was enriched when primary students wrote Logo programs to create 3D virtual worlds. The analysis of results found deep learning in mathematics, as well as in technology and engineering areas. This prompted a rethinking about the nature of learning mathematics and a need to employ and examine a more holistic learning approach for the learning in science, technology, engineering, and mathematics (STEM) areas.

A Historical Approach to Children s Physics Education : Modelling of DC-circuit Phenomena in a Small Group

This three-phase design research describes the modelling processes for DC-circuit phenomena. The first phase presents an analysis of the development of the DC-circuit historical models in the context of constructing Volta s pile at the turn of the 18th century. The second phase involves the designing of a teaching experiment for comprehensive school third graders. Among other considerations, the design work utilises the results of the first phase and research literature of pupils mental models for DC-circuit phenomena. The third phase of the research was concerned with the realisation of the planned teaching experiment. The aim of this phase was to study the development of the external representations of DC-circuit phenomena in a small group of third graders. The aim of the study has been to search for new ways to guide pupils to learn DC-circuit phenomena while emphasing understanding at the qualitative level. Thus, electricity, which has been perceived as a difficult and abstract subject, could be learnt more comprehensively. Especially, the research of younger pupils learning of electricity concepts has not been of great interest at the international level, although DC-circuit phenomena are also taught in the lower classes of comprehensive schools. The results of this study are important, because there has tended to be more teaching of natural sciences in the lower classes of comprehensive schools, and attempts are being made to develop this trend in Finland. In the theoretical part of the research an Experimental-centred representation approach, which emphasises the role of experimentalism in the development of pupil s representations, is created. According to this approach learning at the qualitative level consists of empirical operations like experimenting, observations, perception, and prequantification of nature phenomena, and modelling operations like explaining and reasoning. Besides planning teaching, the new approach can be used as an analysis tool in describing both historical modelling and the development of pupils representations. In the first phase of the study, the research question was: How did the historical models of DC-circuit phenomena develop in Volta s time? The analysis uncovered three qualitative historical models associated with the historical concept formation process. The models include conceptions of the electric circuit as a scene in the DC-circuit phenomena, the comparative electric-current phenomenon as a cause of different observable effect phenomena, and the strength of the battery as a cause of the electric-current phenomenon. These models describe the concept formation process and its phases in Volta s time. The models are portrayed in the analysis using fragments of the models, where observation-based fragments and theoretical fragements are distinguished from each other. The results emphasise the significance of the qualitative concept formation and the meaning of language in the historical modelling of DC-circuit phenomena. For this reason these viewpoints are stressed in planning the teaching experiment in the second phase of the research. In addition, the design process utilised the experimentation behind the historical models of DC-circuit phenomena In the third phase of the study the research question is as follows: How will the small group s external representations of DC-circuit phenomena develop during the teaching experiment? The main question is divided into the following two sub questions: What kind of talk exists in the small group s learning? What kinds of external representations for DC-circuit phenomena exist in the small group discourse during the teaching experiment? The analysis revealed that the teaching experiment of the small group succeeded in its aim to activate talk in the small group. The designed connection cards proved especially successful in activating talk. The connection cards are cards that represent the components of the electric circuit. In the teaching experiment the pupils constructed different connections with the connection cards and discussed, what kinds of DC-circuit phenomena would take place in the corresponding real connections. The talk of the small group was analysed by comparing two situations, firstly, when the small group discussed using connections made with the connection cards and secondly with the same connections using real components. According to the results the talk of the small group included more higher-order thinking when using the connection cards than with similar real components. In order to answer the second sub question concerning the small group s external representations that appeared in the talk during the teaching experiment; student talk was visualised by the fragment maps which incorporate the electric circuit, the electric current and the source voltage. The fragment maps represent the gradual development of the external representations of DC-circuit phenomena in the small group during the teaching experiment. The results of the study challenge the results of previous research into the abstractness and difficulty of electricity concepts. According to this research, the external representations of DC-circuit phenomena clearly developed in the small group of third graders. Furthermore, the fragment maps uncover that although the theoretical explanations of DC-circuit phenomena, which have been obtained as results of typical mental model studies, remain undeveloped, learning at the qualitative level of understanding does take place.

A aprendizagem dos números racionais através das conexões entre as suas representações:uma experiência de ensino no 2º ciclo do ensino básico

Tese de doutoramento, Educação (Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2014

O desenvolvimento do pensamento algébrico de alunos do 4º ano de escolaridade : uma experiência de ensino

Tese de doutoramento, Educação (Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2014