Abstract In this paper we document the advantages of utilising technology to enhance teachers’ instructional activities. In particular we showcase the potential and impact that the use of Geometer’s Sketchpad may have on the teaching and learning of geometry at school. A series of five, two-hour teacher development workshops in which Geometer’s Sketchpad was used were attended by 12 Grade 11 and 12 teachers. The findings revealed that teachers had a better understanding of the same geometry that they initially disliked. This finding was supported by a quantitative analysis which showed a positive change in the understanding of and beliefs about geometry from when the teachers started to the end of the workshops.

No description available.

No description available.

This study describes the first study conducted in Thailand that resulted in changes in science teachers' classroom environments. The aim of this study was to assess the effectiveness of constructivist teaching on improving learning environments in Thai secondary school science classrooms. The study involved three phases. First, the Constructivist Learning Environment Survey (CLES), an instrument for assessing students' perceptions of the actual and preferred classroom environment through the constructivist perspective, was validated for use in Thailand. Second, typical Thai secondary school science classrooms were described using quantitative and qualitative methods. Finally, the effectiveness of constructivist teaching on promoting improvement in classroom environments was evaluated through an action research process, involving the use of feedback on actual and preferred classroom environments. The sample consisted of seven secondary school science teachers and their 17 classes of 606 students in Nakornsawan Province, Thailand. Student Actual and Preferred Forms of the CLES, assessing Personal Relevance, Uncertainty, Critical Voice, Shared Control and Student Negotiation, were administered. Factor analysis and internal consistency reliability measures supported a five-factor structure for both actual and preferred forms. Students' attitudes to science were also measured. The actual and preferred environments of different classes were described based on profiles of classroom environment scores. / The results suggested that the average classroom in this study had relatively high levels of student perceived actual Uncertainty, Student Negotiation, and Personal Relevance, but the levels of Shared Control and Critical Voice were consistently lower. On all five scales, students preferred a more favourable classroom environment than what they perceived as being actually present. Three teachers, selected from the original sample, then participated in an attempt to improve their classroom environments through the use of a constructivist teaching approach. Changes in classrooms did occur, thus supporting the effectiveness of constructivist teaching in improving classroom learning environments and students' attitudes towards science in Thailand.

The goal in mathematics has shifted towards an emphasis on both procedural knowledge and conceptual understanding. The importance of gaining procedural knowledge and conceptual understanding is aligned with Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000), which encourages fluency, reasoning skills, and ability to justify decisions. Possession of only procedural skills will not prove useful to students in many situations other than on tests (Boaler, 2000). Teachers and researchers can benefit from this study, which examined the effects of representations, constructivist approaches, and engagement on middle school students' algebraic understanding. Data from an algebra pretest and posttest, as well as 16 algebra video lessons from an NSF-IERI funded project, were examined to determine occurrences of indicators of representations, constructivist approaches, and engagement, as well as student understanding. A mixed methods design was utilized by implementing multilevel structural equation modeling and constant comparison within the analysis. Calculation of descriptive statistics and creation of bar graphs provided more detail to add to the findings from the components of the statistical test and qualitative comparison method. The results of the final structural equation model revealed a model that fit the data, with a non-significant model, p > .01. The new collectively named latent factor of constructivist approaches with the six indicators of enactive representations, encouragement of student independent thinking, creation of problem-centered lessons, facilitation of shared meanings, justification of ideas, and receiving feedback from the teacher was shown to be a significant predictor of procedural knowledge (p < .05) and conceptual understanding (p < .10). The indicators of the original latent factor of constructivist approaches were combined with one indicator for representations and two indicators for engagement. Constant comparison revealed similar findings concerning correlations among the indicators, as well as effects on student engagement and understanding. Constructivist approaches were found to have a positive effect on both types of student learning in middle school mathematics.

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As a result of two years working with the pre-service primary teachers in a College in Fiji I became aware of the difficulty many of the students were having understanding the primary school mathematics they would be required to teach. During that time I had attempted to help them overcome the difficulties by using different teaching approaches and activities but was far from satisfied with my efforts. Hence I decided to make a concerted effort to help the students by planning, implementing and partially evaluating a mathematics education unit, known as the Teaching Program for the first semester of their course. This work formed the basis of my study. For the Teaching Program I chose a constructivist teaching approach with number sense as the underlying theme. To examine the aspects of the Program I used my observations and those of the students especially ones reported in their mathematics journals. To evaluate the effectiveness of the Teaching Program I collected and analysed quantitative data from traditional testing of the class of forty students as well as data from case studies of six of the pre-service teachers in the class. To determine what features of the Teaching Program were linked to positive changes my main source of data was the case studies, especially entries from their journal writings. The findings suggested that a significant development of the cognitive aspects of the students’ number sense did occur during the time of the Teaching Program but not as much as was hoped for. As a result of the analysis of the data I came to a greater realisation of the importance of the non-cognitive aspects of number sense and the necessity for a greater consideration of them in the development of a Program. I also realise now that a major development that did occur was in my understanding of the knowledge and learning of mathematics. My ideas of a teaching paradigm of social constructivism had not guided me sufficiently to incorporate activities and procedures to develop the non-cognitive aspects. I suggest that a paradigm which extends the theory of social constructivism to give greater consideration of these aspects of learning in general, and hence numeracy and number sense in particular, was needed. As a result of this study, my introduction to the theory of enactivism appears to be giving me some direction in this search at this stage.

Current curriculum trends promote inquiry-based student-centered strategies as a way to foster critical thinking and learning. Problem-based learning (PBL), a type of inquiry focusing on an issue or “problem,” is an instructional approach taught on the basis that science reform efforts increase scientific literacy. PBL is a constructivist approach to learning real life problems where understanding is a function of content, context, experiences, and learner goals; historical PBL situates the lesson in a historical context and provides opportunities for teaching NOS concepts. While much research exists on the benefits of historical PBL to student learning in general, more research is warranted on how teachers implement PBL in the secondary science curriculum. The purpose of this study was to examine the classroom-learning environment of four science teachers implementing a historical PBL instructional unit to identify the teachers’ understandings, successes and obstacles. By identifying teachers’ possible achievements and barriers with implementing a constructivist philosophy when executing historical PBL, educators and curriculum designers may improve alignment of the learning environment to constructivist principles. A qualitative interpretive case study guided this research study. The four participants of this study were purposefully and conveniently selected from biology teachers with at least three years of teaching experience, degrees in education, State Licensure, and completion of a PBL workshop. Data collection consisted of pre and post questionnaires, structured interviews, a card sort activity in which participants categorized instructional outcomes, and participant observations. Results indicated that the four teachers assimilated reform-based constructivist practices to fit within their preexisting routines and highlighted the importance of incorporating teachers’ current systems into reform-based teacher instruction. While participating teachers addressed a few NOS tenets, emphasizing the full range of possible NOS objectives included in historical PBL is warranted. This study also revealed the importance of creating a collaborative classroom culture and building positive student-teacher relationships when implementing PBL instruction. The four teachers agreed that the historical PBL instructional unit provided a context for learning state standards, and they positively viewed their experiences teaching the lesson. Thus findings from this study suggest that teaching science in a historical context using PBL can be effective.

The aim of this research was to investigate how I engaged in constructivist teaching (CT) when helping a group of low-performing Grade 7 students to develop new meanings of notation as they started to learn formal algebra. Data was collected over a period of one scholastic year, in which I explored the teacher-student dynamics during my mathematics lessons, where students learnt new representations and interpretations of notation with the help of the computer software Grid Algebra. Analysing video recordings of my lessons, I observed myself continuously changing my teaching purpose as I negotiated between the mathematics I intended to teach and the mathematics being constructed by my students. These shifts of focus and purpose were used to develop a conceptual framework called Mathematics-Negotiation-Learner (M-N-L). Besides serving as a CT model, the M-N-L framework was found useful to determine the extent to which I managed to engage in CT during the lessons and also to identify moments where I lost my sensitivity to students constructions of knowledge. The effectiveness of my CT was investigated by focusing on students learning, for which reason I developed the analytical framework called CAPS (Concept-Action-Picture-Symbol). The CAPS framework helped me to analyse how students developed notions about properties of operational notation, the structure and order of operations in numerical and algebraic expressions, and the relational property of the equals sign. Grid Algebra was found to be a useful tool in helping students to enrich their repertoire of representations and to develop new interpretations of notation through what I defined as informal- and formal-algebraic activities. All students managed to transfer these representations and interpretations of notation to pen-and-paper problems, where they successfully worked out traditionally set substitution-and-evaluation tasks.

Les enquêtes internationales montrent qu’en France, les élèves issus de milieux défavorisés ont moins de chances de réussir à l’école que les autres. Or, des données probantes attestent que l’enseignement socioconstructiviste utilisé majoritairement dans les classes françaises n’est pas celui qui donne les meilleurs résultats. A contrario, l’enseignement explicite est porteur auprès des élèves en difficulté scolaire. Cette recherche a pour objectif de comparer l’efficacité de l’enseignement explicite et de l’enseignement socioconstructiviste en mathématiques, auprès d’enfants scolarisés en éducation prioritaire. Elle est réalisée en France (Martinique), dans des classes de CE1, CM1, CM2 situées en éducation prioritaire où les performances des élèves sont faibles en mathématiques. L’hypothèse testée est la suivante : lorsqu’un professeur enseigne une notion mathématique, les résultats des élèves sont meilleurs s’il utilise un enseignement explicite plutôt que s’il utilise un enseignement socioconstructiviste ou usuel. Cette prédiction est testée dans trois études qui ciblent respectivement la technique opératoire de la soustraction en CE1, la technique opératoire de la division en CM1 et la notion d’aire en CM2. Les résultats obtenus révèlent que tous les élèves progressent. Toutefois, ceux des classes ayant reçu un enseignement explicite obtiennent des performances supérieures à ceux des classes ayant reçu un enseignement socioconstructiviste ou usuel. Enfin, les résultats indiquent que l’enseignement explicite est globalement plus efficace pour les élèves moyens à risque ou en difficulté. / International surveys show that in France, students from disadvantaged social backgrounds are much less likely to succeed at school than others students. However, evidence from studies on the effectiveness of teaching methods shows that the socioconstructivist pedagogies mainly used in the French classrooms do not give the best results. On the contrary, explicit teaching is particularly effective for students with learning difficulties. The work carried out in this present thesis aims to compare the effectiveness of explicit teaching and socioconstructivist teaching with students enrolled in priority education networks, in mathematics. This research is carried out in France (Martinique), in elementary school classes of schools from the priority education networks, where overall students’ performance is low in mathematics. The hypothesis tested is the following: when a teacher teaches a specific mathematical notion, students' results are better if he or she uses explicit instruction rather than socioconstructivist or usual instruction. This prediction is being tested in three studies that respectively focus on learning the partitioning technique of subtraction in second grade class, on learning the technique of the division in fourth grade class and on learning the concept of area in fifth grade class. The results show that all students do progress. But, the students in classes that have received explicit instruction outperform students in classes that have received socioconstructivist or usual instruction. Finally, the results indicate that explicit instruction is generally more effective for underachieving students or in difficulty.