9 resultados para Mathematics Classroom
em Helda - Digital Repository of University of Helsinki
Resumo:
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
Resumo:
One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.
Resumo:
The purpose of this research was to examine teacher’s pedagogical thinking based on beliefs. It aimed to investigate and identify beliefs from teachers’ speech when they were reflecting their own teaching. Placement of beliefs in levels of pedagogical thinking was also examined. The second starting point for a study was the Instrumental Enrichment -intervention, which aims to enhance learning potential and cognitive functioning of students. The goal of this research was to investigate how five main principles of the intervention come forward in teachers’ thinking. Specifying research question was: how similar teachers’ beliefs are to the main principles of intervention. The teacher-thinking paradigm provided the framework for this study. The essential concepts of this study are determined exactly in the theoretical framework. Model of pedagogical thinking was important in the examination of teachers’ thinking. Beliefs were approached through the referencing of varied different theories. Feuerstein theory of Structural cognitive modifiability and Mediated learning experience completed the theory of teacher thinking. The research material was gathered in two parts. In the first part two mathematics lessons of three class teachers were videotaped. In second part the teachers were interviewed by using a stimulated recall method. Interviews were recorded and analysed by qualitative content analysis. Teachers’ beliefs were divided in themes and contents of these themes were described. This part of analysis was inductive. Second part was deductive and it was based on theories of pedagogical thinking levels and Instrumental Enrichment -intervention. According to the research results, three subcategories of teachers’ beliefs were found: beliefs about learning, beliefs about teaching and beliefs about students. When the teachers discussed learning, they emphasized the importance of understanding. In teaching related beliefs student-centrality was highlighted. The teachers also brought out some demands for good education. They were: clarity, diversity and planning. Beliefs about students were divided into two groups. The teachers believed that there are learning differences between students and that students have improved over the years. Because most of the beliefs were close to practice and related to concrete classroom situation, they were situated in Action level of pedagogical thinking. Some teaching and learning related beliefs of individual teachers were situated in Object theory level. Metatheory level beliefs were not found. Occurrence of main principles of intervention differed between teachers. They were much more consistent and transparent in the beliefs of one teacher than of the other two teachers. Differences also occurred between principles. For example reciprocity came up in every teacher’s beliefs, but modifiability was only found in the beliefs of one teacher. Results of this research were consistent with other research made in the field. Teachers’ beliefs about teaching were individual. Even though shared themes were found, the teachers emphasized different aspects of their work. Occurrence of beliefs that were in accordance with the intervention were teacher-specific. Inconsistencies were also found within teachers and their individual beliefs.
Resumo:
This research examines three aspects of becoming a teacher, teacher identity formation in mathematics teacher education: the cognitive and affective aspect, the image of an ideal teacher directing the developmental process, and as an on-going process. The formation of emerging teacher identity was approached in a social psychological framework, in which individual development takes place in social interaction with the context through various experiences. Formation of teacher identity is seen as a dynamic, on-going developmental process, in which an individual intentionally aspires after the ideal image of being a teacher by developing his/her own competence as a teacher. The starting-point was that it is possible to examine formation of teacher identity through conceptualisation of observations that the individual and others have about teacher identity in different situations. The research uses the qualitative case study approach to formation of emerging teacher identity, the individual developmental process and the socially constructed image of an ideal mathematics teacher. Two student cases, John and Mary, and the collective case of teacher educators representing socially shared views of becoming and being a mathematics teacher are presented. The development of each student was examined based on three semi-structured interviews supplemented with written products. The data-gathering took place during the 2005 2006 academic year. The collective case about the ideal image provided during the programme was composed of separate case displays of each teacher educator, which were mainly based on semi-structured interviews in spring term 2006. The intentions and aims set for students were of special interest in the interviews with teacher educators. The interview data was analysed following the modified idea of analytic induction. The formation of teacher identity is elaborated through three themes emerging from theoretical considerations and the cases. First, the profile of one s present state as a teacher may be scrutinised through separate affective and cognitive aspects associated with the teaching profession. The differences between individuals arise through dif-ferent emphasis on these aspects. Similarly, the socially constructed image of an ideal teacher may be profiled through a combination of aspects associated with the teaching profession. Second, the ideal image directing the individual developmental process is the level at which individual and social processes meet. Third, formation of teacher identity is about becoming a teacher both in the eyes of the individual self as well as of others in the context. It is a challenge in academic mathematics teacher education to support the various cognitive and affective aspects associated with being a teacher in a way that being a professional and further development could have a coherent starting-point that an individual can internalise.
Resumo:
Continuous growth in the number of immigrant students has changed the Finnish school environment. The resulting multicultural school environment is new for both teachers and students. In order to develop multicultural learning environments, there is a need to understand immigrant students everyday lives in school. In this study, home economics is seen as a fruitful school subject area for understanding these immigrant students lives as they cope with school and home cultures that may be very different from each other. Home economics includes a great deal of knowledge and skills that immigrant students need during their everyday activities outside of school. -- The main aim of the study is to clarify the characteristics of multicultural home economics classroom practices and the multicultural contacts and interaction that take place between the students and the teacher. The study includes four parts. The first part, an ethnographical prestudy, aims to understand the challenges of multicultural schoolwork with the aid of ethnographical fieldwork done in one multicultural school. The second part outlines the theoretical frames of the study and focuses on the sociocultural approach. The third part of the study presents an analysis of videodata collected in a multicultural home economics classroom. The teacher s and students interaction in the home economics classroom is analyzed through the concepts of the sociocultural approach and the cultural-historical activity theory. Firstly, this is done by analyzing the focusedness of the teacher s and the students actions as well as the questions presented and apparent disturbances during classroom interaction. Secondly, the immigrant students everyday experiences and cultural background are examined as they appear during discussions in the home economics lessons. Thirdly, the teacher s tool-use and actions as a human mediator are clarified during interaction in the classroom. The fourth part presents the results, according to which a practice-based approach in the multicultural classroom situation is a prerequisite for the teacher s and the students shared object during classroom interaction. Also, the practice-based approach facilitates students understanding during teaching and learning situations. Practice in this study is understood as collaborative teaching and learning situations that include 1) guided activating learning, 2) establishing connections with students everyday lives and 3) multiple tool-use. Guided activating learning in the classroom is defined as situations that occur and assignments that are done with a knowledgeable adult or peer and include action. The teacher s demonstrations during the practical part of the lessons seemed to be fruitful in the teaching and learning situations in the multicultural classroom. Establishing connections with students everyday lives motivated students to follow the lesson and supported understanding of meaning. Furthermore, if multiple tools (both psychological and material) were used, the students managed better with new and sometimes difficult concepts and different working habits, and accomplished the practical work more smoothly . The teacher s tool-use and role as a mediator of meaning are also highlighted in the data analysis. Hopefully, this study can provide a seedbed for situations in which knowledge produced together, as well as horizontally oriented tool-use, can make school-learned knowledge more relevant to immigrant students everyday lives, and help students to better cope with both classroom work and outside activities. KEY WORDS: home economics education, multicultural education, sociocultural perspective, classroom interaction, videoanalysis