This study conducted to examine the distribution of problem-solving tasks in mathematics textbook related to mathematical literacy. The aim of the study was to analyze the extent to which mathematical literacy is addressed through problem-solving tasks in two grade 4 mathematics textbooks. To analyze the types and distribution of problem-solving tasks within the textbooks the study employed a quantitative approach where the analysis tool was based on four main components that contribute to development of mathematical literacy. The findings revealed that the distribution of problem-solving tasks over had overall was similar with a few differences in percentage in both textbooks. The textbook Matte Direkt 4A provided a greater emphasis on mathematical literacy through problem-solving tasks compared to Koll på matematik 4A. The results also indicated that problem-solving tasks who had a context within the real-world were more prevalent than others in the materials analyzed. These findings implicate the need for a more balanced and comprehensive approach to incorporating problem-solving tasks that promote mathematical literacy in educational materials.

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[pt] Este trabalho tem como objetivo apresentar uma proposta de ensino mediada pela tecnologia, em especial, através da criação de jogos digitais para apoiar a alfabetização matemática de alunos com Transtorno do Espectro Autista. Para que se possa compreender melhor a relevância deste tema, apresenta-se o percurso histórico da educação especial até os dias atuais, abordando a história do autismo e apresentando as características desse transtorno e suas especificidades. Faz-se uma análise da inclusão de alunos com autismo na classe regular e a importância do Plano Educacional Individualizado para o desenvolvimento desses educandos. Ao longo do trabalho, discute-se como se dá o aprendizado da matemática por alunos autistas e explora-se a eficácia do uso da tecnologia como recurso educacional. Ademais, reflete-se sobre a utilização de jogos digitais como estratégia facilitadora do processo de alfabetização matemática, ao suscitar habilidades e competências que vão além de conteúdos matemáticos. O trabalho reforça a criação de jogos digitais como uma importante ferramenta para apoiar a alfabetização matemática e o desenvolvimento global de alunos com transtorno do espectro autista. / [en] This work aims to present a teaching proposal mediated by technology, in particular, through the creation of digital games to support the mathematical literacy of students with Autism Spectrum Disorder. In order to have better understand of this topic relevance, the historical path of special education up to the present day is presented, covering the history of autism and presenting the characteristics of this disorder and its specificities. This research makes an analysis of autistic students inclusion in regular classes and the importance of the Individualized Educational Plan for the development of these students. Throughout the work, we discuss how mathematics is learned by autistic students and explore the effectiveness of using technology as an educational resource. Furthermore, it reflects on the use of digital games as a strategy to facilitate the mathematical literacy process, by raising skills and competencies that go beyond mathematical content. The work reinforces the creation of digital games as an important tool to support mathematical literacy and the global development of students with autism spectrum disorder.

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Made available in DSpace on 2014-06-11T19:31:42Z (GMT). No. of bitstreams: 0 Previous issue date: 2004-12-20Bitstream added on 2014-06-13T20:22:45Z : No. of bitstreams: 1 jacobini_or_dr_rcla.pdf: 1226882 bytes, checksum: 334ebeb4b436a3efc244c87f112026fc (MD5) / Com esta pesquisa busquei analisar as possibilidades de crescimento político dos estudantes, quando a modelagem matemática é adotada como estratégia de ensino-aprendizagem. Considero essas possibilidades como reflexões que se identificam com questionamentos, críticas, ações e transformações. Ao inserir este estudo no contexto da Educação Matemática Crítica baseei minha pesquisa bibliográfica em autores que se identificam com esse movimento. Adotei na pesquisa uma abordagem qualitativa e para a coleta de dados organizei três ambientes de aprendizagem, denominados cenários para investigação, com estudantes voluntários das séries iniciais dos Cursos de Matemática e de Engenharia de Computação, ambos da PUC-Campinas. A análise dos dados indica que o crescimento político dos atores nos cenários associa-se, de um lado, com a conscientização política resultante da sua atuação em investigações diretamente relacionadas com os temas dos projetos de modelagem, nas discussões que acompanham os resultados obtidos e no debate sobre o alcance desses resultados e sobre as conseqüências sociais do trabalho realizado. Do outro lado, esse crescimento associa-se com uma ação política que se concretiza por meio do envolvimento do estudante com a comunidade. Concluo este estudo indicando que o processo de crescimento político dos estudantes deve ser pensado como uma forma de alfabetização matemática, estreitamente relacionada com o núcleo de uma literacia matemática voltada para mudanças sociais. / With this research I intended to analyze the possibilities of the students' political growth when the mathematical modelling is adopted as teaching-learning strategy. I consider those possibilities as reflections that identify with questioning, critics, actions and transformations. When inserting this study in the context of the Critical Mathematics Education I based my bibliographical research on authors that identify with this movement. The research was performed within a qualitative approach, starting from the construction of three learning environment, denominated scenarios to investigation, organized with voluntary students from the initial series of the courses of Mathematics and Engineering of Computation, both of PUC-Campinas University. The analysis of the data indicates that the actors' political growth in the sceneries associates, on a side, with the political awareness as a result of their involvement in investigations directly related with the themes of the modelling projects, in the discussions that accompany the obtained results and in the debate about the reach of those results, and about the social consequences of the accomplished work. On the other hand, that growth associates with a political action that is rendered through the student's involvement with the community. I conclude this study indicating that the process of the students' political growth should be thought as a form of mathematical literacy, strictly related with the nucleus of a mathematical literacy focused on social changes.

Syftet med denna studie var att undersöka lärares syn och undervisningspraxis när det handlar om matematisk vardagskompetens. Fyra lärare intervjuades var för sig. När lärarnas svar analyserades framkom en likartad syn, att matematisk vardagskompetens handlar om den matematik man behöver för att klara sig i sin egen vardag. Denna syn går i linje med den definition som Organisation for Economic Co-operation and Development, OECD, har tagit fram och som dessutom är den som forskning i allmänhet refererar till. De uppgifter med fokus på matematisk vardagskompetens som lärarna ger till sina elever handlar både om att klara den egna vardagen och att klara sig i en framtida vardag som vuxen och yrkesarbetare.  Lärarnas undervisningspraxis skiljer sig åt då det kommer till matematisk vardagskompetens. En av lärarna har ett tydligt samarbete med yrkeslärarna och eleverna får således mycket matematisk vardagskompetens i undervisningen. Lärarna försöker i övrigt få med det i matematikundervisningen för att motivera eleverna för densamma. Hur detta sker är mer eller mindre strukturerat beskrivet. Brist på tid, för stora undervisningsgrupper och avsaknad av samarbete med yrkeslärarna nämns som faktorer som begränsar hur stort fokus lärarna har på matematisk vardagskompetens i undervisningen. / The aim of this study was to investigate teachers’ views and teaching praxes when it comes to mathematical literacy. Four teachers were interviewed individually. When the teachers’ answers were analyzed, an analogous view was displayed, that mathematical literacy is about the mathematics one needs to be able to cope with one’s own everyday life. This view corresponds to the definition Organisation for Economic Co-operation and Development, OECD, has presented and that research in general refers to. The assignments with focus on mathematical literacy, that the teachers give their students, deals both with managing one’s own everyday life and a future everyday as an adult and skilled worker.  The teachers’ teaching praxes differ when it comes to mathematical literacy. One of the teachers has a clear cooperation with the vocational teachers and the students receive therefore much mathematical literacy in the teaching. The teachers try, otherwise, to teach mathematical literacy to motivate the students for the teaching. How this is fulfilled is more or less structurally described. Deficiency of time, too large teaching groups and want of cooperation with the vocational teachers are mentioned as factors confining the focus the teachers have on mathematical literacy in the teaching.

South Africa is the first country in the world to offer Mathematical Literacy as a school subject. This subject was introduced in 2006 as an alternative to Mathematics in the Further Education and Training band. The purpose of this subject is to provide learners with an awareness and understanding of the role that mathematics plays in the modern world, but also with opportunities to engage in real-life problems in different contexts. A problem is the beliefs some people in and outside the classroom have regarding this subject such as teachers believing ML is the dumping ground for mathematics underperformers (Mbekwa, 2007). Another problem is the belief of some principals that any nonmathematics teacher can teach ML. In practice there is Mathematics teachers who teach ML in the same way that they teach Mathematics; non-Mathematics teachers who in many cases lack the necessary mathematical content knowledge and skills to teach ML competently; and Mathematics teachers who adapted their practices to teach ML using different approaches than those required for teaching Mathematics. Limited in-depth research has been done on the ML teachers, what they believe and what knowledge is required to teach this subject effectively and proficiently. The purpose of this study is to investigate the way in which ML is taught in a limited number of classrooms with the view to exploring the relationship between ML teachers’ knowledge and beliefs and their instructional practices. According to Artzt, Armour-Thomas and Curcio (2008) the instructional practice of the teacher plays out in the classroom where teachers’ goals, knowledge and beliefs serve as the driving force behind their instructional efforts to guide and mentor learners in their search for knowledge. To accomplish this aim, an in-depth case study was conducted to explore the nature of teachers’ knowledge and beliefs about ML as manifested in their instructional practices. A qualitative research approach was used in which observations and interviews served as data collection techniques enabling me to interpret the reality as I became part of the lives of the teachers. My study revealed that there is a dynamic but complex relationship between ML teachers’ knowledge and beliefs and their instructional practices. The teachers’ knowledge, but not their stated beliefs were reflected in their instructional practices. Conversely, in one case, the teacher’s instructional practice also had a positive influence on her knowledge and beliefs. It was further revealed that mathematics teacher training and teaching experience played a significant role in the productivity of the teachers’ practices. The findings suggest that although mathematical content knowledge is required to develop PCK, it is teaching experience that plays a crucial role in the development of teachers’ PCK. Although the study’s results cannot be generalised due to the small sample, I believe that the findings concerning the value of teachers’ knowledge and the contradictions between their stated beliefs and practices could possibly contribute to teacher training. Curriculum decision-makers should realise that the teaching of ML requires specially trained, competent, dedicated teachers who value the subject. This exploratory study concludes with recommendations for further research. / Thesis (PhD)--University of Pretoria, 2011. / Science, Mathematics and Technology Education / unrestricted

Mathematics has always been a problem at schools, colleges and universities and to address this problem the South African government has introduced a new subject called Mathematical Literacy into schools and colleges. Since this subject places the emphasis on real-life contexts, there has been a special focus on its management at schools and colleges so that its implementation is done in an efficient way. This study therefore focuses on the experiences and interactions of managers of this new subject and how their leadership can improve performance in it. In addition to the literature review, an empirical investigation based on a qualitative approach and involving semi-structured interviews with managers of three public TVET colleges in the Western Cape was conducted to collect data. The other method used was the analysis of documents relevant to the study. The research found that managers of Mathematical Literacy have varying experiences in both their roles and the implementation of the subject. They also face varied challenges in relation to lecturers and students although there are also similarities regarding these at the different colleges in the study. The strategies of instructional leadership in intervention methods to improve performance in the subject which are encouraged by managers also differ, and some have better results than others. Various methods to empower lecturers are recommended. Recommendations are also made on what was found in this study, as are recommendations for further study. / Educational Leadership and Management / M. Ed. (Education Management)

Thesis (MEd (Curriculum Studies)--Stellenbosch University, 2010. / ENGLISH ABSTRACT: The aim of this research is three-fold. Firstly I aimed to show the difficulty of the concept of proportional reasoning through empirical research. Several researchers have shown the degree of difficulty learners experience with proportional reasoning and have even indicated that many university students (and adults) do not have sound proportional reasoning skills. Piaget’s controversial developmental levels classify proportional reasoning as a higher order thinking skill in his highest level of development, formal operational thought, and claims that most people do not reach this level. The difficulty of proportional reasoning and the fact that it is a skill needed within all Learning Outcomes of Mathematical Literacy creates a predicament in terms of the difficulty of the subject in general. Is it then fair to classify Mathematical Literacy as an inferior subject in the way it has been done over the last few years if it is a subject that requires learners to operate at such a high level of thought through proportional reasoning? Secondly, I would like to confirm with the use of a baseline assessment that learners entering Grade 10 Mathematical Literacy have poor proportional reasoning skills and have emotional barriers to Mathematics and therefore Mathematical Literacy. The research will be done in three private schools located in the West Coast District of the Western Cape in South Africa. If learners in these educationally ideal environments demonstrate poor proportional reasoning skills even though they were privileged enough to have all the possible support since their formative years, then results from overcrowded government schools may be expected to be even worse. The learners in Mathematical Literacy classes often lack motivation, interest and enthusiasm when it comes to doing mathematics. Through the baseline assessment I confirm this and also suggest classroom norms and values that will help these learners to become involved in classroom activities and educational discourse. Thirdly and finally this research will focus on the design of activities that will aim to build on learners’ prior knowledge and further develop their proportional reasoning skills. I argue that activities to develop proportional reasoning should take equivalence of fractions as basis to work from. The activities will aim to help learners to set up questions in such a way that they can solve it with techniques with which they are familiar. Interconnectivity will form a vital part to this investigation. Not only do I indicate the interconnectivity between concepts in the Mathematical Literacy Learning Outcomes of the National Curriculum Statement, but I would like to make these links clear to learners when working through the proposed activities. Making links between concepts is seen as a higher order thinking skill and is part of meta-cognition which involves reflection on thoughts and processes. In short, this research can be summarised as the design of activities (with proposed activities) that aims to develop proportional reasoning by making connections between concepts and requires of learners to be active participants in their own learning. / AFRIKAANSE OPSOMMING: Die doel van hierdie navorsing is drieledig. Eerstens will ek die probleme met die konsep van proporsionele denke uitlig deur eksperimentele ontwerp navorsing. Verskeie navorsers verwys na die moeilikheidsgraad van probleme wat leerders ondervind met proporsionele denke. Sommige van hierdie navorsers het ook bevind dat verskeie universiteitstudente (en ander volwassenes) nie oor die vaardigheid van proporsionele denke beskik nie. Piaget se kontroversiële ontwikkelingsvlakke klassifiseer proporsionele denke as ‘n hoër orde denkvaardigheid in sy hoogste vlak van ontwikkeling, formele operasionele denke, en noem dat meeste mense nooit hierdie vlak bereik nie. Die hoë moeilikheidsgraad van proporsionele denke en die feit dat dit ‘n vaardigheid is wat binne al die Leeruitkomste van Wiskundige Geletterdheid benodig word veroorsaak ‘n dilemma as mens dit vergelyk met die moeilikheidsgraad van die vak oor die algemeen. Tweedens wil ek met behulp van ‘n grondfase assessering bewys dat leerders wat Graad 10 Wiskunde Geletterdheid betree swak proporsionele denkvaardighede het, gepaardgaande met emosionele weerstand teenoor Wiskunde en Wiskunde Geletterdheid. Die navorsing sal gedoen word in drie privaatskole in die Weskus distrik van die Wes-Kaap van Suid-Afrika. Indien leerders in hierdie ideale opvoedkundige omstandighede swak proporsionele denkvaardighede ten toon stel, ten spyte van die feit dat hulle bevoorreg was om sedert hulle vormingsjare alle moontlike opvoedkundige ondersteuning te geniet, dan kan verwag word dat resultate komende van oorvol staatskole selfs swakker mag wees. By leerders in Wiskunde Geletterdheid klasse kan daar gereeld ‘n gebrek aan motivering, belangstelling en entoesiasme ten opsigte van Wiskunde bespeur word. Deur gebruik van die grondfase assessering wil ek hierdie stelling bewys en ook voorstelle maak vir klaskamernorme en waardes wat sal help om die leerders meer betrokke te maak by klaskameraktiwiteite en opvoedkundige gesprekke.

This diploma thesis deals with problems of mathematical skills. Unlike previous research carried out in Czech education, this diploma thesis focuses on university students. Specifically, the focus is on aspirants of the bachelor degree studying geography at the Faculty of Science of Charles University in Prague. The main aim of this work is to determine the mathematical skills, with which students have the greatest problems, if these problematical skills change over time, whether they are problematic independently of the group of the students or each student group has problems with other mathematical skills. In order to meet the goals the credit tests of mathematical geography were used. Because this type of test is not commonly used to determine the level of mathematical skills, it was necessary to develop an own assessment methodology. In total, 1920 credit tests were analyzed from the six academic years 2011/2012 to 2016/2017. The results show that the most problematic mathematical skills are "unit transfers", "using the appropriate formula in the correct form" and "calculating the angles". GeKa + FGG and UZ students also have problems with "formulating a verbal answer or reasoning". All studied study fields did together the smallest proportion of mistakes in mathematical skill "expression the...