The aim of this research is to explore the question of how farmers learn, in constructing knowledge both in and for practice. It seeks to identify how they gain new ideas, make changes, develop to a level of expertise and who and what contribute to this process. The rapidity of change in a high tech environment, combined with globalisation, the new economy and the knowledge age, means that farmers are living their lives in 'fast forward' mode. There is so much new technology, research and development available that the ability to identify information relevant to a particular farming practice and to process it to knowledge is an increasing challenge. Six central South Island (N.Z.) farmers were selected purposively as case studies. The range of case profiles provides for comparison and contrast of the relative importance of formal qualifications, differences between sheep/beef farmers and dairy farmers, levels of expertise, age and experiences. The self-rating of the farmers enables a comparison of lower and higher performers, identifying characteristics which enable insight into why some farmers consistently lead new practice and why others are reluctant followers. The research is qualitative in design and approached from a constructlVIst and interpretive paradigm. Socially and experientially based, it seeks to understand the experiences of the subjects through in-depth interviews and observations. This study identifies farmers as social learners although working independently, in relative geographical isolation and often, social isolation. It concludes that these farmers learn through participation in the practice of farming. This practice includes a constellation of cOmInunities of practice, which may be resource-rich or resource-poor, depending on the range and depth of the farmer's involvement. Through full and committed participation in these practice communities and associate constellations, the practitioner's identity evolves, encouraging new practices, ideas and innovation. This study emphasises that expertise is not a permanent state but requires evolving identity, knowledge and dispositional ability; for maintenance and growth within a culture of practice. Emergent grounded theory suggests that dispositional knowledge underpins construction and use of all knowledge; that construction and use of high-order propositional and procedural knowledge requires higher-order dispositional knowledge and that mastery is developed through evolving identity, dispositions, leadership and learning, socioculturally constructed through resource-rich constellations of communities of practice.

The performance of mathematics and physical science students are very low in South Africa. These students lack algebraic knowledge and skills in physics education. They tend to treat mathematics and science as separate entities; to them the two subjects are not related. Even the teachers seem not to realise the interrelationship of the two subjects, because according to the research, they perpetuate this attitude. A possible reason could be that they are unfamiliar with common objectives and applications. Knowledge of science is enhanced by the application of mathematics, but the role of mathematical knowledge and skills in the understanding of physical science is uncertain. Even in the new National Curriculum Statement (NCS) of South Africa the relationship between mathematics and physical science is not clearly indicated. Algebraic language is a main tool used in physics, but students still display a lack of understanding of mathematical concepts and problem solving skills. The study was aimed at identifying the mathematical knowledge and skills that would enable students to solve physics problems in grades 11 and 12. The aim was also to identify the specific problems experienced by students in applying these skills and knowledge in physics at grades 11 and 12 level. The empirical study was conducted amongst a group of 120 students in four schools in the Rustenburg Region, North- West Province, South Africa and 28 teachers of which 10 were from these schools and 18 were teachers participating in the Sediba project of the North-West University. The investigation was done by means of a self constructed test and questionnaires. The results indicate that the biggest problem lies with a lack of conceptual knowledge, especially with a basic understanding of proportional reasoning. Other problems were identified and possible remedies proposed. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006.

Enligt Läroplanen för förskolan (Skolverket, 2016) har förskollärare en skyldighet att undervisa i naturvetenskap samt ett ansvar att inspirera barnen och väcka deras nyfikenhet för ämnet. Syftet med studien är att upptäcka eventuella samband mellan förskollärares attityder och deras val av undervisningsmetoder gällande naturvetenskap. Vi vill uppfylla syftet med hjälp av följande frågeställningar: (1) vilka attityder till naturvetenskap finns hos förskollärare? och (2) vilka metoder används vid undervisning av naturvetenskap i förskolan? I studien används ett sociokulturellt perspektiv på lärande och utveckling, då detta synsätt menar att tanke, språk, erfarenheter, attityder och handlingar hör ihop (Säljö, 2014a). Studien är kvalitativ och datainsamlingen har skett via semistrukturerade intervjuer av sex legitimerade förskollärare. Studiens resultat visar följande: (1) att det inte kan påvisas något samband mellan förskollärares attityder och deras val av arbetssätt (2) att både kunskapsinriktat och processinriktat arbetssätt integreras i den naturvetenskapliga undervisningen, samt (3) att det finns ett samband mellan förskollärares intresse och val av naturvetenskapligt innehåll i verksamheten. Utifrån diskussionen har följande slutsatser dragits: att förskollärares attityder i någon form påverkar förskolans verksamhet, och att intresset spelar större roll än faktorerna omgivningens önskningar och krav samt tilliten till den egna förmågan, vilka ingår i Ajzens (1991) modell The theory of planned behaviour.

京都大学 / 0048 / 新制・課程博士 / 博士(人間・環境学) / 甲第21866号 / 人博第895号 / 新制||人||214(附属図書館) / 2018||人博||895(吉田南総合図書館) / 京都大学大学院人間・環境学研究科共生人間学専攻 / (主査)准教授 中森 誉之, 教授 服部 文昭, 准教授 PETERSON Mark / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DFAM

The learning difficulties prevalent among mathematics students are widely documented. This case study explores the difficulties experienced by National Certificate (Vocational) Level 2 mathematics students at a Technical and Vocational Education and Training (TVET) College in Gauteng in the learning of functions. The primary research question was: What conceptual and procedural knowledge difficulties do NC(V) L2 students experience when learning the concept of functions in mathematics? Qualitative data was generated from the students (n=17) through lesson observations, test responses and interviews. The convenient sample of students all belonged to one L2 mathematics class. The findings revealed that the students experience conceptual knowledge difficulties in terms of defining a function, identifying functions, translating between representations of functions, and interpreting the behaviour of a function. The findings also revealed procedural knowledge difficulties prevalent among the students. The errors that students committed in this regard included factorisation errors, structural errors, misapplication and modification of the rules. In general, the findings indicated that the students in this sample lack procedural knowledge and conceptual understanding of functions. The lesson observations revealed a prevalence of several misconceptions regarding functions among the students which were seemingly not recognised nor remedied by the teacher. The teacher’s instructional practices thus appeared to be among the possible sources of the difficulties that the students experience in the learning of functions. This finding was also confirmed by the students during the interviews. Shaky foundations from previous grades were also a factor. / Dissertation (MEd)--University of Pretoria, 2020. / Science, Mathematics and Technology Education / MEd / Unrestricted

Ratio is one of the key mathematics concepts included in the South African Mathematics curriculum. It is applied in other topics of the Grade 7 curriculum, including geometry, functions and relationships, algebra, similarity and congruency. The aim of this qualitative research study was to explore the difficulties that learners experience in learning ratio. The primary research question for the study was: What is Grade 7 learners’ knowledge of ratio? This research question was answered through the following secondary research questions: How do learners solve problems involving ratio? What is learners’ conceptual knowledge of ratio? And what learning difficulties do learners experience when learning about ratio? The study was informed by Kilpatrick, Swafford and Findell’s (2001) five strands of mathematical proficiency; however, the focus was on conceptual and procedural knowledge of ratio. The interpretivist paradigm and the single exploratory case study design were used to gain insight into the learning of ratio. Data was collected from Grade 7 learners (23 of the 35 learners originally sampled) through a self-developed test that followed the prescripts of the Grade 7 Mathematics curriculum in South Africa and through semi-structured interviews. The test scripts were analysed using the Atlas.tiTM windows coding system and the results were used to construct questions for the semi-structured interviews. The interviews were used to corroborate data emerging from the test. The results of the study indicated that Grade 7 learners can do simple and routine manipulations of ratio as well as non-proportional ratio problems but struggle to solve problems that require multiplicative thinking and proportional reasoning skills. Although there could be other factors contributing to learners’ struggle to tackle proportional ratio problems requiring multiplication and proportional reasoning, a lack of conceptual knowledge seemed to contribute significantly. / Dissertation (MEd)--University of Pretoria, 2020. / Science, Mathematics and Technology Education / MEd / Unrestricted

Magister Educationis - MEd / A DESCRIPTION OF ENTRY LEVEL TERTIARY STUDENTS' MATHEMATICAL ACHIEVEMENT (Towards an analysis of student texts) M.S. Jacobs PhD Thesis, School of Mathematics and Science Education, University of the Western Cape. This research provides insights into the mathematical achievement of a cohort of tertiary mathematics students. The context for the study is an entry level mathematics course, set in an engineering programme at a tertiary institution, the Cape Peninsula University of Technology (CPUT). The participant members are first year, first semester students. The materials for the inquiry are student produced test scores and examination scripts taken from their entry level course. The characteristics of the mathematical achievement of the cohort concern the understanding of procedural and conceptual knowledge and problem solving abilities in mathematics. The facility with mathematics is another central concern of this study as it forms the dominant aspect of mathematical achievement which is accessible to research in the materials employed for the study. This research also develops a mathematical achievement profile for individual members of the cohort. The methodology makes use of content - and textual analytic methods for profiling the students. When viewed across the different kinds of profiling techniques adopted, this study suggests that these techniques complement one another: the profiles developed provide a cohesive and complementary overview of the achievement of the cohort. 111 This study challenges perceptions that responses to constructed response questions offer little information about the mathematical knowledge of students. This study investigates the possibilities of providing a bridge between the assessment of students by means of tests scores and a taxonomy of mathematical objectives, on the one hand, and the critical analysis of student produced texts, on the other. Findings suggest that diagnostic uses of paper and pencil tests can be revealing about the achievement of students. The wide range of responses to test items revealed a distribution of incompleteness in terms of employing algorithmic techniques. This research revealed that even in cases of wrong solutions, participant members' responses were reasonable, meaningful, clear and logical. The participants responded in many ways as predicted by the research literature. Evidence could be found for the use of child methods; poor use of reflective abstraction for coordination; accessing the wrong cognitive frames; not seeing the underlying structure of the mathematics and treating letters as objects. Findings suggest that the use of a textual analytic method, which led to the creation of critical indicators as a way of sign-posting events, enhanced the achievement profile of the students. / The Grassmate Project (SothAfrica/Norway)

Persons with Swedish as their first language often find it hard to learn subject-verb agreement when studying English. In Swedish this grammatical difficulty does not exist and it is therefore hard to introduce to learners that have Swedish as their native language.This investigation is based on the texts of 28 ninth graders of whom four were interviewed. My interest was in finding out how the students reflect on their own written work with a focus on subject-verb agreement with a particular focus on the third person singular s.My study shows that the four interviewed students claim that they never reflect on grammar in their spontaneous writing and that they never consciously try to apply rules that they have studied in school through being offered grammatical explanations. Instead they make their grammatical choices intuitively, using their procedural knowledge.

Several factors that are known to influence attitudes of students towards learning have been documented. Some of these factors have been found to affect the achievement of students. In this study the relationship of the attitudinal disposition of students to their learning outcomes were assessed. Chemistry attitude questionnaire was used to assess the attitude of students and a pen and paper examination comprising of questions requiring declarative and procedural knowledge were used to assess learning outcomes of students. Correlation analysis and multiple linear regression analysis were used to assess relationship between attitude of students and their learning outcomes. The results showed that attitude of students had a positive but moderate influence on their performance. The ANOVA results showed a statistical significant relationship between attitude of students and students’ learning outcomes (F= 38.383, p=0.000). / Institute of Science and Technology Education / M.Sc. (Mathematics, Science and Technology Education)

Thesis advisor: Lillie Richardson Albert / The purpose of this research is to identify the categories of South Korean elementary teachers' knowledge for teaching mathematics. Operating under the assumption that elementary teachers' knowledge for teaching affects students' learning, eleven South Korean elementary teachers volunteered to participate in this study. Emerging from the data collected and the subsequent analysis are five categories of South Korean elementary teachers' knowledge for teaching mathematics: Mathematics Curriculum Knowledge, Mathematics Learner Knowledge, Fundamental Mathematics Conceptual Knowledge, Mathematics Pedagogical Content Knowledge, and Mathematics Pedagogical Procedural Knowledge. The first three categories of knowledge play a significant role in mathematics instruction as an integrated form within Mathematics Pedagogical Content Knowledge. A notable conclusion of this study is that Pedagogical Content Knowledge might not be the sum of the other categories of knowledge for teaching mathematics. These findings may be connected to results from relevant studies in terms of the significant role of teachers' knowledge in their mathematics instruction. This study contributes to the existing literature in that it provides empirical bases for understanding teachers' knowledge for teaching mathematics and reveals the relationship among categories of knowledge for teaching mathematics. / Thesis (PhD) — Boston College, 2014. / Submitted to: Boston College. Lynch School of Education. / Discipline: Teacher Education, Special Education, Curriculum and Instruction.