Det är allmänt accepterat att lärare bör använda sig av evolutionsteorin som ett sätt att binda ihop undervisningen i biologi. Åtskilliga studier har dock påvisat att flertalet elever har missuppfattningar och föreställningar inom evolution som motverkar deras inlärning av evolutionsteorin. Det samma gäller för begreppsförståelse och konflikten mellan betydelsen av ett ord i vardagsspråket och i ämnesspråket. Tidigare forskning har också kartlagt att biologilärare inte alltid är medvetna om elevers svårigheter eller utformar en evolutionsundervisning som utmanar elevers begreppsförståelse. Denna kvalitativa studie som genomfördes med hjälp av intervjuer med sex olika lärare visar på samma mönster och pekar på några möjliga lösningar för att förbättra elevers förståelse för de evolutionära mekanismerna.  Samtidigt som det finns en stor samstämmighet bland de intervjuade biologilärarna kring begreppsförståelse, precis som i många andra ämnen, resonerar de olika om vilka delar som är viktiga i evolutionsundervisningen och varför. En del fokuserar mer på att lära ut innehållet enligt den lärobok som används medan en del förklarar mer om varför eleverna ska lära sig om evolution.  Som ett resultat av denna studie föreslås bland annat att undervisningen om evolution borde inledas så tidigt som möjligt för att i största möjliga mån minimera risken för att olika missuppfattningar och föreställningar kring evolution inte ska cementeras tidigt. I detta sammanhang bör också information kring ämneskunskap förmedlas vid överlämningarna från ett stadium till ett annat i grundskolan. Vidare föreslås att användandet av CoRe-verktyget implementeras i planeringen av undervisningen och att det införs som ett moment under VFU- arbetet för blivande ämneslärare. Det faktum att tid är en bristvara för lärare innebär att det sällan finns tid för egen reflektion. Därför måste arbetet med CoRe-verktyget schemaläggas på samma sätt som många skolor idag arbetar med kooperativt lärande.

School science education prepares learners to study science at a higher level, prepares them to follow a career in science and to become scientific literate citizens. It is the responsibility of the educator to ensure the learners’ conceptual framework is developed to the extent that secures success at higher level studies. The purpose of this study was to test the effectiveness of conceptual change teaching strategies on the conceptual development of grade 11 learners on Newton’s second law of motion. The two strategies employed were the cognitive conflict strategy and the development of ideas strategy. A sequential explanatory mixed-method research design was used during this study. The qualitative data were used to elucidate the quantitative findings. The quantitative research consisted of a quasi-experimental design consisting of a single-group pre-test–post-test method. During the qualitative part of the research a phenomenological research approach was utilised to gain a better understanding of participants’ learning experiences during the intervention. The quantitative research made use of an adapted version of the Force Concept Inventory (FCI). The data collected from the pre-test were used to inform the intervention. The intervention was videotaped and the video analysis or qualitative data analysis was done. After the intervention the post-test was written by the learners. Hake’s average normalised learning gain <g> from pre- to post-scores was analysed to establish the effectiveness of the intervention. The two sets of results (quantitative and qualitative) were integrated. Information from the qualitative data analysis was used to support and explain the quantitative data. The quantitative results indicate that there was an improvement in the students’ force conception from their initial alternative conceptions, such as that of an internal force. Especially the learners’ understanding of contact forces and Newton’s first law of motion yielded significant improvement. The qualitative data revealed that the understanding of Newton’s second law of motion by the learners who partook in this study did improve, since the learners immediately recognised the mistakes made when confronted with the anchor concept. The cognitive conflict teaching strategy was effective in establishing the anchor concept of force which proved to be useful as bridging concept in the development of ideas teaching strategy. The data from both datasets revealed that the cognitive conflict teaching strategy for the initial part of the intervention was effective. It was evident that for development of the idea teaching strategy the two data sets revealed mixed results. Recommendations were made for future research and implementation of conceptual development teaching strategies. / MEd (Natural Sciences Education), North-West University, Potchefstroom Campus, 2014

School science education prepares learners to study science at a higher level, prepares them to follow a career in science and to become scientific literate citizens. It is the responsibility of the educator to ensure the learners’ conceptual framework is developed to the extent that secures success at higher level studies. The purpose of this study was to test the effectiveness of conceptual change teaching strategies on the conceptual development of grade 11 learners on Newton’s second law of motion. The two strategies employed were the cognitive conflict strategy and the development of ideas strategy. A sequential explanatory mixed-method research design was used during this study. The qualitative data were used to elucidate the quantitative findings. The quantitative research consisted of a quasi-experimental design consisting of a single-group pre-test–post-test method. During the qualitative part of the research a phenomenological research approach was utilised to gain a better understanding of participants’ learning experiences during the intervention. The quantitative research made use of an adapted version of the Force Concept Inventory (FCI). The data collected from the pre-test were used to inform the intervention. The intervention was videotaped and the video analysis or qualitative data analysis was done. After the intervention the post-test was written by the learners. Hake’s average normalised learning gain <g> from pre- to post-scores was analysed to establish the effectiveness of the intervention. The two sets of results (quantitative and qualitative) were integrated. Information from the qualitative data analysis was used to support and explain the quantitative data. The quantitative results indicate that there was an improvement in the students’ force conception from their initial alternative conceptions, such as that of an internal force. Especially the learners’ understanding of contact forces and Newton’s first law of motion yielded significant improvement. The qualitative data revealed that the understanding of Newton’s second law of motion by the learners who partook in this study did improve, since the learners immediately recognised the mistakes made when confronted with the anchor concept. The cognitive conflict teaching strategy was effective in establishing the anchor concept of force which proved to be useful as bridging concept in the development of ideas teaching strategy. The data from both datasets revealed that the cognitive conflict teaching strategy for the initial part of the intervention was effective. It was evident that for development of the idea teaching strategy the two data sets revealed mixed results. Recommendations were made for future research and implementation of conceptual development teaching strategies. / MEd (Natural Sciences Education), North-West University, Potchefstroom Campus, 2014

Not only is Quantum Mechanics (QM) conceptually rich, it is also a theory that physics students have found abstract and technically formidable. Nevertheless, compared to other classical topics of physics, university students’ understanding of QM has received minimal attention in the physics education literature. The principal purpose of this study was to characterize the variation in the ways that undergraduate physics students depict the basic concepts of QM and to extrapolate the results to scaffold possible changes to instructional practices at the university that provided the context for the study. In so doing, an adaptation of a developmental phenomenographic perspective was chosen. Empirically, the study was approached through in-depth interviews with 35 physics students from two Ethiopian governmental universities after they had been exposed to the traditional QM course for one-third of a semester. Interview responses were analyzed using phenomenographic approach where a picture of students’ depictions was established for each quantum concept by expounding the given responses. For each basic quantum concept addressed, the structure of the description categories was separately constructed, and overall, it was found that naive, quasi-classical ontology and/or variants of classical ways of visualization are dominant in students’ responses. For example, it was found that students’ depictions of the photon concept could be described with three distinct categories of description, which are (a) classical intuitive description, (b) mixed model description and (c) quasi-quantum model description. Similarly, the findings revealed that it is possible to establish three qualitatively different categories of description to picture students’ depictions of matter waves, namely, (a) classical and trajectory-based description, (b) an intricate blend of classical and quantum description and (c) incipient quantum model description. Likewise, it was found that students’ depictions of uncertainty principle can be described as: (a) uncertainty as classical ignorance, (b) uncertainty as measurement disturbance and (c) uncertainty as a quasi-quantum principle. With regard to learning QM, the categories of description made clear several issues: most students did not have enough knowledge to depict the basic concepts of QM properly; they were influenced by the perspective of classical physics and their perceptions in making explanations about QM; and they also applied mixed ideas, one based on their classical model and the other from newly introduced QM. These results are also supported by the findings of previous studies in similar domains. Findings from the study were used to guide the design of multiple representations-based instructions and interactive learning tutorials on the conceptual aspects of QM that has been shown to address specific difficulties identified in the study. Theoretical and practical implications of the study, as well as potential future considerations are drawn. / Mathematics, Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education)

Not only is Quantum Mechanics (QM) conceptually rich, it is also a theory that physics students have found abstract and technically formidable. Nevertheless, compared to other classical topics of physics, university students’ understanding of QM has received minimal attention in the physics education literature. The principal purpose of this study was to characterize the variation in the ways that undergraduate physics students depict the basic concepts of QM and to extrapolate the results to scaffold possible changes to instructional practices at the university that provided the context for the study. In so doing, an adaptation of a developmental phenomenographic perspective was chosen. Empirically, the study was approached through in-depth interviews with 35 physics students from two Ethiopian governmental universities after they had been exposed to the traditional QM course for one-third of a semester. Interview responses were analyzed using phenomenographic approach where a picture of students’ depictions was established for each quantum concept by expounding the given responses. For each basic quantum concept addressed, the structure of the description categories was separately constructed, and overall, it was found that naive, quasi-classical ontology and/or variants of classical ways of visualization are dominant in students’ responses. For example, it was found that students’ depictions of the photon concept could be described with three distinct categories of description, which are (a) classical intuitive description, (b) mixed model description and (c) quasi-quantum model description. Similarly, the findings revealed that it is possible to establish three qualitatively different categories of description to picture students’ depictions of matter waves, namely, (a) classical and trajectory-based description, (b) an intricate blend of classical and quantum description and (c) incipient quantum model description. Likewise, it was found that students’ depictions of uncertainty principle can be described as: (a) uncertainty as classical ignorance, (b) uncertainty as measurement disturbance and (c) uncertainty as a quasi-quantum principle. With regard to learning QM, the categories of description made clear several issues: most students did not have enough knowledge to depict the basic concepts of QM properly; they were influenced by the perspective of classical physics and their perceptions in making explanations about QM; and they also applied mixed ideas, one based on their classical model and the other from newly introduced QM. These results are also supported by the findings of previous studies in similar domains. Findings from the study were used to guide the design of multiple representations-based instructions and interactive learning tutorials on the conceptual aspects of QM that has been shown to address specific difficulties identified in the study. Theoretical and practical implications of the study, as well as potential future considerations are drawn. / Mathematics, Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education)

In 2005 the opportunity to apply the New Zealand ‘Numeracy’ approach to teaching Mathematics was extended into the secondary school sector. The goal was to alter teachers’ pedagogy so that ‘sense making’ rather than ‘instruction’ was the core objective of their lessons. Ultimately it is hoped that along with a familiarity and comprehension of Number will come a relatively seamless acquisition of the fundamentals of Algebra. This paper will present details of this approach for teaching Number, the status of Number in the secondary school curriculum, the focus and ramifications of teaching for understanding, as opposed to assimilating and learning to apply algorithms, and will also consider evidence of the effectiveness of the initiative.

The study investigated errors made by Grade 9 learners when simplifying algebraic expressions. Eighty-two (82) Grade 9 learners from a rural secondary school in Limpopo Province, South Africa participated in the study. The sequential explanatory design method which uses both quantitative and qualitative approaches was used to analyse errors in basic algebra. In the quantitative phase, a 20-item test was administered to the 82 participants. Learners’ common errors were identified and grouped according to error type. The qualitative phase involved interviews with selected participants. The interviews focused on each identified common error in order to establish the reasons why learners made the identified errors. The study identified six (6) common errors in relation to simplifying algebraic expressions. The causes of these errors were attributed to poor arithmetic background; interference from new learning; failure to deal with direction and operation signs; problems with algebraic notation and misapplication of rules. / Mathematics Education / M. Ed. (Mathematics Education)

The following study aims to examine the special mathematical knowledge needed in order to teach mathematics. Furthermore, the study attempts to explore how teachers’ views on the knowledge needed in order to teach mathematics affects their student’s opportunities to develop their conceptual understanding. Qualitative and quantitative empirical data was attained by observations and complementary interviews. A total of three teachers, all working at the same school, was observed and interviewed. The study used Ball, Thames &amp; Phelps (2008) practice-based theory of mathematical knowledge for teaching, MKT, as its theoretical framework when analyzing the empirical data. The result of the observations displays that math teachers tend to use common content knowledge far more than specialized content knowledge during their lessons. The outcome of this also study reveals that there is a tendency among teachers to interfuse mathematical concepts with terminology. Conceptual understanding is equated with the use of correct terminology. The students are not exposed to the underlying ideas of the mathematical concepts. The study also concludes that there seems to be a sectioning between the mathematical content taught in grade 4-6 from the rest of the content being taught in elementary school, with a low number of connections being made between mathematical topics and concepts included in the curriculum.

In 2005 the opportunity to apply the New Zealand ‘Numeracy’ approach to teaching Mathematics was extended into the secondary school sector. The goal was to alter teachers’ pedagogy so that ‘sense making’ rather than ‘instruction’ was the core objective of their lessons. Ultimately it is hoped that along with a familiarity and comprehension of Number will come a relatively seamless acquisition of the fundamentals of Algebra. This paper will present details of this approach for teaching Number, the status of Number in the secondary school curriculum, the focus and ramifications of teaching for understanding, as opposed to assimilating and learning to apply algorithms, and will also consider evidence of the effectiveness of the initiative.

The study aimed to explore misconceptions that Grade 9 learners at a school in Soweto had concerning the topic of fractions. The study was based on the ideas of constructivism in a bid to understand how learners build on existing knowledge as they venture deeper into the development of advanced constructions in the concept of fractions. A case study approach (qualitative) was employed to explore how Grade 9 learners describe the concept of fractions. The approach offered a platform to investigate how Grade 9 learners solve problems involving fractions, thereby enabling the researcher to discover the misconceptions that learners have/display when dealing with fractions. The research allowed the researcher to explore the root causes of the misconceptions held by learners concerning the concept of fractions. Forty Grade 9 participants from a township school were subjected to a written test from which eight were purposefully selected for an interview. The selection was based on learners’ responses to the written test. The researcher was looking for a learner script that showed application of similar but incorrect procedures under specific sections of operations of fractions, for example, multiplication of fractions. Both performance extremes were also considered, the good and the worst performers overall. The written test and the interviews were the primary sources of data in this study. The study revealed that learners have misconceptions about fractions. The learners’ definitions of what a fraction is were neither complete nor precise. For example, the equality of parts was not emphasised in their definitions. The gaps brought about by the learner conception of fractions were evident in the way problems on fractions were manipulated. The learners did not treat a fraction as signifying a specific point on the number system. Due to this, learners could not place fractions correctly on the number line. Components of the fraction were separated and manipulated as stand-alone whole numbers. Consequently, whole number knowledge was applied to work with fractions. A lack of conceptual understanding of equivalent fractions was evident as the common denominator principle was not applied. In the multiplication of fractions, procedural manipulations were evident. In mixed number operations, whole numbers were multiplied separately from the fractional parts of the mixed number. Fractional parts were also multiplied separately, and the two answers combined to yield the final solution. In the division of fractions, the learners displayed a lack of conceptual knowledge of division of fractions. Operations were made across the division sign numerators separate from the denominators. This reveals that a fraction was not taken as an outright number on its own by learners but viewed as one number put on top of the other which can be separated. Dividing across, learners rendered division commutative. A procedural attempt to apply the invert and multiply procedure was also evident in this study. Learners made procedural errors as they showed a lack of conceptual understanding of the keep-change-flip division algorithm. The study revealed that misconceptions in the concept of fraction were due to prior knowledge, over-generalisation and presentation of fractions during instruction. Constructivism values prior knowledge as the basis for the development of new knowledge. In this study, learners revealed that informal knowledge they possess may impact negatively on the development of the concept of fractions. For example, division by one-half was interpreted as dividing in half by learners. The prior elaboration on the part of a whole sub-construct also proved a barrier to finding solutions to problems that sought knowledge of fractions as other sub-constructs, namely, quotient, measure, ratio and fraction as an operator. Over generalisation by learners in this study led to misconceptions in which a procedure valid in a particular concept is used in another concept where it does not apply. Knowledge on whole numbers was used in manipulating fractions. For example, for whole numbers generally, multiplication makes bigger and division makes smaller. The presentation of fractions during instruction played a role in some misconceptions revealed by this study. Bias towards the part of a whole sub-construct might have limited conceptualisation in other sub-constructs. Preference for the procedural approach above the conceptual one by educators may limit the proper development of the fraction concept as it promotes the use of algorithms without understanding. The researcher recommends the use of manipulatives to promote the understanding of the fraction concept before inductively guiding learners to come up with the algorithm. Imposing the algorithm promotes the procedural approach, thereby depriving learners of an opportunity for conceptual understanding. Not all correct answers result from the correct line of thinking. Educators, therefore, should have a closer look at learners’ work, including those with correct solutions, as there may be concealed misconceptions. Educators should not take for granted what was covered before learners conceptualised fractions as it might be a source of misconceptions. It is therefore recommended to check prior knowledge before proceeding with new instruction. / Mathematics Education / M. Ed. (Mathematics Education)