The aim of this study was to investigate the comparative effects of Constructivist-Based Teaching Method (CBTM) and the Traditional Teaching Method (TTM) on Grade 11 Mathematics learners’ errors in algebra. The constructivist learning theory (CLT) was used to frame this study. Mainly, CLT was used to influence the design of CBTI to hone participants’ errors in algebra that militate against their performance in Mathematics. The study was conducted in the Mpumalanga Province of South Africa with a four-week intervention programme in each of the two participating secondary schools. Participants consisted of n=78 Grade 11 Mathematics learners and one Grade 11 Mathematics teacher. A non-equivalent control group design consisting of a pre-test and post-test measure was employed. The Grade 11 teacher in the control school employed the TTM while the researcher implemented CBTM in the experimental school. The main aspects of CBTM entailed participants’ construction of their own knowledge from the base of prior knowledge and through group learning approach and exploratory talk in which discussions included argumentation, verbalising explanations, justifications and reflections. Participants in experimental school became familiar with the basic principles of CBTI such as group work, which enhanced the construction of conceptual understanding of algebraic concepts. This reduced most of the errors they commit in algebra and elevated their performance in Mathematics. The principal instruments for data collection consisted of a standardised Algebra Concept Achievement Test and lesson observations. The pre-test was used to determine participants’ initial errors in algebra before the intervention. A post-test was given at the end of intervention to ascertain change in participants’ errors in algebra over a four-week intervention period. Using descriptive and inferential statistical techniques, the study found that participants in experimental school significantly reduced their errors in algebra than those in control school. The study showed that CBTM was a more effective pedagogy that improved the errors Grade 11 learners commit in algebra than the TTM. / College of Education / M. Ed. (Mathematics Education)

The aim of this study was to investigate the effect of context-based problem solving instruction (CBPSI) on the problem solving performance of Grade 10 learners, who performed poorly in mathematics. A cognitive load theory (CLT) was used to frame the study. In addition, CLT was used to: 1) facilitate the interpretation and explanation of participants‟ problem solving performance; and, 2) influence the design of CBPSI to hone participants‟ problem solving skills. The study was conducted in the Gauteng province of South Africa and involved a two-week intervention program in each of the nine participating high schools. Participants consisted of 783 learners and four Grade 10 mathematics teachers. A non-equivalent control group design was employed, consisting of a pre- and post- measure. In addition, classroom observations and semi-structured interviews were conducted with teachers and learners. Teachers employed conventional problem solving instructions in four control schools while the researcher implemented CBPSI in five experimental schools. Instruction in experimental schools entailed several worked-out context-based problem solving examples given to participants in worksheets. The main aspects of CBPSI embraced elements of the effects of self-explanation and split-attention, as advocated by CLT. Due to the design of CBPSI participants in experimental schools became familiar with the basic context-based problem solving tasks that were presented to them through the worked-out example samples. In turn, the associated cognitive load of problem solving tasks was gradually reduced. The principal instrument for data collection was a standardized Functional Mathematics Achievement Test. The pre-test determined participants‟ initial problem solving status before intervention. A post-test was given at the end of intervention to benchmark change in the functionality of CBPSI over a two-week period. Using one-way analysis of covariance (ANCOVA), Analysis of Variance (ANOVA), and other statistical techniques the study found that participants in experimental schools performed significantly better than participants in control schools on certain aspects of problem solving performance. In addition, semi-structured interviews and classroom observations revealed that participants rated CBPSI highly. On the whole, the study showed that CBPSI is an effective instructional tool to enhance the problem solving performance of Grade 10 mathematics learners. / Mathematics Education / D. Phil. (Mathematics, Science and Technology Education)

För att lyckas lösa problem och använda kunskap behöver en person först ha lärt sig grundläggande kunskap om problemområdet. Sådant lärande kräver att den lärandes arbetsminne inte överbelastas med oändamålsenlig information. Studien undersöker effekten av lärandetekniken worked examples, som visats vara effektiv för att inte överbelasta arbetsminnet inom ämnen som fysik och matematik. Worked examples kommer från cognitive load theory och här undersöks teknikens effekt inom biologiundervisning, med fokus på ämnesområdet ekologi. Högstadieelevers kunskap inom ekologi mättes, varpå de inom undervisning antingen arbetade med worked examples eller instuderingsfrågor. Därefter mättes deras kunskapsnivå återigen, för att på så vis jämföra metodernas effekt på deltagarnas lärande. Elever som lärts med worked examples visade på en större kunskapsutveckling gällande snarlika uppgifter som de övat på, medan kunskapsutveckling för frågor med andra lösningsmetoder gav tvetydigt resultat. Tekniken worked examples har härmed visats sig vara en användbar teknik inom ämnesområdet ekologi inom biologiundervisningen. Den kan med fördel användas under initial-inlärningsfas inom biologiämnet för att hjälpa elever förvärva kunskap.

Cette recherche démontre que, compte tenu des tendances passées dans les comportements individuels face à la participation au marché du travail, l’augmentation de l’âge normal de la retraite n’est ni urgente ni nécessaire au Canada si son seul objectif est de pallier une augmentation de la durée de la retraite. Par ailleurs, si l’accueil d’un nombre toujours grandissant d’immigrants alimente la croissance de la main-d’œuvre, il entraîne aussi un déficit fiscal non négligeable. Celui-ci est toutefois en bonne partie lié au sous-emploi de cette main-d’œuvre potentielle; sous-emploi qui affecte aussi la population native, alimentant ainsi les risques de pénurie de main-d’œuvre. D’une part, et contrairement à l’opinion répandue selon laquelle l’allongement de la vie a été accompagné d’un rétrécissement du nombre d’années dédiées au travail, la durée de vie au travail en 2016 a augmenté de 4,96 ans et représente une part plus importante de l’espérance de vie, soit 3,55 points de pourcentage, comparé à son niveau en 1981. En outre, bien que l’évolution de la structure par âge de la population ait exercé une pression à la baisse (−11,7%) sur la croissance de l’offre agrégée de travail, les changements de comportement individuel quant à la participation au travail (19,3%) et les heures travaillées (5,8%) ont plus que compensé cet effet, entre 1981 et 2016. Au cours de cette période, les comportements individuels, notamment la participation des femmes au marché du travail, ont connu de profonds changements. Si ces changements étaient déjà connus et pleinement documentés, la quantification de leur contribution à l’offre individuelle et agrégée de travail le sont moins. Cette étude vient combler ce vide. Par exemple, et comme on pouvait s’y attendre, la participation des femmes au marché du travail a été la principale source de l’offre additionnelle de travail entre 1981 et 2016, contribuant 9,6 ans (contre 0,25 an pour les hommes) au changement de la durée de vie au travail. Au vu de ces résultats, le vieillissement de la population n’a pas encore entraîné une diminution de la durée de la vie active qui justifierait une augmentation de l’âge normal de la retraite au Canada. D’autre part, si l’immigration explique à elle seule 32,9% de l’augmentation de l’offre de travail entre 1981 et 2016, cette contribution n’est pas à coût nul. Par exemple, entre 1997 et 2015, les immigrants, comparés aux natifs du même âge, ont reçu 110$ de plus et contribué 3 520$ de moins en transferts publics. Ainsi, au même âge, l’immigrant moyen a reçu 3 640 en transferts nets de plus que le natif moyen. Toutefois, 85% de ce surplus provient des déséquilibres sur le marché du travail, dont le sous-emploi de cette main-d’œuvre potentielle. En effet, les résultats de cette recherche montrent que le sous-emploi représente un défi important dans un contexte de vieillissement de la population et de pénurie de main-d’œuvre appréhendée. S’il touche plus durement la population immigrante, il affecte aussi les natifs. Ainsi, en moyenne entre 1981 et 2016, 20,1% des travailleurs canadiens ont été en situation de sous-emploi, alors que le plein emploi aurait contribué à l’ajout de 1,5 million (±0,2) de travailleurs équivalent temps plein. Ces résultats découlent de l’application de plusieurs méthodes notamment la méthode de Sullivan (Sullivan, 1971), le modèle de changement continu (Horiuchi et al., 2008) ainsi que l’optimal matching et l’analyse des clusters sur un large éventail de données. Les sources de données incluent les recensements, les estimations de la population, les enquêtes sur la main-d’œuvre, la santé, et la consommation, au Canada et aux États-Unis. Cette recherche vient nuancer certaines des conséquences prétendues du vieillissement de la population sur la main-d’œuvre canadienne, tout en apportant un nouvel éclairage sur les solutions à mettre de l’avant afin de faire face à certains défis au cours des prochaines décennies. Si l’immigration peut ici jouer un rôle non négligeable, un meilleur arrimage entre l’offre et la demande de travail réduirait le sous-emploi parmi l’ensemble de la population canadienne, tout en améliorant leur niveau de vie. Les discussions sur l’augmentation de l’âge normal de la retraite ou des quotas d’immigration ne peuvent ignorer un tel constat. / This research demonstrates that, given past trends in individual behaviour in the labour market, increasing the normal retirement age is neither urgent nor necessary in Canada if its sole purpose is to offset an increase in the duration of retirement. Moreover, while the inflow of ever-increasing numbers of immigrants fuels labour force growth, it also creates a significant fiscal deficit. However, this deficit is largely related to the underemployment of this potential workforce, which also affects the native population, thus fuelling the risk of labour shortages. On the one hand, and contrary to the widespread opinion that population ageing has led to shrinking worklife for financing longer lifespan, Worklife Duration increased by 4,96 years and 3,55 percentage points of life expectancy over the last four decades. Furthermore, although the change in the age structure of the population has put a slight downward pressure (−11,7%) on the growth of aggregated labour supply, changes in individual behaviour regarding labour participation (19,3%) and worked hours (5,8%) have more than compensated for this effect between 1981 and 2016. During this period, individual behaviours, including women’s participation in the labour market, have undergone profound changes. While these changes were already known and fully documented, their contribution to individual and aggregate labour supply is less so. This study fills this gap. For example, and not surprisingly, women’s participation in the labour market was the main source of additional labour supply between 1981 and 2016, contributing 9,6 years (compared to 0,25 year for men) to the change in worklife duration. Given these results, population aging has not yet resulted in a decrease in working life which would justify an increase in the normal retirement age in Canada. On the other hand, while immigration alone accounts for 32,9% of the increased labour supply between 1981 and 2016, this contribution is at not zero cost. For example, between 1997 and 2015, immigrants, compared to natives at the same age, received $110 more and contributed $ 3 520 less, in public transfer. As a result, the average immigrant has received $3 640 in net transfer more than the average native. However, 85% of this deficit arises from the labour market imbalances such as the underemployment of this potential labour supply. Indeed, the results of this research show that underemployment represents a major challenge in the context of an aging population and a perceived labour shortage. While it affects the immigrant population most severely, it is also prevalent among native workers. Thus, on average, between 1981 and 2016, 20,1% of Canadian workers were underemployed, while full employment would have contributed an additional 1,5 million (±0,2) full-time equivalent workers. This study uses various methods, including the Sullivan method (Sullivan, 1971) and the model of continuous change (Horiuchi et al., 2008), as well as optimal matching and cluster analysis on a wide range of data. The data sources include censuses, population estimates, labour force, and health and consumer surveys in Canada and the United States. This research brings new evidence to the debates around the consequences of population aging on the Canadian workforce while shedding new light on the solutions to be put for facing the challenges in the coming decades. While immigration can play an important role, a better match between labour supply and demand would reduce underemployment among the Canadian population while improving their standard of living. Discussions about increasing the normal retirement age or immigration quotas cannot ignore such a finding.

SAMMANFATTNING Bakgrund Elevers grupparbeten utgör en betydande del av HKK-undervisningen. Tidigare forskning kring elevers grupparbeten i allmänhet är omfattande, men forskning gällande elevers grupparbeten inom HKK är ytterst begränsad. Som utpräglat processämne är det av största vikt att eleverna ges möjlighet att träna på praktiska moment inom hem- och konsumentkunskap (HKK), för att eleverna ska kunna utveckla kunskap i handling vilket sedermera ska bedömas av undervisande lärare. Syfte Syftet med studien var att utforska lärares uppfattningar, upplevelser och erfarenheter av grupparbete i HKK. Metod Kvalitativa intervjuer genomfördes med tio HKK-lärare runtom i Sverige. Intervjuerna analyserades med stöd av kvalitativ innehållsanalys. Resultat Det mest framträdande resultatet i studien var att arbetsformen grupparbete var dominerande i såväl praktiskt som teoretiskt arbete inom HKK. Ramfaktorer påverkade, styrde och begränsade undervisningen. Samarbete, kamratlärande, trygghet och praktisk träning var främsta syften med grupparbeten inom HKK. Det sociala klimatet, elevernaskunskapsnivå och särskilda behov var de faktorer som främst togs i beaktning vid sammansättning av elevgrupper. Lärarnas arbete kring elevgruppernas varaktighet skilde sig åt. Observationer var den vanligaste bedömningsformen när elever arbetade i grupp. Bedömning av elever som arbetade i grupp upplevdes vara svårt och utmanande bland lärarna i studien. Slutsats Grupparbete som undervisningsmetod framstår som rådande kutym inom ämnet. Studien påvisade brister med denna undervisningsmetod, främst utifrån bedömningsaspekten. Med mer noggrant uttänkta strategier för varför, hur och när det vore lämpligt att använda grupparbete som undervisningsmetod anser vi att HKK-läraren har möjlighet att höja kvaliteten på såväl undervisning som bedömning. / ABSTRACT  Background Students' group work constitutes a significant part of the teaching in Home and Consumer Studies (HCS). Previous research on students 'group work in general is extensive, but research on students' group work within HCS is extremely limited. As a distinct process subject, it is of the utmost importance that students are given the opportunity to practice practical elements in HCS, so that students can develop ”knowledge in action”, which will be assessed by the teacher.  Objective The aim of the study was to explore the teachers’ perceptions and experiences regarding group work in HCS.  Method Qualitative interviews were conducted with ten teachers in HCS within Sweden. The interviews were analyzed on the basis of content analysis.  Results The most prominent result in the study was that group work was dominant in both practical and theoretical work within HCS. Framework factors influenced, controlled and limited teaching. Cooperation, peer learning, safety and practical training were the main purposes of group work within HCS. The social climate, the students' level of knowledge and special needs were the factors that were mainly taken into account when composing student groups. The teachers' work on the duration of the student groups differed. Observations were the most common form of assessment when students worked in groups. Assessment of students who worked in groups was perceived as difficult and challenging among the teachers in the study.  Conclusion Group work as a teaching method appears to be the prevailing custom within the subject. The study demonstrated shortcomings with this teaching method, mainly based on the assessment aspect. With more carefully thought out strategies for why, how and when it would be appropriate to use group work as a teaching method, we believe that the HCS teacher has the opportunity to raise the quality of both teaching and assessment.