Den här studien syftar till att undersöka hur elevers matematikprestationer påverkas av eventuell prov- och / eller matematikångest, om det finns åtgärder som reducerar eventuellprov- och / eller matematikångest och om lärarens sätt att examinera har betydelse. För att besvara syftet söker studien svar på hur matematiklärare förstår prov- och / eller matematikångest, på vilket sätt de beskriver att de försöker hjälpa elever att reducera sådan ångest och om matematiklärare ser examinationsformen som faktor för utlösande av prov- och/ eller matematikångest. Resultaten visar att provångest är situationsbunden och utlöses i stressande situationer när personer tror att de befinner sig i en bedömningssituation. Det kan leda till sämre förmåga att koncentrera sig på uppgifterna. Det finns utöver detta risk att den utlösta provångesten triggarigång matematikångest, vilket i sin tur kan leda till ytterligare sämre förmåga att koncentrera sig på uppgifterna, försämrad prestation och dåliga provresultat. Matematikångest kan också utlösas på grund av social påverkan, dåligt självförtroende samt biologiska faktorer, den beror således inte enbart på provångest. För att reducera provångest krävs att lärare får kunskap om hanteringen av känslor som uppstår så att de kan hjälpa elevernaatt förstå och handskas med sina känslor. Åtgärder mot matematikångest handlar om att förebygga att elever hamnar efter i grundläggande kunskaper i matematik, alternativt reparera brister så fort de upptäcks och att undvika och bearbeta negativa associationer förknippat med matematik. Lärare som intervjuades i denna studie hade endast begränsad kunskap om provångest ochmatematikångest och om hur dessa kan reduceras eller förebyggas. Deras svar antydde dessutom att de inte hade kännedom om att det är två olika typer av ångest och att dessa behöver olika sätt för att reduceras eller åtgärdas. De använde inte variation av examinationsformer som ett medel för att hjälpa sina elever trots att de i princip var överens om att olika examinationsformer kan uppfattas som olika stressande och att alternativa examinationsformerskulle kunna reducera denna stress som leder till provångest och eventuellt vidare till utlösandet av matematikångest. Konsekvensen av detta är att elever inte får den hjälpen de behöver, eller att de får fel hjälp och att de därmed riskerar att misslyckas trots att det hade varit möjligt att lösa.

In introductory biology, college students are taught to predict how populations will grow and change over time by using population growth models. These models are commonly represented as mathematical equations. However, students consistently struggle when math and biology concepts intersect in the classroom, and these struggles lead to suboptimal understanding of how mathematical population models are designed and used. Education literature suggests that students may struggle with population modeling because of math anxiety, the high cognitive load of the task, and the lack of scaffolding for abstract concepts. In our study, we sought to improve student mastery modeling exponential growth, logistic growth, and Lotka-Volterra predator-prey interactions through using pictorial diagrams in modeling pedagogy. We predicted that these diagrams would reduce the amount of triggered math anxiety, lower the cognitive load of the task through reducing element interactivity, and allow for a more scaffolding for abstract symbols through a pictorial representation bridge. To test the effectiveness of population diagrams, we created two versions of a population modeling lesson plan: one version taught using diagrams then equations, while the other taught using purely equations. We also designed practice and assessment questions that tested calculation and model-building ability. We assessed math anxiety, scientific reasoning ability, and math ability at the beginning of the semester and state anxiety, effort of tasks, and difficulty of tasks during each lesson. Over 200 students from a non-major biology course were randomly assigned to each group, and all were given a pre-assessment, four lessons, a practice test, and a unit test on population modeling. Our findings show that while the addition of pictorial models to the traditional pedagogy did not have a significant effect on exponential and logistic growth model mastery, students that were exposed to predator-prey diagrams were more able to create a new model for a three-level predator-prey interaction than students that were only given traditional pedagogy. In addition, students who were exposed to predator-prey interaction diagrams before they derived equations reported a lower cognitive load than students who were only exposed to equations. Although diagrams were not a more helpful calculation tool for students than traditional equations, using population diagrams before to equation derivation may help improve student mastery of growth model creation.

This research study was motivated by a hypothesis, generated on the basis of formal and informal observations, personal and professional experiences, discussions with prospective teachers and a pilot study conducted by this author; that pre-service teachers have a high level of mathematics anxiety and negative attitudes about mathematics. The primary purpose of this research was to examine the relationship between mathematics anxiety and pre-service teachers. The secondary purposes of this study were to examine the relationship between anxiety and performance and to examine the relationship between math anxiety, test anxiety, and stereotype threat. A quantitative experimental research design was used to investigate the research questions. The population consisted of prospective teachers at colleges and universities in Louisiana. The sets of data are mathematics anxiety of prospective teachers, a test anxiety inventory and a mathematics performance task. A personal data questionnaire was used to gather demographic information and attitudinal information about the participants. The implications of this study for elementary teacher education programs point to increased attention on the mathematics anxiety of pre-service teachers. This process is two-fold. One, it is recommended that pre-service teachers be made aware of their mathematics anxiety level and their attitudes about mathematics and two, it is recommended that teacher education programs acknowledge and address the importance of these affective variables and their role in pedagogy.

本研究主要目的是以文獻分析、問卷調查、潛在成長模式等方法探討數學焦慮、數學學習動機與數學學業成就等三個變項的縱貫模式及因果結構模式。根據五百二十九位國三學生所填的五波調查問卷資料，進行兩部分研究。 研究一乃在估算數學焦慮、數學學習動機、數學學業成就的潛在改變量模式及 數學焦慮、數學學習動機、數學學業成就兩兩之間的因果結構模式。結果發現1.數學焦慮縱貫模式上，符合「焦慮遞增理論」；2.數學學習動機縱貫模式上，符合「動機先升後降理論」；3.數學學業成就縱貫模式上，符合「成就先升後降理論」； 4.數學焦慮與數學學習動機因果結構模式上，符合「動機焦慮交互激發效果理論」；5.數學焦慮與數學學業成就因果結構模式上，符合「焦慮成就交互抑制效果理論」；6.數學學習動機與數學學業成就因果結構模式上，符合「動機成就交互激發效果理論」。 研究二則依據研究一二變項因果結構統計驗證成立的三套理論，建構出三變項因果結構六模式，並驗證有無中介效果。結果顯示，1.前焦慮、中動機、後學業成就因果模式上，符合「動機未完全中介前焦慮、後學業成就理論」；2. 前動機、中焦慮、後學業成就因果模式上，符合「焦慮未完全中介前動機、後學業成就理論」；3.前焦慮、中學業成就、後動機因果模式上，符合「學業成就未完全中介前焦慮、後動機理論」；4.前學業成就、中焦慮、後動機因果模式上，符合「焦慮未完全中介前學業成就、後動機理論」；5. 前動機、中學業成就、後焦慮因果模式上，符合「學業成就未完全中介前動機、後焦慮理論」；6.前學業成就、中動機、後焦慮因果模式上，符合「動機未完全中介前學業成就、後焦慮理論」。 除了上述結果外，研究也對數學焦慮、數學學習動機與數學學業成就縱貫模式的趨勢與時間效果量，國三學生轉折點界定，數學焦慮、數學學習動機與數學學業成就適當模式產出及個別中介角色剖析有深入探討。 / This study, using literature review, questionnaire survey, and latent growth model, investigated the longitudinal model and causal model among math anxiety, learning motivation, and academic achievement. After collecting 529 students with 5 waves, I conducted two studies. The purpose of study 1 was to estimate the latent change model and the causal model of math anxiety, learning motivation, and academic achievement. Results showed that 1. The anxiety increasing theory was supported by the math anxiety longitudinal model. 2. The first increasing then decreasing theory was supported by the math learning motivation longitudinal model. 3. The first increasing then decreasing theory was supported by the math academic achievement longitudinal model. 4. The reciprocal activated effect theory was supported by the math anxiety and learning motivation causal models. 5. The reciprocal inhibitive effect theory was supported by the math anxiety and academic achievement causal models. 6. The reciprocal activated effect theory was supported by the math learning motivation and academic achievement causal models. According to the final three theories stated above and proved by study 1, I constructed the six causal models in order to verify the mediated effects of math anxiety, math learning motivation, and math academic achievement. I found that 1. Math learning motivation did not mediate fully the effects on early math anxiety and late math academic achievement. 2. Math anxiety did not mediate fully the effects on early math learning motivation and late math academic achievement. 3. Math academic achievement did not mediate fully the effects on early math anxiety and late math learning motivation. 4. Math anxiety did not mediate fully the effects on early math academic achievement and late math learning motivation. 5. Math academic achievement did not mediate fully the effects on early math learning motivation math and late math anxiety. 6. Math learning motivation did not mediate fully the effects on early math academic achievement and late math anxiety. In addition, the research also explored the longitudinal model trend and effect, the key period for 3rd year junior high school students, the proper models, and the mediated roles among math anxiety, learning motivation, and academic achievement.

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2017-01-03T13:16:07Z No. of bitstreams: 1 TeseACM.pdf: 1747171 bytes, checksum: d5d56450329e9a9a208138faa6c9a898 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2017-01-16T17:21:51Z (GMT) No. of bitstreams: 1 TeseACM.pdf: 1747171 bytes, checksum: d5d56450329e9a9a208138faa6c9a898 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2017-01-16T17:22:04Z (GMT) No. of bitstreams: 1 TeseACM.pdf: 1747171 bytes, checksum: d5d56450329e9a9a208138faa6c9a898 (MD5) / Made available in DSpace on 2017-01-16T17:22:13Z (GMT). No. of bitstreams: 1 TeseACM.pdf: 1747171 bytes, checksum: d5d56450329e9a9a208138faa6c9a898 (MD5) Previous issue date: 2016-10-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Mathematics anxiety is characterized by a specific set of unpleasant physiological, cognitive and behavioral reactions to any mathematical stimuli or mathematics learning contingencies. This paper had as a general objective to look for evidence of validity of assessment and intervention tools related to mathematics anxiety and to this end, the research was divided into two studies. The study part is intended to search for evidence of validity of the Mathematics Anxiety Scale (MAS). It is divided into three steps aiming in order to investigate the main objectives such as verify evidence of the inner structure of the MAS; check out correlations between high and low scores on the MAS and school performance in subject matters like mathematics, portuguese, history and geography; expand the application of the MAS in the South, Midwest and Northeast in Brazil and observe possible differences in average scores of mathematics anxiety in each region, taking into account students’ gender, school year (grades) and term. The second study aimed to verify the effectiveness of an intervention program to math anxiety and it was done in a single step. On the first study, the results in step 1, by Exploratory and Confirmatory Data Analysis, indicated that the MAS tends to show a structure with two dimensions. In part 2, the results showed that there was significant and positive correlation between MAS total score and performance in mathematics, in eleven two-month terms analyzed; Portuguese, in six two-month terms; History; in twomonth terms; Geography, in six two-month terms. In the third part, the results showed significant difference in MAS average in relation to the gender variable in the Midwest, southern regions and in the general sample. Referring to the period variable, there was also a significant difference in the Midwest, Southeast and also, in the general sample. On the school year variable, the significant differences in MAS average occurred in the Midwest and in the general sample. In the Midwest, the significant differences in MAS scores occurred between the 1st year of high school (9th grade) and the 6th and 7th years of elementary school. Significant differences were also observed between the 3rd grade and the 8th grade; the 6th grade and 8th and 1st grades; the 7th grade and 1st and 8th grades; and the 8th grade and 3rd, 6th and 7th grades. In the general sample, the differences between the 1st grade of high school (9th grade) and the 6th and 7th grades of elementary school. In relation to the general objective of this paper which is about the search for evidence of validity of an assessment tool and the effectiveness of an intervention, both concerned with math anxiety, data supporting positive evidence for carrying on using MAS and to the intervention were found in this research. Although the last one was only an initial study and thus it is still not possible to indicate whether it is effective, but the results are promising. / A ansiedade à matemática é caracterizada por um conjunto específico de reações fisiológicas desagradáveis, cognitivas e comportamentais diante de qualquer estímulo matemático ou contingências de aprendizagem de matemática. Esse trabalho teve como objetivo geral buscar evidências de validade de ferramentas de avaliação e intervenção relacionadas à ansiedade à matemática e para isso o trabalho foi dividido em dois estudos. O primeiro estudo é a busca de evidências de validade da Escala da Ansiedade à Matemática – EAM – dividida em três etapas para a investigação dos respectivos objetivos específicos: verificar evidências da estrutura interna da EAM; verificar correlações entre altos e baixos escores na escala EAM e desempenho escolar nas disciplinas de matemática, português, história e geografia; ampliar a aplicação da EAM na região Sul, Centro-Oeste e Nordeste e observar possíveis diferenças de média de escores de ansiedade à matemática em cada região, considerando as variáveis gênero, ano escolar e período. O segundo estudo teve como objetivo verificar a eficácia de um programa de intervenção de ansiedade à matemática e abrangeu apenas uma etapa. Sobre o primeiro estudo, os resultados na etapa 1 por meio da Análise Fatorial Exploratória e Confirmatória, indicaram que o instrumento EAM tende a apresentar uma estrutura com duas dimensões. Na etapa 2, os resultados mostraram que houve correlação significativa e positiva entre escore total da EAM e desempenho em: matemática, em onze bimestres analisados; português, em seis bimestres; história; em dois bimestres; geografia, em seis bimestres. Na terceira etapa, os resultados apontaram diferença significativa de média na EAM, em relação à variável gênero nas regiões Centro-Oeste, Sul e na amostra geral. Referente à variável período, também houve diferença significativa quando analisadas as regiões Centro-Oeste, Sudeste e também, na amostra geral; sobre a variável série, as diferenças significativas na média. da EAM ocorreram na região Centro-Oeste e na amostra geral. Na região Centro-Oeste as diferenças significativas na pontuação da EAM ocorreram entre o 1º ano do Ensino Médio e o 6º e 7º anos do Ensino Fundamental. Também foram observadas diferenças significativas entre o 3º ano e o 8º ano; o 6º ano e 8º e 1º anos; o 7º ano e 1º e 8º anos; e o 8º ano e 3º, 6º e 7º anos; na amostra geral as diferenças entre o 1º ano do Ensino Médio e a 6º e 7º anos do Ensino Fundamental. Em relação ao objetivo geral do estudo, sobre a busca de evidências de validade para um instrumento de avaliação e da eficácia de uma intervenção, ambos para ansiedade à matemática, na presente pesquisa foram encontrados dados que sustentam evidências positivas para a continuação dos estudos com a EAM e para a intervenção, embora esse último tenha sido apenas um estudo inicial e por isso, ainda não é possível indicar se possui eficácia, mas os resultados são favoráveis.

En systematisk litteraturstudie om vilka faktorer som kan orsaka matematikängslan hos elever i grundskolan och hur lärare kan arbeta för att stärka elevernas självförtroende och hjälpa dem att minska denna ängslan. Vi människor föds inte med matematiska förmågor och automatiskt blir antingen bättre eller sämre på matematik, utan vi utvecklas och lär med tiden att bli matematiska. I studien lyfts normer och attityder till matematik fram och problematiseras i samband med elevers matematikängslan. Studiens resultat visar att det framför allt är yttre sociala faktorer,normer och negativa handlingar som påverkar elevers matematikängslan. Detta kan leda till att elever utvecklar ett lägre självförtroende och negativa attityder till ämnet matematik. Det kan därmed vara svårt att bryta detta då det blir en negativ spiral, vilket kan resultera i att elever ser på sig själva som mindre matematiska. Men genom att bygga bra lärar-elev-relationer, stärka elevens självförtroende och skapa positiva attityder och goda normer till ämnet matematik så 3kan lärare hjälpa eleven att minska denna ängslan. Därför ligger ett stort ansvar på att lärare utvecklar kunskaper i hur de kan bemöta elever med matematikängslan. / A systematic literature review on factors that could cause math anxiety in primary school students and how teachers can work to strengthen students' self-confidence and help them reduce this anxiety. We humans are not born with mathematical abilities and automatically become either better or worse at mathematics, but we develop and learn over time to become mathematical. We highlight norms and attitudes to mathematics in the study and problematize them in connection with students' mathematics anxiety. The results of the study indicate that it is most social factors, norms and negative acts and comments that affect students' math anxiety. This leads to developing lower self-confidence and negative attitudes towards the subject of mathematics. This could be difficult to break as it becomes a negative spiral, which results in the student seeing themselves as less mathematical. But by building good teacher-student relationships, building the student's self-confidence, and creating positive attitudes and good norms towards the subject of mathematics, teachers can help the student to reduce this anxiety. Therefore, teachers have a responsibility to learn how they can help students with math anxiety.

La présente étude s’intéresse aux choix de filières de formation des filles comparées aux garçons. La présence des filles dans les filières de formation dans le domaine des sciences, de la technologie, du génie et de la mathématique (STGM) est moins importante que celle des garçons. Ce fait est documenté dans la plupart des pays industrialisés (OCDE, 2013). Les décideurs sont préoccupés par cette sous-représentation des filles et des femmes dans ces domaines et s’affairent à comprendre le phénomène, dans le but d’agir pour changer la situation (Drouin et al., 2008; MCCCF, 2011). Or, les facteurs d’influence pour expliquer cet écart entre les garçons et les filles sont nombreux et ne font pas l’objet d’un consensus dans la littérature (Ceci et al., 2009). Toutefois, plusieurs s’entendent pour dire que les mathématiques, importantes dans les profils de formation en STGM, et la façon dont les filles les perçoivent pourraient expliquer, en partie, leurs choix (Rowan-Kenyon et al., 2012 et Wang et al., 2013). Ces auteurs ont aussi suggéré que le contexte social et les croyances des filles au sujet des mathématiques seraient déterminants dans le processus de choix impliquant cette discipline. Un modèle théorique sociocognitif, inspiré par les travaux de Lent et al, (1994-2006), expliquant le processus de choix scolaires et professionnels a permis de conceptualiser les liens entre les déterminants socio-motivationnels spécifiques aux mathématiques. L’objectif général de la présente étude était de mieux documenter l’importance des mathématiques dans les choix de filières de formation menant aux carrières en STGM. Spécifiquement, nous avons examiné les relations entre le rendement en mathématiques, la perception des élèves quant au contexte social (soutien des parents et enseignants), leurs attentes de réussite, la valeur qu’ils accordent aux mathématiques (sentiment d’autoefficacité, anxiété, perception de l’utilité et intérêt) et les choix de filières de formation générale après leur secondaire (sciences humaines sans mathématiques, sciences humaines avec mathématiques, sciences de la santé et sciences pures). Nous avons exploré les distinctions entre les filles et les garçons. Pour ce faire, 1129 élèves finissants ont été questionnés au sujet de leurs motivations en mathématiques et de leurs intentions de formation post-secondaire. Par la suite, une comparaison entre les 583 filles et les 543 garçons a été réalisée par des analyses de régression logistiques multinomiales. Les résultats montrent que plusieurs déterminants permettent de dégager des similitudes et des différences quant aux choix de filières de formation des filles et des garçons. D’abord, il semble que pour la plupart des élèves, filles ou garçons, un rendement élevé et un important soutien des enseignants tel que perçu par les élèves à la fin du secondaire est davantage lié aux choix de filières en sciences pures et en sciences de la santé qu’en sciences humaines avec ou sans mathématiques. Toutefois, le soutien des parents perçu est plus déterminant pour les filles qui choisissent les sciences de la santé que pour les garçons. Le soutien des enseignants perçu est plus déterminant pour les garçons qui choisissent les sciences humaines que pour les filles. Aussi, un faible sentiment d’autoefficacité en mathématiques serait associé au choix de filières en sciences humaines, alors qu’une forte anxiété en mathématiques chez les filles serait associée aux filières en sciences de la santé. Pour les garçons, c’est davantage l’intérêt en mathématiques qui est déterminant pour choisir la filière des sciences pures. La perception de l’utilité des mathématiques est déterminante à la fois pour les garçons et pour les filles qui choisissent les filières de sciences les menant à des carrières en STGM. En somme, nos résultats suggèrent que le soutien en mathématiques de la part des adultes significatifs, tel que perçu par les élèves, est moins prépondérant que les attentes de réussite (sentiment d’autoefficacité et anxiété) et la valeur accordée aux mathématiques (intérêt et utilité perçue) pour comparer les garçons et les filles dans leurs choix de filières. À la lumière des résultats obtenus, il nous semble que l’implantation de mesures, dans les milieux scolaires, pour renforcer le sentiment d’autoefficacité des jeunes filles en mathématiques et surtout pour diminuer leur taux d’anxiété dans cette matière serait une voie prometteuse pour atteindre la parité entre les garçons et les filles dans les filières en STGM. / This study focuses on the choice of training options for girls compared to boys choice. The presence of girls in training courses in the field of science, technology, engineering and mathematics (STEM) is less important than that of boys. This is documented in most industrialized countries (OECD, 2013). Policymakers are concerned about the under-representation of girls and women in these areas and are working to understand the phenomenon in order to take action to change the situation (Drouin et al., 2008; MCCCF, 2011). However, the influencing factors to explain this difference between boys and girls are numerous and are not the subject of a consensus in the literature (Ceci et al., 2009). However, many agree that the mathematics major in STEM’s training profiles, and how girls perceive it might explain, in part, their choices (Rowan-Kenyon et al., 2012 and Wang et al ., 2013). These authors also suggested that, for girls, the social context and beliefs about mathematics would be decisive in the choice process involving the discipline. A socio-cognitive theoretical model, inspired by the work of Lent et al, (1994-2006), explaining the process of educational and occupational choices could help conceptualize the relationship between socio-motivational determinants in the field of mathematics. The main objective of this study was to better document the role of mathematics in the process of choice making leading to careers in STEM. Specifically, we examined the predictive value of mathematics performance, students' perception about the support of the social context (parents and teachers), their expectations of success and the value of mathematics (self-efficacy, perceived usefulness, interest and anxiety) on the choice of general education field after high school (social sciences/humanities with and without mathematics, health sciences and pure sciences). A comparison between girls and boys was made. To reach our goal, 1129 graduating students were questioned about their motivation in mathematics and their post-secondary education intentions. Thereafter, a comparison of the 583 girls and 543 boys was performed by multinomial logistic regression analyzes. The results show that several determinants can both compare and differentiate the choice of training options for girls and boys. First, it seems that for most students, boys and girls, high performance in mathematics and important support from teachers as perceived by the students at the end of high school is more related to the choice of pure science field and health sciences than humanities. However, the support of parents seemed to be more relevant for girls, than for boys, who choose the health sciences. Surprisingly, teacher support as perceived seems to be more relevant for boys than for girls who choose humanities. Also, a low sense of mathematical competence is associated with the choice of humanities courses, while a strong mathematics anxiety in girls is associated with health sciences sectors. For boys, it's greater interest in mathematics which is critical to choose the pure sciences field. The perception of the usefulness of mathematics is crucial for both boys and girls who choose science field leading them to careers in STEM. In sum, our results suggest that support in mathematics from the significant adults, as perceived by students, is less dominant than expectations of success (self-efficacy and anxiety) and the value placed on mathematics (interest and utility perceived) to compare boys and girls in their choice of field. In the light of the results obtained, we believe that the implementation of measures in schools to strengthen the self-efficacy of girls in mathematics and especially to reduce their anxiety levels in this area would be a promising way to achieve parity between boys and girls in STEM fields.