79 research outputs found
The didactic transposition of the fundamental theorem of calculus
No full textUsing the tools of praxeological analysis and didactical transposition analysis, the treatments of the Fundamental Theorem of Calculus in one Norwegian, Grade 13 textbook is analysed, with a particular focus on the development of the logos block of the FTC. The terms structure, functioning and utility, first introduced by Chevallard in 2022, is further to describe different dimensions of the mathematical object at stake. Through the analysis, a lack in the logos relating to the concept of integrability is identified in the textbook, and consequences of this is explored in relation to a set of tasks found in the book.publishedVersio
Introduksjon av tekstbasert programmering i matematikk 1T forankret i matematikk
No full textDenne studien har som utgangspunkt utvikling, realisering og videreutvikling av undervisningsopplegg innenfor introduksjon av programmering i matematikk 1T. Gjennom analyse av utviklingsprosessen og realiseringen ved bruk av didaktisk ingeniørvirksomhet (Strømskag, 2020a) og ATD - den antropologiske teorien for det didaktisk (Chevallard & Bosch, 2020a) - etableres grunnlaget for videreutvikling av undervisningsopplegget basert på datamateriale i form av intervjuer og observasjoner. Innenfor rammeverket ATD tas blant annet praksologi, didaktiske transposisjoner og det å stille spørsmål til verden i bruk, hvorpå prakseologi har størst rolle i analyse og kategorisering av datamateriale fra både utvikling og intervjuer.
Et viktig poeng å understreke i denne studien er ønsket om å ha en matematisk forankring i introduksjonen av tekstbasert programmering. Realiseringen har funnet sted i en 1T klasse, og fra samme klasse finner vi deltakerne som tok del i fokusgruppe intervjuer i etterkant av gjennomføringen.
Studien min viser blant annet at det å ha et veldig åpent undervisningsopplegg, selv innenfor et tema som programmering i matematikk med tilhørende mange løsningsmetoder, kan virke mot sin hensikt. I tillegg har jeg sett at mange elever gir uttrykk for at forkunnskapene de sitter med gjennom blokkprogrammering føles lite anvendbare i overgangen til tekstbasert programmering. En sentral del i videreutviklingen ble derfor å fjerne noe av åpenheten, uten å ta bort muligheten for videre utforskning og heller inkludere flere løsningsmetoder gjennom spesifikke oppgaver. Overgangen mellom blokk- og tekstbasert programmering fikk også en større rolle i videreutviklingen enn hva jeg originalt hadde sett for meg, men basert på intervjuene var dette utvilsomt et viktig element å løfte fram.This study has as its starting point the development, realization and further development of a teaching plan within the introduction of programming in mathematics 1T. Through analysis of the development process and realization using didactic engineering (Strømskag, 2020a) and ATD - the anthropological theory for the didactics (Chevallard & Bosch, 2020a) - the basis for further development of the teaching program is established based on data material in the form of interviews and observations. Within the ATD framework, among other things, praxeology, didactic transpositions and the paradigm of questioning the world are used, whereupon praxeology has the greatest role in the analysis and categorization of data material from both development and interviews.
An important point to emphasize in this study is the desire to have a mathematical foundation in the introduction of text-based programming. The realization took place in a first year high-school class, and from the same group of pupils we find the participants who took part in focus group interviews after the implementation.
My study shows, among other things, that having a very open teaching plan, even within a topic such as programming in mathematics and its many possible solutions, can be counterproductive. In addition, I have seen that many students express that the prior knowledge they have through block programming feels of little use in the transition to text-based programming. A central part of the further development was therefore to remove some of the openness, without taking away the possibility of further exploration and rather including extra methods for solving the same problem through specific tasks. The transition between block and text-based programming also played a bigger role in the further development than I had originally envisioned, but based on the interviews this was undoubtedly an important element to highlight
En prakseologisk analyse av matematikk 1T-elevers arbeid med bokstaver i algebra
No full textI denne studien undersøker jeg en gruppe elever i matematikk 1T sin bruk av bokstaver i algebra. Studien skiller mellom tre forskjellige måter man behandler bokstaver på i matematikk inspirert av Ely og Adams (2012), plassholdere, ukjente og variabler. Plassholdere står for et tall som både er bestemt og kjent innen den samme matematiske konteksten. Ukjente er et tall som er bestemt innenfor en matematisk kontekst, men er ikke kjent, og variabler kan variere innen den samme matematiske konteksten. Studien er en kvalitativ undersøkelse, der det ble gjennomført oppgavebaserte intervjuer med seks elever i matematikk 1T. Formålet er å undersøke hvordan elevenes prakseologier kommer til uttrykk i arbeidet med oppgaver som omhandler plassholdere, ukjente og variabler.
Studien benytter seg av den antropologiske teorien for det didaktiske (ATD) som teoretisk og analytisk rammeverk (Chevallard, 2006). Det ble gjort en prakseologisk analyse av oppgavene som ble gitt til elevene i intervjuene. Basert på de prakseologiske elementene type oppgave T, teknikk τ, teknologi θ og teori Θ blir elevenes muntlige og skriftlige besvarelse analysert. Studien undersøker hvordan elevene uttrykker de prakseologiske elementene i oppgaver som stiller krav til forståelse av plassholdere, ukjente og variabler.
Studien viser at denne gruppen elever i matematikk 1T har manglende teknologi θ og teori Θ knyttet til oppgaver som omhandler plassholdere, ukjente og variabler. Den teknologi θ som elevene innehar er ofte knyttet til tidligere erfaringer med andre lignende oppgaver. I flere tilfeller har elevene tilgang til teknikkene τ som kreves for å løse oppgavene, men kobler ikke teknikkene τ sammen med type oppgave T. Dette fører til at elevene ikke evner å løse oppgavene på grunn av den manglende teknologien θ. Den konseptuelle vanskelighetsgraden på oppgavene påvirker elevenes evne til å løse oppgavene. På grunn av dette blir den manglende evnen til å koble typen oppgave T til teknikker τ tydeligere i oppgaver som omhandler variabler enn plassholdere, siden den konseptuelle forståelsen av en variabel er vanskeligere. Undersøkelsen viser at den mangelfulle logos-blokken begrenser elevenes evne til å løse oppgaver som inneholder bokstaver.In this study, I analyze a group of “matematikk 1T” students' use of letters in mathematics. The study distinguishes between three different ways of treating letters in mathematics inspired by Ely and Adams (2012), placeholders, unknowns and variables. Placeholders stand for a number that is determined and known within the same mathematical context. Unknowns stand for a number that is determined within a mathematical context but is not known, and variables can vary within the same mathematical context. The study is a qualitative study, where task-based interviews were conducted with six “matematikk 1T” students. The purpose is to identify how the students' praxeology is expressed in their work with tasks dealing with placeholders, unknowns, and variables.
The study uses the anthropological theory of the didactic (ATD) as a theoretical and analytical framework (Chevallard, 2006). It is a praxeological analysis of the tasks given to the students in the interview. Based on the praxeological elements type of task T, technique τ, technology θ and theory Θ, the students' oral and written responses are analyzed. The study examines how the students express the praxeological elements in tasks that require understanding of placeholders, unknowns, and variables.
The study shows that this group of “matematikk 1T” students has a lack of technology θ and theory Θ related to tasks involving placeholders, unknowns and variables. The technology θ possessed by the students is often linked to previous experiences with other similar tasks. In many cases, the students have access to the techniques τ required to solve the tasks, but do not connect the techniques τ to the type of task T. This leads to students not being able to solve the tasks due to the lack of technology θ. The conceptual difficulty of the tasks affects the students' ability to solve the tasks. Because of this, the inability to connect the type of task T to techniques τ becomes more significant in tasks dealing with variables than placeholders, since the conceptual understanding of a variable is more difficult. The study shows that the deficient logos block limits students' ability to solve tasks containing letters
Analysis of a university student’s construction of a praxeology for integration tasks
No full textThis study utilizes the model of didactic moments from the Anthropological Theory of the Didactic to examine a university student’s praxeological work pertaining to a set of four integration tasks. The research focuses on themes related to the Fundamental Theorem of Calculus (FTC), which elucidate the technological aspects of the employed techniques. By analyzing the integral calculus content in the textbook used by the student at upper secondary level, the study identifies a potential causal relationship between the textbook’s treatment of integration and shortcomings in the student’s praxeological equipment. Specifically, it is found that an essential element of the FTC—interpreting area in terms of a function—was missing in the textbook’s logos block on integration. Furthermore, the analysis reveals a predominance of algebraic techniques over graphical ones in the student’s performance of the set of tasks. The findings underscore the impact of educational resources on students’ praxeological equipment and highlight the need for a critical evaluation of these resources using didactic transposition analysis. The study advocates developing a praxeological organization for integral calculus in order to guide curriculum designers and textbook authors, thereby bridging the educational gap between secondary and tertiary education and enhancing students’ comprehension of integral calculus.publishedVersio
Korleis forstår nokre elevar på mellomtrinnet og ungdomstrinnet likskapsteiknet?
No full textDenne studien omhandlar elevar på mellomtrinnet og ungdomstrinnet si forståing av likskapsteiknet. Likskapsteiknet er synleg på alle matematiske nivå og er eit symbol som elevar nyttar seg av frå dei startar på skulen. I eigen undervisningskvardag har eg observert misoppfatningar og misbruk av likskapsteiknet hos elevane, og eg har lurt på kvifor det er slik. Derfor enda eg opp med eit forskingsspørsmål for å belyse dette: Korleis forstår nokre elevar på mellomtrinnet og ungdomstrinnet likskapsteiknet? Føremålet med oppgåva er å få ei forståing av korleis elevar kan forstå og nytte likskapsteiknet, og finne ut kva som kan påverke forståinga deira. Det er tidlegare gjort ein del forsking på elevar si forståing av likskapsteiknet (m.a. Falkner et al., 1999; Kieran, 1981; McNeil et al., 2006) og det kjem fram at likskapsteiknet ofte vert tolka som eit operasjonelt symbol, som fortel at ein skal rekne ut eller finne svaret, av elevar. Ekvivalenstolkinga av likskapsteiknet, som viser til at uttrykka på begge sider av likskapsteiknet har same verdi, kan ta lenger tid å få på plass. Det viser seg likevel at med undervisning som legg til rette for det kan elevar utvikle ei slik forståing. Forskingsdesignet i oppgåva er kvalitativt og eg nytta meg av materiale som tidlegare var samla inn av tre forskarar ved Høgskulen i Volda. Materialet som er analysert i studien er transkripsjonar av lydopptak av sju oppgåvebaserte intervju med elevar i femte og åttande klasse. Intervjua vart analysert ut frå to rammeverk som omhandlar matematisk forståing og elevar si forståinga av likskapsteiknet. Med eit lite utval vil ein ikkje kunne sei noko om korleis alle elevar forstår likskapsteiknet, men funna som kjem fram i studien kan gjelde fleire og det kan ha nytteverdi for andre.Funna som er gjort i studien viser at elevane i femte klasse i stor grad forstår likskapsteiknet som ein operator, og at dei har ei instrumentell forståing som kan vere avgrensande for vidare læring. Dei viser likevel teikn til at dei kan utvide forståinga si gjennom rettleiing og diskusjon. Elevane i åttande klasse ser i større grad ut til å forstå likskapsteiknet som eit ekvivalensteikn, sjølv om det truleg ikkje vil gjelde for alle. Dei som viser ei ekvivalenstolking viser også teikn til at dei ser fleire samanhengar og kan vere på veg mot relasjonell forståing. Ut frå funna kan det sjå ut til at elevane si forståing heng saman med deira matematiske kompetanse, kva erfaringar dei har med seg frå tidlegare og korleis dei er eksponert for likskapsteiknet i undervisningThis master thesis examines how students in primary school and lower secondary school understand the equal sign. The equal sign is visible in all levels of mathematics and it is a symbol that students use from the moment they begin their education. In my own teaching I have observed misconceptions and misuse of the equal sign within the classroom and I have wondered what the cause of this could be. Therefore, I formulated a research question that reads as follows: How do some students in primary school and lower secondary school understand the equal sign? The goal of this thesis is to achieve an understanding of how students can understand and use the equal sign and find out which factors can influence their understanding. Former research has been done in the field of students understanding of the equal sign (e.g. Falkner et al., 1999;Kieran, 1981; McNeil et al. 2006) and it is put forward that the equal sign often is interpreted by students as an operational symbol that tells the student to equate or find the answer. The equivalence interpretation, which tells us the expressions on both sides of the equal sign has the same value, can take longer time for students to possess. But it shows that with teaching that facilitates an equivalence interpretation, students can develop this. This is a qualitative study where I have used data previously collected by three researchers at Volda University College. The data analyzed in this study is transcriptions of voice recordings from seven task-based interviews with students in the fifth and eight grade. The interviews were analyzed using two frameworks which deal with mathematical understanding and students` understanding of the equal sign. With limited data it is not possible to say something about how all students understands the equal sign, but the findings may apply to and have value for others. The findings show that the students in fifth grade generally have an operational understanding of the equal sign, and an instrumental understanding which can limit further learning. Even so, they show signs to be able to expand their understanding through guidance and discussion. It looks like the eight grade students to a greater extent can understand the equivalence interpretation of the equal sign. Those who show this interpretation also seem to see more connections and can be on their way to develop a relational understanding as well. One could infer that the students’ understanding is connected to their mathematical competence, alongside the experiences they have had and how they previously have been exposed to the equal sign in their education
The Efficiency of a Mewis Duct in Waves
No full textIn this thesis, the efficiency of a Mewis Duct in waves has been investigated with the use of model tests in the large towing tank at MARINTEK in Trondheim. A ?load-varying? self-propulsion method was used, allowing for calculations without the need for results from a resistance test. Still water, regular and irregular wave conditions have been tested. The vessel model used, M3030 A, was originally used to test the Mewis Duct in still water.Results in still water have been compared to the original test results. Deviations from the original tests have been found, which could be due to increased resistance of the model and bias in the tow force and thrust measurements.Results in regular waves show a consistent increase in the effective wake with the Mewis Duct fitted, but the thrust deduction contains a high amount of scatter. This results in scatter in the hull efficiency, and further in the propulsive efficiency.Uncertainty analysis has been carried out and shows that scatter in the tow force are probably the reason for inaccurate results. It indicates the necessity of accurate measurements of the tow force with the load-varying self-propulsion method
The Efficiency of a Mewis Duct in Waves
No full textIn this thesis, the efficiency of a Mewis Duct in waves has been investigated with the use of model tests in the large towing tank at MARINTEK in Trondheim. A ?load-varying? self-propulsion method was used, allowing for calculations without the need for results from a resistance test. Still water, regular and irregular wave conditions have been tested. The vessel model used, M3030 A, was originally used to test the Mewis Duct in still water.Results in still water have been compared to the original test results. Deviations from the original tests have been found, which could be due to increased resistance of the model and bias in the tow force and thrust measurements.Results in regular waves show a consistent increase in the effective wake with the Mewis Duct fitted, but the thrust deduction contains a high amount of scatter. This results in scatter in the hull efficiency, and further in the propulsive efficiency.Uncertainty analysis has been carried out and shows that scatter in the tow force are probably the reason for inaccurate results. It indicates the necessity of accurate measurements of the tow force with the load-varying self-propulsion method
A Comparative Analysis of Translator Style in the Translation of Jo Nesbø's Harry Hole Series
No full textDet overordna målet med denne oppgåva er å samanlikne to litterære omsetjarar sine stilar i omsetjing frå norsk til engelsk med fokus på kulturspesifikke gjenstandar, faste uttrykk og dialekt. Dette er gjort gjennom å analysere element frå kjeldeteksten og dei tilsvarande omsetjingane i målteksten, og identifisere prosedyrane som vert brukte av omsetjaren. Desse prosedyrane er så kategorisert som enten domestiserande eller framandgjerande for å kunne samanlikne på tvers av hovudkategoriane. Omsetjingane som er analyserte er Police og The Thirst, omsetje av Don Bartlett og Neil Smith, som er omsetjingar av romanane Politi og Tørst skrive av Jo Nesbø. Kvar måltekst (TT) vert analyserte for seg før dei vert samanlikna med kvarandre for å sjå etter likskapar og skilnader mellom omsetjarane sine val. Det er også gjennomført eit intervju med Neil Smith for å få eit klarare syn på korleis omsetjingane til Don Bartlett har påverka omsetjingane hans, og kva andre faktorar som har påverka stilen hans i denne spesifikke omsetjinga. Det denne studien viser er at når det gjeld dei overordna omsetjingsstrategiane, har begge omsetjarane gått for domestisering, noko som bringer omsetjingane nærare målgruppa. Skilnadane mellom omsetjarane kan sjåast på dei lågare nivåa av omsetjingar. Dette kan ein sjå i prosedyrane som er valde, spesielt for kulturspesifikke gjenstandar. Desse skilnadane er det som kan tilskrivast stilen til omsetjarane.The overall aim of this thesis is to compare two literary translators’ styles in translations from Norwegian to English, with a focus on culture-specific items, fixed expressions, and dialect. This has been done through analyzing items from the source text and the corresponding translations in the target text, identifying the procedures used by the translator. These procedures have then been categorized as either domesticating or foreignizing to be able to compare across the main categories. The translations that have been studied are Police and The Thirst, translated by Don Bartlett and Neil Smith respectively, which are translations of the novels Politi and Tørst written by Jo Nesbø. Each target text (TT) is analyzed on its own before the TTs are compared, looking for the similarities and differences between the translators’ choices. An interview with Neil Smith has also been carried out to get a clearer view on how the translations of Don Bartlett has impacted his translations, and what other factors have affected his style in this particular translation. What this study shows is that when it comes to the over-all translational strategies both translators have gone for domestication, bringing the translations closer to the target audience. Where the translators differ are on the lower levels of translations. This can be seen in the procedures chosen, especially for culture-specific items. These differences are what can be ascribed to the style of the translators
Analysis of a University Student’s Construction of a Praxeology for Integration Tasks
No full textThis study utilizes the model of didactic moments from the Anthropological Theory of the Didactic to examine a university student’s praxeological work pertaining to a set of four integration tasks. The research focuses on themes related to the Fundamental Theorem of Calculus (FTC), which elucidate the technological aspects of the employed techniques. By analyzing the integral calculus content in the textbook used by the student at upper secondary level, the study identifies a potential causal relationship between the textbook’s treatment of integration and shortcomings in the student’s praxeological equipment. Specifically, it is found that an essential element of the FTC—interpreting area in terms of a function—was missing in the textbook’s logos block on integration. Furthermore, the analysis reveals a predominance of algebraic techniques over graphical ones in the student’s performance of the set of tasks. The findings underscore the impact of educational resources on students’ praxeological equipment and highlight the need for a critical evaluation of these resources using didactic transposition analysis. The study advocates developing a praxeological organization for integral calculus in order to guide curriculum designers and textbook authors, thereby bridging the educational gap between secondary and tertiary education and enhancing students’ comprehension of integral calculus
The didactic transposition of the fundamental theorem of calculus
No full textUsing the tools of praxeological analysis and didactical transposition analysis, the treatments of the Fundamental Theorem of Calculus in one Norwegian, Grade 13 textbook is analysed, with a particular focus on the development of the logos block of the FTC. The terms structure, functioning and utility, first introduced by Chevallard in 2022, is further to describe different dimensions of the mathematical object at stake. Through the analysis, a lack in the logos relating to the concept of integrability is identified in the textbook, and consequences of this is explored in relation to a set of tasks found in the book.Utilizando las herramientas del análisis praxeológico y el análisis de transposición didáctica, se analizan los tratamientos del Teorema Fundamental del Cálculo en un libro de texto noruego de grado 13, con un enfoque particular en el desarrollo del bloque logos de la FTC. Los términos estructura, funcionamiento y utilidad, introducidos por primera vez por Chevallard en 2022, describen además diferentes dimensiones del objeto matemático en juego. A través del análisis, se identifica en el libro de texto una carencia en los logos relacionada con el concepto de integrabilidad, y se exploran las consecuencias de esto en relación con un conjunto de tareas que se encuentran en el libro
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