Studiens syfte är att undersöka hur behöriga matematiklärare värderar matematikuppgifter och till vilken betygsnivå de kan relateras. Studien har genomförts som en kvalitativ studie baserad på tematisk analys. Åtta professionella matematiklärare har intervjuats och deras uttalanden har analyserats. Studien är inriktad på kursen matematik 3c på gymnasiet. Studien visar att lärare värderar uppgifterna olika vilket kan tyda på utmaningar med att tolka betygskriterier i matematik på gymnasiet. I undersökningen framkommer hur de som är nyexaminerade behöriga lärare visar på en mer generös värdering och relaterar till högre betygsnivå jämfört med de lärare som är mer erfarna. De mer erfarna lärarna visar också gögre grad av samstämmighet när det gäller hur de beskriver kunskapsnivå motsvarande de olika betygsnivåerna jämfört med de nyexaminerade lärarna. De nyexaminerade lärarna uttrycker i vissa fall bristande matematiska kunskaper kopplat till de högre kurser i matematik på gymnaisenivån som de förväntas undervisa på. / The purpose of the study is to investigate how qualified mathematics teachers value mathematics tasks and to which grade level they can be related. The study has been conducted as a case study. Eight actively working mathematics teachers have been interviewed and their statements have been analyzed. The study is focused on the course mathematics 3c at the upper secondary school. The study shows that teachers value the tasks differently, which may indicate challenges with interpreting grading criteria in mathematics at upper secondary school. The survey reveals how those who are newly qualified teachers show a more generous assessment and relate to a higher grade level compared to the teachers who are more experienced. The more experienced teachers also show a higher degree of agreement when it comes to how they describe the level of knowledge corresponding to the different grade levels compared to the newly qualified teachers. In some cases, the newly graduated teachers express a lack of mathematical knowledge linked to the higher courses in mathematics at the upper secondary level that they are expected to teach.

No description available.

Although the Internet is widely used in many areas, its use in school mathematics is at best in its infancy. Studies show that Mathematics teachers have fewer uses for the Internet than teachers of other disciplines. Hence, this research adopted a mixed method approach to investigate what mathematics materials are on the Internet, how teachers are teaching mathematics with the Web and mathematic students' perceptions and engagement with the Internet. This research reviewed the World Wide Web for mathematics materials and found three major groupings of online resources namely interactive resources, non-interactive resources, and communications possibilities. A typology of Web objects was constructed and a database based on a Task-Web object approach was proposed for teacher use. A broad survey was used to elicit information about Internet usage among mathematic teachers. A total of 103 mathematics teachers responded and 15 were interviewed to gain further insight into their usage. Observations of Internet use were also conducted in the classrooms of 4 teachers. The results show that most teachers would like to use the Internet more in their teaching of mathematics but many do not know where and how to do so in an effective way. Statistics, Business Mathematics and Number operations appear to be the more popular topics. Using statistics data from the Web seem to be the Web feature that is most common followed by using the Internet as a resource centre for word problems. Web communications are seldom used. Common constraints teachers face include lack of time, difficulty in planning, lack of knowledge of good Web sites that map to curricula, slow download times, and limited booking times. Students perceive doing activities on the Internet as better than from the textbook because of the amount and variety of information, the better explanations and the change in mode of presentation. Students who have a low comfort level with mathematics wish their teachers would use the Internet. The power of interactive activities on the Internet to engage and motivate these students is due to a variety of reasons such as the element of game play, a change from the routine, its ability to present different conceptual visuals, the independent self paced learning, and quick feedback that came with the use of the Internet. The Internet also enabled students to access difficult to find information and saved them time. The findings also suggest that teachers' persistence in using the Internet could bring about a routine that helps students settle down to the task and stay on task. Teachers' choice and discernment of Web-based activities that are engaging and motivating are paramount to the success of this learning tool. Four Web-based strategies for teaching mathematics were documented and a model of underlying knowledge for teacher practice with the Web was suggested.

For the problem of producing pedagogical step-by-step solutions to mathematical problems in education, standard methods and algorithms used in construction of computer algebra systems are often not suitable. A method of using rules to manipulate mathematical expressions in small steps is suggested and implemented. The problem of creating a step-by-step solution by choosing which rule to apply and when to do it is redefined as a graph search problem and variations of the A* algorithm are used to solve it. It is all put together into one prototype solver that was evaluated in a study. The study was a questionnaire distributed among high school students. The results showed that while the solutions were not as good as human-made ones, they were competent. Further improvements of the method are suggested that would probably lead to better solutions. / För problemet att producera pedagogiska steg-för-steg-lösningar till matematiska problem inom utbildning, är vanliga metoder och algoritmer som används i konstruktion av datoralgebrasystem ofta inte lämpliga. En metod som använder regler för att manipulera matematiska uttryck i små steg föreslås och implementeras. Problemet att välja vilka regler som ska appliceras och när de ska göra det för att skapa en steg-för-steg-lösning omdefineras som ett grafsökningsproblem och varianter av algoritmen A* används för att lösa det. Allt sätts ihop till en prototyp av en lösare vilken utvärderas i en studie. Studien var ett frågeformulär som delades ut till gymnasiestudenter. Resultaten visade att även fast lösningar skapade av programmet inte var lika bra som lösningar skapade av människor, så var de anständiga. Fortsatta föbättringar av metoden föreslås, vilka troligtvis skulle leda till bättre lösningar.

Syftet med denna studie är att undersöka lärarnas upplevelse av elevers missuppfattningar vid inlärning av bråk och sannolikhet samt om det är möjligt att minska missuppfattandet med hjälp av kategorisering av dessa. Genom att fråga matematiklärare om de upplever att eleverna de undervisar ofta har missuppfattningar och om samma missuppfattningar är återkommande, kan vi få en bild av vilka delar av de matematiska begreppen som kan uppfattas svåra av eleverna. De missuppfattningar som tenderar att återkomma kan komma att behöva mer fokus på förklaring. Studien genomfördes genom en surveyundersökning i enkätform som publicerades i grupper som samlar matematiklärare på sociala medier, samt skickades till matematiklärare via mail. Det resulterade i 41 enkätsvar som analyserades genom beskrivande statistik i kombination med en induktiv innehållsanalys. Studien visar att orsaken till att missuppfattningar kopplade till matematiska begrepp kan bero på ett för stort fokus på procedurinriktad undervisning i de tidigare skolåren. Detta upplever lärarna medför att eleverna inte har tillräcklig begreppsförståelse när de börjar på gymnasiet. Det vanligaste åtgärdsförslaget är kopplat till undervisningsstrategier med mer sociokulturella inslag i undervisningen. De allra flesta av studiens deltagare upplever att begreppsförståelse är viktigt och utgör en förutsättning för att klara av både problemlösning och mer avancerad matematik. För att skapa förståelse för matematiska begrepp är det nyttigt för lärare att känna till vanliga missuppfattningar. Kategorisering av missuppfattningar kan därför vara till nytta för lärarna i undervisningen, som ett stöd i lektionsplanering och som ett pedagogiskt verktyg för att utveckla elevernas matematiska kunskaper. / The purpose of this study is to investigate the teachers' experience of students' misconceptions when learning fractions and probability, and whether it is possible to reduce misconceptions by categorizing them. By asking mathematics teachers if they feel that the students they teach often have misconceptions and if the same misconceptions are repeated, we can get a picture of which parts of the mathematical concepts may be perceived as difficult by the students. The misconceptions that tend to recur may need more focus on explanation. The study was carried out through a survey in questionnaire form that was published in groups that bring together mathematics teachers on social media and was also sent to mathematics teachers via email. This resulted in 41 survey responses that were analysed through descriptive statistics in combination with an inductive content analysis. The study shows that the reason for misconceptions connected to mathematical concepts may be due to too much focus on procedure-oriented teaching in the earlier school years. The teachers feel that this means that the students do not have sufficient conceptual understanding when they start high school. The most common proposed measure is linked to teaching strategies with more socio-cultural elements in the teaching. The vast majority of the study's participants feel that conceptual understanding is important and constitutes an essentiality for being able to cope with both problem solving and mathematics at more advanced levels. In order to create an understanding of mathematical concepts, it is useful for teachers to know about common misconceptions. Categorization of misconceptions can therefore be useful for teachers in teaching, as a support in lesson planning and as a pedagogical tool to develop students' mathematical knowledge.

Skolmatematiken och matematikdidaktiken har under de senaste årtiondena genomgått en förändring från ett historiskt fokus på ren räkning och utantillkunskaper mot alltmer processorientering. Det pågår en aktiv debatt om hur framgångsrik dagens matematikundervisning egentligen är då de svenska elevernas resultat i internationella jämförelser så som PISA är inte lysande. Historiskt har den svenska matematikundervisningen hämtat influenser från amerikansk matematikdidaktikutveckling. I detta examenarbete görs jämförelse av förespråkad matematikdidaktik vid två olika lärarkurser i Sverige och en lärarkurs på Stanford, USA. Syftet är att undersöka likheter och skillnader i synen på ”god” matematikundervisning på dessa kurser. Som huvudsaklig analysmetod valdes en diskursanalys. De tre olika lärarkurserna ses som tre diskurser. Fyra frågor ställts till respektive diskurs: Vad lyfts fram om matematikdidaktik? Hur talas det omdetta? Vad utesluts eller tonas ner? Vad framställs som god matematik-undervisning? Huvudinriktningen mot en processorienterad matematik är tydlig i alla tre diskurserna. Samtidigt så nämns i diskurserna att ”kunna vissa saker utantill är också viktigt” så det är inte helt entydigt men ändå en tydlig riktning. Alla diskurser tar också upp uppgifternas betydelse för lärandet. Val av uppgifter är en viktig del av matematikdidaktiken. Några skillnader som framkommer är att den amerikanska diskursen lyfter fram betydelsen av mjuka faktorer som attityd, självförtroende, motivation, tilltro, uppmuntran betydligt mer än de två svenska. Sammanfattningsvis visar min analys av de tre diskurserna att den amerikanska diskursen tydligare lyfter fram värderingar och undervisar lärarstudenterna i vad som är god matematikundervisning. God matematikundervisning innefattar många mjuka aspekter som motivation, självförtroende och jämlikhet. Budskapet i de två svenska diskurserna är sakligare och med mer bredd – god matematikundervisning omfattar ett spektrum av förmågor, kunskaper, ämnesområden. Lärarstudenten får ett ”smörgåsbord” och får sedan, på gott och ont, plocka ihop sin egen tallrik av hur matematikundervisningen ska bedrivas. / In recent decades, school mathematics and mathematics education have undergone a change from a historical focus on pure arithmetic and facts knowledge towards an increasingly process orientation. There is an active debate about how successful today's mathematics education really is and the Swedish students' results in international comparisons such as PISA are not brilliant. Historically, Swedish mathematics teaching has taken influences from American mathematics didactic trends. In this thesis, a comparison is made of advocated mathematic education at two different teacher courses in Sweden and a teacher course at Stanford, USA. The purpose is to investigate similarities and differences in the view of “good mathematics education” in these courses. A discourse analysis was chosen as the main analysis method. The three different teacher courses are seen as three discourses. Four questions are asked for each discourse: What mathematics didactics is highlighted? How is this talked about? What is excluded or toned down? What is presented as good mathematics teaching? In all three discourses a clear focus on a process-oriented mathematics is seen. At the same time, it is mentioned in the discourses that "knowing certain things by heart is also important" so it is not completely unambiguous but still a clear direction. All discourses also address the importance of the math problems. Choice of problems and exercises is an important part of mathematics didactics. One difference that emerge is that the American discourse highlights the importance of soft factors such as attitude, self-confidence, motivation, confidence, encouragement significantly more than the other two. In summary, my analysis of the three discourses shows that the American discourse more clearly highlights values and educates student teachers what is good mathematics teaching. Good mathematics education includes many soft aspects such as motivation, self-confidence and equality. The message in the two Swedish discourses is more objective and with more breadth - good mathematics education encompasses a spectrum of abilities, knowledge, subject areas. The teacher student gets a "smorgasbord" and then has to fill his own plate with theories and methods how the mathematics teaching should be conducted.

Made available in DSpace on 2016-04-27T16:57:53Z (GMT). No. of bitstreams: 1 dissertacao_eduardo_sad_costa.pdf: 3568903 bytes, checksum: 4e09f1b15f7714b64ad56708b0bd9974 (MD5) Previous issue date: 2007-05-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work involves a qualitative study about whether and how mathematics High-School teachers work with their students the trouble-situations regarding linear Diophantine equations. The study was performed by means of analyzing semi-structured interviews applied on six mathematics teachers from the states of São Paulo and Minas Gerais, teaching at high-school level. The Numbers Elementary Theory has been treated by several researchers on Mathematical Education, as Campbell e Zazkis (2002), Resende (2007), as an adequate subject for the introduction and development of fundamental Mathematical ideas in High- School. However, the results of such investigation show that, although the interviewed teachers affirmed that they did work with problems of discreet mathematics that can be modeled through linear Diophantine equations, none of them seemed to work with their students using the knowledge of these equations properties in order to decide whether they have solution, and what these solutions would be / Neste trabalho apresento um estudo qualitativo sobre se, e como, professores de Matemática do Ensino Médio trabalham com seus alunos situações-problema que recaem em equações diofantinas lineares. O estudo foi feito por meio da análise de entrevistas semi-estruturadas realizadas com seis professores de Matemática dos estados de São Paulo e Minas Gerais que lecionam no Ensino Médio. A Teoria Elementar dos Números vem sendo tratada por diversos pesquisadores de Educação Matemática, como Campbell & Zazkis (2002), Resende (2007), como assunto propício para a introdução e desenvolvimento de idéias Matemáticas fundamentais no Ensino Básico. No entanto os resultados desta investigação indicam que embora os professores entrevistados afirmassem trabalhar com problemas de matemática discreta modeláveis via equação diofantina linear, nenhum deles deu indícios de trabalhar com seus alunos utilizando conhecimentos das propriedades dessas equações para decidir se as mesmas tem solução e quais seriam essas soluções

In 2004, the Transition Mathematics Project (TMP), funded by the state of Washington and The Bill and Melinda Gates Foundation, was established to create projects to help high school students gain the necessary skills to become college and work-ready. Aligned to TMP's College Readiness Mathematics Standards, a fourth-year capstone mathematics course was developed and implemented, titled Applications in Mathematical Reasoning (AMR), a rigorous course option for students to take during their senior year of high school. The purpose of this study was to explore any relationship between taking the AMR course and preparation for college level mathematics. Using causal-comparative study design and matching participants in the sample, variables were examined based on the number of precollege courses taken; college level math course completed and grade earned; and placement test results for students who took the AMR course compared to those students who took no mathematics during their high school senior year. Though findings for precollege and college level course-taking were inconclusive, mathematics placement test scores were found to be significantly higher for those students who completed the AMR course. The placement test findings supported other research that links rigorous mathematics courses taken in high school with improved college placement and persistence. Based on the research examined and the study findings, there was support to consider the following: (a) creating alternate but rigorous math course offerings for the high school senior year; (b) striving toward a four-years of mathematics graduation requirement for all high schools; (c) enacting mandatory placement at the community college for students placing into precollege courses; and (d) reducing barriers to successful transition between high schools and post secondary institutions by fostering K-16 communication, aligning standards, and improving course alignment. / Graduation date: 2012

No description available.