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En formalisering av matematiken i svensk gymnasieundervisning
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2011 (Swedish)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesisAlternative title
A Formalisation of Swedish Upper Secondary School Mathematics (English)
Abstract [en]

This study examines how formal mathematics can be taught in the Swedish secondary school with its new curriculum for mathematics. The study examines what a teaching material in formal mathematics corresponding to the initial content of the course Mathematics 1c could look like, and whether formal mathematics can be taught to high school students.

The survey was conducted with second year students from the science programme. The majority of these students studied the course Mathematics D. The students described themselves as not being motivated towards mathematics.

The results show that the content of the curriculum can be presented with formal mathematics. This both in terms of requirements for content and students being able to comprehend this content. The curriculum also requires that this type of mathematics is introduced in the course Mathematics 1c.

The results also show that students are open towards and want more formal mathematics in their ordinary education. They initially felt it was strange because they had never encountered this type of mathematics before, but some students found the formal mathematics to be easier than the mathematics ordinarily presented in class.

The study finds no reason to postpone the meeting with the formal mathematics to university level. Students’ commitment to proof and their comprehention of content suggests that formal mathematics can be introduced in high school courses. This study thus concludes that the new secondary school course Mathematics 1c can be formalised and therefore makes possible a renewed mathematics education.

Abstract [sv]

Denna studie undersöker hur formell matematik kan undervisas i den nya svenska gymnasieskolan med dess nya ämnesplan för matematik. I studien undersöks hur ett undervisningsmaterial i formell matematik motsvarande det inledandeinnehållet i kursen Matematik 1c kan se ut och huruvida denna matematik kan undervisas med gymnasieelever.

Undersökningen genomfördes med elever från det naturvetenskapliga programmets andra årskurs. Majoriteten av dessa elever läste då kursen Matematik D. Eleverna beskrev sig själva som ej motiverade i matematik.

Resultatet visar att innehållet i ämnesplanen kan presenteras med formell matematik. Detta både med avseende ämnesplanens krav på innehåll och atteleverna kan förstå innehållet. Ämnesplanen kräver dessutom att denna typ av matematik tas upp som en del av innehållet i kursen Matematik 1c.

Resultatet visar också att eleverna är öppna för och vill ha mer formell matematik i undervisningen. De tyckte att det kändes ovant eftersom att de aldrig tidigare stött på denna typ av matematik, men vissa elever fann formell matematik som enklare än matematiken som normalt presenteras på lektionerna.

Studien finner ingen anledning till att skjuta upp mötet med formell matematik till universitetsnivå. Elevernas engagemang för bevis och tillgodogörandet av innehållet talar också för att formell matematik kan introduceras i gymnasiekurserna. Studiens slutsats är således att nya gymnasieskolans kurs Matematik 1c kan formaliseras och öppna för en förnyad matematikundervisning.

Place, publisher, year, edition, pages
2011. , 106 p.
Series
Trita-MAT. MA, ISSN 1401-2278
Keyword [en]
Mathematics, Education, Formal mathematics, Proof
Keyword [sv]
Matematik, Undervisning, Formell matematik, Bevis
National Category
Didactics Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-91398OAI: oai:DiVA.org:kth-91398DiVA: diva2:509959
Educational program
Master of Science in Engineering - Engineering and of Education
Presentation
2011-06-14, E32, Lindstedtsvägen 3, Stockholm, 09:00 (Swedish)
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2013-10-05 Created: 2012-03-14 Last updated: 2013-10-05Bibliographically approved

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