Förlorad i övergången från aritmetik till algebra : Hur gymnasieelever översätter aritmetik till algebra

The aim of this thesis is to look for signs of students’ understanding of algebra by studying how they make the transition from arithmetic to algebra. Students in an Upper Secondary class on the Natural Science program and Science and Technology program were given a questionnaire with a number of algebraic problems of different levels of difficulty. Especially important for the study was that students leave comments and explanations of how they solved the problems. According to earlier research, transitions are the most critical steps in problem solving. The Algebraic Cycle is a theoretical tool that can be used to make different phases in problem solving visible. To formulate and communicate how the solution was made may lead to students becoming more aware of their thought processes. This may contribute to students gaining more understanding of the different phases involved in mathematical problem solving, and to students becoming more successful in mathematics in general.The study showed that the students could solve mathematical problems correctly, but that they in just over 50% of the cases, did not give any explanations to their solutions.

Gymnasieelevers uppfattningar om algebra och problemlösning : En undersökning med utgångspunkt i elevernas kön, slutbetyg i grundskolan och val av gymnasieprogram

Syftet med den här uppsatsen är att undersöka elevers uppfattningar om algebra och problemlösning samt granska hur dessa uppfattningar påverkas beroende på elevernas val av gymnasieprogram, kön och slutbetyg i grundskolan. Syftet är vidare att ta reda på vilka eventuella hinder och svårigheter eleverna själva uppfattar då de använder algebra för att lösa matematiska problem. Som metod för att söka svar på syfte och frågeställningar har valts att genomföra en enkätundersökning med elever som går första året på gymnasiet och som läser antingen naturvetenskapsprogrammet eller bygg- och anläggningsprogrammet. Enkätundersökningen består av två delar, en del som undersöker elevers uppfattningar om matematik i allmänhet och algebra och problemlösning i synnerhet, samt en del som försöker reda ut vilka svårigheter eleverna uppfattar då de ska lösa matematiska problem med algebra. Svaren sammanställs genom en analys av vilka eventuella skillnader och likheter som finns beroende på elevernas val av gymnasieprogram, kön och betyg i grundskolan. Resultatet visar på att elever på naturvetenskapsprogrammet som hade MVG i betyg i grundskolan har en mer positiv inställning till algebra och problemlösning i jämförelse med elever från bygg- och anläggningsprogrammet som fått G i betyg. Vad gäller elevernas kön finns det inte några indikationer på att denna faktor har någon större påverkan på deras uppfattningar. Resultatet kan vara en indikation på att elevernas uppfattningar främst påverkas av deras förståelse för det algebraiska tankesättet. Det eleverna upplever som svårast när de ska lösa problem med hjälp av algebra är att översätta den skrivna texten till en algebraisk framställning. När eleverna löser matematiska problem indikerar även resultatet att de till stor del styrs av sina förväntningar och förutfattade föreställningar om uppgiften. Resultatet ger en indikation om att eleverna behöver arbeta mer med problemlösning i olika former för att genom det kunna träna upp sin resonemangsförmåga och sin förmåga att behärska alla de tre faserna, översättning, omskrivning och tolkning, i den algebraiska cykeln.

Relative durations of post-vocalic consonants in readaloud Spanish by native Swedish L2-learners

Prosody is said to be a persistent feature in foreign accents, particularly in the speech of adult learners. Native Swedish speakers have been reported to lengthen vowels in Spanish as well as post-vocalic consonants in English and German, more than native speakers of the respective languages. The aim of the present study is to examine whether native Swedish learners of Spanish produce increased postvocalic consonant durations in a reading aloud exercise. The text contains certain words that could be expected to trigger complementary consonant lengthening in native Swedish speakers. The result shows that there is no general tendency for native Swedes to lengthen post-vocalic consonants more than native speakers of Spanish in the present speech material. There are examples of longer consonant durations in the speech of the native,Swedish subjects, but it could be a coincidence. A conclusion is that the text used in the study, and probably Spanish as a language, contains few words that are ideal for triggering lengthening of post-vocalic consonants in native Swedish speakers.

The relative perceptual weight of two Swedish prosodic contrasts

Abstract. In addition to 9 vowel and 18 consonant phonemes, Swedish has three prosodic phonemic contrasts: word stress, quantity and tonal word accent. There are also examples of distinctive phrase or sentence stress, where a verb can be followed by either an unstressed preposition or a stressed particle. This study focuses on word level and more specifically on word stress and tonal word accent in disyllabic words. When making curriculums for second language learners, teachers are helped by knowing which phonetic or phonological features are more or less crucial for the intelligibility of speech and there are some structural and anecdotal evidence that word stress should play a more important role for intelligibility of Swedish, than the tonal word accent. The Swedish word stress is about prominence contrasts between syllables, mainly signaled by syllable duration, while the tonal word accent is signaled mainly by pitch contour. The word stress contrast, as in armen [´arːmən] ‘the arm’ - armén [ar´meːn] ‘the army’, the first word trochaic and the second iambic, is present in all regional varieties of Swedish, and realized with roughly the same acoustic cues, while the tonal word accent, as in anden [´anːdən] ‘the duck’ - anden [`anːdən] ‘the spirit’ is absent in some dialects (as well as in singing), and also signaled with a variety of tonal patterns depending on region. The present study aims at comparing the respective perceptual weight of the two mentioned contrasts. Two lexical decision tests were carried out where in total 34 native Swedish listeners should decide whether a stimulus was a real word or a non-word. Real words of all mentioned categories were mixed with nonsense words and words that were mispronounced with opposite stress pattern or opposite tonal word accent category. The results show that distorted word stress caused more non-word judgments and more loss, than distorted word accent. Our conclusion is that intelligibility of Swedish is more sensitive to distorted word stress pattern than to distorted tonal word accent pattern. This is in compliance with the structural arguments presented above, and also with our own intuition.