scholarly journals Quadratic equations in Swedish textbooks for upper-secondary school

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Wang Wei Sönnerhed
Keyword(s):  
Secondary School ◽  
Procedural Knowledge ◽  
Secondary Level ◽  
Learning Opportunities ◽  
Learning Trajectory ◽  
Upper Secondary School ◽  
Quadratic Equations ◽  
Upper Secondary ◽  
Hypothetical Learning Trajectory ◽  
Upper Secondary Level

This paper analyzes the content and tasks involving quadratic equations in eight mathematics textbooks published during the period 2000-2012 at the upper-secondary level in Sweden. The study applies the theoretical hypothetical learning trajectory (HLT) framework combining conceptual and procedural knowledge. The analysis includes horizontal and vertical dimensions within an HLT. The aim is to explore embedded HLTs and learning opportunities from both dimensions in these textbooks. A total of 250 examples and 1,068 tasks have been examined. Results show that all the textbooks contain algebra identities and four different methods for solving quadratic equations as well as their applications as a core hypothetical learning trajectory but differ in how an HLT starts and ends. Geometrical representations for some algebra identities and completing the square are widely used in both theoretical presentations and tasks, which implies that conceptual learning is encouraged among the Swedish textbooks. At the same time, procedural knowledge is still emphasized as a basic but important learning process.  

GeoGebra as a tool for visualisation in geometry education

2019 ◽  
pp. 169-176
Author(s):  
Ján Guncaga ◽  
László Budai ◽  
Tibor Kenderessy
Keyword(s):  
Mathematics Education ◽  
Secondary School ◽  
Secondary Level ◽  
Upper Secondary School ◽  
Geometric Concepts ◽  
Upper Secondary ◽  
Spatial Imagination ◽  
Support Students ◽  
Upper Secondary Level ◽  
Geometry Education

There are problems in geometry education in lower and upper secondary school, which students have with the spatial imagination and with the understanding of some geometric concepts. In this article, we want to present tasks that show some advantages of the software GeoGebra. We use this software as a tool to visualize and to explain some geometric concepts, as well as to support students’ spatial imagination. Classification: D30, G10. Keywords: space imagination, GeoGebra, mathematics education at lower and upper secondary level.

scholarly journals Matematiikan parhaiden osaajien siirtyminen toiselle asteelle: koulutusvalinnat ja matematiikan osaamisen kehittyminen

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Laura Niemi ◽  
Jari Metsämuuronen ◽  
Markku Hannula ◽  
Anu Laine
Keyword(s):  
Secondary School ◽  
Secondary Level ◽  
Upper Secondary School ◽  
Related Factors ◽  
Mathematical Competence ◽  
9Th Grade ◽  
High Achieving Students ◽  
Upper Secondary ◽  
High Achieving ◽  
Upper Secondary Level

Tutkimus on osa pitkittäistutkimusta, jossa samaan ikäluokkaan kuuluvia oppilaita seurattiin perusopetuksen kolmannelta vuosiluokalta toisen asteen koulutuksen loppuun neljällä eri mittauskerralla. Tutkimuksessa käytetään Opetushallituksen ja Kansallisen koulutuksen arviointikeskuksen vuosien 2005–2015 aikana keräämää kansallisesti edustavaa tutkimusaineistoa. Tutkimusaineisto käsittää kaikkiaan 3896 oppilasta. Tutkimuksessa keskitytään tarkastelemaan matematiikan parhaita osaajia, joita on yhteensä 292 (7,5 %). Poikien osuus on 64,0 % (n = 187) ja tyttöjen 36,0 % (n = 105). Osaaminen määritetään yhdeksännen vuosiluokan kokeessa menestymisen perusteella. Kansallisten matematiikan kokeiden lisäksi oppilaat ovat vastanneet erilaisiin kyselyihin, joissa heiltä on kerätty tietoa yksilöön, kouluun ja kotitaustaan liittyvistä tekijöistä. Tutkimuksessa selvitetään näiden tekijöiden yhteyttä toisen asteen koulutusvalintaan ja osaamisen kehittymiseen toisen asteen opintojen aikana. Tulosten analysoinnissa käytettiin päätöspuuanalyysia (DTA) ja regressioanalyysia. Tutkimuksessa havaittiin, että suurin osa (60,0 %) yhdeksännen vuosiluokan parhaista osaajista oli parhaita osaajia myös toisen asteen päättyessä ja muiden osaaminen laski hyvien tai keskitason osaajien tasolle. Yksilöön liittyvät tekijät selittävät parhaiten matematiikassa menestymistä myös toisella asteella. Myönteiset asenteet matematiikkaa kohtaan ja vahva matematiikan osaamisen pohja perusopetuksessa luovat edellytyksiä menestyä matematiikassa erinomaisesti toisella asteella. Matematiikan parhaiden osaajien osaamisen taso heikkenee todennäköisemmin, jos oppilas ei mene lukioon tai ei suorita lukiossa vähintään 11 matematiikan kurssia. Yhdeksännen vuosiluokan parhaista osaajista lukioon hakeutuivat todennäköisemmin ne, jotka menestyivät arvosanatiedon perusteella erinomaisesti äidinkielessä. In English The study is part of a longitudinal research. Same students were followed from 3rd grade of primary education to the end of upper secondary level. The data was collected by EDUFI and FINEEC during 2005–2015. The data consists of 3896 students and the target group consists of mathematically high-achieving students. Total number of them is 292 (7,5 %). Definition of high-achieving students is based on success in the mathematics examination of 9th grade.  In addition to math examinations it has been gathered information about students’ individual-, school- and home-related factors. The study examines the relationship between these factors and the choice between upper secondary vocational education and general upper secondary school. The aim is to investigate how high-achieving students’ mathematical competence develop during these studies and which factors are related to development. Decision tree analysis (DTA) and regression analysis were used to analyse the data. The results indicated that 60,0 % of mathematically high-achieving students were also high-achieving students at the end of upper secondary level. The individual-related factors were explanatory factors for mathematical success at the upper secondary level. Positive attitudes towards mathematics and strong mathematical competence in basic education predicted excellent success in mathematics later. The competence of high-achieving student most likely decreased if a student didn’t go to the general upper secondary school or didn’t complete at least 11 mathematics courses. They, who performed excellently in their studies of mother tongue in 9th grade, most likely applied to the general upper secondary school.

scholarly journals Matematiikan parhaat osaajat lukion lopussa ja heidän matematiikka-asenteissaan tapahtuneet muutokset

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Laura Niemi ◽  
Jari Metsämuuronen ◽  
Markku Hannula ◽  
Anu Laine
Keyword(s):  
Secondary School ◽  
Primary Education ◽  
Longitudinal Research ◽  
Secondary Level ◽  
Self Concept ◽  
Upper Secondary School ◽  
High Achieving Students ◽  
Upper Secondary ◽  
High Achieving ◽  
Upper Secondary Level

Tutkimus perustuu Opetushallituksen ja Kansallisen koulutuksen arviointikeskuksen keräämään pitkittäisaineistoon. Samaan ikäluokkaan kuuluvat oppilaat ovat osallistuneet kansallisiin matematiikan kokeisiin ja matematiikka-asenteita kartoittaviin kyselyihin vuosien 2005–2015 aikana neljällä eri mittauskerralla perusopetuksen kolmannelta vuosiluokalta toisen asteen loppuun. Tutkimusaineiston kokonaisotos käsittää yhteensä 3896 oppilasta. Tutkimuksessa keskitytään tarkastelemaan matematiikassa parhaiten menestyneitä opiskelijoita. Matematiikan parhaiksi osaajiksi määritetään kansalliseen matematiikan kokeeseen osallistuneet lukiolaiset, jotka saivat pitkän matematiikan ylioppilaskokeesta arvosanan laudatur tai eximia cum laude approbatur (n = 146). Ensin tutkimuksessa selvitetään, miten parhaiden osaajien matematiikka-asenteet muuttuivat perusopetuksesta lukion loppuun ja toiseksi, miten opetuksen pedagogiset ratkaisut yläkoulussa ja lukiossa selittävät osaamiseltaan parhaiden tyttöjen ja poikien asenteissa tapahtuneita muutoksia. Selittävien tekijöiden analyysissa käytetään päätöspuuanalyysia (DTA) ja lineaarista regressioanalyysia. Matematiikan parhaiden osaajien matematiikasta pitäminen kasvoi lukio-opintojen aikana, mutta minäkäsitys ja kokemus matematiikan hyödyllisyydestä laskivat. Matematiikassa parhaiten menestyneiden tyttöjen asenteissa tapahtuneet muutokset poikkesivat asenteiden yleisestä muutossuunnasta. Parhaiden tyttöjen minäkäsitys kasvoi yläkoulun ja lukion aikana lähes parhaiten menestyneiden poikien tasolle ja tytöt pitivät matematiikasta lukion lopussa poikia enemmän. Matematiikassa parhaiten menestyneiden tyttöjen ja poikien asenteiden kehittymistä selittivät erilaiset opetuksen pedagogiset ratkaisut. Molemmilla myönteisiä asenteita vahvistivat yleisesti oppilaskeskeisyyteen, yhteistoiminnallisuuteen ja oppijoiden tarpeiden huomioimiseen liittyvät pedagogiset ratkaisut. In English The study is part of a longitudinal research. Students belonging to the same age group were followed from the third grade of primary education to the end of upper secondary level. The data was collected by EDUFI and FINEEC during 2005–2015. The data consists of 3896 students. The target group consists of mathematically high-achieving students at the end of their studies in upper secondary school. The definition of high-achieving students based on success in matriculation examination of advanced math (n = 146). First we examine how high-achieving students’ attitudes towards mathematics change from primary education to the end of upper secondary level and then how pedagogical solutions in grades 7–9 and in upper secondary level explain boys’ and girls’ changes in attitudes. Decision tree analysis (DTA) and regression analysis were used to analyse the data. The results indicated that high-achieving students liked more mathematics during upper secondary school but self-concept and experience of usefulness of mathematics decreased. The changes of high-achieving girls’ attitudes differed from the general trend of change. High-achieving girls’ self-concept increased almost to the same level than high-achieving boys’ during grades 7–9 and in upper secondary school. Additionally, girls liked mathematics more than boys at the end of upper secondary level. The development of high-achieving girls’ and boys’ attitudes was explained by different pedagogical solutions. Both girls’ and boys’ positive attitudes were generally reinforced by pedagogical solutions related to student-centeredness, cooperative learning and paying attention to students’ needs. Fulltext in Finnish.

scholarly journals UPPER-SECONDARY SCHOOL STUDENTS’ APPROACHES TO SCIENCE EXPERIMENTS IN AN EXAMINATION DRIVEN CURRICULUM CONTEXT

2020 ◽  
Vol 19 (4) ◽  
pp. 523-535
Author(s):  
Tamirirofa Chirikure
Keyword(s):  
Secondary School ◽  
Scientific Reasoning ◽  
Secondary School Students ◽  
Procedural Knowledge ◽  
Upper Secondary School ◽  
Iterative Approach ◽  
School Students ◽  
Linear Approach ◽  
Upper Secondary ◽  
Teaching Learning

This research explored upper-secondary school students’ approaches when they engage in planning and conducting science experiments. Approaches to science experiments are important because they provide insight into students’ scientific reasoning and their enactment of scientific methods. An explanatory mixed-methods design was employed to determine and explain students’ approaches to science experiments. Data were generated by administering a 15-item Approaches to Science Experiments Questionnaire (ASEQ) on 211 participants and interviewing a smaller sample of 33. The linear approach was predominant while the divergent approach was least adopted by the participants. The teaching-learning context, substantive and procedural knowledge lead to specific approaches and the emergence of subcategories of the three broad approaches. Capable students engaged in a self-directed iterative approach while external help resulted in an assisted iterative approach. Rigid and contrived linear approaches were a result of time constraints, substantive and procedural shortcomings. Scattergun and blanking divergent approaches emerged from extreme weaknesses in substantive and procedural knowledge. Assessing practical skills through long-term projects is recommended to focus more on developing students’ scientific reasoning and process skills. Research with the ASEQ in other teaching-learning cultures, observing students in action and analysing their write-ups could provide deeper insights into approaches to science experiments. Keywords: science experiments, divergent approach, iterative approach, linear approach, mixed methods.

scholarly journals Excelling in Exam Through Narrative Writing: A Connection of Creative and Descriptive Expressions

2019 ◽  
Vol 7 (4) ◽  
pp. 46
Author(s):  
Roseline David ◽  
Joseph Alagiaraj Thambu Raj
Keyword(s):  
Action Research ◽  
Secondary School ◽  
Limited English Proficiency ◽  
Teaching And Learning ◽  
English Language ◽  
English Proficiency ◽  
Writing Skills ◽  
Secondary Level ◽  
Upper Secondary ◽  
Upper Secondary Level

This paper discusses the impacts of an action research on how students can excel in writing skills regardless of their level of competency especially for those taking the English Language paper (SPM 1119) in the Malaysian Secondary School Public Exam in 2018. This action research aims to exert the need for realigning our focus to incorporate an approach of teaching and learning at upper secondary level. The research was carried out from January to October in a secondary school in Kota Kinabalu, Sabah. Two classes of 37 Limited English Proficiency students and 24 High English Proficiency Students who were sitting for SPM 1119 in 2018 were the subjects. The students were exposed to creative expressions under various topics which were then emphasized to be utilized in continuous writing. As a result, the performance of students had improved significantly in their continuous writing where they eventually scored 100 percent pass in SPM1119 in 2018. All 24 Highly Competent students were able to score ranging from “A-” to “A+” with grade A being the median grade. On the other hand, all the students from the Limited English Proficiency students passed with grades ranging from “A”+ to “E” (minimum passing grade) with grade “B” as the median.

scholarly journals The challenges of learning and teaching chemical bonding at different school levels using electrostatic interactions instead of the octet rule as a teaching model

2018 ◽  
Vol 19 (3) ◽  
pp. 932-953 ◽  
Author(s):  
Jarkko Joki ◽  
Maija Aksela
Keyword(s):  
Secondary School ◽  
Chemical Bonding ◽  
Electrostatic Interactions ◽  
Secondary Level ◽  
Teaching Model ◽  
Electrostatic Model ◽  
Upper Secondary School ◽  
Learning And Teaching ◽  
Upper Secondary ◽  
Octet Rule

Teaching chemical bonding using the octet rule as an explanatory principle is problematic in many ways. The aim of this case study is to understand the learning and teaching of chemical bonding using a research-informed teaching model in which chemical bonding is introduced as an electrostatic phenomenon. The study posed two main questions: (i) how does a student's understanding of chemical bonding evolve from lower- to upper-secondary school when an electrostatic model of chemical bonding was used at the lower-secondary level? (ii) How does the teaching of octets/full shells at the upper-secondary level affect students’ understanding? The same students were interviewed after lower-secondary school and again during their first year at upper-secondary school. Their upper-level chemistry teachers were also interviewed. The interview data were analysed using the grounded theory method. The findings showed that the students’ earlier proper understanding of the electrostatic-interactions model at the lower-secondary level did not prevent the later development of less-canonical thinking. Teachers’ pedagogical content knowledge (PCK) of the explanatory principles of chemical bonding and how to use explanations in science education needs to be promoted in both pre-service teacher education and during in-service training.

Cooperative Learning in Italian Secondary School

2004 ◽  
Vol 143-144 ◽  
pp. 1-35
Author(s):  
Emilia Di Martino
Keyword(s):  
Action Research ◽  
Cooperative Learning ◽  
Secondary School ◽  
Secondary Level ◽  
Action Research Project ◽  
Research Project ◽  
Teaching Situation ◽  
Upper Secondary ◽  
Specific Teaching ◽  
Upper Secondary Level

This paper presents the results of an Action Research project aimed at exploring (1) the possibility of implementing Cooperative Learning and (2) the possible benefits of doing so in the author’s specific teaching situation at Upper Secondary level in Italy.

Assessing the transition between school and university: Differences in assessment between A level and university in English

2016 ◽  
Vol 16 (2) ◽  
pp. 188-208 ◽  
Author(s):  
Frances Wilson ◽  
Simon Child ◽  
Irenka Suto
Keyword(s):  
Higher Education ◽  
Secondary School ◽  
English Literature ◽  
Secondary Level ◽  
First Year ◽  
High Stakes ◽  
Undergraduate Study ◽  
Upper Secondary ◽  
Upper Secondary Level

High stakes assessments are commonly used at the end of secondary school to select students for higher education. However, growing concerns about the preparedness of new undergraduates for university study have led to an increased focus on the form of assessments used at upper secondary level. This study compared the structure and format of assessments used at upper secondary level (GCE A level qualifications), and the first year of undergraduate study of English literature in England. Greater diversity of assessment was found at university compared to A level, while there was little difference in the level of scaffolding and guidance provided in assessment materials. We conclude that it seems inevitable that some students will meet forms of assessment with which they are unfamiliar at university. Implications for the design of first-year undergraduate courses are discussed.

scholarly journals CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks

2019 ◽  
Vol 8 (3) ◽  
pp. 232
Author(s):  
Uffe Thomas Jankvist ◽  
Morten Misfeldt
Keyword(s):  
Secondary School ◽  
Teaching And Learning ◽  
School Mathematics ◽  
Upper Secondary School ◽  
Mathematics Textbooks ◽  
Secondary School Mathematics ◽  
Proof Schemes ◽  
Mathematical Proofs ◽  
Upper Secondary ◽  
Upper Secondary Level

This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are identified in ten different textbooks. The CAS based proofs in these textbooks are of three types: complete outsourcing of the proof to CAS; partial outsourcing of the proof to CAS; and additional verification of the proof’ correctness by CAS. Analyses of examples of each of these types are provided. The analyses draw on theoretical constructs related to both proofs and proving (e.g. proof schemes) and to use of digital technologies in mathematics education (lever potential, blackboxing, instrumental genesis). In particular, the analyses make use of a distinction between epistemic, pragmatic and justificational mediations. Results suggest both potential problems with using CAS as an integrated part of deductive mathematical proofs in textbooks, since it appears to promote undesired proof schemes with the students, and difficulties with understanding these problems using the constructs of epistemic and pragmatic mediations that are often adopted in the literature regarding CAS use in mathematics teaching and learning.

scholarly journals ADAPTING THE SURVEY OF ATTITUDES TOWARDS STATISTICS (SATS-36) FOR ESTONIAN SECONDARY SCHOOL STUDENTS

2017 ◽  
Vol 16 (1) ◽  
pp. 228-239
Author(s):  
CARITA HOMMIK ◽  
PIRET LUIK
Keyword(s):  
Factor Analysis ◽  
Secondary School ◽  
Secondary School Students ◽  
Statistics Education ◽  
Reliability And Validity ◽  
Secondary Level ◽  
School Students ◽  
Upper Secondary ◽  
Students Attitudes ◽  
Upper Secondary Level

The purpose of this study is to adapt the Survey of Attitudes Towards Statistics (SATS-36) for Estonian secondary school students in order to develop a valid instrument to measure students’ attitudes within the Estonian educational context. The SATS-36 was administered to Estonian-speaking secondary school students before their compulsory statistics course. Because the fit indices for confirmatory factor analysis did not indicate a good fit, an exploratory factor analysis was conducted to find a new model. It validated a four-factor structure of the scale, excluding nine items. Good indices for both reliability and validity were obtained. Trends in secondary school students’ attitudes were also examined to investigate the effects of gender and gender combined with the level of education. Results showed that students tended to feel rather positively about statistics at the beginning of the course. All four factors displayed differences between boys and girls. Comparison of lower and upper secondary level students showed that students from the upper secondary level value statistics more highly. The authors recommend SATS with some small proposed changes to make it even more suitable for the secondary level. First published May 2017 at Statistics Education Research Journal Archives

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