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 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.  

scholarly journals Att utveckla elevers förmåga att formulera undersökningsbara frågor i naturvetenskap: Mangling av en didaktisk modell

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Sara Planting-Bergloo ◽  
Maria Andrée ◽  
Josefin Reimark ◽  
Emma Henriksson ◽  
Sebastian Björnhammer ◽  
...  
Keyword(s):  
Science Education ◽  
Secondary School ◽  
School Science ◽  
Upper Secondary School ◽  
Scientific Investigations ◽  
Video Recordings ◽  
Upper Secondary ◽  
Epistemological Analysis ◽  
Support Students ◽  
Ultimate Purpose

En viktig målsättning för naturvetenskaplig undervisning är att utveckla förmågan att formulera undersökningsbara frågor. Syftet med den här studien är att undersöka hur undervisning som utformats med hjälp av metoden Question Formulation Technique (QFT) kan stödja utveckling av elevers förmåga att formulera naturvetenskapligt undersökningsbara frågor.  QFT är en modell för att utveckla elevers förmåga att formulera och värdera sina egna frågor i allmänhet. I studien prövas QFT i en svensk skolkontext och inom ramen för naturvetenskaplig undervisning. Studien genomfördes som en interventionsstudie i gymnasieskolan och inom ramen för kursen Gymnasiearbete. I kursen ska eleverna genomföra en egen naturvetenskaplig undersökning. QFT användes för att utforma undervisning som del av introduktionen till kursen. Data består av videoinspelningar av elevsamtal från undervisning som har analyserats utifrån ett pragmatiskt ramverk med organiserande syften och praktisk epistemologisk analys. Resultaten visar vilka närliggande syften som etableras i elevernas samtal om undersökningsbara frågor i undervisningen: (A) att producera så många frågor som möjligt, (B) att bedöma vilka frågor som är mest relevanta, (C) att kategorisera frågor, (D) att hitta och specificera ett undersökningsobjekt och (E) att planera för att genomföra en undersökning. Slutsatsen är att QFT kan fungera som stöd för lärares planering av undervisning om naturvetenskapligt undersökningsbara frågor under förutsättning att läraren aktivt stödjer eleverna i att uppmärksamma centrala kvaliteter avseende undersökningsbarhet och genom att binda samman närliggande syften med det övergripande syftet.  In English An important goal for science education is to develop students’ ability to formulate questions of inquiry. The aim of this study is to investigate if science teaching designed from the method “Question Formulation Technique” (QFT) can support the development of this ability. QFT is a model for developing students' ability to phrase and evaluate questions in general which has been developed in a US context. In this study QFT is used in a Swedish context and within upper secondary school science education. The study is an intervention study where QFT was used as part of the introduction to Diploma work in the final year of upper secondary school. During the diploma work students are expected to conduct their own scientific investigations. The data consists of video recordings of student conversations while working with the formulation of questions for inquiry as part of a research lesson designed using QFT. Data was analyzed using a pragmatic approach of combining practical epistemological analysis (PEA) and organising purposes. The results show that five proximate purposes were established in the student conversations while the students engaged in formulating and refining questions of inquiry based on the QFT model. The five proximate purposes were: (A) to produce as many questions as possible, (B) to assess which questions are most relevant, (C) to categorize questions, (D) to find and specify the object of inquiry and (E) plan to conduct an inquiry. In conclusion, QFT can support the planning of teaching in relation to the ultimate purpose regarding how to formulate and refine questions of inquiry provided that the teacher actively participates to support students in connecting the established proximate purposes with the ultimate purpose. Fulltext in Swedish.

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 Study of the Presence of Sustainability Competencies in Teacher Training in Mathematics Education

2021 ◽  
Vol 13 (10) ◽  
pp. 5629
Author(s):  
Francisco M. Moreno-Pino ◽  
Rocío Jiménez-Fontana ◽  
José María Cardeñoso Domingo ◽  
Pilar Azcárate Goded
Keyword(s):  
Higher Education ◽  
Early Childhood ◽  
Mathematics Education ◽  
Teacher Training ◽  
Secondary School ◽  
Upper Secondary School ◽  
Childhood Education ◽  
Secondary School Education ◽  
Upper Secondary ◽  
Didactics Of Mathematics

This article presents the results of the analysis of the presence of the sustainability competencies proposed by the Sectoral Commission of the Conference of Rectors of Spanish Universities in three degrees in the area of Didactics of Mathematics of the Faculty of Education Sciences at the Universidad de Cádiz (Spain): the degree in Early Childhood Education, the degree in Primary Education, and the Master’s degree in Teacher Training for Compulsory Secondary and Upper Secondary School Education (specialisation in mathematics). The research method used is content analysis, reflected in the syllabi of the subjects of the degrees analysed. To carry out the analysis, two instruments were used: an adaptation of the model of the Green Curriculum in Higher Education and the map of generic competencies in sustainability of the EDINSOST project. The global results show a very low relative presence of sustainability competences in the area of Didactics of Mathematics (25%), the competency related to ethical aspects having the lowest relative presence (10%). For the most part, the competencies related to sustainability are established for the lowest level of mastery, “know”. When comparing the degree programmes, the Master’s degree in Teacher Training for Compulsory Secondary and Upper Secondary School Education (specialisation in mathematics) is the degree that contributes the most to the development of the sustainability competency (32%), followed by the degree in Early Childhood Education (25%), and the degree in Primary Education (18%). Including sustainability in the curriculum of mathematics education in higher education can improve the training of professionals who engage in reflective and critical thinking. However, these results show there is still a long way to go.

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.

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