Utilising student profiles in mathematics course arrangements

This thesis develops a method for identifying students struggling in their mathematical studies at an early stage. It helps in directing support to students needing and benefiting from it the most. Thus, frustration felt by weaker students may decrease and therefore, hopefully, also drop outs of potential engineering students. The research concentrates on a combination of personality and intelligence aspects. Personality aspects gave information on conation and motivation for learning. This part was studied from the perspective of motivation and self-regulation. Intelligence aspects gave information on declarative and procedural knowledge: what had been taught and what was actually mastered. Students answered surveys on motivation and self-regulation in 2010 and 2011. Based on their answers, background information, results in the proficiency test, and grades in the first mathematics course, profiles describing the students were formed. In the following years, the profiles were updated with new information obtained each year. The profiles used to identify struggling students combine personality (motivation, selfregulation, and self-efficacy) and intelligence (declarative and procedural knowledge) aspects at the beginning of their studies. Identifying students in need of extra support is a good start, but methods for providing support must be found. This thesis also studies how this support could be taken into account in course arrangements. The methods used include, for example, languaging and scaffolding, and continuous feedback. The analysis revealed that allocating resources based on the predicted progress does not increase costs or lower the results of better students. Instead, it will help weaker students obtain passing grades.

Developing multiple - choice questions in mathematics

In this paper we wish to illustrate different perspectives used to create Multiple-Choice questions and we will show how we can improve these in the construction of math tests. As it is known, web technologies have a great influence on student’s behaviour. Based on an on-line project beginning at 2007 which has been contributing to help students on their individual work, we would like to share our experience and thoughts with colleagues who have a common concern when they have the task of constructing Multiple-Choice tests. We feel that Multiple-Choice tests play an important and a very useful supporting role in selfevaluation or self-examination of our students. Nonetheless, good Multiple–Choice Test Items are generally more complex and time-consuming to create than other types of tests. It requires a certain amount of skill. However, this skill maybe increases through study, practice and experience. This paper discusses a number of issues related to the use of Multiple-Choice questions, lists the advantages and disadvantages of this question format contrasting it with open questions. Some examples are given in this context.

New challenges in mathematics for the european higher education

In this paper we will talk about a math project submitted to the Lifelong Learning Programme. European higher education needs a reform in order to play its full role in the Europe of Knowledge. Modernisation of higher education is necessary in the areas of curricula (Bologna process), funding and governance so that higher education institutions can face the challenges posed by globalisation and contribute more effectively to the training and retraining of the European workforce. On the other hand Mathematics is an essential component of all educational systems. Mathematical literacy is being scrutinized in assessment efforts such as the OCDE Programme for International Student Assessment (PISA). This showed a low level in Europe. Due to the Bologna Process, which brought several didactical implications for Higher Education (HE) institutions, there is the need of lifelong learning. This evolution is in conflict with the earlier mentioned lack of competencies on basic sciences, such as Mathematics. Forced by this duality, efforts are combined to share expertise in the Math field and the integration of pedagogical methodologies becomes a necessity. Thus, several European countries have proposed an International Project to the Lifelong Learning Programme, Action ERASMUS Modernisation of Higher Education, to make institutions more attractive and more responsive to the needs of the labour market, citizens and society at large. One of the main goals of the project is to attract students to math through high-quality instructional units in an understandable, exciting and attractive way.

E-assessment in mathematics courses with multiple-choice questions tests

With the implementation of the Bologna Process several challenges have been posed to higher education institution, particularly in Portugal. One of the main implications is related to the change of the paradigm of a teacher centered education, to a paradigm that is student centered. This change implies the change of the way to assess courses in higher education institutions. Continuous and formative assessments emerged as the focus, catalyzed by electronic assessment, or e-assessment. This paper presents a case of the implementation of an e-assessment strategy, implemented in order to allow continuous, formative assessment in numerous mathematics classes using multiple-choice questions tests implement in Moodle open-source learning management system. The implementation can be considered a success.

E-assessment in mathematics courses with multiple-choice questions tests

With the implementation of the Bologna Process several challenges have been posed to higher education institution, particularly in Portugal. One of the main implications is related to the change of the paradigm of a teacher centered education, to a paradigm that is student centered. This change implies the change of the way to assess courses in higher education institutions. Continuous and formative assessments emerged as the focus, catalyzed by electronic assessment, or e-assessment. This paper presents a case of the implementation of an e-assessment strategy, implemented in order to allow continuous, formative assessment in numerous mathematics classes using multiple-choice questions tests implement in Moodle open-source learning management system. The implementation can be considered a success.

Are figures accessible in mathematics academic journals?

Are figures accessible in mathematics academic journals? An analysis of current image accessibility in highly cited mathematics journals.

Are figures accessible in mathematics academic journals?

Are figures accessible in mathematics academic journals? An analysis of current image accessibility in highly cited mathematics journals.

¿Para qué sirven los problemas en la clase de matemáticas? = What is the use of problems in Mathematics lessons?

The results obtained in several yield tests, at an international level (mainly the famous PISA 2003 report, by the OCDE), have raised a multiplicity of performances in order to improve the students' yield regarding problem solving. In this article we set a clear guideline on how problems should be used in Mathematics lessons, not for obtaining better scores in the yield tests but for improving the development of Mathematical thinking in students. From this perspective, the author analyses, through eight reflections, how the concept of problem, transmitted both in the school and from society, influences the students

Assessment of Young Learners’ English Proficiency in Bilingual Content Instruction CLIL

This applied linguistic study in the field of second language acquisition investigated the assessment practices of class teachers as well as the challenges and visions of language assessment in bilingual content instruction (CLIL) at primary level in Finnish basic education. Furthermore, pupils’ and their parents’ perceptions of language assessment and LangPerform computer simulations as an alternative, modern assessment method in CLIL contexts were examined. The study was conducted for descriptive and developmental purposes in three phases: 1) a CLIL assessment survey; 2) simulation 1; and 3) simulation 2. All phases had a varying number of participants. The population of this mixed methods study were CLIL class teachers, their pupils and the pupils’ parents. The sampling was multi-staged and based on probability and random sampling. The data were triangulated. Altogether 42 CLIL class teachers nationwide, 109 pupils from the 3rd, 4th and 5th grade as well as 99 parents from two research schools in South-Western Finland participated in the CLIL assessment survey followed by an audio-recorded theme interview of volunteers (10 teachers, 20 pupils and 7 parents). The simulation experimentations 1 and 2 produced 146 pupil and 39 parental questionnaires as well as video interviews of volunteered pupils. The data were analysed both quantitatively using percentages and numerical frequencies and qualitatively employing thematic content analysis. Based on the data, language assessment in primary CLIL is not an established practice. It largely appears to be infrequent, incidental, implicit and based on impressions rather than evidence or the curriculum. The most used assessment methods were teacher observation, bilingual tests and dialogic interaction, and the least used were portfolios, simulations and peer assessment. Although language assessment was generally perceived as important by teachers, a fifth of them did not gather assessment information systematically, and 38% scarcely gave linguistic feedback to pupils. Both pupils and parents wished to receive more information on CLIL language issues; 91% of pupils claimed to receive feedback rarely or occasionally, and 63% of them wished to get more information on their linguistic coping in CLIL subjects. Of the parents, 76% wished to receive more information on the English proficiency of their children and their linguistic development. This may be a response to indirect feedback practices identified in this study. There are several challenges related to assessment; the most notable is the lack of a CLIL curriculum, language objectives and common ground principles of assessment. Three diverse approaches to language in CLIL that appear to affect teachers’ views on language assessment were identified: instrumental (language as a tool), dual (language as a tool and object of learning) and eclectic (miscellaneous views, e.g. affective factors prioritised). LangPerform computer simulations seem to be perceived as an appropriate alternative assessment method in CLIL. It is strongly recommended that the fundamentals for assessment (curricula and language objectives) and a mutual assessment scheme should be determined and stakeholders’ knowledge base of CLIL strengthened. The principles of adequate assessment in primary CLIL are identified as well as several appropriate assessment methods suggested.

Portfolio as an Indicator of Young Learners’ English Proficiency in Mainstream Language Instruction (EFL) and Bilingual Content Instruction (CLIL)

Tämä soveltavan kielitieteen ja kielitaidon arvioinnin toimintatutkimus tarkasteli kieliportfolion ominaisuuksia ja mahdollisuuksia nuorten oppijoiden englannin kielen arvioinnissa kahdessa eri oppimiskontekstissa: englanti oppiaineena (EFL) ja kaksikielinen sisällönopetus (CLIL). Tutkielman itsenäiset, kahteen eri englannin kielen rekisteriin (arkikieli ja akateeminen kieli) kohdistuneet portfoliokokeilut olivat erillisiä tapaustutkimuksia. Molemmat portfoliot perustuivat väljästi Eurooppalaiseen kielisalkkumalliin, ja ne olivat osa tutkielmantekijän luokkaopetusta ja -toimintaa. EFL -portfoliokokeilu 9-10-vuotiaille kolmasluokkalaisille toteutettiin marraskuun 2011 ja toukokuun 2012 välisenä aikana, kun CLIL -portfoliokokeilu n. 7-9-vuotiallle ensimmäisen ja toisen luokan oppilaille kesti kaksi lukuvuotta 2012–2014. Molemmissa kokeiluissa myös oppilaiden vanhemmat kuuluivat tutkimusjoukkoon, samoin CLIL -portfolion toteutuksessa avustaneet ja opettajanäkökulmaa edustaneet opettajaopiskelijat. Portfoliokokeilun aloitti myös kaksi muuta CLIL -opettajaa, mutta kumpikin kokeilu päättyi alkuvaiheeseensa. Tarkemman tarkastelun kohteina olivat tutkimuksen osallistujien kokemukset ja mielipiteet portfoliokokeiluista. Erityisesti tavoitteena oli selvittää, miten informatiivisena englannin kielitaidon indikaattorina kieliportfoliota pidettiin. Myös kehitysehdotuksia kerättiin. Trianguloitu aineisto koottiin sekä puolistrukturoiduin kyselyin että vapaaehtoisin teemahaastatteluin, jotka äänitettiin. EFL -aineisto koostui 18 oppilaskyselystä, 17 huoltajakyselystä ja 7 oppilashaastattelusta. CLIL -aineistoon sisältyi 19 oppilaskyselyä, 18 huoltajakyselyä, 7 oppilashaastattelua ja yksi opettajaopiskelijoiden (N=3) ryhmähaastattelu. Aineisto analysoitiin pääosin kvalitatiivisin menetelmin temaattisen sisältöanalyysin keinoin, mutta myös laskien frekvenssejä ja prosenttisosuuksia. Osallistujien mielipiteet ja kokemukset olivat hyvin samankaltaiset ja positiiviset kummassakin portfoliokokeilussa. Merkittävä enemmistö sekä oppilaista että huoltajista koki, että portfolion avulla on mahdollista osoittaa englannin kielitaitoa ja sen kehittymistä. Oppilaat kuvailivat portfoliotyötä hauskaksi ja kivaksi, ja heidän mielestään portfoliotehtävien pitäisi olla tarpeeksi haastavia, sisältää taiteellisia ja luovia elementtejä sekä kohdistua tuttuihin, mielenkiintoisiin aiheisiin. He totesivat, että portfolion avulla voi oppia lisää kieltä. Vanhempien mielestä portfolio kertoo koulun vieraiksi jääneistä oppisisällöistä, auttaa ymmärtämään lapsen ajatusmaailmaa ja motivaatiotasoa sekä paljastaa heidän kielitaidostaan uusia ulottuvuuksia. Opettajaopiskelijat havaitsivat, että portfolion avulla voi tutustua oppilaiden kieli- ja kulttuuritaustoihin sekä kartoittaa heidän kielellisiä tarpeitaan. Tämän tutkielman teoreettisen tarkastelun ja tulosten mukaan kieliportfolio tukee erinomaisesti uuden Perusopetuksen Opetussuunnitelman (NCC 2014) tavoitteita ja arvioinnin uudistuspyrkimyksiä sekä lainsäädännön arvioinnille asettamia edellytyksiä. Portfolio on erittäin suositeltava nuorten oppijoiden kielitaidon arviointimenetelmä perinteisten rinnalle.

The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

Gender bias in the Trends in Mathematics and Science Study 2003 (TIMMS) for Canadian students /

This study is a secondary data analysis of the Trends in Mathematics and Science Study 2003 (TIMSS) to determine if there is a gender bias, unbalanced number of items suited to the cognitive skill of one gender, and to compare performance by location. Results of the Grade 8, math portion of the test were examined. Items were coded as verbal, spatial, verbal /spatial or neither and as conventional or unconventional. A Kruskal- Wallis was completed for each category, comparing performance of students from Ontario, Quebec, and Singapore. A Factor Analysis was completed to determine if there were item categories with similar characteristics. Gender differences favouring males were found in the verbal conventional category for Canadian students and in the spatial conventional category for students in Quebec. The greatest differences were by location, as students in Singapore outperformed students from Canada in all areas except for the spatial unconventional category. Finally, whether an item is conventional or unconventional is more important than whether the item is verbal or spatial. Results show the importance of fair assessment for the genders in both the classroom and on standardized tests.

Introduction to engineering : a case study of an interdisciplinary course in Mathematics, Science and Technology

This thesis research was a qualitative case study of a single class of Interdisciplinary Studies: Introduction to Engineering taught in a secondary school. The study endeavoured to explore students' experiences in and perceptions of the course, and to investigate the viability of engineering as an interdisciplinary theme at the secondary school level. Data were collected in the form of student questionnaires, the researcher's observations and reflections, and artefacts representative of students' work. Data analysis was performed by coding textual data and classifying text segments into common themes. The themes that emerged from the data were aligned with facets of interdisciplinary study, including making connections, project-based learning, and student engagement and affective outcomes. The findings of the study showed that students were positive about their experiences in the course, and enjoyed its project-driven nature. Content from mathematics, physics, and technological design was easily integrated under the umbrella of engineering. Students felt that the opportunity to develop problem solving and teamwork skills were two of the most important aspects of the course and could be relevant not only for engineering, but for other disciplines or their day-to-day lives after secondary school. The study concluded that engineering education in secondary school can be a worthwhile experience for a variety of students and not just those intending postsecondary study in engineering. This has implications for the inclusion of engineering in the secondary school curriculum and can inform the practice of curriculum planners at the school, school board, and provincial levels. Suggested directions for further research include classroom-based action research in the areas of technological education, engineering education in secondary school, and interdisciplinary education.

Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.