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Dissertation examined the impact of the application of ICT on IV-th grade students mathematical competence development(sef-development). / Disertacijoje nagrinėjamas IKT taikymo poveikis IV klasės mokinių matematinės kompetencijos ugdymui(si).

What students should learn in school and therefore also what teachers should teach is an important issue worldwide. Mathematics teaching (and teaching in other subjects) is often regulated by some form of governing text in a written curriculum communcating a set of standards. Another common mean through which policy is communicated is assessments, which for example can convey policy by communicating desirable outcomes in student learning. A common problem with regulating what teachers do through policy means is that it often is difficult to achieve intended changes. This study investigates the impact of a national reform in Sweden initiated in 1994, introducing mathematical competency goals by communicating them through the national curriculum and national assessments. The study is based on analysis of data obtained from the Swedish Schools Inspectorate (SSI), which conducted a quality review of upper secondary school mathematics teaching. During this quality review, the SSI collected data on a representative sample of 145 upper secondary mathematics teachers through interviews, observations, and surveys. This was done in 2009 and 2010, which means that the reform from a time perspective has had ample time to exert influence on teachers. In the study the data obtained from the SSI was analyzed in order to answer two questions:  have teachers changed their beliefs about the goals of upper secondary school mathematics in line with the intentions of the reform, and why have, or have they not, changed their beliefs about the goals of upper secondary school mathematics in line with the intentions of the reform? In research on teachers’ reception of policy messages, similar to the one introduced in Sweden, it has been found that a common response to these messages is that teachers are positive to the message. However, although positive, teachers have often been found to only adopt superficial properties of the reform while still maintaining a highly traditional view of teaching and the goals of teaching, not consistent with the intentions of the reform. Therefore, the questions in this study were examined by using a model that can explain why teachers, when confronted with a reform message, change their beliefs in profound or superficial ways, or not at all. Through analysis of the SSI-data, measures on constructs of the model were obtained, and with statistical means it was examined whether the model can account for the changes in teachers’ beliefs about the goals of upper secondary school mathematics. The results of the study suggest that the Swedish reform has had a relatively small impact, and that the model can give an explanation to why some Swedish upper secondary teachers of mathematics have changed their beliefs in line with the reform, some have changed them in superficial ways, and some have not changed them in any discernable way. Whether teachers perceive the reform as entailing an important and non-trivial change for them seems to be of utmost importance. The results of this study suggest that if teachers do not perceive this, they will not process the message deeply, which by the results of this study suggest that there is little chance for them to change their beliefs in a profound way. If they however do perceive the message as entailing an important and non-trivial change, this study suggests that chances are greater that teachers will change their beliefs in line with the reform. Teachers’ interest in the subject and their perceptions of the usefulness of the documents communicating the message are then in this study suggested to be important factors influencing whether teachers will process the reform message systematically, which in turn heavily influences whether they will change their beliefs in a profound way. One practical implication, suggested by this study is that when policy communicates a new and non-trivial message with the intention of influencing teachers, it is important that the message is communicated clearly. Such clarity makes it more difficult for a teacher to superficially interpret the message as being in accordance with the teacher’s earlier beliefs, and thus not entail any need for change. However, to attain such clarity of a complex message is not an easy task to accomplish.

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La presente investigación denominada “Actividades interactivas con Jclic-Hot potatoes para lograr la competencia resuelve problemas de movimiento, forma y localización”, de enfoque cuantitativo, y tipo cuasi experimental, tuvo el objetivo de determinar en qué medida influyen las actividades interactivas ut supra, en el logro de la competencia matemática mencionada, en alumnas de 4° “B” de Educación Secundaria de la Institución Educativa Sara Antonieta Bullón Lamadrid de la ciudad de Lambayeque, en el año 2019, aplicando el modelo de diseño instruccional ADDIE El estudio consideró una muestra estadística conformada por los grupos experimental y control con 30 discentes de cuarto grado, pertenecientes a una población de 210 alumnas. Se aplicó el instrumento ficha de registro y la data obtenida fue procesada mediante el estadístico T Student, interpretándose y discutiéndose, a la luz del marco teórico. Finalmente, se demostró la hipótesis que Las actividades interactivas con Jclic-Hot Potatoes influyen en el logro de la competencia Resuelve Problemas de Movimiento, Forma y Localización en estudiantes de 4° “B” de educación secundaria de la entidad educativa Sara Antonieta Bullón Lamadrid de la ciudad de Lambayeque, en el año 2019; concluyéndose con la pertinencia del empleo de los softwares educativos mencionados. / The present investigation called "Interactive activities with Jclic-Hot potatoes to achieve competence solves problems of movement, shape and location", of a quantitative approach, and quasi-experimental type, had the objective of determining to what extent the activities influence interactive ut supra, in the achievement of the aforementioned mathematical competence, in students of 4th "B" of Secondary Education of the Sara Antonieta Bullón Lamadrid Educational Institution of the city of Lambayeque, in the year 2019, applying the ADDIE instructional design model The study considered a statistical sample made up of the experimental and control groups with 30 fourth grade students, belonging to a population of 210 female students. The registration form instrument was applied and the data obtained was processed using the T Student statistic, interpreting and discussing it, in light of the theoretical framework. Finally, the hypothesis was demonstrated that the interactive activities with JclicHot Potatoes influence the achievement of the competence Solve Problems of Movement, Shape and Location in students of 4th "B" of secondary education of the educational entity Sara Antonieta Bullón Lamadrid de the city of Lambayeque, in the year 2019; concluding with the relevance of the use of the mentioned educational software.

<p>Students’ use of superficial reasoning seems to be a main reason for learning difficulties in mathematics. It is therefore important to investigate the reasons for this use and the components that may affect students’ mathematical reasoning development. Assessments have been claimed to be a component that significantly may influence students’ learning.</p><p>The purpose of the study in Paper 1 was to investigate the kind of mathematical reasoning that is required to successfully solve tasks in the written tests students encounter in their learning environment. This study showed that a majority of the tasks in teacher-made assessment could be solved successfully by using only imitative reasoning. The national tests however required creative mathematically founded reasoning to a much higher extent.</p><p>The question about what kind of reasoning the students really use, regardless of what theoretically has been claimed to be required on these tests, still remains. This question is investigated in Paper 2.</p><p>Here is also the relation between the theoretically established reasoning requirements, i.e. the kind of reasoning the students have to use in order to successfully solve included tasks, and the reasoning actually used by students studied. The results showed that the students to large extent did apply the same reasoning as were required, which means that the framework and analysis procedure can be valuable tools when developing tests. It also strengthens many of the results throughout this thesis. A consequence of this concordance is that as in the case with national tests with high demands regarding reasoning also resulted in a higher use of such reasoning, i.e. creative mathematically founded reasoning. Paper 2 can thus be seen to have validated the used framework and the analysis procedure for establishing these requirements.</p><p>Paper 3 investigates the reasons for why the teacher-made tests emphasises low-quality reasoning found in paper I. In short the study showed that the high degree of tasks solvable by imitative reasoning in teacher-made tests seems explainable by amalgamating the following</p><p>factors: (i) Limited awareness of differences in reasoning requirements, (ii) low expectations of students abilities and (iii) the desire to get students passing the tests, which was believed easier when excluding creative reasoning from the tests.</p><p>Information about these reasons is decisive for the possibilities of changing this emphasis. Results from this study can also be used heuristically to explain some of the results found in paper 4, concerning those teachers that did not seem to be influenced by the national tests.</p><p>There are many suggestions in the literature that high-stake tests affect practice in the classroom. Therefore, the national tests may influence teachers in their development of classroom tests. Findings from paper I suggests that this proposed impact seem to have had a limited effect, at least regarding the kind of reasoning required to solve included tasks. What about other competencies described in the policy documents?</p><p>Paper 4 investigates if the Swedish national tests have had such an impact on teacher-made classroom assessment. Results showed that impact in terms of similar distribution of tested competences is very limited. The study however showed the existence of impact from the national tests on teachers test development and how this impact may operate.</p>

Students’ use of superficial reasoning seems to be a main reason for learning difficulties in mathematics. It is therefore important to investigate the reasons for this use and the components that may affect students’ mathematical reasoning development. Assessments have been claimed to be a component that significantly may influence students’ learning. The purpose of the study in Paper 1 was to investigate the kind of mathematical reasoning that is required to successfully solve tasks in the written tests students encounter in their learning environment. This study showed that a majority of the tasks in teacher-made assessment could be solved successfully by using only imitative reasoning. The national tests however required creative mathematically founded reasoning to a much higher extent. The question about what kind of reasoning the students really use, regardless of what theoretically has been claimed to be required on these tests, still remains. This question is investigated in Paper 2. Here is also the relation between the theoretically established reasoning requirements, i.e. the kind of reasoning the students have to use in order to successfully solve included tasks, and the reasoning actually used by students studied. The results showed that the students to large extent did apply the same reasoning as were required, which means that the framework and analysis procedure can be valuable tools when developing tests. It also strengthens many of the results throughout this thesis. A consequence of this concordance is that as in the case with national tests with high demands regarding reasoning also resulted in a higher use of such reasoning, i.e. creative mathematically founded reasoning. Paper 2 can thus be seen to have validated the used framework and the analysis procedure for establishing these requirements. Paper 3 investigates the reasons for why the teacher-made tests emphasises low-quality reasoning found in paper I. In short the study showed that the high degree of tasks solvable by imitative reasoning in teacher-made tests seems explainable by amalgamating the following factors: (i) Limited awareness of differences in reasoning requirements, (ii) low expectations of students abilities and (iii) the desire to get students passing the tests, which was believed easier when excluding creative reasoning from the tests. Information about these reasons is decisive for the possibilities of changing this emphasis. Results from this study can also be used heuristically to explain some of the results found in paper 4, concerning those teachers that did not seem to be influenced by the national tests. There are many suggestions in the literature that high-stake tests affect practice in the classroom. Therefore, the national tests may influence teachers in their development of classroom tests. Findings from paper I suggests that this proposed impact seem to have had a limited effect, at least regarding the kind of reasoning required to solve included tasks. What about other competencies described in the policy documents? Paper 4 investigates if the Swedish national tests have had such an impact on teacher-made classroom assessment. Results showed that impact in terms of similar distribution of tested competences is very limited. The study however showed the existence of impact from the national tests on teachers test development and how this impact may operate.

According to the Swedish curriculum for the compulsory school, every teacher has an obligation to differentiate students’ education to promote their development and learning needs. The study carried out in this paper is a qualitative interview study with Swedish teachers that have experience teaching particularly gifted students in mathematics. The study is based on the implementation theory where the aim of the study is to present an overview of different challenges that teachers encounter when trying to implement the decisions made regarding education of gifted students in mathematics. Furthermore, the aim of the study was to see if there were differences, and what those differences were, between the challenges that Swedish teachers mentioned versus the challenges that are acknowledged in previous international research.  A deductive approach is used rooting the analysis in key concepts based on previous research. The key concepts or challenges we found were mathematical competence, student interests and motivations, appropriate challenge for students, inclusion, identification, prioritizing, time, materials, lack of education and collegial cooperation. We found plenty of similarities to the previous research on the area but could however also see tendencies in our study which hasn’t been discussed in the presented previous research. For example, we noticed that teachers in our study mentioned the importance of experience. We also noticed that some of the key challenges from the previous research didn’t seem to be as prominent in this study.