Topics from elementary number theory; divisibility, prime numbers, the Euclidian Algorithm, solutions of Diophantine equations and some theorems involving congruences like the Chinese Remainder Theorem and Fermat’s Little Theorem. Rational numbers and irrational numbers.

Course description: The fundamental concepts of calculus will be discussed. Subjects: Limits and continuous functions. Differentiable functions, rules for derivatives, derivatives of higher order, antiderivatives. Applications of differential calculus: Extremal value problems, linear approximation. The main functions in calculus: logarithms, exponential functions and trigonometric functions. The mean value theorem. Integration: The definite integral and rules of integration. The fundamental theorem of calculus. Techniques of integration, improper integrals. Series and sequences. Ordinary differential equations. Vectors and matrix calculations.

The course will cover topics in algebra, school algebra and the history of algebra. The teaching of algebra at different school levels will be examined as well as the developement of algebraic thinking in different age groups.

 Part of the course are in-field studies where students prepare and teach algebra.

This course intertwines mathematics and mathematics education. Students get an introduction to probability and statistics, build mathematical models, and learn to approach the teaching of mathematics from a modelling perspective. Among topics covered are combinations, permutations, the counting of the number of outcomes, the binomial distribution, and probability distributions in general. Students will explore how conclusions are drawn about probability based on data and how computer simulations can be used for that purpose. Different types of mathematical models will be introduced, such as linear models, exponential growth models, inverse proportion models, power functions models, linear optimization models in two variables, and graph theoretical models.

The didactics of probability and statistics will be explored and analysed from a modelling perspective. Students will select and adapt exercises and problems for the teaching of probability and statistics, and plan teaching processes. An emphasis will be put on mathematics teaching that touches on important issues of the modern times, such as climate change and pandemics.

In the course there is emphasis on students‘ mathematical reasoning and ability to write simple proofs.

The term group and related terms will be defined. Many examples based on traditional arithmetic in known sets of numbers will be examined, but also more abstract examples such as finite groups and permutation groups. Rings and fields are introduced. Connections between arithmetic and algebra at secondary school level with groups, rings and fields are examined.

Topics from Euclidian geometry. Foundations and systematic development of elementary geometry of the plane. Concepts, postulates, definitions, and theorems involving parallel lines polygons and circles. Attention is given to reasoning and proving theorems. A brief discussion of the geometry of solids. Calculation of area and volume.

This course focuses on theories and research related to learning, teaching and the teacher profession. Relations with on-site activities are emphasised, and that participants become familiar with the working environment of compulsory school teachers, compulsory school act and regulations.

Learning and teaching are discussed from various points of view and with respect to various learning theories. Participants organise their own teaching processes by making aims, organising teaching and learning, and organising interaction and collaboration. All this work is related do the conceptions of professionalism and practice theories.

Course design and procedure: Lectures, reflective studies, seminars, individual and group work, projects, interactive lectures, field work and training

Content: The main goal of the course is to give insight into the sociology and philosophy of education. Selected sociological and philosophical ideas that are useful to study education and the school reality will be discussed. There is emphasis on three things. A. To understand ideas and concepts og be able to explain them. B. To compare ideas and concepts to the education and the school reality that we are familiar with. C. To think critically about the ideas and the reality that they are meant to throw light on.

 Methods: There are weekly lectures and discussions. Lectures will be recorded and uploaded to the course‘s Canvas site. Students study them and then take part in discussions that will not be recorded. At the beginning of the semester students register for discussion groups which are then fixed for the semester. There is obligatory attendance (80%) for discussion classes, but students can choose to attend at Stakkahlíð or in realtime on Zoom. Students do two group assignments, two individual assignments and a final assignment.

The course aims to expose students to perspectives on curriculum and assessment in compulsory education, from theory to practice. Students discuss and learn about basic concepts and issues related to curriculum theory as they appear in public schools. Issues and ideologies reflected in official curricula, laws, directives, and other policy briefings are discussed both theoretically and as they appear in praxis. Special focus is laid on the role of teachers and administrators in curriculum development and assessment, and alternatively their professional role in developing learning programs for groups of pupils as well as individual pupils with special needs. Nature, purpose, and strategies regarding assessment and curriculum are addressed (cf. formative assessment, summative assessment, writing test items and other test instruments, and marking and reporting). Students discuss and learn about controversial issues and different ideological currents concerning central questions about the purpose and aims of compulsory education.

The working process of the course consists of lectures, and critical discussion through seminars and group assignments

Course description in English:*  This course aims to prepare students to use programming and computational thinking strategies to create computer graphics and solve problems of various kinds, and furthermore to prepare students for teaching these same topics to pupils in compulsory school and upper secondary school. No previous experience or knowledge of programming is required before starting the course.

The courses mathematical topics are mainly coordinate geometry and the fundamentals of computational thinking: abstraction, decomposition, algorithmic thinking, debugging, automation and generalization. Students will learn about the use of variables, functions, loops, and logical operators in programming. Students will learn to use computational thinking strategies to build simple computer models, such as computer games or art, and to use programming for solving mathematical tasks.

Students will also learn to plan lessons in compulsory and upper secondary school, aiming for the development of students’ computational thinking and creative programming skills, along with the use of programming for investigating mathematical topics. The dynamic geometry software GeoGebra will be put into a computational thinking perspective and its possibilities for mathematics teaching will be explored. The position of programming and computational thinking in society and the educational system will be discussed, also in connection with other school subjects.

Course participation involves mostly the solving of tasks, reading, and participation in a critical discussion.

The central objective of this course is for students to develop their ideas about literacy and how to intergrade literacy across subjects so that they will be better equipped to teach their own subject.

During their studies student develop their own personal theory, i.e. research and mould their ideas about how they will or want to perform as teachers.

An emphasis will be placed on a coherent and creative approach towards planning and organising teaching across subjects and that students will be introduce to research and novelties in teaching methods that enhance literacy and subject-based vocabulary in all school levels.

The purpose of this course is to work with conceptual issues in sustainability and global initiative such as those being implemented by the UNESCO. Examples of problems in the environment and nature will be explored, f.ex. climate change, decrease in number of species, soil erosion and pollution. Emphasis will be on the role of teachers in dealing with controversial issues and how they can teach children to analyse problems, evaluate information and put forward possible solutions. Participants read and use research about sustainability education. Participants will also examine their own angle to sustainability, their values and behaviour. 

It is obligatory to attend classes during On Campus weeks, according to the academic calendar for School of Education.

This course focuses on providing the student teachers with competences for becoming professionals in their field, with focus on their subject area, and supporting them in laying the foundation for their own professional working theory. This will be obtained by building up knowledge and understanding of the responsibilities which is imbued in teaching and the skills needed for self evaluation in various situations in the field. An emphasis is also put on providing the student teachers with skills regarding the role of the classroom teacher and classroom management; team-teaching and co-operative skills; how to deal with traumatic experiences and children's welfare; and working with parents. Furthermore, research on school development, school evaluation and school ethos will be looked into together with research on teachers. Finally this will be linked with practicum.

Emphasis is on interactive lectures, inquiry and reflective studies, seminars, group work, projects, portfolios, field studies and fieldwork.

The main task of this course is field work, subject teaching at middle and lower secondary level compulsory school. The emphasis is on actual teaching practise and giving the students opportunities to discuss, evaluate, reflect and develop their teaching. Students will develop a teaching plan based on the national curriculum guide and school curricula. They will analyse incidents from their practice to learn from and improve their teaching. A range of teaching methods will be explored and applied in teaching in the field.

Teaching methods: Students are in the field the whole semester in both courses and attend regular classes at the university. Emphasis is on interactive lectures, self-study, group work and projects. The course of study is directly related to field practice. Various issues will be explored with concrete examples from school practice. Students read chosen materials and research on school practice, both provided by lecturers and chosen by students.

In this course the focus is on Icelandic as a second language and the education of multilingual students in Icelandic compulsory schools. Language acquisition and language upbringing will be examined and the difference between acquiring skills in a first and a second language. The emphases will be on what it is that teachers in general need to know about the Icelandic language to be able to help their students make progress in the subject being taught.

The structure of the Icelandic language system, pronunciation, word formation, inflections, sentence structure, meaning of words and phrases, the three layers of the vocabulary, and various things related to language use will be studied. The purpose is to figure out what is most likely to be demanding for multilingual students in preschools who are acquiring the language, both in general but also due to personal differences, such as different first languages.

Based on this special attention will be paid to the teaching of different subjects and how they can be planned, taking in account students’ different level of Icelandic. Important aspect of that is how subject texts can be simplified to fit the needs of multilingual students.

In this course, students learn about some of the main theories in mathematics education and about research on mathematics learning and teaching. In focus is mathematics teaching in schools, individual learning and the societal roles of mathematics and mathematics education. Students also deepen their understanding of mathematics and mathematics education by engaging with mathematics tasks and working on ways to adapt and develop mathematics tasks for primary and secondary school students. Emphasis is placed on how teachers can make use of theory in order to plan and implement mathematics teaching for all, such that it is based on care for mathematics learning.

Topics from elementary number theory; divisibility, prime numbers, the Euclidian Algorithm, solutions of Diophantine equations and some theorems involving congruences like the Chinese Remainder Theorem and Fermat’s Little Theorem. Rational numbers and irrational numbers.

Course description: The fundamental concepts of calculus will be discussed. Subjects: Limits and continuous functions. Differentiable functions, rules for derivatives, derivatives of higher order, antiderivatives. Applications of differential calculus: Extremal value problems, linear approximation. The main functions in calculus: logarithms, exponential functions and trigonometric functions. The mean value theorem. Integration: The definite integral and rules of integration. The fundamental theorem of calculus. Techniques of integration, improper integrals. Series and sequences. Ordinary differential equations. Vectors and matrix calculations.

The course will cover topics in algebra, school algebra and the history of algebra. The teaching of algebra at different school levels will be examined as well as the developement of algebraic thinking in different age groups.

 Part of the course are in-field studies where students prepare and teach algebra.

This course intertwines mathematics and mathematics education. Students get an introduction to probability and statistics, build mathematical models, and learn to approach the teaching of mathematics from a modelling perspective. Among topics covered are combinations, permutations, the counting of the number of outcomes, the binomial distribution, and probability distributions in general. Students will explore how conclusions are drawn about probability based on data and how computer simulations can be used for that purpose. Different types of mathematical models will be introduced, such as linear models, exponential growth models, inverse proportion models, power functions models, linear optimization models in two variables, and graph theoretical models.

The didactics of probability and statistics will be explored and analysed from a modelling perspective. Students will select and adapt exercises and problems for the teaching of probability and statistics, and plan teaching processes. An emphasis will be put on mathematics teaching that touches on important issues of the modern times, such as climate change and pandemics.

In the course there is emphasis on students‘ mathematical reasoning and ability to write simple proofs.

The term group and related terms will be defined. Many examples based on traditional arithmetic in known sets of numbers will be examined, but also more abstract examples such as finite groups and permutation groups. Rings and fields are introduced. Connections between arithmetic and algebra at secondary school level with groups, rings and fields are examined.

Topics from Euclidian geometry. Foundations and systematic development of elementary geometry of the plane. Concepts, postulates, definitions, and theorems involving parallel lines polygons and circles. Attention is given to reasoning and proving theorems. A brief discussion of the geometry of solids. Calculation of area and volume.

This course focuses on theories and research related to learning, teaching and the teacher profession. Relations with on-site activities are emphasised, and that participants become familiar with the working environment of compulsory school teachers, compulsory school act and regulations.

Learning and teaching are discussed from various points of view and with respect to various learning theories. Participants organise their own teaching processes by making aims, organising teaching and learning, and organising interaction and collaboration. All this work is related do the conceptions of professionalism and practice theories.

Course design and procedure: Lectures, reflective studies, seminars, individual and group work, projects, interactive lectures, field work and training

Content: The main goal of the course is to give insight into the sociology and philosophy of education. Selected sociological and philosophical ideas that are useful to study education and the school reality will be discussed. There is emphasis on three things. A. To understand ideas and concepts og be able to explain them. B. To compare ideas and concepts to the education and the school reality that we are familiar with. C. To think critically about the ideas and the reality that they are meant to throw light on.

 Methods: There are weekly lectures and discussions. Lectures will be recorded and uploaded to the course‘s Canvas site. Students study them and then take part in discussions that will not be recorded. At the beginning of the semester students register for discussion groups which are then fixed for the semester. There is obligatory attendance (80%) for discussion classes, but students can choose to attend at Stakkahlíð or in realtime on Zoom. Students do two group assignments, two individual assignments and a final assignment.

The course aims to expose students to perspectives on curriculum and assessment in compulsory education, from theory to practice. Students discuss and learn about basic concepts and issues related to curriculum theory as they appear in public schools. Issues and ideologies reflected in official curricula, laws, directives, and other policy briefings are discussed both theoretically and as they appear in praxis. Special focus is laid on the role of teachers and administrators in curriculum development and assessment, and alternatively their professional role in developing learning programs for groups of pupils as well as individual pupils with special needs. Nature, purpose, and strategies regarding assessment and curriculum are addressed (cf. formative assessment, summative assessment, writing test items and other test instruments, and marking and reporting). Students discuss and learn about controversial issues and different ideological currents concerning central questions about the purpose and aims of compulsory education.

The working process of the course consists of lectures, and critical discussion through seminars and group assignments

Course description in English:*  This course aims to prepare students to use programming and computational thinking strategies to create computer graphics and solve problems of various kinds, and furthermore to prepare students for teaching these same topics to pupils in compulsory school and upper secondary school. No previous experience or knowledge of programming is required before starting the course.

The courses mathematical topics are mainly coordinate geometry and the fundamentals of computational thinking: abstraction, decomposition, algorithmic thinking, debugging, automation and generalization. Students will learn about the use of variables, functions, loops, and logical operators in programming. Students will learn to use computational thinking strategies to build simple computer models, such as computer games or art, and to use programming for solving mathematical tasks.

Students will also learn to plan lessons in compulsory and upper secondary school, aiming for the development of students’ computational thinking and creative programming skills, along with the use of programming for investigating mathematical topics. The dynamic geometry software GeoGebra will be put into a computational thinking perspective and its possibilities for mathematics teaching will be explored. The position of programming and computational thinking in society and the educational system will be discussed, also in connection with other school subjects.

Course participation involves mostly the solving of tasks, reading, and participation in a critical discussion.

The central objective of this course is for students to develop their ideas about literacy and how to intergrade literacy across subjects so that they will be better equipped to teach their own subject.

During their studies student develop their own personal theory, i.e. research and mould their ideas about how they will or want to perform as teachers.

An emphasis will be placed on a coherent and creative approach towards planning and organising teaching across subjects and that students will be introduce to research and novelties in teaching methods that enhance literacy and subject-based vocabulary in all school levels.

The purpose of this course is to work with conceptual issues in sustainability and global initiative such as those being implemented by the UNESCO. Examples of problems in the environment and nature will be explored, f.ex. climate change, decrease in number of species, soil erosion and pollution. Emphasis will be on the role of teachers in dealing with controversial issues and how they can teach children to analyse problems, evaluate information and put forward possible solutions. Participants read and use research about sustainability education. Participants will also examine their own angle to sustainability, their values and behaviour. 

It is obligatory to attend classes during On Campus weeks, according to the academic calendar for School of Education.

This course focuses on providing the student teachers with competences for becoming professionals in their field, with focus on their subject area, and supporting them in laying the foundation for their own professional working theory. This will be obtained by building up knowledge and understanding of the responsibilities which is imbued in teaching and the skills needed for self evaluation in various situations in the field. An emphasis is also put on providing the student teachers with skills regarding the role of the classroom teacher and classroom management; team-teaching and co-operative skills; how to deal with traumatic experiences and children's welfare; and working with parents. Furthermore, research on school development, school evaluation and school ethos will be looked into together with research on teachers. Finally this will be linked with practicum.

Emphasis is on interactive lectures, inquiry and reflective studies, seminars, group work, projects, portfolios, field studies and fieldwork.

The main task of this course is field work, subject teaching at middle and lower secondary level compulsory school. The emphasis is on actual teaching practise and giving the students opportunities to discuss, evaluate, reflect and develop their teaching. Students will develop a teaching plan based on the national curriculum guide and school curricula. They will analyse incidents from their practice to learn from and improve their teaching. A range of teaching methods will be explored and applied in teaching in the field.

Teaching methods: Students are in the field the whole semester in both courses and attend regular classes at the university. Emphasis is on interactive lectures, self-study, group work and projects. The course of study is directly related to field practice. Various issues will be explored with concrete examples from school practice. Students read chosen materials and research on school practice, both provided by lecturers and chosen by students.

In this course the focus is on Icelandic as a second language and the education of multilingual students in Icelandic compulsory schools. Language acquisition and language upbringing will be examined and the difference between acquiring skills in a first and a second language. The emphases will be on what it is that teachers in general need to know about the Icelandic language to be able to help their students make progress in the subject being taught.

The structure of the Icelandic language system, pronunciation, word formation, inflections, sentence structure, meaning of words and phrases, the three layers of the vocabulary, and various things related to language use will be studied. The purpose is to figure out what is most likely to be demanding for multilingual students in preschools who are acquiring the language, both in general but also due to personal differences, such as different first languages.

Based on this special attention will be paid to the teaching of different subjects and how they can be planned, taking in account students’ different level of Icelandic. Important aspect of that is how subject texts can be simplified to fit the needs of multilingual students.

In this course, students learn about some of the main theories in mathematics education and about research on mathematics learning and teaching. In focus is mathematics teaching in schools, individual learning and the societal roles of mathematics and mathematics education. Students also deepen their understanding of mathematics and mathematics education by engaging with mathematics tasks and working on ways to adapt and develop mathematics tasks for primary and secondary school students. Emphasis is placed on how teachers can make use of theory in order to plan and implement mathematics teaching for all, such that it is based on care for mathematics learning.

Topics from elementary number theory; divisibility, prime numbers, the Euclidian Algorithm, solutions of Diophantine equations and some theorems involving congruences like the Chinese Remainder Theorem and Fermat’s Little Theorem. Rational numbers and irrational numbers.

Course description: The fundamental concepts of calculus will be discussed. Subjects: Limits and continuous functions. Differentiable functions, rules for derivatives, derivatives of higher order, antiderivatives. Applications of differential calculus: Extremal value problems, linear approximation. The main functions in calculus: logarithms, exponential functions and trigonometric functions. The mean value theorem. Integration: The definite integral and rules of integration. The fundamental theorem of calculus. Techniques of integration, improper integrals. Series and sequences. Ordinary differential equations. Vectors and matrix calculations.

In the course there is emphasis on students‘ mathematical reasoning and ability to write simple proofs.

The term group and related terms will be defined. Many examples based on traditional arithmetic in known sets of numbers will be examined, but also more abstract examples such as finite groups and permutation groups. Rings and fields are introduced. Connections between arithmetic and algebra at secondary school level with groups, rings and fields are examined.

Topics from Euclidian geometry. Foundations and systematic development of elementary geometry of the plane. Concepts, postulates, definitions, and theorems involving parallel lines polygons and circles. Attention is given to reasoning and proving theorems. A brief discussion of the geometry of solids. Calculation of area and volume.

In this course students explore teaching of diverse groups in inclusive settings, emphasizing strategies to address diverse educational and sociological needs of students, guided by human values, democracy and social justice. The emphasis is on evidence-based strategies to address the most common students´ special needs related to reading difficulties, behavioral difficulties, attention deficit, hyperactivity, and autism spectrum disorder. At the same time the use of respectful, person-first language, putting strengths and talents of students in the foreground, is stressed. Multicultural teaching and teaching of students learning Icelandic as a second language will be addressed. Students will be introduced to classroom management strategies, individualized behavior support, multi-disciplinary and parent collaboration. The course focus is on inclusive, evidence-based practices that aim to provide students with special needs opportunities equal to those of their classmates.

Issues, concepts and theories in the field of distance education will be explored. Development and trends will be examined from the emphasis on independent study to emphasis on social activities and shared knowledge construction online and global. The focus will also be on research on distance education at different school levels in Iceland and other countries, distance learners and their needs, and teaching methods with different types of media. The design of distance or online courses and programs will be explored as well as international standards for such courses.

Students participate in online synchronous and asynchronous discussion about theory and practice concerning distance education (DE), engage in problem-based learning (group work) and do an individual project that could involve design of a DE course, a study concerning DE, or a paper on topics related to DE.

Objectives
The objectives of the course are threefold. First, to provide insight into selected learning theories. Second, to enable  students to gain understanding of how these theories can be applied to upbringing, teaching, and the organization of learning for people of all ages. Third, to increase knowledge of research on the effects of different approaches to teaching and evidence-based practices to reach a variety of learning objectives.   

Content

• Among the main learning theories covered in the course are those from the cognitive, behavioural, and motivational domains.
• Main concepts related to the learning theories will be introduced and discussed in relation to how learning can be defined in different ways.
• Students will read research articles where these learning theories are studied and applied in practice.
• Emphasis will be placed on understanding what constitutes evidence-based practice. 
• Students will design a learning plan for a student or a group of students, based upon one of the learning theories approaches discussed in the course. Through this assignment the students will deepen their understanding of the learning theory in question and how to apply it in practice. 

Content: The main goal of the course is to give insight into the sociology and philosophy of education. Selected sociological and philosophical ideas that are useful to study education and the school reality will be discussed. There is emphasis on three things. A. To understand ideas and concepts og be able to explain them. B. To compare ideas and concepts to the education and the school reality that we are familiar with. C. To think critically about the ideas and the reality that they are meant to throw light on.

 Methods: There are weekly lectures and discussions. Lectures will be recorded and uploaded to the course‘s Canvas site. Students study them and then take part in discussions that will not be recorded. At the beginning of the semester students register for discussion groups which are then fixed for the semester. There is obligatory attendance (80%) for discussion classes, but students can choose to attend at Stakkahlíð or in realtime on Zoom. Students do two group assignments, two individual assignments and a final assignment.

The course focuses on:

• the effects of information and communications technology (ICT) on education and schools
• ICT-related policy, curriculum and school practice
• Concepts, theories and research related to the use of ICT in schools
• technology integration in schools
• teaching methods, professional development of teachers, software and digital learning materials
• students' and teachers' digital competence, ICT skills, and media literacy
• ICT as part of everyday life

Approach:
Reading and discussion about curriculum, policy, theory, research and practice. Students work alone or in smaller groups on literature research and introduce various topics of their choice. They share their ideas and experiences of ICT uses in learning and teaching and contribute to the construction of a learning and professional community in the area of ICT in education.

This course deals with the spectrum of teaching methods from direct and formal approaches to informal methods. Emphasis is put on theoretical underpinnings and research on teaching methods, especially Icelandic research. Special attention is put on examining differentiated and responsive approaches (such as the open school concept, flexible teaching, cooperation, multi-age teaching, problem-based learning, holistic education, project-based learning, negotiating the curriculum and authentic learning).

In this course, students learn about some of the main theories in mathematics education and about research on mathematics learning and teaching. In focus is mathematics teaching in schools, individual learning and the societal roles of mathematics and mathematics education. Students also deepen their understanding of mathematics and mathematics education by engaging with mathematics tasks and working on ways to adapt and develop mathematics tasks for primary and secondary school students. Emphasis is placed on how teachers can make use of theory in order to plan and implement mathematics teaching for all, such that it is based on care for mathematics learning.

Course description in English:*  This course aims to prepare students to use programming and computational thinking strategies to create computer graphics and solve problems of various kinds, and furthermore to prepare students for teaching these same topics to pupils in compulsory school and upper secondary school. No previous experience or knowledge of programming is required before starting the course.

The courses mathematical topics are mainly coordinate geometry and the fundamentals of computational thinking: abstraction, decomposition, algorithmic thinking, debugging, automation and generalization. Students will learn about the use of variables, functions, loops, and logical operators in programming. Students will learn to use computational thinking strategies to build simple computer models, such as computer games or art, and to use programming for solving mathematical tasks.

Students will also learn to plan lessons in compulsory and upper secondary school, aiming for the development of students’ computational thinking and creative programming skills, along with the use of programming for investigating mathematical topics. The dynamic geometry software GeoGebra will be put into a computational thinking perspective and its possibilities for mathematics teaching will be explored. The position of programming and computational thinking in society and the educational system will be discussed, also in connection with other school subjects.

Course participation involves mostly the solving of tasks, reading, and participation in a critical discussion.

In this course, students learn to plan mathematics teaching in upper secondary school using various approaches to provide access for all. An emphasis will be put on exploring different teaching environments and teaching methods that build on research on the teaching and learning of mathematics. In the course, the aims of learning mathematics both in Iceland and its neighboring countries will be discussed based on curricular and governmental documents. Students will read about and get a chance to try out various ways to assess and analyze students’ mathematical achievements. The course format includes lectures, project work, presentations, topic studies connected to practice, and critical topic discussion. An emphasis will be put on students’ discussion about challenges and their search for solutions to problems related to the teaching and learning of mathematics.

The course aims to prepare participants to draw on their resources in their work with diverse groups of students. In the course, we draw on inclusive education theories and research, emphasizing a holistic and creative approach to preparation and teaching at the forefront. Furthermore, a focus is put on teaching strategies and educative assessment that works for diverse groups of students, and adapting teaching and learning to students with special needs.

Content
The focus of the course is on inclusive practices. How to create a learning environment that cares for all students learning is introduced. The focus is also on collaboration with parents, colleagues, professionals, and paraprofessionals. 

Work process
The course is a blended course online and on campus. It is divided into four main themes. All the themes connect to teaching in inclusive educational settings. The focus on each theme is three or four weeks.

The teaching is through lectures, projects, collaboration, discussions in class, on canvas, and in formal assignments. The course is grounded in students' independence, responsibility, and participation.

This course focuses on qualitative research methods. It looks at different movements and traditions in research methodology and their relationship to the structure and execution of research. The course also touches on the ethics of research, validity and different views of these concepts. Students will conduct a small research project, which provides training in a literature review, data collection, data analysis, and presentation of research findings. Students work as a team throughout the semester.

Readings, lectures, in-class discussion and group work. Sessions for distance students are held twice during the semester and participation is mandatory

Students in this course are expected to deepen their knowledge and skills in quantitative research methodology. Students will use a computer program for data analysis, with emphasis on interpretation and writing about research results. Students are expected to develop positive attitudes toward research and the value of research in educational and social settings.

Topic 
Participants familiarize themselves with research on mathematics studies and how an understanding of mathematics develops. They learn to analyze the knowledge and understanding of the student group and evaluate their learning process. They learn about difficulties in mathematics that students encounter, their impact on learning, and the methods for diagnosing them. Participants acquire knowledge of teaching methods and resources for students of different backgrounds, including diverse linguistic and cultural backgrounds.

Activities
Building a learning community where all participants are expected to be active in shaping the learning culture is at the core of the course. Students can participate on campus, online, and through the course webpage. The coursework is based on lectures, seminars, and individual and group assignments.

Students conduct a small-scale investigation on mathematical learning. Based on their learning in the course, they plan a developmental study within schools. Emphasis is on how they can build a learning community that supports children in learning mathematics.

Topic:
The focus of the couse is on new research on children's mathematical thinking. Students study the development of children's understanding of mathematics and mathematical content knowledge. Emphasis is on the foundation of mathematics learning that develops in the early years and how to build a learning community that supports children in learning mathematics through play and everyday activities. Research methodologies applied in research on children's mathematical thinking will be explored. 

Activities:
Building a learning community where all participants are expected to be active in shaping the learning culture is at the core of the course. Students can participate on campus, online and through the course webpage. The course readings will be discussed and explored. Students participate in activities that will support them in being able to work in a creative way within their schools. 

Students conduct a small scale investigation on young children's mathematical learning. Based on their learning at the course they plan a developmental study within preschool or in primary grades.  Emphasis is on how they can build a learning community that supports children in learning mathematics through play and everyday activities.

The course focuses on:

• the effects of information and communications technology (ICT) on education and schools
• ICT-related policy, curriculum and school practice
• Concepts, theories and research related to the use of ICT in schools
• technology integration in schools
• teaching methods, professional development of teachers, software and digital learning materials
• students' and teachers' digital competence, ICT skills, and media literacy
• ICT as part of everyday life

Approach:
Reading and discussion about curriculum, policy, theory, research and practice. Students work alone or in smaller groups on literature research and introduce various topics of their choice. They share their ideas and experiences of ICT uses in learning and teaching and contribute to the construction of a learning and professional community in the area of ICT in education.

Topics from elementary number theory; divisibility, prime numbers, the Euclidian Algorithm, solutions of Diophantine equations and some theorems involving congruences like the Chinese Remainder Theorem and Fermat’s Little Theorem. Rational numbers and irrational numbers.

Course description: The fundamental concepts of calculus will be discussed. Subjects: Limits and continuous functions. Differentiable functions, rules for derivatives, derivatives of higher order, antiderivatives. Applications of differential calculus: Extremal value problems, linear approximation. The main functions in calculus: logarithms, exponential functions and trigonometric functions. The mean value theorem. Integration: The definite integral and rules of integration. The fundamental theorem of calculus. Techniques of integration, improper integrals. Series and sequences. Ordinary differential equations. Vectors and matrix calculations.

In the course there is emphasis on students‘ mathematical reasoning and ability to write simple proofs.

The term group and related terms will be defined. Many examples based on traditional arithmetic in known sets of numbers will be examined, but also more abstract examples such as finite groups and permutation groups. Rings and fields are introduced. Connections between arithmetic and algebra at secondary school level with groups, rings and fields are examined.

Topics from Euclidian geometry. Foundations and systematic development of elementary geometry of the plane. Concepts, postulates, definitions, and theorems involving parallel lines polygons and circles. Attention is given to reasoning and proving theorems. A brief discussion of the geometry of solids. Calculation of area and volume.

In this course students explore teaching of diverse groups in inclusive settings, emphasizing strategies to address diverse educational and sociological needs of students, guided by human values, democracy and social justice. The emphasis is on evidence-based strategies to address the most common students´ special needs related to reading difficulties, behavioral difficulties, attention deficit, hyperactivity, and autism spectrum disorder. At the same time the use of respectful, person-first language, putting strengths and talents of students in the foreground, is stressed. Multicultural teaching and teaching of students learning Icelandic as a second language will be addressed. Students will be introduced to classroom management strategies, individualized behavior support, multi-disciplinary and parent collaboration. The course focus is on inclusive, evidence-based practices that aim to provide students with special needs opportunities equal to those of their classmates.

Issues, concepts and theories in the field of distance education will be explored. Development and trends will be examined from the emphasis on independent study to emphasis on social activities and shared knowledge construction online and global. The focus will also be on research on distance education at different school levels in Iceland and other countries, distance learners and their needs, and teaching methods with different types of media. The design of distance or online courses and programs will be explored as well as international standards for such courses.

Students participate in online synchronous and asynchronous discussion about theory and practice concerning distance education (DE), engage in problem-based learning (group work) and do an individual project that could involve design of a DE course, a study concerning DE, or a paper on topics related to DE.

Objectives
The objectives of the course are threefold. First, to provide insight into selected learning theories. Second, to enable  students to gain understanding of how these theories can be applied to upbringing, teaching, and the organization of learning for people of all ages. Third, to increase knowledge of research on the effects of different approaches to teaching and evidence-based practices to reach a variety of learning objectives.   

Content

• Among the main learning theories covered in the course are those from the cognitive, behavioural, and motivational domains.
• Main concepts related to the learning theories will be introduced and discussed in relation to how learning can be defined in different ways.
• Students will read research articles where these learning theories are studied and applied in practice.
• Emphasis will be placed on understanding what constitutes evidence-based practice. 
• Students will design a learning plan for a student or a group of students, based upon one of the learning theories approaches discussed in the course. Through this assignment the students will deepen their understanding of the learning theory in question and how to apply it in practice. 

Content: The main goal of the course is to give insight into the sociology and philosophy of education. Selected sociological and philosophical ideas that are useful to study education and the school reality will be discussed. There is emphasis on three things. A. To understand ideas and concepts og be able to explain them. B. To compare ideas and concepts to the education and the school reality that we are familiar with. C. To think critically about the ideas and the reality that they are meant to throw light on.

 Methods: There are weekly lectures and discussions. Lectures will be recorded and uploaded to the course‘s Canvas site. Students study them and then take part in discussions that will not be recorded. At the beginning of the semester students register for discussion groups which are then fixed for the semester. There is obligatory attendance (80%) for discussion classes, but students can choose to attend at Stakkahlíð or in realtime on Zoom. Students do two group assignments, two individual assignments and a final assignment.

The course focuses on:

• the effects of information and communications technology (ICT) on education and schools
• ICT-related policy, curriculum and school practice
• Concepts, theories and research related to the use of ICT in schools
• technology integration in schools
• teaching methods, professional development of teachers, software and digital learning materials
• students' and teachers' digital competence, ICT skills, and media literacy
• ICT as part of everyday life

Approach:
Reading and discussion about curriculum, policy, theory, research and practice. Students work alone or in smaller groups on literature research and introduce various topics of their choice. They share their ideas and experiences of ICT uses in learning and teaching and contribute to the construction of a learning and professional community in the area of ICT in education.

This course deals with the spectrum of teaching methods from direct and formal approaches to informal methods. Emphasis is put on theoretical underpinnings and research on teaching methods, especially Icelandic research. Special attention is put on examining differentiated and responsive approaches (such as the open school concept, flexible teaching, cooperation, multi-age teaching, problem-based learning, holistic education, project-based learning, negotiating the curriculum and authentic learning).

In this course, students learn about some of the main theories in mathematics education and about research on mathematics learning and teaching. In focus is mathematics teaching in schools, individual learning and the societal roles of mathematics and mathematics education. Students also deepen their understanding of mathematics and mathematics education by engaging with mathematics tasks and working on ways to adapt and develop mathematics tasks for primary and secondary school students. Emphasis is placed on how teachers can make use of theory in order to plan and implement mathematics teaching for all, such that it is based on care for mathematics learning.

Course description in English:*  This course aims to prepare students to use programming and computational thinking strategies to create computer graphics and solve problems of various kinds, and furthermore to prepare students for teaching these same topics to pupils in compulsory school and upper secondary school. No previous experience or knowledge of programming is required before starting the course.

The courses mathematical topics are mainly coordinate geometry and the fundamentals of computational thinking: abstraction, decomposition, algorithmic thinking, debugging, automation and generalization. Students will learn about the use of variables, functions, loops, and logical operators in programming. Students will learn to use computational thinking strategies to build simple computer models, such as computer games or art, and to use programming for solving mathematical tasks.

Students will also learn to plan lessons in compulsory and upper secondary school, aiming for the development of students’ computational thinking and creative programming skills, along with the use of programming for investigating mathematical topics. The dynamic geometry software GeoGebra will be put into a computational thinking perspective and its possibilities for mathematics teaching will be explored. The position of programming and computational thinking in society and the educational system will be discussed, also in connection with other school subjects.

Course participation involves mostly the solving of tasks, reading, and participation in a critical discussion.

In this course, students learn to plan mathematics teaching in upper secondary school using various approaches to provide access for all. An emphasis will be put on exploring different teaching environments and teaching methods that build on research on the teaching and learning of mathematics. In the course, the aims of learning mathematics both in Iceland and its neighboring countries will be discussed based on curricular and governmental documents. Students will read about and get a chance to try out various ways to assess and analyze students’ mathematical achievements. The course format includes lectures, project work, presentations, topic studies connected to practice, and critical topic discussion. An emphasis will be put on students’ discussion about challenges and their search for solutions to problems related to the teaching and learning of mathematics.

The course aims to prepare participants to draw on their resources in their work with diverse groups of students. In the course, we draw on inclusive education theories and research, emphasizing a holistic and creative approach to preparation and teaching at the forefront. Furthermore, a focus is put on teaching strategies and educative assessment that works for diverse groups of students, and adapting teaching and learning to students with special needs.

Content
The focus of the course is on inclusive practices. How to create a learning environment that cares for all students learning is introduced. The focus is also on collaboration with parents, colleagues, professionals, and paraprofessionals. 

Work process
The course is a blended course online and on campus. It is divided into four main themes. All the themes connect to teaching in inclusive educational settings. The focus on each theme is three or four weeks.

The teaching is through lectures, projects, collaboration, discussions in class, on canvas, and in formal assignments. The course is grounded in students' independence, responsibility, and participation.

This course focuses on qualitative research methods. It looks at different movements and traditions in research methodology and their relationship to the structure and execution of research. The course also touches on the ethics of research, validity and different views of these concepts. Students will conduct a small research project, which provides training in a literature review, data collection, data analysis, and presentation of research findings. Students work as a team throughout the semester.

Readings, lectures, in-class discussion and group work. Sessions for distance students are held twice during the semester and participation is mandatory

Students in this course are expected to deepen their knowledge and skills in quantitative research methodology. Students will use a computer program for data analysis, with emphasis on interpretation and writing about research results. Students are expected to develop positive attitudes toward research and the value of research in educational and social settings.

Topic 
Participants familiarize themselves with research on mathematics studies and how an understanding of mathematics develops. They learn to analyze the knowledge and understanding of the student group and evaluate their learning process. They learn about difficulties in mathematics that students encounter, their impact on learning, and the methods for diagnosing them. Participants acquire knowledge of teaching methods and resources for students of different backgrounds, including diverse linguistic and cultural backgrounds.

Activities
Building a learning community where all participants are expected to be active in shaping the learning culture is at the core of the course. Students can participate on campus, online, and through the course webpage. The coursework is based on lectures, seminars, and individual and group assignments.

Students conduct a small-scale investigation on mathematical learning. Based on their learning in the course, they plan a developmental study within schools. Emphasis is on how they can build a learning community that supports children in learning mathematics.

Topic:
The focus of the couse is on new research on children's mathematical thinking. Students study the development of children's understanding of mathematics and mathematical content knowledge. Emphasis is on the foundation of mathematics learning that develops in the early years and how to build a learning community that supports children in learning mathematics through play and everyday activities. Research methodologies applied in research on children's mathematical thinking will be explored. 

Activities:
Building a learning community where all participants are expected to be active in shaping the learning culture is at the core of the course. Students can participate on campus, online and through the course webpage. The course readings will be discussed and explored. Students participate in activities that will support them in being able to work in a creative way within their schools. 

Students conduct a small scale investigation on young children's mathematical learning. Based on their learning at the course they plan a developmental study within preschool or in primary grades.  Emphasis is on how they can build a learning community that supports children in learning mathematics through play and everyday activities.

The course focuses on:

• the effects of information and communications technology (ICT) on education and schools
• ICT-related policy, curriculum and school practice
• Concepts, theories and research related to the use of ICT in schools
• technology integration in schools
• teaching methods, professional development of teachers, software and digital learning materials
• students' and teachers' digital competence, ICT skills, and media literacy
• ICT as part of everyday life

Approach:
Reading and discussion about curriculum, policy, theory, research and practice. Students work alone or in smaller groups on literature research and introduce various topics of their choice. They share their ideas and experiences of ICT uses in learning and teaching and contribute to the construction of a learning and professional community in the area of ICT in education.