LU1-MAT115 Mathematics 1a

Contents and structure

This course plan is based on what the "National guidelines for teacher training for primary and secondary education years 1-7" say about mathematics, the purpose being to educate mathematics teachers who can facilitate complete mathematics teaching in line with relevant research and the current curriculum.

This involves various types of competence such as being able to:

• analyse the pupils' mathematical development
• be good mathematical guides and partners
• select and create good mathematical examples and tasks
• evaluate and select material for use in teaching mathematics
• look at mathematics as a creative process and stimulate pupils into using their creative abilities

In order to develop the necessary competence, students will use mathematics for levels 1-7 to develop teaching knowledge of mathematics that includes both academic and didactic knowledge. The students will have a solid and reflective understanding of the mathematics that pupils will learn and how this is further developed in the next stages of the educational system. Among other things, this means that they must be able to implement and understand mathematical processes and arguments. The students must also have knowledge of mathematics that is specific to the teaching profession. This means that they are also able to analyse mathematical processes and arguments proposed by others and evaluate their soundness and potential.

Students will have the didactic competence that enables them to become familiar with the pupils' perspective and learning processes and to use variation and adaptation to prepare mathematics teaching for pupils with different needs and with different cultural and social backgrounds, in such a way that mathematics is perceived as a meaningful subject for all pupils.

Mathematics 1 is divided in two subjects that build on each other: Mathematics 1A (15 cr) and Mathematics 1B (15 cr).

The subject comprises mathematical didactic and mathematical topics that are important for those teaching mathematics in years 1-7. Most topics will be relevant in both subjects, but we will concentrate on selected topics in the various subjects in order to develop theoretical and practical tools that can be used for further work. In total, these disciplines will enable students to have the learning outcome for mathematics 1 described in the "National guidelines for teacher training for primary and secondary education years 1-7".

Contents

The mathematical topics in particular focus in this subject are: numbers and understanding numbers, algebra and functions.

This covers all aspects of numbers and handling numbers: the basic number concept in children, development of the use of numbers from an informal level to a more systematic one and the position system's significance in this context. Algorithms linked to knowledge about additive and multiplicative structures. A feeling for numbers by means of experimentation and generalisation with numbers and how this leads on to algebraic thinking. Extension of number quantities, especially fractions and decimals, is handled in detail.

In algebra, algebraic thinking and experimentation, generalising and formalising of patterns and connections, formulae and similarities will be covered. The role of letters and children's development and understanding of these. In functions, variables and different function types are important, especially linear functions, proportionality and reverse proportionality. This knowledge is linked to teaching material at primary level.

There is work on relevant mathematical didactic theory in different topics, so as to give students the theoretical and practical tools to be able to develop teaching knowledge in mathematics. Work on this aspect will include:

The basic skills such as being able to use maths in all subjects and read and write in mathematics. Work on spreadsheets will be part of the digital skills. Interaction patterns and communication, with a special focus on different communication patterns in the classroom. Semiotic representation forms, with movement between concrete and abstract representation forms, informal and formal maths language and the role of language in the pupils' learning. Participation and appropriation perspectives in respect of pupils' learning, particularly individual perspectives on learning as the constructivistic and cognitive requirement of different levels of thinking. Formative evaluation as feedback and feedforward to pupils in their learning process. Understanding and skills in mathematics and how different academic views and types of assignment can affect learning and teaching. Working methods as investigative landscape, pupil activators, instructions and diagnostic teaching.

Skills in practice will mainly relate to work on the middle level in this subject.

Learning Outcome

Knowledge

The student

• has detailed teaching knowledge of the mathematics the pupils work on at primary level, in particular understanding numbers and arithmetic and the transition from arithmetic to algebra, with special focus on teaching for beginners
• has knowledge of algebra and functions and can connect this knowledge with teaching material for the primary stage
• has knowledge of mathematics' historical development of number concepts and systems
• has knowledge of the content of mathematics in the kindergarten and in primary school as well as the transitions between kindergarten and primary and between primary and lower secondary school
• has teaching knowledge on the significance of arithmetic as a basic skill in all school subjects
• has knowledge on oral expression, reading, written expression and using digital tools in mathematics
• has knowledge of common interaction patterns and communication related to teaching mathematics
• has knowledge of the significance semiotic representation forms have in mathematics, and which challenges that are related to transitions between representation forms
• has knowledge of the role of language in learning mathematics
• has knowledge of different theories for learning, and on the connection between learning views and subject and knowledge views
• has knowledge of a repertoire of methods for teaching mathematics

Skills

The student

• can plan, implement and assess mathematics teaching for all pupils in the middle stage, with focus on variation and pupil activity, based on research, theory and practice
• has good practical skills in oral and written communication in mathematics, and the competence to promote such skills in pupils
• can use work methods that promote pupils' wonder, creativity and ability to work systematically with exploring activities, justifications, arguments and evidence
• can use various observation and assessment methods, in order to adapt teaching to the pupils' varying needs
• can communicate with pupils, individually and in various group settings, listen to, assess and make use of pupil suggestions
• can analyse and assess pupils' ways of thinking, argumentation and solution methods from different perspectives on knowledge and learning

General competence

The student

• has insight into the role of mathematics in other subjects and society in general
• has insight into the significance of mathematics for participation in a democratic society

Entry requirements

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Teaching methods

The students are themselves responsible for acquiring the knowledge, skills and competence expressed in the learning outcome above. The teachers will be the driving force in this and will facilitate this work through teaching, guidance, theoretical and practical studies, tasks and other activities. We will emphasise forms of work that promote curiosity, research, reflection and creative problem solving with and without digital tools. This will involve a great deal of student activity throughout the course of study.

Work on academic and didactic mathematical themes will ensure an interaction between academic and didactic knowledge and skills that facilitates the student's academic and didactic development and reflection. Relevant research is guiding for this work. Through work with literature the student develops knowledge and skills for reflection and development. Practice is an arena in which the student gains experience in using, reflecting on and developing knowledge and skills, for which reason practice will be a natural partner. Teaching will be an arena in which literature and practice are brought together, where knowledge, experience and skills are revealed and developed by means of specific activities, lectures, discussions and guidance. There will be collaboration with other subjects. During the studies the student will work on assignments individually and in groups to support the student's academic and didactic development and reflection.

Compulsory learning activities

1.Oral and written assignments as specified in the semester plan

2. 80% class attendance is obligatory

Assessment

written exam

Examination support material

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