EVL-MA115 Mathematics 1A (5-10)

Contents and structure

Mathematics 1, levels 5-10, is based on national guidelines for mathematics in the teacher training for primary and lower secondary school, the Curriculum for Knowledge Promotion in Primary and Secondary Education and Training and the harmonisation document prepared by the resource group for mathematics in Competence for Quality. The programme consists of two courses of 15 credits each: Mathematics 1A and Mathematics 1B.

The goal of the programme is to expand the disciplinary and didactic repertoire of mathematics teachers to enhance their teaching through exploratory and performative studies of their own practices and of relevant research.

This involves the development competencies such as being able to:

analyse the mathematical development of the pupils, be good guides to mathematics and good interlocutors in relation to mathematics

select and create good mathematical examples and tasks

evaluate and select appropriate teaching and assessment materials look at mathematics as a creative process and stimulate pupils to use their creative abilities and evaluate the use of digital tools and resources in teaching

communicate mathematical knowledge with the pupils Through mathematics for grades 5-10, students shall develop teaching knowledge in mathematics. This means that students must have a solid and reflective understanding of the mathematics that pupils will learn and how this is further developed in the next levels of the educational system. Further, students must have knowledge of mathematics that is specific to the teaching profession. In addition to themselves being able to complete and understand mathematical processes and arguments, such knowledge includes being able to analyse mathematical processes and arguments proposed by others, in order to assess their soundness and potential. Teaching knowledge entails having the didactic competence that enables students to become familiar with the pupils' perspectives 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 by all pupils. Mathematics 1 is divided in two courses that build on each other: Mathematics 1A (15 credits) and Mathematics 1B (15 credits).

The mathematical topics in this subject are: numbers and numeracy, number theory, additive and multiplicative thinking and algebra. This entails working with the development of the concept of numbers from integers to rational and real numbers, and corresponding development of algorithms for calculation. Various aspects of fractional and coherence between fractions, decimals and percentages, link to proportionality and congruence and congruence arithmetic are treated in-depth. Different aspects of algebra, including the function aspect and variable concept are dealt with.

Learning Outcome

Knowledge

The student

has detailed knowledge of teaching the mathematics the students work with in grades 5-10,particularly numeracy and arithmetic, the transition from arithmetic to algebra, as well as algebra and functions has knowledge about the role of language in learning mathematics

has knowledge of communication and reasoning 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 teaching knowledge about the significance of arithmetic as a basic skill in all school subjects has knowledge about verbal expression, reading and written expression and can use digital tools in mathematics has knowledge of the content of mathematics in the different grades in primary and lower secondary school, and of the transitions between the grades in primary and lower secondary school has knowledge of different theories of learning, and of the connection between views of learning and views of the subject-matter and knowledge has knowledge of a broad repertoire of methods for teaching mathematics

has insight into and experience with the use of different teaching aids, both digital and others, and opportunities and limitations in such aids

 

Skills:

The student

can plan, implement and assess mathematics teaching for all pupils in grades 5-10, 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 and evaluate mapping tests and various observation and assessment methods, in order to adapt teaching to the pupils' varying needs

is able to evaluate pupils' goal fulfilment with and without marks and to give reasons for the assessments can communicate with pupils, individually and in various group settings, listen to, assess and make use of pupil suggestions and institutionalise knowledge

can analyse and assess pupils' ways of thinking, argumentation and solution methods from different perspectives on knowledge and learning

can prevent and detect mathematics difficulties and facilitate mastery in pupils with various types of mathematics difficulties

can teach basic skills, especially arithmetic as a basic skill in all school subjects, can use mathematical language, communicate and reason, and use varied forms of representation

 

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

None

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 wonder, exploration, reflection and creative problem-solving with and without digital tools. Work requirements and communication are supported by digital resources. Among other things, we will use videos of lectures and we will work collectively on online assignments. Video will also be a central learning tool, both in modelling teaching and in analysing our own and others' teaching practice. During sessions, we will among other things study, plan, perform and reflect on central teaching practices such as mathematical conversations, explanations and activities. A great deal of student activity is expected throughout the course of study. Work requirements will mainly relate to exploratory and practical studies of students' own practice.

Compulsory learning activities

Course requirement 1Testing new disciplinary and didactic knowledge of algebra/pre-algebra in the student's own school This course requirement is to lead to knowledge sharing among the student's colleagues.The testing shall be filmed.

Course requirement 2 Developing teaching knowledge

Course requirement 3 Assessing textbooks

Assessment

Written examination

Examination support material

None

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