Course syllabus - Learning and Understanding Mathematical Concepts

Objectives

The main aim of the course is to deepen the student's understanding of concepts covered in the mathematics curriculum of lower and upper secondary schools from mathematical and learning perspectives. The course is intended primarily for students undergoing teacher training who wish to become teachers in mathematics and for practicing teachers who already have a degree.

Course content

The concept of numbers from natural numbers to complex numbers and how the understanding of the concept of numbers develops. Calculation rules as properties of numbers and how they are explained, for example models of explanation for the relations (-1)(-1)=1 and 1/(1/a)=a. The concepts of axiom, proof and how to draw conclusions from assumptions, applied to fields like geometry. Experimental investigation work in mathematics. The equality sign and its use in various contexts such as equations and in the simplification of mathematical expressions. Congruency as an algebraic idea and its application to common items, such as the clock. Problem solving and modelling giving examples such as the concept of function and the solution of equations. Learning and teaching strategies for use in mental arithmetic. Analytical geometry compared with coordinate free geometry illustrated with examples such as conical sections. Analysis of relevant software for mathematics and technical tools used in teaching mathematics.

Tuition

Classroom lessons, seminars and field studies.

Specific requirements

Numbers, algebra and functions, 7,5 credits and A problem solving approach to geometry, 7,5 credits or equivalent.

Examination

Examination (EXA1), 7.5 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass, Fail