Academic regulations for MA (Ed) programme in Educational Theory and Curriculum Studies (Mathematics)

1. The outline provisions of the academic regulations
The academic regulations for MA (Ed) programme in Educational Theory and Curriculum Studies (Mathematics) (2009) have been drawn up by the Board of studies and have been approved by the Dean of The Danish School of Education on 21-08-2009

The academic regulations take effect on 01-09-2009

On successful completion of the MA (Ed) programme in Educational Theory and Curriculum Studies (Mathematics), the student will be entitled to use the title Master of Arts (Education) in Educational Theory and Curriculum Studies: Mathematics
The academic direction and primary subject areas of the programme
The MA (Ed) programme in Educational Theory and Curriculum Studies (Mathematics) aims, based on a qualifying first degree, to further develop students’ knowledge and skills within the fields of general didactics, the didactics of mathematics and mathematics in order to qualify them for educational, development and management tasks, as well as to participate in research contexts within the field of the didactics of mathematics on the basis of the understanding gained of research work and research ethics.
Academic skills and qualifications

Insights and competences
Students should develop their:
• Competence in defining, analysing and discussing problems on a theoretical basis in relation to learning, education and teaching in institutional frameworks, and in arguing for and making well-informed choices in relation to the planning of subject-specific and cross-disciplinary teaching.
• Insight into and competence in relation to the theory of science in general and within the discipline in question, as well as in relation to the potential and limitations of qualitative and quantitative research methods.
• Insight into and comprehensive knowledge of selected central theories and problem areas within the didactics of mathematics and/or science, as well as competence in recognising and analysing the significance of these theories and problem fields for current and/or potential teaching practice within the field.
• Comprehensive knowledge and judgement concerning a) the interplay between theory and practice within the didactics of mathematics; b) the potential and limitations of qualitative and quantitative research methods in relation to the didactics of mathematics; and c) content/didactic perspectives in a limited area of mathematics as a subject area and/or concerning the historical development of mathematics as a teaching subject.
• Competence in relation to mathematical thinking, problem-solving, modelling, reasoning, representation, symbolisation, formalism, communication and the use of aids; in interaction with their development of insight into and comprehensive knowledge of numbers, algebra, geometry, functions, infinitesimal calculation, dynamic systems, probability calculation and statistics; as well as their competence in dealing with and analysing these skills and areas of study from the perspective of the didactics of mathematics.
• Skills in defining and working academically with problems.


Formal competences
The programme enables students to
• Carry out teaching in mathematics at teacher-training colleges and perhaps upper-secondary schools.
• Act as consultants in various educational contexts focusing on the didactics of mathematics.
Authority
The MA (Ed) programme in Educational Theory and Curriculum Studies (Mathematics) is one of the programmes offered by the Danish School of Education, Aarhus University pursuant to Act no. 1368 of 7 December 2007 on universities (the University Act). The national legal foundation for the programme is Ministerial Order no. 338 of 6 May 2004 on Bachelor’s and Master’s degree programmes at universities (the Education Order), which refers to the ministerial orders in force on exams, external examiners and grading.
Admission requirements and prerequisites

Admission to the MA (Ed) programme in Educational Theory and Curriculum Studies (Mathematics) requires applicants to have one of the following degrees:

1) A Bachelor’s degree in Mathematics.
2) A professional Bachelor’s degree as a primary or lower-secondary teacher specialising in Mathematics and a Bachelor’s project in connection with this.

Admission to the supplementary programme in preparation for the MA (Ed) programme in Educational Theory and Curriculum Studies (Mathematics) requires applicants to have one of the following degrees:

3) A Bachelor’s degree in a relevant subject other than Mathematics.
4) A professional Bachelor’s degree as a primary or lower-secondary teacher specialising in Mathematics.
5) An intermediate degree as a primary or lower-secondary teacher specialising in Mathematics.

The supplementary programme in preparation for the MA (Ed) programme in Educational Theory and Curriculum Studies (Mathematics) consists of one module corresponding to 30 ECTS credits: Mathematics as a Theoretical Construct. Further information can be found in the academic regulations for the Supplementary Programme in Preparation for the MA (Ed) programme in Educational Theory and Curriculum Studies (Mathematics).

Tuition fees are charged in connection with the supplementary programme, which is offered by the Danish School of Education, University of Aarhus, in accordance with Ministerial Order no. 423 of 21 May 2008 on supplementary programmes in preparation for the Master of Education programmes.

The Danish School of Education, University of Aarhus, may admit students who do not fulfil the requirements stated, if the student is deemed to have equivalent qualifications.

In order to realise the stated programme objectives, on registration students must be able to:
• Read academic literature in English and Scandinavian languages.
• Write academically, including defining research problems and arguments based on the academic use of theories and methods.
• Read academically – be able to extract theoretical perspectives and reflect on the assumptions on which they are based, and to interpret empirical results in relation to theoretical arguments.
• Use net-based communications and teaching technology.
• Conduct literature searches and use electronic databases.
• Communicate academic problems to other academics within the field.
This programme grants access to:

The programme may form the basis for the three-year research training programme leading to a PhD.
Transitional regulations

These academic regulations enter into force on 1 September 2009 and apply to all students enrolled on the MA (Ed) programme in Educational Theory and Curriculum Studies (Mathematics), and to students starting the Master’s degree programme on or after 1 September 2009.

Examinations passed by students admitted under the previous academic regulations will be converted into corresponding examinations under these academic regulations as follows:

• The former module called “Curriculumteori og institutionsdidaktik” is the equivalent of the new module called “Theory of Curriculum and Didactics”.
• The former module called “Naturvidenskabernes videnskabsteori og metode” is the equivalent of the new module called “Philosophy and Methodology of the Natural Sciences”.


2. The Structure of the programme
Overview of exams -
Module / first-year exam Exam title / type of examination Subject type / marking Sem./ECTS
Theory of Curriculum and Didactics Mandatory 1. sem.
- External exam with an external examiner Graded 15 ECTS
Mandatory Modules Didactics of Mathematics Mandatory 1. sem.
- External exam with an external examiner Graded 10 ECTS
project A Mandatory 1. sem.
- External exam with an external examiner Pass/fail 5 ECTS
Mathematics I Mandatory 2. sem.
- External exam with an external examiner Graded 15 ECTS
Philosophy and Methodology of the Natural Sciences Mandatory 2. sem.
- External exam with an external examiner Graded 10 ECTS
Project B Mandatory 2. sem.
- External exam with an external examiner Graded 5 ECTS
Mathematics II Mandatory 3. sem.
- External exam with an external examiner Graded 15 ECTS
Elective Modules
(15 ECTS / 3. sem.)		 elective module on Elective course 3. sem.
- External exam with an external examiner Graded 15 ECTS
6B. In-depth study module: Mathematics Elective course 3. sem.
- External exam with an external examiner Graded 15 ECTS
Mathematics B Elective course 3. sem.
- External exam with an external examiner Graded 10 ECTS
Project C Elective course 3. sem.
- External exam with an external examiner Graded 5 ECTS
Thesis thesis Mandatory 4. sem.
- External exam with an external examiner Graded 30 ECTS



Diagram of the programme's structure -
1. semester 2. semester 3. semester 4. semester
Theory of Curriculum and Didactics
15 ECTS















Didactics of Mathematics
10 ECTS










project A
5 ECTS





Mathematics I
15 ECTS















Philosophy and Methodology of the Natural Sciences
10 ECTS










Project B
5 ECTS





Mathematics II
15 ECTS















Elective Modules
15 ECTS















thesis
30 ECTS































Rules and regulations for academic progression -

The MA (Ed) programme must be completed no more than five years after the date of registration.
Students are entitled to leave of absence subject to the rules of Aarhus University regarding leave of absence. Applications for leave of absence must be submitted in writing to the board of studies.


Assessment criteria and concepts used in module descriptions


Development of an “academic basis”


On completion of each module, students should have gained competence on an academic basis in the module concerned. This means that in an examination situation students should be able to provide answers that are critically, systematically, theoretically and empirically well-founded. These criteria may be given different weight in different modules, depending on whether the module has a primarily theoretical or empirical focus, for instance.


Critical answers mean that students problematise the subject content and define (new) problems or theses.


Systematic answers mean that students argue for the strengths and weaknesses of the methods used, use clearly defined concepts consistently, make logical arguments and structure the subject content.


Theoretically well-founded answers mean that students apply relevant theory in their analyses based on primary literature (possibly in translation).


Empirically well-founded answers mean that students include relevant empirical material based on primary studies (either existing or collected by the students).


Concepts used in module descriptions:


Demonstrate comprehensive knowledge of and insight into: show knowledge of the entire subject area covered by the module (breadth), and be able to identify key issues (depth) in the field.


Analyse: be able to identify and differentiate between elements in a subject area


Assess: be able to substantiate the quality of various statements


Discuss: be able to synthesise elements in a theoretical or practical subject area, assess them in relation to one another, and put the results of the assessment into perspective


Define (e.g. practice-related issues, study design or solution proposals): be able to describe and explain how issues within a subject area can be addressed


Communicate: be able to communicate academic expertise about a subject area to a specific target group


Carry out: be able to perform a task in practice and explain the reasons for performing the task (e.g. a study, an evaluation, supervision, or a teaching plan)


Grades are given on the basis of a general assessment of the extent to which the student is able, in an examination situation, to demonstrate an academic basis in relation to the module requirements.


The grade “12” requires complete fulfilment of the goals of the module on a highly qualified academic basis.


Deficiencies with regard to fulfilling the goals are evaluated as an overall assessment of whether the goals of the module have been fulfilled and of the quality of the academic basis.


Spelling and expression abilities are taken into account in the overall assessment.

3. The programme's individual subjects and exams:
1. Theory of Curriculum and Didactics
Objective:
After completing this module students should be capable of the following on an academic basis (i.e. on a critical, systematic, theoretical and empirical basis) :

• Demonstrating comprehensive knowledge of and insight into central fundamental educational ideas.
• Analysing and discussing general didactic, specialised didactic and curriculum issues in relation to teaching and learning in institutional settings.
• Discussing the didactic basis for the planning of teaching in institutional settings.
• Assessing and discussing didactic practice.



Content
-Curriculum theory and educational theory: traditions and basic concepts.
-Comparative subject didactics.
-Institutional didactics.
-Learning theory.
Method of instruction:
Lectures, presentations by participants and group work.
Language of instruction:
danish
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral - 45 minutes

Submission
Remarks
The exam comprises an oral examination lasting 45 minutes
including the discussion of the exam performance based on a
written assignment of between 15 and 20 standard pages
(between 36,000 and 48,000 characters).
2
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Group Combined written and oral - 45 minutes

Submission
Remarks
The exam comprises an individual oral examination lasting 45
minutes
including the discussion of the exam performance based on a
synopsis handed in by a group (maximum three participants) the
total number of pages must still be between 5 and 8 standard
pages.
3
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral - 45 minutes

Submission
Remarks
The exam comprises an oral examination lasting 45 minutes
including the discussion of the exam performance based on a
synopsis of between 5 and 8 standard pages (between 12,000 and
19,200 characters).
4
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Group Combined written and oral - 45 minutes

Submission
Remarks
The exam comprises an individual oral examination lasting 45
minutes
including the discussion of the exam performance based on active
participation, documented in a portfolio consisting of 2-4 short
texts (survey papers about the themes of the lectures) of a
maximum total of 20 standard pages (48,000 characters).
5
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral - 45 minutes

Submission
Remarks
The exam comprises an oral examination lasting 45 minutes
including the discussion of the exam performance based on active
participation, documented in a portfolio consisting of 2-4 short
texts (survey papers about the themes of the lectures) of a
maximum total of 20 standard pages (48,000 characters).
6
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Group Combined written and oral - 45 minutes

Submission
Remarks
The exam comprises an individual oral examination lasting 45
minutes
including the discussion of the exam performance based on a
portfolio handed in by a group (maximum three participants) the
length must be between 10 and 15 standard pages (between 24,000
and 36,000 characters) per extra group member.

The general conditions for submitting portfolios for exam form
cb) will be announced in the course schedule before the start of
the semester.

Mandatory Modules
The module consist of the following exams:
1. Didactics of Mathematics
Objective:

Goals
After completing this module students should be capable of the following on an academic basis (i.e. on a critical, systematic, theoretical and empirical basis) :
• Demonstrating comprehensive knowledge of selected theories and problems within the didactics of mathematics.
• Analysing and assessing the significance of the selected theories and problems for teaching practice.


Content
Selected central theories and problems within the didactics of mathematics, including:
• Justification problems.
• Equality and differentiation.
• Content descriptions.
• Evaluation.
• Theories of learning.
• Theories of teaching.
• Forms of communication in the teaching of mathematics.
• Attitudes and professional cultures.
• Teacher competences and teacher training.
Method of instruction:
Language of instruction:
Curriculum:
The course alternates between lectures, group work and joint discussions.
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral - 45 minutes

Presentation
Remarks
For the course, the internal approval of 3-5 individual or group
assignments is required. These assignments vary in nature, and
are set and carried out within stated deadlines during the
course of the teaching. Taken together, these approved
assignments constitute a portfolio which must be revised and
submitted to the administrative office (Studieadministrationen)
by the deadlines stated by this office. Failure to comply with
these terms precludes students from entering an individual oral
examination, which lasts a maximum of 45 minutes including
discussion of the exam performance. The oral examination is
based on an assignment drawn in advance from the assignments
that have been submitted, but will also include the entire
portfolio of assignments. The assignment drawn from the
portfolio will be accompanied by a text from the course which
must be included in the dialogue between the student, the
external examiner and the examiner. The administrative office
will inform students no later than one week after the submission
deadline of the assignment that has been drawn from the
portfolio and the text that has been chosen by the examiner to
accompany it. Assessment is based on evaluation of the part of
the portfolio that has been drawn and the student’s individual
oral performance at the exam

2. project A
Objective:
Project A: That the students develop comprehensive knowledge and judgement with regard to the interplay between theory and practice within the didactics of mathematics.

Each project must be based on a mathematical problem or problem concerning the didactics of mathematics which is explicitly related to the project goals listed above. Within this framework, the problem is defined by the student(s) in such a way that the project can be carried out within a period of time corresponding to 5 ECTS credits (1/12 of a year of full-time study).
Method of instruction:
Each project is organised around the fact that a written report in Danish or English, documenting the insight gained as well as comprehensive knowledge and judgement, must be submitted by a group or an individual student. The maximum number of students in any project group is five. A supervisor will be appointed for each project group.

Project reports written by one author may not exceed 20 standard pages. This number is increased by 10 pages for each additional participant in the project group.
Language of instruction:
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral - 45 minutes

Submission
Remarks
Project, worth 5 ECTS credits, is organised based on the
production of an individual or group -written report in Danish
or English documenting the insight, comprehensive knowledge and
judgement that has been gained. A project group may not consist
of more than five students. A supervisor will be appointed for
each project group. The project report may not consist of more
than 20 standard pages with a single author. This number of
pages is increased by 10 pages for each additional member of the
project group. The project report is followed by an oral
examination lasting a maximum of 45 minutes including discussion
of the exam performance. The oral defence takes place
individually. Assessment is based on evaluation of the project
report and the student’s individual oral performance at the
exam.

3. Mathematics I
Objective:

Goals
After completing this module students should be capable of the following on an academic basis (i.e. on a critical, systematic, theoretical and empirical basis) :
• Demonstrating comprehensive knowledge of and insight into selected aspects of probability calculations, statistics and dynamic systems.
• Demonstrating comprehensive knowledge of and insight into selected professional competences, including:
o Competence in dealing with problems: defining and solving mathematical problems and assessing the approaches of others in dealing with mathematical problems.
o Competence in modelling: performing and assessing all parts of a mathematical modelling process.
• Analysing and discussing various subject areas and professional competences in a subject-didactic perspective.


Content
• Competence in mathematical problem-solving and modelling.
• The concept of randomness and probability, combination probability calculation, selected standard distributions for stochastic variables; statistics, including parameter estimation, hypothesis testing and regression analysis; differential equation systems and their numerical and analytical solutions.
• A spreadsheet and a general CAS toolkit.


 
Method of instruction:
The course alternates between lectures, group work and joint discussions.
Language of instruction:
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral - 45 minutes

-
Remarks
For the course the internal approval of 3-5 individual or group
assignments is required. These assignments vary in nature, and
are set and carried out within stated deadlines during the
course of the teaching. Taken together, these approved
assignments constitute a portfolio which must be revised and
submitted to the administrative office (Studieadministrationen)
by the deadlines stated by this office. Failure to comply with
these terms precludes students from entering an individual oral
examination, which lasts a maximum of 45 minutes including
discussion of the exam performance. The oral examination is
based on an assignment drawn in advance from the assignments
that have been submitted, but will also include the entire
portfolio of assignments. The assignment drawn from the
portfolio will be accompanied by a text from the course which
must be included in the dialogue between the student, the
external examiner and the examiner. The administrative office
will inform students no later than one week after the submission
deadline of the assignment that has been drawn from the
portfolio and the text that has been chosen by the examiner to
accompany it. Assessment is based on evaluation of the part of
the portfolio that has been drawn and the student’s individual
oral performance at the exam

4. Philosophy and Methodology of the Natural Sciences
Objective:

Goals
After completing this module students should be capable of the following on an academic basis (i.e. on a critical, systematic, theoretical and empirical basis) :
• Demonstrating comprehensive knowledge of the theory and methodology of science and insight into the didactics of mathematics.
• Analysing the potential and limitations of qualitative and quantitative research methods within the didactics of mathematics.


Content
• The history of the didactics of mathematics.
• Mathematics and the didactics of mathematics as academic disciplines.
• Theory and methodology of science perspectives – selected directions in the humanities and science.
• Qualitative and quantitative research methods in a theory of science perspective.
Method of instruction:
The course alternates between lectures, group work and joint discussions.
Language of instruction:
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral - 45 minutes

Submission
Remarks
For the course the internal approval of 3-5 individual or group
assignments is required. These assignments vary in nature, and
are set and carried out within stated deadlines during the
course of the teaching. Taken together, these approved
assignments constitute a portfolio which must be revised and
submitted to the administrative office (Studieadministrationen)
by the deadlines stated by this office. Failure to comply with
these terms precludes students from entering an individual oral
examination, which lasts a maximum of 45 minutes including
discussion of the exam performance. The oral examination is
based on an assignment drawn in advance from the assignments
that have been submitted, but will also include the entire
portfolio of assignments. The assignment drawn from the
portfolio will be accompanied by a text from the course which
must be included in the dialogue between the student, the
external examiner and the examiner. The administrative office
will inform students no later than one week after the submission
deadline of the assignment that has been drawn from the
portfolio and the text that has been chosen by the examiner to
accompany it. Assessment is based on evaluation of the part of
the portfolio that has been drawn and the student’s individual
oral performance at the exam.

5. Project B
Objective:
Project B: That the students develop comprehensive knowledge and judgement with regard to the potential and limitations of qualitative and quantitative research methods in relation to the didactics of mathematics.

Each project must be based on a mathematical problem or problem concerning the didactics of mathematics which is explicitly related to the project goals listed above. Within this framework, the problem is defined by the student(s) in such a way that the project can be carried out within a period of time corresponding to 5 ECTS credits (1/12 of a year of full-time study).
Method of instruction:
Each project is organised around the fact that a written report in Danish or English, documenting the insight gained as well as comprehensive knowledge and judgement, must be submitted by a group or an individual student. The maximum number of students in any project group is five. A supervisor will be appointed for each project group.

Project reports written by one author may not exceed 20 standard pages. This number is increased by 10 pages for each additional participant in the project group.
Language of instruction:
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral - 45 minutes

Submission
Remarks
Project, worth 5 ECTS credits, is organised based on the
production of an individual or group -written report in Danish
or English documenting the insight, comprehensive knowledge and
judgement that has been gained. A project group may not consist
of more than five students. A supervisor will be appointed for
each project group. The project report may not consist of more
than 20 standard pages with a single author. This number of
pages is increased by 10 pages for each additional member of the
project group. The project report is followed by an oral
examination lasting a maximum of 45 minutes including discussion
of the exam performance. The oral defence takes place
individually. Assessment is based on evaluation of the project
report and the student’s individual oral performance at the
exam.

6. Mathematics II
Objective:

Goals
After completing this module students should be capable of the following on an academic basis (i.e. on a critical, systematic, theoretical and empirical basis) :
• Demonstrating comprehensive knowledge of and insight into selected aspects of geometry and algebra.
• Demonstrating comprehensive knowledge of and insight into selected professional competences, including:
o Competence in reasoning: engaging in and assessing mathematical reasoning, such as mathematical argumentation, as well as analysing and discussing mathematical statements, such as definitions, theorems and examples.
o Competence in representation: analysing, discussing and assessing representations of mathematical cases.
• Analysing and discussing various subject areas and professional competences in a subject-didactic perspective.


Content
• Competence in mathematical reasoning and representation.
• Deductive and analytical geometry; linear algebra.
• A geometry programme and a general CAS toolkit.
Method of instruction:
The course alternates between lectures, group work and joint discussions.
Language of instruction:
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral - 45 minutes

Submission
Remarks
For the course the internal approval of 3-5 individual or group
assignments is required. These assignments vary in nature, and
are set and carried out within stated deadlines during the
course of the teaching. Taken together, these approved
assignments constitute a portfolio which must be revised and
submitted to the administrative office (Studieadministrationen)
by the deadlines stated by this office. Failure to comply with
these terms precludes students from entering an individual oral
examination, which lasts a maximum of 45 minutes including
discussion of the exam performance. The oral examination is
based on an assignment drawn in advance from the assignments
that have been submitted, but will also include the entire
portfolio of assignments. The assignment drawn from the
portfolio will be accompanied by a text from the course which
must be included in the dialogue between the student, the
external examiner and the examiner. The administrative office
will inform students no later than one week after the submission
deadline of the assignment that has been drawn from the
portfolio and the text that has been chosen by the examiner to
accompany it. Assessment is based on evaluation of the part of
the portfolio that has been drawn and the student’s individual
oral performance at the exam.

Elective Modules

The following general goals apply to elective modules in addition to the goals applying to specific elective modules.

After completing this module students should be capable of the following on an academic basis (i.e. on a critical, systematic, theoretical and empirical basis) :
• Demonstrating insight into the subject area and issues of the elective module and into relevant theoretical angles on (and empirical investigations of) the module.
• Analysing, assessing and discussing major theoretical, empirical and/or practice-related issues associated with the area of study that has been selected – including the relations between these issues and other areas and issues of the didactics of mathematics.
The module consist of the following exams:
1. 6B. In-depth study module: Mathematics
Objective:
On agreement with the study board and the programme coordinator, one or more students may study in depth an area of relevance for mathematics or the didactics of mathematics. The form may be project work with supervision and/or an actual course, if the number of participants permits this.
Method of instruction:
The course alternates between lectures, group work and joint discussions.
Language of instruction:
In parts of the programme, teaching may be in English.
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual - -


-
Remarks
For Module 6b: Reflection module (15 ECTS credits) the exam
may be taken either as described under a) or b). The choice of
options a) or b) is made by the teachers responsible for the
modules and announced in the course schedule before the start
of the semester.

2. elective module on
Objective:

Elective subjects taken on another Master’s degree programme, perhaps at a university elsewhere in Denmark or abroad are subject to the approval of the board of studies.
Method of instruction:
Language of instruction:
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual - -


-
Remarks
The exam in an elective module on another Master’s degree
programme observes the regulations stipulated for the module in
question.

3. Mathematics B
Objective:

Goals
After completing this module students should be capable of the following on an academic basis (i.e. on a critical, systematic, theoretical and empirical basis) :
• Demonstrating comprehensive knowledge of and insight into selected aspects of: numbers, algebra, and infinitesimal calculation.
• Demonstrating comprehensive knowledge of and insight into selected professional competences, including:
o Competence in reasoning: engaging in and assessing mathematical reasoning, such as mathematical argumentation, as well as analysing and discussing mathematical statements, such as definitions, theorems and examples.
o Competence in symbols and formalism: analysing, discussing and assessing mathematical symbol language and formalism.

Content
• Competence in mathematical reasoning and symbols and formalism.
• The concept of numbers and the classical foundation of the main number sets; algebraic structures; classical real analysis of functions of several variables, convergence and divergence of number sequences and number series.
• A general CAS toolkit.
Method of instruction:
The course alternates between lectures, group work and joint discussions.
Language of instruction:
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral -


Submission
Remarks
For the courses associated with modules 1-6b (cf. Appendix 1)
the internal approval of 3-5 individual or group assignments is
required. These assignments vary in nature, and are set and
carried out within stated deadlines during the course of the
teaching. Taken together, these approved assignments constitute
a portfolio which must be revised and submitted to the
administrative office (Studieadministrationen) by the deadlines
stated by this office. Failure to comply with these terms
precludes students from entering an individual oral examination,
which lasts a maximum of 45 minutes including discussion of the
exam performance. The oral examination is based on an assignment
drawn in advance from the assignments that have been submitted,
but will also include the entire portfolio of assignments. The
assignment drawn from the portfolio will be accompanied by a
text from the course which must be included in the dialogue
between the student, the external examiner and the examiner. The
administrative office will inform students no later than one
week after the submission deadline of the assignment that has
been drawn from the portfolio and the text that has been chosen
by the examiner to accompany it. Assessment is based on
evaluation of the part of the portfolio that has been drawn and
the student’s individual oral performance at the exam. The exam
is assessed in cooperation with an external examiner according
to the Danish 7-step grading scale.

4. Project C
Objective:
Project C: That the students develop comprehensive knowledge and judgement with regard to the content/didactic perspectives in a limited area of mathematics as a subject area and/or with regard to the historical development of mathematics as a teaching subject.

Each project must be based on a mathematical problem or problem concerning the didactics of mathematics which is explicitly related to the project goals listed above. Within this framework, the problem is defined by the student(s) in such a way that the project can be carried out within a period of time corresponding to 5 ECTS credits (1/12 of a year of full-time study).
Method of instruction:
Each project is organised around the fact that a written report in Danish or English, documenting the insight gained as well as comprehensive knowledge and judgement, must be submitted by a group or an individual student. The maximum number of students in any project group is five. A supervisor will be appointed for each project group. Project reports written by one author may not exceed 20 standard pages. This number is increased by 10 pages for each additional participant in the project group.
Language of instruction:
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral - 45 minutes

Submission
Remarks
Project, worth 5 ECTS credits, is organised based on the
production of an individual or group -written report in Danish
or English documenting the insight, comprehensive knowledge and
judgement that has been gained. A project group may not consist
of more than five students. A supervisor will be appointed for
each project group. The project report may not consist of more
than 20 standard pages with a single author. This number of
pages is increased by 10 pages for each additional member of the
project group. The project report is followed by an oral
examination lasting a maximum of 45 minutes including discussion
of the exam performance. The oral defence takes place
individually. Assessment is based on evaluation of the project
report and the student’s individual oral performance at the
exam.

Thesis
The module consist of the following exams:
1. thesis
Objective:
Method of instruction:
Language of instruction:
METHOD OF EVALUATION
1
Examinees Product Product framework Duration Preparation time Materials permitted Basis for assessment
Individual Combined written and oral Self-chosen subject 60 minutes

Submission
Remarks
The Master’s thesis (30 ECTS credits) comprises the final part
of the MA (Ed) programme. The Master’s thesis consists of an
individual or group written thesis within the field of didactics
with special focus on mathematics, followed by an oral
examination. The maximum number of members of a thesis group is
three. The thesis may not be more than 80 standard pages if it
is written by one student, 120 standard pages if it written by
two students, and 160 standard pages if it written by three
students. The oral examination is done individually, and must
take place no more than two months after submission of the
thesis. It lasts no more than 60 minutes per student. The
assessment is made on the basis of an evaluation of the written
thesis and the student’s individual oral performance. An
individual assessment is made. The assessment is made in
cooperation with an external examiner according to the Danish 7-
step grading scale.

The thesis must document the ability of students to apply
academic theories and methods in working with a specific
academic topic. The choice of topic is up to the students
concerned. The topic is subject to the approval of a supervisor
appointed by the director of studies. When students register to
write their theses, they will be informed of the deadline for
handing in the thesis.

In addition to a thorough knowledge of the topic chosen and the
relevant academic literature, the Master’s thesis must develop
the insight of the student(s) into and skills in educational
theory and curriculum studies in relation to mathematics,
including familiarity with the terminology and methods of the
field, as well as developing the ability to define and work with
a problem on an academic basis.

In addition to academic content, the spelling and expression
abilities of students are also taken into account in the
assessment. The assessment of language skills is based on
orthographic and grammatical correctness as well as style.
However, academic content is always given most weight.

If the Master’s thesis is written in Danish, it must include a
summary in English. If it is written in English, it must include
a summary in Danish. The summary must be between one and three
standard pages (2,400 characters per page, including spaces).
Subject to agreement with the supervisor appointed by the
director of studies, the summary may be written in German. The
summary is taken into account in the overall assessment of the
Master’s thesis. The main emphasis must be on the clear
communication of the specific academic contribution and the
basis on which this is achieved.

The final grade for the thesis is determined immediately after
the oral presentation and discussion of the exam performance.
The examiner and external examiner then jointly produce a
written assessment that takes into account both the thesis and
the oral presentation. The written assessment is sent to the
examinee at the latest one month after the oral presentation.



4. Other rules and regulations
Credit and flexibility
The Board of Studies is able to approve credit from a Danish or foreign higher education insti-tution, cf. the Examination Executive Order no. 867 of 19 August 2004 regarding university degree programme examinations, VTU, section 35, see http://www.au.dk/en/rules/2004/bek867 and the Education Executive Order no. 338 of 6 May 2004 regarding Bachelor’s and Master’s degree programmes at universities, VTU, section 72, see http://www.au.dk/en/rules/2004/bek338

Written application stating reasons for credit must be submitted to the Board of Studies. Appli-cations must be written on the application form available at http://www.au.dk/da/adm/indskriv/skema.htm
Registration and withdrawal
Registration for examinations is via the self-service for students, see http://www.au.dk/en/students.htm
For registration and deregistration, as well as procedures, see the university’s regulations re-garding examinations at http://www.au.dk/en/rules/2006/au1

If there is enrolment in a teaching programme that involves one or more examinations, registration for the teaching will entail registration for an examination, cf. the Examination Executive Order, section 27 subsection 1. Students have a duty to ensure that registration for examinations is correct. The self-service facility can be used by students to check their own registration no later than immediately prior to the deadline for deregistration.
Spelling and fluency
Each student’s spelling and phrasing skills make up part of the assessment of all written ex-aminations, irrespective of the language used. More importance is placed on the academic con-tent, but spelling and phrasing skills are a modifying factor in the overall assessment of the achievement of set objectives.

Each student’s oral presentation skills make up part of the assessment of all oral examinations, irrespective of the language used. More importance is placed on the academic content, but oral presentation skills are a modifying factor in the overall assessment of the achievement of set objectives.
Regulations for assignments
Stipulations regarding the extent of written dissertations are stated in the description of the individual study element.
A normal page for written submissions is 2400 characters (with spaces). To calculate normal pages, both text and notes are included, but not the front page, table of contents and bibliog-raphy.
Written submissions that do not comply with these stipulations cannot be accepted for assess-ment.
Using computers for examinations
For the university’s regulations regarding the use of computers for examinations, see http://www.au.dk/en/rules/2002/au6
Project-oriented procedures
Options for project-oriented procedures are stated in the description of the individual study element.
Exemption
An exemption is a deviation from that or those regulations that normally apply for the area in question. Exemption can be granted on the basis of an application sent to the authority that has the power to grant such exemption.
An application for exemption must be submitted to the Board of Studies. If another authority has the power to grant exemption, the Board of Studies forwards the application to the appro-priate authority (e.g. the dean, rector or ministry).
An application for exemption must be made in writing, stating reasons, and submitted as soon as possible. For the application to be processed immediately, it must include a precise account of the regulation from which exemption is sought, and what such exemption is intended to achieve (e.g. permission to use special aids, extension of examination time, postponement of time limits). Documentation for the unusual conditions that justify exemption must be enclosed with the application. Importance will not normally be attached to such conditions if they are not documented.
Appeals and complaints

Complaints must be submitted to the Board of Studies. A prerequisite for immediate process-ing is that the complaint must be made in writing, stating reasons. The complaint must state both the cause of the complaint and what the complainant expects to achieve.

Complaints regarding examinations must be submitted no later than 14 days following the re-lease of the examination results, cf. the Examination Executive Order no. 867 of 19 August 2004 regarding university degree programme examinations, VTU, section 8, see http://www.au.dk/en/rules/2004/bek867

Complaints regarding legal issues against the Danish School of Education’s decisions may be submitted to the Danish University and Property Agency. Complaints should be submitted to the administrative office of the School of Education (Studieadministrationen). The School of Education will issue a statement giving the complainant one week to respond. Complaints will then be sent to the Danish University and Property Agency, enclosing the statement and any comments by the complainant.
Examinations

Closer regulations regarding how and to what extent the student must have participated in classes in which the type of examination involves such participation are stated in the description of the individual study element.


In the assessment of all written examinations, emphasis will be placed on the student’s ability to present an academic problem area and manage an academic task, including compliance with formal academic requirements (references, quotations, etc.).


In the assessment of all oral examinations, emphasis will be placed on the student’s ability to present academic material, organise an oral presentation and enter into academically constructive dialogue.


The results of all examinations are stated in the examination result (the diploma), including their ECTS value.
An average is calculated with one decimal place of all graded assessments. Each assessment is included in the calculation of the ECTS value.


Acts and executive orders, as well as the university’s rules and regulations relating to education, are available in the electronic rules and regulations of Aarhus University at http://www.au.dk/en/rules/index.html


The external examiner requirement cannot be waived.


Individual assessments are made in connection with group exams. The maximum number of students in any group assignment is five.


Each module must be passed separately. Exams which have been passed cannot be re-taken.


Students have a maximum of three attempts to pass a module. The board of studies may permit a fourth and fifth exam attempt if exceptional circumstances apply.


Exams must be taken in Danish. Subject to agreement with the examiner, students may take exams in English.


In order to enable the Danish School of Education, Aarhus University, to contribute to the development of exam forms, other exam forms than those suggested above may be approved by the Board of Studies for Master’s degree programmes at the Department of Curriculum Studies at the Danish School of Education, Aarhus University, as long as they meet the requirements of the regulations in force. Initiatives to experiment with alternative exam forms may be taken by the board of studies, supervisors or students. Alternative exam forms are always subject to the approval of the board of studies, and the students must be informed of them before they register for the exam in question.


Exams passed at other educational institutions in Denmark or abroad may qualify for credit transfer as part of the programme subject to individual assessment and the approval of the board of studies. Exams passed abroad are transferred as “passed”. However, normally no more than two modules may be replaced by exams taken at other institutions. The Master’s thesis may not be replaced by exams/theses completed as part of other Master’s degree programmes.
Udskrevet den 07-09-2009