Didactical Elements
Didactic TriangleI/didactical System
Teacher
Student
Subject
Didactic Triangle/didactical System
Teacher
Student
Examples:
Subject
Mathematics/Science
Didactic Triangle/didactical System
Student
Teacher
Examples:
Subject
Mathematics/Science
Didactic Triangle/didactical System
Subject
Mathematics/Science
Student
Examples:
Teacher
Subject didactics
Basic asumption about whether it makes
sense to talk about didactics:
Despite individuals involved we will find
some general phenomena and mechanisms
characterazing teaching and learning
Subject didactics has as it’s domain to
describe teaching and learning processes
within a given teaching subject.
Didactic positions

Teaching and learning is just a simple
transfer of knowledge from teacher to
student (copy – paste)

The mind is not a vessel to be filled but a
fire to be ignited.
(Plutarch 46-119 AC)
Reference
Write down the description of a (small)
part of a teaching course which in some
way because of teacher student
interaction seems interesting to you.
(age group, topic, ………….)
This situation will be your reference for the
concepts and theories we are going to
present.
External didactical transformation

Analyze your teaching topic for scientific
knowledge and for every day knowledge
and evaluate who and what affected what
it was about and the choice of teaching
methods.
Didactic transpositions
Subject didactics has as it’s domain to
describe teaching and learning processes
within a given teaching subject.
Scientific
Knowledge
Practice
and every
day
knowledge
External
didactical
transposition
Teaching
Knowledge
Internal
didactical
transposition
Teaching Institution
Subject/topic in a
didactical system
External didactical transformation
Ontology: Clarify the existence and
characteristics of the subject domain.
Two positions:
Platonism: Real reality is the world of ideas
and concepts – what we see are
reflections or shadows
Materialism: Ideas are tools created to
understand the reality.
Do we invent or discover mathematics??
External didactical transposition
Stakeholders:
Political, public, scientific and educational
institutions
Critical perspectives:
Ethics (atomic bomb, pollution), model
critic
gender agenda, western dominated
External didactical transposition
Why teach mathematics/science?
The discourse on stating the reasons for
teaching a subject is important becuase the
actual reasons
- constitute the (teaching) subject
- refer to relations between (teaching) subject
and the underlying scientific subject
- Play a role in planning teaching and
communicating about teaching
External didactical transposition
Categories of reasons
 Personly utility (utility argument)
 Collective utility (economy argument)
 Personly formation (culture argument)
 Collective formation (democracy
argument)
External didactical transposition
Constituting the school subject
Demarcation and identification:
Mathematics as a school subject is found in
all countries with almost same content
Science is found as different school subject
constructions
External didactical transposition
Constituting the school subject
 To be described in terms of goal and
content ideally mutually referring in a
balanced way
 In practice you find either clear goal with
weak examples of content or clear list of
content with less reference to goal
 New trend: specifying core topics and
values of the subject along with
presentation of paradigmatic examples
External didactical transposition
Constituting the school subject:
In practice the following are very strong
players in the constitutioning process:
 The textbook
 External tests and examinations
 Teacher communities
 Physical and material conditions
Knowledge – how?
Knowledge - how
A model for acknowledgment in science and mathematics in a
didactical context
”Short cut”
Didactical transpositions
Subject didactics has as it’s domain to
describe teaching and learning processes
within a given teaching subject.
Scientific
Knowledge
Practice
and every
day
knowledge
External
didactical
transposition
Teaching
Knowledge
Internal
didactical
transposition
Teaching Institution
Subject/topic in a
didactical system
Didactical TriangleI/didactical System
Teacher educator
Teacher
Student
How to teach
Mathematics
Mathematics
Didactical TriangleI/didactical System
Teacher
Student
Subject
Didactical relation model
Hiim and Hippe.
Prerequsites for learning
assesment
frame conditions (set up)
Learning process
goal
content
Didactical relation model
Hiim and Hippe.






Prerequisites for learning: The students’ skills, knowledge,
understanding, feelings, values, general background
Frame conditions: Rules and regulations, economy, material, time,
equipment, tradition and climate for collaboration
Goal: What is the purpose, what are the students expected to
achieve
Content: What is the topic, succession – intellectual as well as
emotional aspects
Learning process: How will learning take place, organizing of
work, involving students in decisions, theory – practice connection
Assessment: What should be assessed (products, learning
process, outcome, participation) and how.
External didactical transformation
Analyze your teaching topic in the
perspectives of the didactic relation
model
 Did it bring in some new lightning on
your teaching situation?

http://www.aausmed.wordpress.com/