didactical elements
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Didactical Elements
Didactic TriangleI/didactical System
Teacher
Student
Subject
Didactic Triangle/didactical System
Teacher
Student
SubjectMathematics/ScienceExamples:
Didactic Triangle/didactical System
Teacher
Student
SubjectMathematics/Science
Examples:
Didactic Triangle/didactical System
TeacherStudent
SubjectMathematics/Science
Examples:
Subject didactics
Subject didactics has as it’s domain to describe teaching and learning processes within a given teaching subject.
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
Didactic positionsTeaching 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 transformationAnalyze 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 transpositionsSubject didactics has as it’s domain to describe teaching and learning processes within a given teaching subject.
Scientific Knowledge
Practice and every day knowledge
Teaching Institution
TeachingKnowledge
Subject/topic in a didactical system
Externaldidactical transposition
Internaldidactical transposition
External didactical transformationOntology: 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 transpositionStakeholders:
Political, public, scientific and educational institutions
Critical perspectives:Ethics (atomic bomb, pollution),
model criticgender agenda, western
dominated
External didactical transpositionWhy 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 transpositionCategories of reasonsPersonly utility (utility argument)Collective utility (economy
argument)Personly formation (culture
argument)Collective formation (democracy
argument)
External didactical transpositionConstituting 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 transpositionConstituting the school subjectTo 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 transpositionConstituting the school subject:
In practice the following are very strong
players in the constitutioning process:
The textbookExternal tests and examinationsTeacher communitiesPhysical and material conditions
Knowledge – how?
Knowledge - how
”Short cut”
A model for acknowledgment in science and mathematics in a didactical context
Didactical transpositionsSubject didactics has as it’s domain to describe teaching and learning processes within a given teaching subject.
Scientific Knowledge
Practice and every day knowledge
Teaching Institution
TeachingKnowledge
Subject/topic in a didactical system
Externaldidactical transposition
Internaldidactical transposition
Didactical TriangleI/didactical System
Teacher
Student
Mathematics
How to teach Mathematics
Teacher educator
Didactical TriangleI/didactical System
Teacher
Student
Subject
Didactical relation modelHiim and Hippe.
Prerequsites for learning
assesment
Learning process
content
goal
frame conditions (set up)
Didactical relation modelHiim 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 transformationAnalyze your teaching topic in
the perspectives of the didactic relation model
Did it bring in some new lightning on your teaching situation?
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