Didactical Elements

Didactic TriangleI/didactical System

Teacher

Student

Subject

Didactic Triangle/didactical System

Teacher

Student

SubjectMathematics/Science

Examples:

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 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 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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