## Methodology

## How Do We Create "New", and Verify Current Knowledge?

# Essential Questions

### 1. How do we approach the creation of new, and the verification of current, knowledge in different AOK's?

### 2. Does the variety of methodologies in different AOK's impact the value of the knowledge claims?

### 3. Is mathematics better defined by its method or by its subject matter?

### 4. What does it mean to say that mathematics is an axiomatic system? How do we choose the axioms underlying mathematics? Is this an act of faith?

### 5.To what extent and in what ways might the arts be regarded as a representation of reality? To what extent does the artist create new knowledge?

### 6. Most arts have used technology, over many centuries (for example, musical instruments, pencils). Has the relationship between the arts and technology changed as a result of the possibilities of mechanical reproduction and digital manipulation?

###

# Assessments

In this unit, you will be completing a variety of formative assessments to prepare you to write a 1200-1600 word essay that will be assessed on all four criteria that are used to assess the TOK essay. The question you will assess will be:

“The methods used to produce knowledge depend on the use to which it will be put.”Discuss this statement in relation to two areas of knowledge. (November 2013 Title # 6)

Download and complete

for each AOK by the end

of the Unit:

How do we approach the creation of new, and the verification of current, knowledge in different AOK's?

Does the variety of methodologies in different AOK's impact the value of the knowledge claims?

In pairs, students draw a "common" task and attempt to create a series of instructions on how to achieve it. They prepare their instructions then exchange it with another partnership. The partnership then attempts to complete the task only using the instructions then compare their results with what the creators of the instructions intended.

Class Discussion: To what extent is the method we use to create something more important than the final product?

Students select one AOK and must create a series of interview questions for an interview with an expert in that AOK about how knowledge is created/verified in their AOK. They must submit a transcript of their interview next lesson.

Student's share their transcripts with other students.

Class Discussion: Does the variety of methodologies in different AOK's impact the value of the knowledge claims?

### Is mathematics better defined by its method or by its subject matter?

### What does it mean to say that mathematics is an axiomatic system? How do we choose the axioms underlying mathematics? Is this an act of faith?

Mathematical Proofs, Axioms and the “language of the Universe” Students should be divided into 6 groups (2-3 students per group) and then assigned a number 1-6. These numbers correspond to questions that are listed at the top of the website-Introduction to Mathematics Methodology

Each group has the remainder of the lesson to create an A3 poster that:

1. Answers the question

2. Provides demonstrative examples

3. Includes no more than 10 words

(excluding the question)

Market Place Activity

After in the second lesson, students select who shall be the teacher (1) and who shall be the student(s) (1-2). Teachers remain with the poster and must present the groups' poster and students must go around the room searching out the answers to the other 5 questions (15 minutes)

After the Market Place Activity, students have 5 minutes to share their findings, then class discussion reviewing the 6 questions.

In the same 6 groups have students go to the Wikipedia link entitled List of Axioms. Assign one axiom to each group and have them create a three to five-minute math lesson that shows how their axiom functions in a "real" math example (15 minutes).

Students present lessons to class next lesson

To what extent does Mathematics fit the definition of a language?

Students are split into groups 3-4 and attempt to create a case for Mathematics as a language or a unique area of knowledge.

Present in groups of 6-8 to share their findings.

Use the remaining time in the lesson to develop notes for SD next lesson (see the link to Guiding Questions)

Socratic Discussion:

Is mathematics its own discipline or the language of the science?

Complete a Knowledge Framework for Mathematics

Guiding Questions for

Socratic Discussion on

the Nature of

Mathematics

To what extent and in what ways might the arts be regarded as a representation of reality?

What kinds of art might be seen as “realistic”?

Methodology and the Arts

What do Artists do all day?

BBC Series on the Methodology of Modern Artists

Links to Past Episodes

Jake and Dinos Chapman (Visual Art): Part 1, Part 2

Evelyn Glennie (Percussionist): Part 1,Part 2

Micheal Landry (Visual Art/Installations): Part 1, Part 2

Albert Watson (Photography): Part 1, Part 2

Akram Khan (Dance): Part 1, Part 2

Most arts have used technology, over many centuries (for example, musical instruments, pencils).

Has the relationship between the arts and technology changed as a result of the possibilities of mechanical reproduction and digital manipulation?

Art Created and Art Experienced

Complete Knowledge Framework for the Arts

Comparing and Contrasting Methodologies

Are all methodologies equally valid or must a methodology be universal in order to be reliable?

Work on Essay

Full TOK Symposium Comparing Methodologies in Arts and Maths

Venn Diagram Comparing the Methodologies of the Arts, Mathematics and Ethics around the concepts of procedures, axioms/assumed truths, application (universal or individual) and malleability over time.

Class Discussion: "To what extent does methodology strengthen an AOK's ability to make reliable knowledge claims?"

Setup Essay Assignment

Peer Edit Essay and Review Assessment Criteria

The Artist and the Mathematician at Work Methodology Symposium:

Create a Venn Diagram Online

A More Fancy Venn Diagram Generator

Another Fancy One