Potential of the Internet for Mathematic Education Outline€¦ · MicroLearning, MOOC, OER,...

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Danube University Krems Department for Interactive Media and Educational Technologies

The Potential of the Internet for Mathematic Education MicroLearning, MOOC, OER, ePortfolio

and other Virtual Monsters

These Slides are licensed under a Creative Commons License :


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•  Learning Management Systems and Blended Learning Strategies"

•  Two Case Studies of Educational Scenarios:"•  Mobile Learning/Microlearning"•  Collaborative Learning "

•  Learning Theory & Educational Design"

•  Conclusions"

Potential of the Internet for Mathematic Education Outline

July 2014 Peter Baumgartner

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Transfer"

• "factual knowledge, “know-that”"

• "Transfer of propositional knowledge"

• "to know, to remember"

• " Production of correct answers"

• "Verbal knowledge, Memorisation"

• " to teach, to explain"

Learning I"

Tutor"

• procedural knowledge, "know-how""

• "Presentation of pre-determined problems "

• to do, to practice"• "Selection of correct

method and its use"• Skill, Ability"

• "to observe, to help, to demonstrate"

Learning II"

Coach"

• "social Practice, "knowing-in-action""

• "Action in real (complex and social) situations"

• to cope, to master"• "Realisation of

adequate action strategies"

• Social Responsibilty"• to cooperate, to

support"

Learning III"



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Transfer material to the learning management system (LMS)

Transfer"

Course Repository"

Upload Material 1:1 to the LMS platform (Word, PDF)

Face-to-face study is supported by distribution of materials

Up-/Download changes responsibility structure

LMS is a tool for administrative support

Implementation step by step but organisation-wide

Transfer"

• "factual knowledge, “know-that”"

• "Transfer of propositional knowledge"

• "to know, to remember"

• " Production of correct answers"

• "Verbal knowledge, Memorisation"

• " to teach, to explain"

Teaching I"


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Communication"

Enrichment"

Material prepared for the learning process („Study-Guide“)

Asynchronous Communication (Forum, email)

Integrate tasks and exercises LMS is a tool for the

communication process E-Moderation, E-Tutoring

necessary

Task, exercises and part of communication process are transferred to the LMS

Tutor"

• procedural knowledge, "know-how""

• "Presentation of pre-determined problems "

• to do, to practice"• "Selection of correct

method and its use"• Skill, Ability"

• "to observe, to help, to demonstrate"

Teaching II"



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Using the educational surplus value of blended learning scenarios systematically

Construction"

Blended Learning"

Special Design of Blended Learning Scenarios

Use of special tools: Wikis, Podcasts, Vodcasts, E-Portfolios

Develop tasks and exercises for virtual settings

LMS is an educational tool for learning and teaching

Self directed learning (projects) with personal responsibilities

Coach"

• "social Practice, "knowing-in-action""

• "Action in real (complex and social) situations"

• to cope, to master"• "Realisation of

adequate action strategies"

• Social Responsibilty"• to cooperate, to

support"

Teaching III"


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Construction"

Blended Learning"

Special Design of Blended Learning Scenarios

Use of special tools: Wikis, Podcasts, Vodcasts, E-Portfolios

Develop tasks and exercises for virtual settings

LMS is an educational tool for learning and teaching

Self directed learning (projects) with personal responsibilities

Transfer"

Repository"

Upload Material 1:1 to the LMS platform (Word, PDF)

Face-to-face study is supported by distribution of materials

Up-/Download changes responsibility structure

LMS is a tool for administrative support

Implementation step by step but organisation-wide

Communication"

Enrichment"

Material prepared for the learning process („Study-Guide“)

Asynchronous Communication (Forum, email)

Integrate tasks and exercises

LMS is a tool for the communication process

E-Moderation, E-Tutoring necessary



Peter Baumgartner July 2014 8

Know-ledge

Cognitive Processes

Remem-ber

Under- stand

Apply Analyze Evaluate Create

Facts

Concepts

Proce- dures

Meta- cognitive

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Know-ledge

Cognitive Processes

Remem-ber

Under- stand


Facts

Concepts

Proce- dures

Meta- cognitive

Transfer" Tutor" Coach"

Teaching I" Teaching II" Teaching III"

Micro" Meso" Meso - Macro"


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Student Workload: 1 ECTS ~ 25-30 Hours of Workload

For Example in our Department:

1 Modul = 3 ECTS = 1 face-to-face Seminar = 4 Months


Monat -2 Monat -1 Monat 1 Monat 2

15h 20h 15h 15hPräsenztag (10h)Modulstart Modulabschluß

Month-1 Month-2 Month 1 Month 2

Start of Module Contact Time face2face

End of Module

Blended Learning Arrangement (Example)

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75 Hours of Self-Study Study-Guide Material Online-Assessment with

(semi)automatic Evaluation

AKT 1-2 Remember, Understand

Study-Guide Discussion forum, Tutoring

Assignments Discussion forum, Tutoring

Oral and/or written Exams

Assignments with Timetable and Interaction

Structure

AKT 3-4 Apply,

Analyse

Assignments Forming Groups, Coaching

Assignments Forming Groups, Coaching

Assignments with Timetable & Interacting of Groups(with self-directed

Coordination

Written Exams Projects,

E-Portfolio

AKT 5-6 Evaluate, Create


Blended Learning Arrangement (DUK)


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e.g. prearrangement and follow-up of complex tasks via LMS 1

e.g. f2f-explanation of a complex task which has to be done via LMS

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e.g. f2f-presentations and reflections of assignments 3

e.g. f2f-explanation of assignments with intermediate f2f-feedback

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e.g. f2f-explanation of assignments with f2f-examinations

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e.g. assignment via LMS with f2f-feedback and f2f-examination

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(Cf. Mastertheses by Sankofi/Szucsich 2007)

= Face to Face (f2f) = Timeline = Start/End of Module

Legend


6 Structural Variations (Example-DUK)

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Educational action is the mapping of semantic relations into the time necessary for knowledge acquisition and competences under the perspective of validity claims.!

Peter Baumgartner Fundamental Theorem of Education

Adopted from (Meder 2006) Meder, N. (2006). Web-Didaktik: Eine neue Didaktik

webbasierten, vernetzten Lernens). Bertelsmann, Bielefeld.

Baumgartner, P. (2011). Taxonomie von Unterrichtsmethoden: Ein Plädoyer für didaktische Vielfalt. Münster: Waxmann.

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Validity Claims References to

the World

subjective objective

social

Theory of Communicative Action

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Validity Claims References to the World

subjective Develpment

of the own Personality

objective Subject, Theme, Material

social (Co-)Learner,

Tutor

Educational Setting

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Donau-Universität Krems Department für Interaktive Medien und Bildungstechnologien

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Konstruktion"

Blended Learning"

Eigenes Design von Blended Learning Szenarien

Wikis, Podcasts, Vodcasts, E-Portfolios

Aufgaben und Übungen für Plattform entwickeln

LMS als pädagogisch-didaktisches Werkzeug

Eigenverantwortliche aktivierende Projekte

Transfer"

Materialdepot"

Materialien 1:1 auf die Plattform stellen (Word, PDF)

Präsenzstudium wird ergänzt

Up-/Download, Bringschuld wird zur Holschuld

LMS als administrative Unterstützung

Schrittweiser flächendeckender Ausbau

Kommunikation"

Anreicherung"

Materialien für das LMS aufbereitet („Study-Guide“)

Kommunikation asynchron (Forum, eMail)

Aufgaben und Übungen integrieren

LMS zur kommunikativen Unterstützung

E-Moderation, E-Tutoring notwendig


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Perceive & Do (Debug)

Produce & Deposit

Practice & Discuss

Teaching & Facilitating

Tutoring & Managing

Coaching & Orchestrating

Interacting with Object

Interacting with Self &

other Subject (Human)

Interacting Self & with Society

Knowing-in-action

Reflecting-in-practice Reflecting-in-action

Artefact Environment

Competence Helix

17 July 2014 Peter Baumgartner


July 2014 Peter Baumgartner 18

Case Study I: Microlearning Microlearning deals with relatively small learning units and short-term learning activities.… More frequently, the term is used in the domain of e-learning and related fields in the sense of a new paradigmatic perspective on learning processes in mediated environments. (Wikipedia)

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Microlearning deals with relatively small learning units and

short-term learning activities. Generally, the term

"microlearning" refers to micro-perspectives in the context of

learning, education and training. More frequently, the term is

used in the domain of e-learning and related fields in the

sense of a new paradigmatic perspective on learning

processes in mediated environments. (Wikipedia)

http://en.wikipedia.org/w/index.php?title=Microlearning&oldid=597955821

Microlearning I: Definition



Microlearning II: Examples

•  reading a paragraph of text •  listening to an informational (short) podcast or an

educational video-clip •  memorizing a definition or formula •  sorting a set of (microcontent) items by

(chrono)logical order •  selecting an answer to a question •  answering questions in quizzes

http://en.wikipedia.org/wiki/Microlearning#Dimensions_of_microlearning

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Educational Policy"

Curricula"

Educational Ensemble"Content Block"

(Several Hours)"

Educational Scenarios"(Minutes – Hours)"

Educational Interaction"(Seconds - Minutes"

Learning Time Workload

(ECTS)

Micro Level"

Meso Level"

Macro Level"


Levels of Educational Design



Microlearning IIIa: Dimensions •  Subject Matter: Microcontent (small chunks of

information, „knowledge nuggets“) – Simple issues •  Time: Microteaching (short learning time, seconds up

to 15 minutes) – Simple tasks, lower cognitive processes

•  Learning Activity: Triggered by push technology to minimize cognitive load – Externally controlled instead of self-determined learning

•  Validity: Facts & objectivity oriented – No other personal (emotional, social) development

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Know-ledge

Cognitive Processes

Remem-ber

Under- stand


Facts

Concepts

Proce- dures

Meta- cognitive M

icro

lear

ning



Microlearning IV: Short-Period & Turbulent Environments

Travelling in tram

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Waiting at the airport




Waiting/Siting in a Café

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Waiting room




Standing in line

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Microlearning V: Mathematic Examples App for quickly finding formulas across multiple disciplines. It is focused on traditional math fields such as Algebra, Geometry and Calculus. MathRef allows users to add notes to equations, to save favorite equations and to copy text from within the app to e-mails or text editor.



Microlearning V: Mathematic Examples Sometimes it is good to brush up on your math skills. Numbler is an innovative game that allows you to compete against the computer or friends in the style of "Words With Friends," but instead of creating words with your tiles, users are tasked with creating equations.

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Microlearning V: Mathematic Examples Offers answers to many math-related or number-centric questions. The computational knowledge engine can compute across 29 disciplines. You can get formula details, graphic representations and brief explanations to help you understand how the app arrived at a given solution.



Microlearning V: Mathematic Examples Those studying advanced mathematics can download an app like Graphing Calculator by Mathlab. This free app provides its users with advanced operators, functions, an intuitive user interface and beautifully laid out graphs featuring slopes, roots and intersections -- just to name a few.

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MicroLearning IIIb: Dimensions •  Subject Matter: Microcontent (small chunks of

information, „knowledge nuggets“) – Simple issues? •  Time: Microteaching (short learning time, seconds up

to 15 minutes) – Simple tasks, lower cognitive processes?

•  Learning Activity: Triggered by push technology to minimize cognitive load – Externally controlled instead of self-determined learning?

•  Validity: Facts & objectivity oriented – No other personal (emotional, social) development?

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Know-ledge

Cognitive Processes

Remem-ber

Under- stand


Facts

Concepts

Proce- dures

Meta- cognitive M

icro

lear

ning

Mic

role

arn

ing

Mic

ro

lea

rn

ing

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1.  Mobile technology creates multiple new learning occasions.

2.  Short (consecutive) learning time is not necessarily linked with simple cognitive tasks.

3.  Learning opportunities outside educational institutions increases

4.  Non-formal learning & informal learning needs to be better acknowledged and integrated into an overall learning design.

Summary Case Study I: Microlearning & Mobile Learning



Case Study II: Peer Production Peer production is a way of producing goods and services that relies on self-organizing communities of individuals who come together to produce a shared outcome. (Wikipedia)

We understand peer production as a mode of commons-based and oriented production in which participation is voluntary and predicated on the self-selection of tasks. (Journal of Peer Production)

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Know-ledge

Cognitive Processes

Remem-ber

Under- stand


Facts

Concepts

Proce- dures

Meta- cognitive P

eer

Pro

duct

ion



Peer Production in Wikipedia

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Peer Production in Open Source Software



Social Software and Web 2.0

“Web 1.0”: Hyperlinks connects websites: one piece of content to another piece of

content

“Web 2.0”: Social Software connects to people with same interests

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http://www.librarything.com http://www.librarything.de




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July 2014

https://www.xing.com/

Peter Baumgartner 44

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Mai 2014

Small World

Peter Baumgartner

Granovetter, Mark S. 1973. The Strength of Weak Ties. American Journal of Sociology 78, Nr. 6 (Juni): 1360–1380. http://www.jstor.org/stable/2776392 (Zugegriffen: 21. April 2013).



1.  Collaborative Voting: Contributions with the best

community voting are placed at top articles.

2.  Collaborative Indexing: Community members provide

relevant metadata.

3.  Creation of networks: The friend of a friend of a

friend…

4.  Communities of common interest: People evaluating

this article had also voted for these other articles.

Action Strategies with Social Software

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e.g. wikipedia: very few people write many articles many people add sentences or correct typos

e.g. amazon: very few books are bestsellers, many books are slow sellers (“shopkeeper”)

Internet: Pareto Distribution

e.g. MOOC: very few participants are active and take all examinations, many people are passive and just bystanders (“witness learning”)


Cranshaw, J., & Kittur, A. (2011). The polymath project: lessons from a successful online collaboration in mathematics. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (pp. 1865–1874). ACM. Retrieved from http://dl.acm.org/citation.cfm?id=1979213


Massive Online Collaboration in Math. The Polymath Project

Currently 9 official Polymath Projects. Each of these projects focuses on a significant unsolved problem in mathematics. 3 published articles: pseudonym D. H. J. POLYMATH Case Study with Polymath1: Hales–Jewett theorem

General Blog: http://polymathprojects.org Wiki: http://michaelnielsen.org/polymath1/

Timothy Gowers Blog http://gowers.wordpress.com/ Terence Tao http://terrytao.wordpress.com/

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The Hales–Jewett Theorem

The Hales–Jewett theorem asserts that for every r and every k there exists n such that every r-colouring of the n-dimensional grid {1,...,k}n contains a combinatorial line. A kind of generalization of game of tic-tac-toe, which cannot end in a draw, no matter how large n is, no matter how many people are playing provided only that it is played on a board of sufficiently high dimensions.



The Polymath Project

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The Hales–Jewett Theorem February 1 - May 23, 2009: 1555 comments on 14 blogs entries (Gowers:8 / Tao: 6) 1228 to the subject, rest meta-comments

Number of Participants Number of Comments 39 1228 1 (Thimothy Gowers) 285 1 (Terrence Tao) 232 13 1 21 5 or less



The Polymath Project

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1.  Online collaboration will increase and foster “Citizen

Science”

2.  Voluntary collaboration, free of charge

3.  Massive Collaboration („The wisdom of crowds“)

4.  Open Culture: Free Access at all levels: Standards, Source

Code, APIs, Innovation, OER, OA… („mash ups“)

5.  Acting Globally: No physical and geographical boundaries

6.  Importance of informal learning will increase

Summary Case Study II: Peer Production


July 2014

For every specified educational objective:

What is the educational surplus value in

using eLearning/technology?

Are there other (traditional) methods which

fit better the intended learning outcome?

Conclusion I Importance of Educational Surplus Value


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Every educational technology, every

technology supported learning environment or

internet application implements a theoretical

learning model – irrespective of opinions and

believes of developers and teachers

July 2014

Conclusion II ICT is not educationally neutral



July 2014

1.  There are different levels of educational design following different rules.

2.  Different learning models are not exclusive but support each other. Educational variety instead of educational monoculture!

3.  Design learning environments with objective, subjective and social learning subjects.

4.  Design different modes of blended learning arrangements (face2face, eLearning) holistically.

Peter Baumgartner

Conclusion III a Educational Design

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July 2014

5.  Learning is a social enterprise and needs active participation and personal responsibility.

6.  For effective learning arrangements we need to design learning content AND the appropriate (technologically supported) communicational structure.

7.  The importance of informal learning in combination with social software and web 2.0 will increase. We will need procedure for the Acknowledgement of Prior Experiential Learning (APEL)

Peter Baumgartner

Conclusion III b Educational Design

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Thank you for your attention!

Peter Baumgartner http://www.donau-uni.ac.at/imb

http://www.peter.baumgartner.name http://twitter.com/pbaumgartner

These slides are licensed under a��Creative Commons License.

58 July 2014 Peter Baumgartner

Potential of the Internet for Mathematic Education Outline€¦ · MicroLearning, MOOC, OER,...

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