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Reacting to challenges for the research in mathematics education: case studies of ICT learning environments. Timo Ehmke (Kiel), Martti Pesonen (Joensuu) and Lenni Haapasalo (Joensuu). Based on the project:

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Reacting to challenges for the research in mathematics education: case studies of ICT learning environments

Timo Ehmke (Kiel), Martti Pesonen (Joensuu) and Lenni Haapasalo (Joensuu)

Based on the project:

From Visual Animations to Mental Models in Mathematics Concept Formation(sponsored by DAAD / Academy of Finland)


Introduction
Introduction education: case studies of ICT learning environments

  • Starting point: - learning of tertiary mathematics

  • Problem: - difference between school and university mathematics- School focus on procedural knowledge- University focus on abstract conceptual knowledge- Challenge: Linking procedural and conceptual knowledge

  • Research interest:- Interactive Graphic Representation (IGR) as tool for learning and assessment

Learning and Instruction Symposium - JULIS'05


Features of interactive graphic representations igr
Features of education: case studies of ICT learning environmentsinteractive graphic representations (IGR)

  • dragging points by mouse

  • automatic animation/movement

     dynamic change in the figure

  • tracing of depending points

  • hints and links (text)

  • hints as guiding objects in the figure

  • response analysis / feedback

Learning and Instruction Symposium - JULIS'05


Theoretical background modem framework

verbal education: case studies of ICT learning environments

graphic

symbolic

Theoretical background:MODEM-Framework

The 5 phases of Multiple representations

concept formation: of concept attributes:

  • Orientation

  • Definition

  • Identification

  • Production

  • Reinforcement

Learning and Instruction Symposium - JULIS'05


Objectives
Objectives education: case studies of ICT learning environments

  • What kind of connection has the representation form (verbal, symbolic, graphic) of the mathematical problem to the difficulty of the task?

  • Does students’ prior knowledge have impact on the solving of the interactive problems?

  • Which kind of levels can be distinguished in students’ conceptual and procedural knowledge of binary operations?

Learning and Instruction Symposium - JULIS'05


Design

Test 1 education: case studies of ICT learning environments

Functions 1

(Web-CT)

Test 2

Functions 2

(Web-CT)

Test 3

Binary Operation 1

(Web-CT)

Test 4

Binary Operation 2

(Web-CT)

Test 5

Examination

(Paper&Pencil)

Design

  • First course on Lineare Algebra (N = 92)

  • Four exercises (tests) are computer-based (WebCT)

  • One paper & pencil test (examination)

  • Schema of course and study design:

Learning and Instruction Symposium - JULIS'05


Design description of items in the two binary operations tests
Design: Description of items in the two binary operations tests

Learning and Instruction Symposium - JULIS'05


Results role of the representation form
Results: testsRole of the representation form

Is the representation form of the task (verbal, symbolic, graphic) connected to the difficulty?

Learning and Instruction Symposium - JULIS'05


Results the role of prior knowledge

ns tests

ns

Results: The role of prior knowledge

Does students’ prior knowledge have impact on the solving of the (interactive) problems?

Learning and Instruction Symposium - JULIS'05


Results different levels of concept understanding
Results: testsDifferent levels of concept understanding

Which kind of levels can be distinguished in students’ conceptual and procedural knowledge of binary operations?

Statistical method: Latent-Class-Analysis

Cases: n = 92 Variables: DIS, DIV, DIG, IGS, IVS, IGV, PGV, PGS

Learning and Instruction Symposium - JULIS'05


Three types of learners concerning conceptual procedural knowledge
Three types of learners concerning conceptual-procedural knowledge

Learning and Instruction Symposium - JULIS'05


Validation of the classification by a comparison of the examination results
Validation of the classification knowledge by a comparison of the examination results

Learning and Instruction Symposium - JULIS'05


Summary conclusions
Summary & conclusions knowledge

  • IGR items could successfully adapted in the MODEM framework for diagnostic purpose.

  • Item difficulty of the sub dimensions (IGR) was not crucial.

  • Solving items with IGR (eg. DIG and IGV) was less dependend from prior knowledge.

  • The class analysis delivered three groups (levels) of concept understanding.

  • Challenge for ongoing work: Fostering links between conceptual and procedural knowledge.

  • Intervention-study: procedural vs. conceptual training about the mathematical function concept.

Learning and Instruction Symposium - JULIS'05


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