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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
  • 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 interactive 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

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
  • 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

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: Role 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

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: Different 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 by a comparison of the examination results

Learning and Instruction Symposium - JULIS'05

summary conclusions
Summary & conclusions
  • 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