The conflict between Minimalist Instruction and versatile tools

1
The conflict between Minimalist Instruction
and versatile tools

• Lenni Haapasalo
• University of Joensuu, Finland

2
Minimalist Instruction

• Carroll, J. M. (1990). The Nurnberg Funnell
  Designing Minimalist Instruction for Practical
  Computer Skill. Cambridge, Massachusetts The MIT
  Press, pp. 710.
• Lazonder, A. W. (2001). Minimalist
  Instruction for
• Learning to Search the World Wide Web.
  Education
• and Information Technologies 6 (3), pp.
  161-176.

3
The main conflict

• How much should students understand for being
  able to do, and vice versa?
• Structure of the topic to be learned
• Instructional variables to utilize technology

4

• Instruction that emphasizes how to can be
  effective in a particular context but may not
  transfer to novel situations because it does not
  teach the knowledge underlying the skills. On
  the other hand, instruction that emphasizes the
  why can provide richer knowledge applicable to
  a variety of contexts but creates discrepancy
  between instruction and applicationthat which we
  teach is not what we expect students to do.
• Shih Alessi (1994, 154)

5
Procedural vs Conceptual

• Merriënboer van, J. J. G. (1997). Training
  Complex Cognitive Skills A Four-Component
  Instructional Design Model for Technical
  Training. Englewood Cliffs, NJ Educational
  Technology Publications.
• Shih, H. Alessi, S. (1994). Mental Models and
  Transfer of Learning in Computer Programming.
  Journal of Research on Computing in Education 26,
  pp. 154-176.
• Ben-Ari, M. (2001). Constructivism in Computer
  Science Education. Journal of Computers in
  Mathematics and Science Teaching 20, pp. 4573.
• Urban-Lurain, M. (2001). Teaching FITness for
  Conceptual Understanding A Computer Science
  Course for Non-Computer Science Majors. Presented
  at Annual Meeting of the AERA, April 2001.
  (http//www.cse.msu.edu/rgroups/cse101/AERA2001/Te
  achingFITness.htm)
• Chatfield, R. (2000). Sustainable Use-Design and
  Skill Social and Material Dimensions of
  Relational Databases. Sociological Perspectives
  43 (4), pp. 573-592.

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Procedural vs Conceptual

• Even though new hardware and software
  applications are produced frequently, the basic
  operational principles of new applications are
  quite constant.
• Procedural skills are not sufficient for a
  transfer effect, if the logic beyond the skills
  is unknown.
• It is easier to remember conceptual knowledge
  than discrete procedural skills without any
  meaning.
• (Urban-Lurain, M. 2002).

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... Procedural vs Conceptual

• One problem of conceptual knowledge is its slow
  applicability.
• When having mere conceptual understanding of an
  application, retriving the needed information
  from the memory and interpretation to concrete
  procedures can be difficult.
• Interpretation or modification of conceptual
  facts for certain situation is slow, reguiring
  often additional tests and functions.
• Applying of more automated procedural knowledge
  is faster, because procedures can be directly
  used in the situation without any time consuming
  interpretations.
• (Neves Anderson)
• (Borgman)
• (Olfman Mandiwalla).

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Conceptual knowledge (C )

• denotes knowledge of and a skilful drive
  along particular networks, the elements of which
  can be concepts, rules (algorithms, procedures,
  etc.), and even problems (a solved problem may
  introduce a new concept or rule) given in various
  representation forms.
• Haapasalo, L. Kadijevich, Dj. (2000).
  Two Types of Mathematical Knowledge and Their
  Relation. Journal für Mathematik-Didaktik 21
  (2), pp.139-157.

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Procedural knowledge (P ) denotes dynamic and
successful utilization of particular rules,
algorithms or procedures within relevant
representation forms. This usually requires not
only the knowledge of the objects being utilized,
but also the knowledge of format and syntax for
the representational system(s) expressing them.
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• P often calls for automated and un-conscious
  steps, whereas C typically requires conscious
  thinking. However, P may also be demonstrated in
  a reflective mode of thinking when, for example,
  the student skillfully combines two rules without
  knowing why they work.

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Four relations between P and C

• Inactivation view (I) P and C are not
  related
  (Nesher 1986 Resnick Omanson 1987).
• Dynamic Interaction view (DI) C is a
  necessary but not sufficient for P (EDU)
  (Byrnes Wasik 1991).
• Simultaneous activation view (SA) P is
  a necessary and sufficient for C (DEV)
  (Hiebert 1986, Byrnes Wasik 1991
  Haapasalo (1997).
• Genetic view (G) P is a necessary but
  not sufficient for C (Kline 1980, Kitcher
  1983, Vergnaud 1990, Gray Tall 1993, Sfard
  1994).

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Educational approach

• is based on the assumtion that P depends on C.
  Thus, the logical background is DI or SA. The
  term refers to educational needs, typically
  requiring a large body of knowledge to be
  transferred and understood.

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assumes that P enables C development. The logical
background is G or SA, and the term reflects the
philogenetic and ontogenetic nature of
mathematical knowledge.

• Developmental approach

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Dynamic interaction and simultaneous activation

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Downloadable at

• http//www.joensuu.fi/lenni/programs.html

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Proportionality - Linear Dependence - Gradient
of a Straight Line through Origin
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Simultaneous activation
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Novice learner (Alien)
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Expert learner
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Utilizing SA method with ClassPad

• http//www.classpad.org/Classpad/Casio_Classpad_30
  0.htm

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Main Application work area

• Currently displayed screen (Graph Editor, Graph,
  Conic Editor, Table, Sequence Editor, Geometry,
  3D Graph Editor 3D Graph, Statistics, List
  Editor, and Numeric Solver).
• Main Application window Geometry window
• Linear equation in x and y An infinite line
• Equation of circle in x and y A circle
• 2-dimensional vector A point or vector
• 2 2 matrix A transformation
• Equation y f(x) A curve
• n 2 matrix A polygon (each column represents a
  vertex)

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Example 1 Gradient / Orientation

• 1. Alg Write y 0. Then copy it.
• 2. Geom Paste, a horizontal line
  appears.
• 3. Geom Rotate 45 degrees. The matching
  line appears.
• 4. Geom Copy it.
• 5. Alg Paste, equation yx appears.
• 6. Alg Change the equation to y2x.
  Then copy this equation.
• 7. Geom Paste it, the matching line
  appears.

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Example 2. Conics

• 1. Draw a circle
• 2. Drag-and-drop it into albegraic window
• 3. Manipulate equation
• 4. Drag-and-drop it into geometric window

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Example 3 Transformations

• 1. Construct a segment CJ.
• 2. Drag-and-drop it to algebraic window.
• 3. Construct a line perpendicular to CJ.
• 4. Drag-and-drop it to algebraic window.
• 5. Make hypotheses concerning the gradients.
• 6. Make any general transformation.
• 7. Two matrices appear in algebraic window,
• 8. Fill them and look what happens!

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Making of informal mathematics

• SA method for enhancing of
• mental links
• made by the student

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Transformation
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adding more interactivity
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Example 4

• Kidware Aquarium Simulation Program
• by Mobius Corporation (2002)
• Animation at
• http//www.edu.joensuu.fi/siekkinen/aquarium.wmv

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New research on ICT learning
Järvelä, J. 2003. Conceptual and Procedural
Knowledge by Learning of Basic Skills in
Information Technology. University of Joensuu.
Faculty of Education. Master Thesis. Aim
To find out how conceptual and procedural
approach affects learning basic skills in ICT.
TG participants in service-in-training for ICT.
Research material portfolios during the
course Viewpoint knowledge-building on
individual level. Results Different
individuals orientate in different ways on
learning ICT Teaching should be tailored
to meet the needs of individuals
34
Three types of learners
Conceptually oriented learners aim to learn
things
advancing from C towards P. Procedurally
oriented learners advance from P towards C.
Procedurally bounded learners concentrate only
on P. Neither procedural nor conceptual
approach, in their most simply forms, does seem
to represent any students way of learning.
Developmental approach seems to act as a
starting point for all learner types.
35
Learning through design

• When designing any learning environment we meet
  the dilemma

Should the learner understand for being able
to do, or vice versa?

• Implementing of technology makes this more
  complicated .

• but opens room for alternative
  teaching/learning paths

• especially when learning through design is
  utilized.

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Challenges for ICT-based design

• Our task is to explore these paths for a better
  education

• ... not only for students but their teachers.

• Even if teachers may not accept ICT-based
  learning, this kind of instruction design can
  improve educational practice..

• ... provided that pedagogy is linked to
  technology..

• ... instructional units are planned
  collaboratively, and a support in their classroom
  utilization is given to teachers.

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Closing remarks 1
Having in mind studies concerning
technology-based learning, such design projects
should also be used in the professional
development of teachers. To benefit from them
fully, we have to realize their main critical
issues and handle them in an adequate way.
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Closing remarks 2

• There is often a conflict between C and P

• We cannot say how, or in which order, students'
  knowledge develops in each situation and in each
  topic

• Even the most abstract concepts can be based on
  their spontaneous ideas.

• This, however, does not predestine any order for
  the activities, because it is the pedagogical
  framework that matters.

• Doing should be coghnitively and psychologically
  meaningful for the student.

• Analyse of TIMSS and PISA reveal

It is not necessarily the school teaching
that impacts on students
mathematical knowledge!!!!
39
If we accept the assumption that the main task
of education is to promote a skilful drive
along knowledge networks so as to scaffold pupils
to utilize their rich activities outside school,
it seems appropriate to speak about an
educational approach in the sense of this paper.
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Geometry link
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The Finnish case study
12 secondary mathematics teachers and 10
primary teachers workshop of 2-3 hours
Aim 1 To get experiences how introduction to
hypermedia could be done in an optimal way when
time is limited (cf. Carrol 1990, Lazonder
2001) Aim 2 To compare conceptual and
procedural approaches in exaggerated way.
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Outcomes
Secondary math. teachers - graphs (ca. 50
) - trigonometry (ca. 30 ) - Pythagorean
theorem - Fourier series - Lorenz
transformations - or physics. Primary teachers
- place value system
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The moving man applet
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Abacus
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Fourier series
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Lorenz transformations
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Procedural group

• eagerly discussed pedagogical issues
• more than .technical issues.
• Some students didnot like that they just
  proceeded without knowing why particular actions
  worked( conceptual barriers of Chatfield
  2000)

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Conceptual group

• students discussed the logical and technical
  structure
• required explanations
• picked up an applet and started to test their
  method
• most students could proceed without using the
  guidelines or the instructors help.