Empiricalmathematical modelling in upper secondary physics

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Empirical-mathematical modelling in upper
secondary physics
- Rationale for and implementation of a modelling
approach in upper secondary physics in Norway

• Carl Angell (UiO)
• Øystein Guttersrud (UiO)
• Ellen Karoline Henriksen (UiO)
• Per Morten Kind (Durham University)

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We will

• Present the background for Project PHYS 21
• Present the rationale for project PHYS 21 in
  terms of six challenges
• Present the view of modelling applied in the
  project
• Present examples of teaching material
• Present some experiences and observations

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Background

• Two overall purposes of science education
• A competent workforce
• Scientifically literate citizens

• A process-centred view of physics

• Physics is concerned with making (mathematical)
  models of reality
• Doing physics in real life is increasingly
  about developing, testing and applying models.

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Six challenges that motivated project PHYS 21

• the use of, and interchange between, multiple
  representations of physical phenomena
• the role and purpose of experiment in physics
• the relationship between mathematics and physics
• understanding the nature of science
• fruitful learning strategies for gaining
  understanding in physics
• skills in scientific reasoning

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Multiple representations in physics

• Physics appears difficult because it requires
  students to cope with a range of different forms
  of representation (experiments, graphs, verbal
  descriptions, formulae) simultaneously and to
  manage the transformations between these (J.
  Dolin, 2002).

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Conceptualizing modelling in physics in project
PHYS 21
Phenomenon
Modeling the phenomenon
Model
Learning the model
Interchanging between forms of representation
Mastering the model
Interchange between and simultaneous application
of the representations constituting the
scientific model
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Project PHYS 21 an overview

• Strategy to introduce the modelling aspects of
  physics to a more extended and systematic degree
  than it is normally done in Norwegian schools
• 10 schools, almost 20 physics teachers and almost
  300 students participated in the project, trying
  out new material and activities involving
  empirical-mathematical modelling along with a
  focus on scientific reasoning
• Introduction and workshops 2003-2004 pilot
  year 2004-2005 full implementation 2005-2006
• Workshops and meetings for participating teachers
  during the whole period

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Printed material for PHYS 21

• Student booklet
• What is physics?
• The aim of physics
• Scientific reasoning
• Types of models
• Mathematical models
• Teacher booklet
• Plan for the academic year
• About models and modelling
• Suggested modelling activities
• Scientific reasoning

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Modelling activities in PHYS 21

• Force on jelly babies as a function of elongation
• Different spring constant for different
  colours?
• Different spring constant from 1st to 2nd try?
• Interval of linearity?

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Modelling activities in PHYS 21

• A quasi-qualitative experiment with falling
  paper cases

R
mg
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Air resistance versus speed
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Air resistance versus speed squared
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Modelling activities in PHYS 21

• The force between two magnets
• Most students found a dependence where
• n was between 1 and 2, and x was the distance
  between the magnets

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Modelling activities in PHYS 21

• Introducing the equations of motion from
  experiment
• Teacher in wheelbarrow at constant speed

General approach Experiment ? graph ? Model
(expressed as a formula)
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Some results and experiences (I)

• Despite mild, but clear directions from the
  project management, the teaching strategies used
  in different PHYS21 classrooms varied widely.
• Questionnaire results indicate that teaching
  approaches were more experiment- and model-based
  in PHYS 21 classrooms than i regular classrooms,
  and that students had reflected on this fact
• Teachers appreciated the chance to give an
  in-depth treatment of fundamental concepts based
  on the empirical-mathematical modelling approach

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Some results and experiences (II)

• Students are uncertain when choosing the
  appropriate axes for plotting independent and
  dependent variables
• Students need training in evaluating mathematical
  models in terms of physical concepts When using
  the trend line and regression tool on their
  calculators, they often come up with complex
  equations including a lot of factors and
  corresponding constants, few of which have any
  physical interpretation. Students seem to have
  the motto the more parameters, the better.

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Conclusion

• The PHYS 21 project has resulted in some new
  suggestions for meaningful activities in physics
  education, but have also revealed some points
  that need further improvement
• Among the many demands expected to be made on
  future citizens and professionals are
  adaptability, ICT skills, flexibility and
  creativity. We argue that empirical-mathematical
  modelling is relevant to fostering such skills
• Empirical-mathematical modelling at its best
  demonstrates how doing physics can be a highly
  creative activity, and may thereby possibly
  contribute to improved recruitment