Understanding the conceptual changes
required in learning science and
mathematics: A cognitive developmental
approach and ...
The Framework Theory Approach to
Conceptual Change
•  1. Knowledge acquisition starts with the construction of a
naïve phy...
Naϊve Physics Naϊve Psychology
Ontology:
Physical Object
Causality:
Mechanical
Ontology:
Psychological Beings
Causality:
I...
Naïve Physics is a Framework Theory
•  Naïve physics does not consist of fragmented
observations but forms an explanatory ...
Learning Science Requires Major
Conceptual Changes in Naïve Physics
•  By the time they start primary school children have...
Naïve and scientific explanations of
the day/night cycle
The sun goes behind
the mountains and
the moon comes up
Earth is ...
(B) From Grade 1 to Grade 5
Major Bodies
Earth Celestial Bodies
Sun Moon Stars
Major Bodies
Celestial Bodies
Sun Planets S...
Changes	
  in	
  Representa.on	
  
Changes in Personal Epistemology
•  Explanation based on simple interpretation of sensory
evidence vs. hypothetical unobse...
The Creation of Misconceptions
•  Instruction-induced conceptual changes
are not sudden, gestalt-types
restructurings
•  T...
Fragmentation
•  Fragmentation can be produced when learners
assimilate scientific information to their naïve physics
crea...
Synthetic Conceptions
•  Synthetic conceptions are formed when learners
assimilate scientific information to their naïve p...
Vosniadou &
Brewer (1992)
Types of Explanation
1st
Grade
3rd
Grade
5th
Grade
Sun occluded by clouds or moves down 7 2 1
Sun and moon move up/down to...
The Role of Domain General Abilities
•  Learning science depends on the complex interplay
between domain specific conceptu...
Other studies of science
concepts
•  Models of the composition and layering
of the earth
•  Mechanics
•  Photosynthesis
• ...
Summary of the Framework Theory
–  Children	
  start	
  the	
  knowledge	
  acquisi.on	
  process	
  
by	
  organizing	
  ...
The Predictive Power of the
Framework Theory
•  The	
  strength	
  of	
  the	
  framework	
  theory	
  is	
  that	
  it	
 ...
Can the framework theory be
applied to mathematics learning?
•  There	
  should	
  be	
  an	
  ini.al	
  framework	
  for	...
Initial Framework for Number
•  By	
  4-­‐5	
  years	
  of	
  age	
  children	
  display	
  elements	
  of	
  an	
  early	...
Natural Numbers vs Fractions
Numerical value Natural number Fraction
Symbolic
Representation
One number (that
carries the
...
Frac.ons	
  are	
  Difficult	
  to	
  Understand
•  Only	
  50%	
  of	
  a	
  na.onally	
  representa.ve	
  sample	
  of	
  ...
Slow	
  Learning	
  of	
  Frac.ons	
  Characterized	
  by	
  
Synthe.c	
  Concep.ons	
  
Students’	
  difficul.es	
  occur	
...
Explanatory Frameworks
5th
Grade
N=40
6th
Grade
N=40
7th
Grade
N=40
8th
Grade
N=40
10th
Grade
N=40
Total
N=200
A. Two Inde...
Students’ Understanding of Density
(Vamvakoussi & Vosniadou, 2010)
Natural numbers Rational numbers Constraint
Discretenes...
Are there any numbers between…
Ø  0.005 & 0.006 0.1 & 0.2
Ø  3/8 & 5/8 1/3 & 2/3
Ø  0.001 & 0.01 0.01 & 0.1
Methodology...
From natural to rational
number
Synthetic models
Initial Model:
Discreteness
§  0.005 - 0.006
(the given numbers are alwa...
Synthetic conceptions of density
Synthetic
conceptions
Open-ended
questionnaires
Forced-choice
questionnaires
9th graders
...
An example
•  Panos, a 9th grader states that:
–  there are 9 numbers between .001 and .01
–  there are infinitely many nu...
Summary
Secondary school students (7th, 9th, 11th graders) with
many years of mathematics instruction
–  transfer the prop...
What Happens to Naïve Concepts when
Scientific Concepts are Learned?
•  Replacement view
•  Conceptual change as some kind...
Summary of the framework theory
–  Children	
  start	
  the	
  knowledge	
  acquisi.on	
  process	
  by	
  
organizing	
  ...
How is the framework theory different from the
‘classical’ Posner et al. (1982) theory?
•  Posner et al., (1982) argue tha...
Instruction for Conceptual Change
Content – Address students’ intuitive
beliefs – Explain not replace
Structure - Order of...
Research-Based Curricula and
Model-Based Instruction
•  Breadth of coverage of the curricula
•  Content of curricula
•  Or...
Sequence of Concepts
Theoretical Framework
Basic Questions -
Entrenched Beliefs
Instructional Interventions
EARTH SHAPE Pe...
Active, intentional and self-regulated
learning
•  Metaconceptual awareness - becoming aware of their own ideas –
understa...
Prof. Stella Vosniadou "Understanding the conceptual changes required in learning science and mathematics: A cognitive dev...
Prof. Stella Vosniadou "Understanding the conceptual changes required in learning science and mathematics: A cognitive dev...
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Prof. Stella Vosniadou "Understanding the conceptual changes required in learning science and mathematics: A cognitive developmental approach and implications for instruction"

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http://sol.edu.hku.hk/summerfest/#vosniadou-keynote-2-abstract
11 June 2014, Wednesday
9:30 – 10:30
Meng Wah Complex T4

Keynote 2:
Understanding the conceptual changes required in learning science and mathematics: A cognitive developmental approach and implications for instruction
By Prof. Stella Vosniadou, Flinders University, Australia
Chair: Terry Au

Keynote 2:
Understanding the conceptual changes required in learning science and mathematics: A cognitive developmental approach and implications for instruction

I will describe my research over the last years designed to describe and explain students’ difficulties in understanding concepts in science and mathematics. More specifically, I will argue that by the time formal instruction starts children have already constructed several relatively coherent explanatory systems or ‘framework theories,’ which are based on their everyday experiences in the context of lay culture. Many scientific and mathematical concepts are however organized within different explanatory theories and their understanding requires major changes in students’ conceptual structures. These conceptual changes are not sudden and stage-like, but happen slowly, through the gradual assimilation of the new information into the initial conceptual structures, creating misconceptions. I will also argue that initial systems of thought are not replaced by more advanced ones but continue to exist and to inhibit access to scientific concepts. The implications of the above for a theory of cognitive development and for learning and instruction will be discussed.

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Transcript of "Prof. Stella Vosniadou "Understanding the conceptual changes required in learning science and mathematics: A cognitive developmental approach and implications for instruction""

  1. 1. Understanding the conceptual changes required in learning science and mathematics: A cognitive developmental approach and implications for instruction Stella Vosniadou Strategic Professor in Education
  2. 2. The Framework Theory Approach to Conceptual Change •  1. Knowledge acquisition starts with the construction of a naïve physics, based on everyday experience and lay culture. Naïve physics is a ‘framework theory’ •  2. Learning science requires fundamental changes in the ontology, epistemology and representations of naïve physics. •  3. These changes are slow and gradual and produce fragmentation and synthetic conceptions •  4. Naïve concepts continue to exist and to inhibit access to scientific concepts even after many years of instruction
  3. 3. Naϊve Physics Naϊve Psychology Ontology: Physical Object Causality: Mechanical Ontology: Psychological Beings Causality: Intentional Framework theories in physics and psychology (Ballargeon, 1990, Carey, 1985, Spelke, 1991)
  4. 4. Naïve Physics is a Framework Theory •  Naïve physics does not consist of fragmented observations but forms an explanatory system with some coherence - a framework theory •  A framework theory is a skeletal conceptual structure that grounds our deepest ontological commitments in terms of which we understand the world. It is not an explicit, socially shared and well formed scientific theory •  We have chosen to call it a ‘theory’ because it is a principle-based system which is characterized by a distinct ontology and causality and which is generative in that it can give rise to prediction and explanation.
  5. 5. Learning Science Requires Major Conceptual Changes in Naïve Physics •  By the time they start primary school children have developed a naïve physics that provides intuitive explanations of everyday phenomena •  These early conceptual structures are very different from the scientific concepts to which children are exposed through formal instruction •  Learning science requires fundamental conceptual changes to take place – new concepts, new ontological categories, new representations, must be formed
  6. 6. Naïve and scientific explanations of the day/night cycle The sun goes behind the mountains and the moon comes up Earth is flat stationary supported by ground, water, etc Sun and the moon are in the sky and they move Sun goes down behind the mountains and the moon comes up Geocentric universe The earth rotates around itself Earth is a spherical planet in space rotating around itself and revolving around the sun. Day/night happens because different parts of the Earth face the sun as the Earth rotates around itself Heliocentric solar system
  7. 7. (B) From Grade 1 to Grade 5 Major Bodies Earth Celestial Bodies Sun Moon Stars Major Bodies Celestial Bodies Sun Planets Satellites Stars MoonEarth Changes in Categorization and the Formation of New Categories Vosniadou & Skopeliti, 2005
  8. 8. Changes  in  Representa.on  
  9. 9. Changes in Personal Epistemology •  Explanation based on simple interpretation of sensory evidence vs. hypothetical unobservable entities •  Development of processes of evidence evaluation, hypothesis testing and problem-solving and reasoning •  Beliefs about knowledge - Nature of knowledge – and the processes of knowing –  Certainty and objectivity of knowledge vs. tentative and evolving –  Simplicity vs. complexity of knowledge - Knowledge outside the self and transmitted vs. constructed - Observation and authority vs. inquiry, evaluation and hypothesis testing
  10. 10. The Creation of Misconceptions •  Instruction-induced conceptual changes are not sudden, gestalt-types restructurings •  They are slow and gradual and characterized by the creation of misconceptions •  Many misconceptions are fragmented or synthetic conceptions
  11. 11. Fragmentation •  Fragmentation can be produced when learners assimilate scientific information to their naïve physics creating internal consistent conceptions. •  Fragmentation can often be produced as the initial result of instruction
  12. 12. Synthetic Conceptions •  Synthetic conceptions are formed when learners assimilate scientific information to their naïve physics, but in the process create an alternative explanation that has some internal consistency and explanatory value. •  Synthetic conceptions are incorrect but sometimes creative solutions to the problem of incompatibility between scientific information and initial conceptions
  13. 13. Vosniadou & Brewer (1992)
  14. 14. Types of Explanation 1st Grade 3rd Grade 5th Grade Sun occluded by clouds or moves down 7 2 1 Sun and moon move up/down to the other side of the earth 6 0 0 Sun and moon revolve around earth 0 2 0 Earth revolves around sun 1 2 1 Earth rotates (up/down) Sun and Moon fixed 1 4 10 Earth turns unspecified 2 2 2 Earth rotates sideways Moon revolves around Earth 0 2 1 Mixed/Undetermined 3 6 5 Total 20 20 20 Frequency of Explanations of the Day/Night Cycle Grade
  15. 15. The Role of Domain General Abilities •  Learning science depends on the complex interplay between domain specific conceptual changes and domain general processes, abilities or skills. –  Representational abilities, –  The ability to take multiple perspectives, –  The ability to distinguish appearance from reality, and –  The understanding that are beliefs are not copies of reality but constructed, hypothetical and subject to hypothesis testing and falsification.
  16. 16. Other studies of science concepts •  Models of the composition and layering of the earth •  Mechanics •  Photosynthesis •  Particulate nature of matter •  Evolution
  17. 17. Summary of the Framework Theory –  Children  start  the  knowledge  acquisi.on  process   by  organizing  their  everyday  experiences  into  a   naïve  physics.   –  Naïve  physics  forms  a  rela.vely  coherent   explanatory  system  -­‐  a  framework  theory.   –  Learning  science  requires  fundamental  ontological,   representa.onal  and  epistemological  changes  in   naïve  physics     –  Fragmenta.on  and  synthe.c  concep.ons  can  be   formed  in  the  process  because  learners  use   construc.ve  types  of  mechanisms  to  assimilate   scien.fic  informa.on  into  their  knowledge  base.  
  18. 18. The Predictive Power of the Framework Theory •  The  strength  of  the  framework  theory  is  that  it  provides   an  account  of  the  transi.on  process  from  ini.al  to   scien.fic  concepts.  It  predicts:     –  A  slow  and  gradual  transi.on   –  The  genera.on  of  fragmenta.on  and  synthe.c  models   •  It  also  allows  us  to  predict  when  and  where  such   misconcep.ons  are  likely  to  occur:   –  When  there  is  incompa.bility  between  the  new,   scien.fic  informa.on  and  exis.ng  beliefs  and   presupposi.ons  
  19. 19. Can the framework theory be applied to mathematics learning? •  There  should  be  an  ini.al  framework  for  number     •  Students  will  have  difficulty  understanding   concepts  and  procedures  that  come  in  conflict   with  the  ini.al  framework  for  number   •  Learning  should  be  slow  and  gradual,   characterized  by  fragmenta.on  and  synthe.c   concep.ons    
  20. 20. Initial Framework for Number •  By  4-­‐5  years  of  age  children  display  elements  of  an  early   understanding  of  number  as  coun%ng  number     •  Early  instruc.on  focuses  on  natural  number  arithme.c   •  Supports  the  externaliza.on  and  systema.za.on  of   students’  ini.al  understandings  about  number  as  natural   number  
  21. 21. Natural Numbers vs Fractions Numerical value Natural number Fraction Symbolic Representation One number (that carries the presuppositions of discreteness) Two numbers and a line (that carry the presuppositions of density) Ordering Supported by the natural numbers’ sequence (counting on) Not supported by the natural numbers’ sequence Existence of a successive or a preceding number There is no unique successor or a unique preceding number No number between two successive numbers Infinitely many numbers between any two different numbers Relationship to the unit The unit is the smallest number No unique smallest number
  22. 22. Frac.ons  are  Difficult  to  Understand •  Only  50%  of  a  na.onally  representa.ve  sample  of  U.S.   8th  graders  were  found  to  be  able  to  correctly  order   three  frac.ons  on  the  Na.onal  Assessment  of   Educa.onal  Progress  (Na.onal  Council  of  Teachers  of   Mathema.cs,  2007).   •   In  a  recent  study  of  6th  graders  with  a  mean  IQ  of  116   only  59%  showed  correct  ordering  of  a  set  of  frac.ons   (Mazzocco  &  Delvin,  2008).     •  This  has  led  the  Na.onal  Mathema.cs  Advisory  Panel   (2008)  to  conclude  that  frac.on  understanding  is  one   of  the  most  important  skills  that  needs  to  be   developed  in  the  mathema.cs  curriculum.    
  23. 23. Slow  Learning  of  Frac.ons  Characterized  by   Synthe.c  Concep.ons   Students’  difficul.es  occur  in  the  areas  where  frac.ons  differ   from  natural  numbers  (Stafylidou  &  Vosniadou,  2004)   1.  Children  start  by  interpre.ng  frac.ons  as  two  independent   natural  numbers.     2.  Ordering  of  frac.ons  is  based  on  natural  number  ordering   (the  bigger  the  numerator  or  denominator  the  bigger  the   frac.on).   3.  Intermediate  hybrid  (synthe.c)  concep.on  -­‐  the  smaller   the  numerator  or  denominator,  the  bigger  the  frac.on)     4.  A  frac.on  always  represents  a  quan.ty  smaller  than  the   unit.     5.  Only  the  older  students  start  to  consider  frac.ons  to   indicate  a  rela.on  between  the  numerator  and  the   denominator.    
  24. 24. Explanatory Frameworks 5th Grade N=40 6th Grade N=40 7th Grade N=40 8th Grade N=40 10th Grade N=40 Total N=200 A. Two Independent Numbers 1) Value increases as N and/or D increase 30% 27.5% 17.5% 7.5% 10% 18.5% 2) Value increases as N and/or D decrease 7.5% 5% 5% 5% 2.5% 5% B. Part of a Whole 1) Naïve part of a unit 10% 17.5% 10% 10% 5% 10.5% 2) Advanced part of a unit 7.5% 12.5% 12.5% 12.5% 12.5% 11.5% 3) Sophisticated part of a unit 2.5% 12.5% 12.5% 7.5% 2.5% 7.5% C. Relation between Numerator/Denominator 1) Relation of Two Numbers (there is a biggest/smaller fraction) 12.5% 12.5% 15% 15% 12.5% 13.5% 2) Relation of Two Numbers (there is no biggest/smaller fraction) 7.5% 7.5% 22.5% 32.5% 42.5% 22.5% 5. Mixed Mixed; Could not be categorized 22.5% 5% 5% 10% 12.5% 11%
  25. 25. Students’ Understanding of Density (Vamvakoussi & Vosniadou, 2010) Natural numbers Rational numbers Constraint Discreteness: Between two successive numbers there is no other number. Density: Between any two different numbers there are infinitely many numbers The belief in discreteness Unique symbolic representation: In the set of natural numbers, every number has a unique symbolic representation (e.g.2) Multiple symbolic representations: In the set of rational number, any numbers has multiple symbolic representation (e.g. 2=2.0=8/4=…) The belief that different symbolic representations refer to different objects. “Homogeneous” structure: In the set of natural numbers there are only natural numbers. “Heterogeneous” structure e.g. natural and non- natural numbers The belief that numbers with different symbolic representations belong to different categories.
  26. 26. Are there any numbers between… Ø  0.005 & 0.006 0.1 & 0.2 Ø  3/8 & 5/8 1/3 & 2/3 Ø  0.001 & 0.01 0.01 & 0.1 Methodology: Open Questionnaires and Multiple-Choice Questionnaires with 9th and 11th grade students (14-17 year olds)
  27. 27. From natural to rational number Synthetic models Initial Model: Discreteness §  0.005 - 0.006 (the given numbers are always considered subsequent) Discreteness(+) Finite number of decimals §  0.0051 - 00.0052 … 0.0059 - 0.006 (the given numbers are not always considered subsequent, finite number of numbers) Intermediate Infinity restricted to decimals only §  infinitely many decimals (but finite number of fractions) Density - Infinity within same symbolic representation §  infinitely many decimals and infinite many fractions §  No fractions between decimals Density §  infinitely many numbers Synthetic Conceptions of Density
  28. 28. Synthetic conceptions of density Synthetic conceptions Open-ended questionnaires Forced-choice questionnaires 9th graders Ν=83 11th graders N=66 9th graders N=81 11th graders N=71 Discreteness 30 % 12,1 % 4,9 % 4,2 % Discreteness(+) 16,9 % 7,6 % 30,9 % 16,9 % Intermediate 43,4 % 66,7 % 40,7 % 42,3 % Density (-) 9,6 % 13,6 % 12,3 % 15,5 % Density 11,1 % 21,1 %
  29. 29. An example •  Panos, a 9th grader states that: –  there are 9 numbers between .001 and .01 –  there are infinitely many numbers between 3/8 and 5/8. •  Following a prompt by the interviewer, he explains: Between  0.001  and  0.01  there  are  nine  numbers.   Or  maybe  ten  –  I m  not  so  sure  about  that.  But  if   you  convert  them  to  fractions,  you  can  find  more   numbers  in  between.  You  can  find  infinitely  many   numbers Vamvakoussi & Vosniadou, 2010
  30. 30. Summary Secondary school students (7th, 9th, 11th graders) with many years of mathematics instruction –  transfer the property of discreteness from natural numbers to non-natural numbers –  do not find necessary for natural numbers, decimals and fractions to behave the same with respect to ordering (dense/discrete) –  are very reluctant to accept that there can be decimals between fractions and vice versa Vamvakoussi & Vosniadou, 2010
  31. 31. What Happens to Naïve Concepts when Scientific Concepts are Learned? •  Replacement view •  Conceptual change as some kind of restructuring – scientific concepts replace naïve physics. •  Co-existence of naïve and scientific concepts •  Findings of recent research support the hypothesis that scientific concepts do not replace naïve physics but the two co-exist,
  32. 32. Summary of the framework theory –  Children  start  the  knowledge  acquisi.on  process  by   organizing  their  everyday  experiences  into  a  naïve  physics   framework  theory  characterized  by  dis.nct  ontological  and   epistemological  commiiments  which  are  fundamentally   different  from  current  science.   –  In  the  process  of  learning  science  the  new,  scien.fic,   informa.on  is  gradually  added  on  to  the  exis.ng  but   incompa.ble  knowledge  base,  crea.ng  fragmenta.on,   inconsistency,  and  synthe.c  models   –  Science  learning  is  complex,  requires  the  acquisi.on  of  new   concepts,  new  ontological  categories,  new  representa.ons,   new  epistemological  beliefs.   –  Intui.ve  –  framework  theories  con.nue  to  exist  even  when   the  scien.fic  theories  have  been  learned    
  33. 33. How is the framework theory different from the ‘classical’ Posner et al. (1982) theory? •  Posner et al., (1982) argue that misconceptions are unitary, faulty conceptions that need to be replaced with the scientific conceptions. •  We argue that misconceptions are ‘synthetic conceptions’ produced because students assimilate scientific information to their intuitive theories. •  Intuitive theories continue to exist even when the scientific theories have been understood. •  The purpose of science teaching is not the replace intuitive theories but to explain how we can go from naïve physics to scientific theories
  34. 34. Instruction for Conceptual Change Content – Address students’ intuitive beliefs – Explain not replace Structure - Order of acquisition of the concepts involved – learning progressions Domain General Mechanisms- perspective taking, representation, hypothesis testing, metacognition
  35. 35. Research-Based Curricula and Model-Based Instruction •  Breadth of coverage of the curricula •  Content of curricula •  Order of presentation of concepts to be taught •  Model-based instruction •  Experiments – hypothesis testing •  Peer collaboration and classroom discussion
  36. 36. Sequence of Concepts Theoretical Framework Basic Questions - Entrenched Beliefs Instructional Interventions EARTH SHAPE Perceived Flatness C: Model of Earth Q: Perception of flatness IM: Globe, Video Demonstrations E: Toy Ship on the Globe EARTH SHAPE and GRAVITY Up/Down Gravity C: Drawing of a man in Australia Q: Life at “bottom” of the earth E: Magnetic globe EARTH, MOON and SUN Relation between size and distance C: Models of earth, sun, moon Q: Perception of sun/moon IM: Scale Models E: Balloons near/far SOLAR SYSTEM and GRAVITY Geocentric Solar System C: Drawing of the Solar System IM: Slides, Video, Maps E: Demonstration of revolution of earth using a toy car (earth) and a ball (sun) EARTH MOVEMENTS, DAY- NIGHT CYCLE and CHANGE OF SEASONS Movement of Earth, Sun, Moon Moon-Earth distance Tilt of the axis of earth Q: Explanation of day/night cycle and of the change of seasons C: Acting out the movements of the earth E: Demonstration of day/night cycle and seasons using a flashlight and a globe CREATION OF UNIVERSE, GALAXY and SOLAR SYSTEM Visit to the planetarium
  37. 37. Active, intentional and self-regulated learning •  Metaconceptual awareness - becoming aware of their own ideas – understanding that their ideas are hypotheses that can be falsified, understanding how to use evidence to evaluate a theory and how to revise a theory in light of disconfirming evidence •  Metacognitive and regulatory skills- plan and control learning processes, self-monitor understanding, evaluate learning. •  Hypothesis testing - learn how to experimentally test ideas, how to formulate hypotheses, how to derive testable propositions from hypotheses, how to test for consistency, etc. •  A constuctivist epistemology of science - understanding that knowledge is not simple, fact-based and certain, but complex, based on ideas and conjectures, and constantly evolving and changing.

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