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- 1. Conceptual learning through learning objects: application in mathematics classrooms in secondary schools <br />Thomas Chiu Kin Fung<br />Acknowledgements to Dr. Daniel Churchill<br />Faculty of Education (HKU)<br />SKH Holy Trinity Church Secondary School<br />
- 2. Overview<br />Background and problems<br />Research question<br />Principles of design for conceptual learning<br />Examples of other IT educational tools <br />Our proposed learning objects.<br />Students’ responses<br />My observations<br />Final words<br />Way forward<br />
- 3. Background<br />Secondary school mathematics focuses on developing algorithmic skills, rather than mathematical understanding. <br /> (Attorps, 2006; Sierpinska, 1994) <br />Teachers spend less time and attention on conceptual knowledge.<br /> (Attorps, 2006; Menzel and Clarke, 1999)<br />
- 4. Background<br />Secondary school algebra in Hong Kong <br /><ul><li>Rich content and skill-based
- 5. The sequence of topics is based mainly on a logical sequence or hierarchy of mathematical concepts and skills</li></ul> (Mok et al, 1999)<br />Teachers in Hong Kong<br /><ul><li>Use most of the teacher-talk time for demonstrating mathematics solutions
- 6. Emphasize developing procedural and conceptual knowledge through rigid practice</li></li></ul><li>Problems<br />Students may <br />Only solve the questions <br /><ul><li>with the methods their teachers taught them
- 7. they have seen before</li></ul>Not be able to understand the relationships between concepts and know ledges<br />Examples:<br /> a) x2+2x+1=0<br /> b) x2+2x = –1<br /> c) x(x+2)+1=0<br />
- 8. What <br />conceptual-model design characteristics <br />optimize <br />problem-solving skill transferof <br />key algebra concepts in the secondary school mathematics curriculum in Hong Kong?<br />
- 9. Conceptual framework<br />
- 10. learning objects & conceptual models<br />Learning Objects<br /><ul><li> Instructional components
- 11. Reusable and digital
- 12. Transported and customized in different contexts
- 13. More effective, pedagogical, reusable and personalized to the learner</li></ul>(Barritt and Lewis, 2000; Churchill, 2007; Hodgins, 2002; Wiley,2000)<br />Conceptual Models<br /><ul><li> One of six types of learning objects
- 14. A representation of key and/or related concepts of a subject knowledge
- 15. A representation of the ‘cognitive resource’</li></ul>(Churchill, 2007)<br />
- 16. Principles for design<br />The design of the proposed conceptual models is based on <br /><ul><li> Design principles of multimedia learning
- 17. Audio: text and spoken word
- 18. Visual: pictures, graphs, animations
- 19. Based on the theory of cognitive load
- 20. 12 design principles for avoiding redundancy to reduce </li></ul> cognitive load of learner<br /><ul><li> Meaningful learning</li></ul>(Mayer, 2009)<br /><ul><li> Recommendations for learning object design
- 21. Moderate color
- 22. Holistic scenario
- 23. Design for interaction</li></ul>(Churchill, in review)<br />
- 24. Principles for design<br /><ul><li>Theory of variation (teaching method)
- 25. Learning is a process that helps student develop a certain way of seeing or experiencing </li></ul>(Marton et al, 2004)<br /><ul><li> Classroom activities are developed to help students establish this kind of connection by experiencing certain dimensions of variation.</li></ul>(Gu et al, 2004).<br />
- 26. Design of the proposed learning objects<br />Learning <br />objects<br />Design of <br />multimedia <br />learning<br />Suggestions <br />for design of <br />learning <br />objects<br />Design of <br />subject <br />matter<br />(theory of variation)<br />
- 27. Five characteristics<br />Alert for important changes to mathematical concepts (signaling principle)<br /><ul><li>Color change or audio alert is made when the concepts are shown.
- 28. It can motivate novice learners.</li></ul> (Mayer, 2009)<br />Representations (multimedia learning, spatial contiguity principle, temporal contiguity principle)<br /><ul><li>Numerically, graphically, algebraically and descriptively simultaneously. Descriptive can be implemented implicitly.</li></ul>(NTCM). <br /> <br />
- 29. Five characteristics<br />Form of representation (multimedia learning, spatial contiguity principle, temporal contiguity principle)<br /><ul><li>Two suggested forms of presentation: pictures and words.
- 30. In the mathematical domain,
- 31. Pictures: graphical representation, diagrams, tables and lines
- 32. Words: equations, expression, numbers and symbols, theorems, notation, symbolic expressions, formula and figures</li></ul>(Mayer, 2009; NTCM)<br /> <br />
- 33. Five characteristics<br />Multi-interactive (segmenting principle)<br /><ul><li> Learners can change parameters (numerically) and graphs (graphically)</li></ul>(Churchill; Mayer, 2009)<br />Sequence of the concepts (pre-training principle)<br /><ul><li> Learners are recommended to have some prerequisite knowledge
- 34. Layout should provide a direction for learning key concepts from some related concepts</li></ul>(Mayer, 2009)<br />
- 35. Some other IT tools<br />Quadratic Equation Calculator<br />GeoGebra<br />Publisher’s Resource(New ways)<br />Students only know <br />what the solutions are/what the graphs look like with those IT tools.<br />
- 36. The proposed learning objects <br />Version 1<br />Decimal, no signaling and large range (-100 to 100) of the control value<br />Version 2<br />Decimal, signaling, smaller ranges (-5 to 5) of control value<br />
- 37. The proposed learning objects <br />Version 3<br />More information – cognitive overload<br />Version 4<br />Fraction, signaling, suitable amount of conceptand suitable range of control value<br />
- 38. The proposed learning objects <br />Version 5<br />Multi-interactivity<br />
- 39. Responses from students<br /><ul><li> During
- 40. Too large ranges of the control values (version 1)
- 41. Too much information in the description (version 3)
- 42. Too bright background color (version 1)
- 43. Disturbing decimal numbers (version 1 & 2)
- 44. No idea of different methods of solving quadratic </li></ul> equations<br /><ul><li>Active and noisy students
- 45. After
- 46. Students talked about the learning objects [motivation]
- 47. Students asked questions about the mathematical </li></ul> problems based on the learning objects<br />
- 48. My observations<br />Students<br /><ul><li>were excited when they manipulated the learning objects
- 49. quoted what they experienced during lesson [longer memory]
- 50. asked questions more often during lessons
- 51. learned actively
- 52. found out some unexpected and untaught concepts
- 53. with higher learning ability, definitely learnt more
- 54. with lower learning motivation, actually “learn”
- 55. remembered the graphical representation and algebraic </li></ul> form after a while<br />
- 56. Final words<br />Ineffective learning <br />Knowledge<br />Procedural knowledge<br />Conceptual knowledge<br />Concept<br />Conceptual knowledge<br />Concept<br />
- 57. Final words<br />Learn with learning objects (effective conceptual learning)<br />Knowledge<br />Conceptual knowledge<br />Concept<br />Concept<br />
- 58. Way forwards<br /><ul><li> Instructions or guidelines must be given to students in advance.
- 59. Other topic with basic concepts are recommended to develop first.
- 60. Apply conceptual models with other types of learning objects.
- 61. More “cognitive resources” should be provided.
- 62. Situated learning may be required.
- 63. Conceptual models become more effective and “real”.
- 64. They may be suggestions for teacher to choose educational tools.</li></ul>Developed by Dr Churchill<br />

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