Conceptual learning through learning objects: application in Mathematics classrooms in secondary schools


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5 March 2010 (Friday) | 16:40 - 17:00 | | CHIU, Kin Fung Thomas, SKH Holy Trinity Chruch Secondary School

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  • There are three principles for designThe first one multimedia learning it is the core for my designMayer defined multimedia learning as leaning with audio and visual. And conducted many tests to develop 12 ways for design a good multimedia learning. He suggest the graphics and word should be placed to each other, no decoration.On the other hand, Churchill suggests that when we design conceptual model, the color should be comfortable and interactive control is necessary.These two suggestions can help optimize student learning outcome.How about subject matter?
  • The final one is about pedagogical knowledge. I use theory of variation in my design. It Is one of the good teaching method to teach algebra. It allows students to see a problem from different perspectives. They also can experience them .It may help students to get the mathematical concept easily.
  • Now we know that what this studies based. On This diagram shows my idea on how to the proposed learning objects. I believe that these three element s does contribute to the design of conceptual models. Based on that, I identify five characteristics.
  • In mathematical domain , we have many notation and terms.I classified them into two categories: pictures and words to implement multimedia learning
  • The final two characteristics are multi-interactive and sequence of the conceptsThe model should allow student to control, to get them involved in the lesson, let them experience, observe and think to have their own understanding. They should learn it on their own pace. Weak students can get motivated . Smart students could learn more.The final characteristics suggest students should have prerequisite knowledge and guideline should be given to them
  • Before I show you my design, I would like to talk about some other It tools.Calculator only helps students to verify their answer.This one only show students how the graph look slikeGeogebra is too complicated. It is too much.Students may find difficulty to learn with them, espeically the one with lower learning ability
  • I adopt a development cycle to construct the conceptual model. I design it and trial and re-design and re-design. It is number, graph, description, algebrabic form. I used the theory of variationThis one the range is too big. Students got confused. The color is too much.They don’t like it at all, I remembered. The first time female students saw it and said it is so disgusting.So I change to this. I even made signals for them. The delta will change color when its value is positive , zero and neagtive
  • Version 3, I tried to put more information. Finally, it didn’t work very well.Students got confused again. And the decimal number means nothing to students.So I change it to this version. I mean them with the coefficient .
  • Finally, I made the final change , I let student to control the curve. Students found it very exciting. It is my final design.I tried them in classroom in three different ways. I teach the concept with it.I also asked students to manipulate them with my instructions.I also asked a smart students to teach the concept he got with this.
  • Here are the students responses. Based on their responses, I made changes .You can see how I change the version.
  • Generally, I found that they become noisy and active, more excited to learn. The classroom become more interactive . They actually talked about the model – subject knowledge on their own will. Even if when I didn’t use them in classroom , they would still ask question based on their experience on the model. I believe that the model let them actually think , they can have longer memory., motivation and better understandingAnd also the model can cater different student with different learning ability.They also helped me to develop a good model.
  • I would like to use two cases to conclude my idea. With ineffective learning, no of learning “income” is equal to no of learning outcome. You provide knowledge, students get procedural knowledge.When you provide concept, students get conceptual knowledge
  • Learning with the models may have an effective conceptual model learningStudents may mixed the knowledge and concept become one big one
  • My design still have some limitations.I think the quadratic equation involved too many concepts. So I should develop other smaller topics with less concepts, like factorization, graph, function. And also it is better to work with other types of learning objects.This is another conceptual model for factorization. It is developed by dr. ChurchillIn hk, teachers may have to buy e-learning material. My idea could be a suggestion for mathematics teacher to choose the educational tools.
  • Conceptual learning through learning objects: application in Mathematics classrooms in secondary schools

    1. 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. 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. 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. 4. Background<br />Secondary school algebra in Hong Kong <br /><ul><li>Rich content and skill-based
    5. 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. 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. 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. 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. 9. Conceptual framework<br />
    10. 10. learning objects & conceptual models<br />Learning Objects<br /><ul><li> Instructional components
    11. 11. Reusable and digital
    12. 12. Transported and customized in different contexts
    13. 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. 14. A representation of key and/or related concepts of a subject knowledge
    15. 15. A representation of the ‘cognitive resource’</li></ul>(Churchill, 2007)<br />
    16. 16. Principles for design<br />The design of the proposed conceptual models is based on <br /><ul><li> Design principles of multimedia learning
    17. 17. Audio: text and spoken word
    18. 18. Visual: pictures, graphs, animations
    19. 19. Based on the theory of cognitive load
    20. 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. 21. Moderate color
    22. 22. Holistic scenario
    23. 23. Design for interaction</li></ul>(Churchill, in review)<br />
    24. 24. Principles for design<br /><ul><li>Theory of variation (teaching method)
    25. 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. 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. 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. 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. 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. 30. In the mathematical domain,
    31. 31. Pictures: graphical representation, diagrams, tables and lines
    32. 32. Words: equations, expression, numbers and symbols, theorems, notation, symbolic expressions, formula and figures</li></ul>(Mayer, 2009; NTCM)<br /> <br />
    33. 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. 34. Layout should provide a direction for learning key concepts from some related concepts</li></ul>(Mayer, 2009)<br />
    35. 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. 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. 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. 38. The proposed learning objects <br />Version 5<br />Multi-interactivity<br />
    39. 39. Responses from students<br /><ul><li> During
    40. 40. Too large ranges of the control values (version 1)
    41. 41. Too much information in the description (version 3)
    42. 42. Too bright background color (version 1)
    43. 43. Disturbing decimal numbers (version 1 & 2)
    44. 44. No idea of different methods of solving quadratic </li></ul> equations<br /><ul><li>Active and noisy students
    45. 45. After
    46. 46. Students talked about the learning objects [motivation]
    47. 47. Students asked questions about the mathematical </li></ul> problems based on the learning objects<br />
    48. 48. My observations<br />Students<br /><ul><li>were excited when they manipulated the learning objects
    49. 49. quoted what they experienced during lesson [longer memory]
    50. 50. asked questions more often during lessons
    51. 51. learned actively
    52. 52. found out some unexpected and untaught concepts
    53. 53. with higher learning ability, definitely learnt more
    54. 54. with lower learning motivation, actually “learn”
    55. 55. remembered the graphical representation and algebraic </li></ul> form after a while<br />
    56. 56. Final words<br />Ineffective learning <br />Knowledge<br />Procedural knowledge<br />Conceptual knowledge<br />Concept<br />Conceptual knowledge<br />Concept<br />
    57. 57. Final words<br />Learn with learning objects (effective conceptual learning)<br />Knowledge<br />Conceptual knowledge<br />Concept<br />Concept<br />
    58. 58. Way forwards<br /><ul><li> Instructions or guidelines must be given to students in advance.
    59. 59. Other topic with basic concepts are recommended to develop first.
    60. 60. Apply conceptual models with other types of learning objects.
    61. 61. More “cognitive resources” should be provided.
    62. 62. Situated learning may be required.
    63. 63. Conceptual models become more effective and “real”.
    64. 64. They may be suggestions for teacher to choose educational tools.</li></ul>Developed by Dr Churchill<br />