### Citations

222 | On cognitive growth - Bruner - 1966 |

154 |
The psychology of invention in the mathematical field
- Hadamard
- 1945
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Citation Context ...ary to use more than one representation. Even mathematicians use different modes of mathematical thinking, including visual and kinetic imagery and less frequently, mental words or algebraic symbols (=-=Hadamard, 1945-=-). In recent years, the principle of multiple representations has attracted much attention among mathematics educators. For example, the Representation Standard of the Principles and Standards for Sch... |

66 | Representations and translations among representations in mathematics. In - Lesh, Post, et al. - 1987 |

41 |
Rethinking “concrete” manipulatives
- Clements, McMillen
- 1996
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Citation Context ...ctive mathematics teaching. Many websites now offer applets that students can use to explore mathematics in an interactive way. This leads to a reconsideration of the roles of concrete manipulatives (=-=Clements & McMillen, 1999-=-). On the other hand, virtual manipulatives are 2-dimensional, flat objects, and some of them are quite restrictive in motion possibilities. Consider the virtual algebraic tiles given in the NCTM webs... |

25 |
The importance of learning styles: Understanding the implications for learning, course design, and education
- Sims, Sims
- 1995
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Citation Context ...nd re-packages these ideas into a practical format for students to use in normal lessons. By working systematically through different modes of representation, students with different learning styles (=-=Sims & Sims, 1995-=-) will have a better chance of mastering the mathematics and enjoying their learning, 1instead of being hampered by a traditionally symbolic rule-based learning milieu. If the students are used to on... |

17 |
The avoidance of visual considerations in calculus students.
- Vinner
- 1989
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Citation Context ...ticians use visual imagery when they solve problems. However, students have been found to avoid using this mode to solve problems even when specifically instructed to do so (Veloo & Lopez-Real, 1994; =-=Vinner, 1989-=-). Thus, the diagram mode has to be carefully developed in mathematics lessons. To develop visual imagery from diagrams, ask students to close their eyes and imagine the results in their mind. Many st... |

10 |
Cooperative learning
- Artzt, Newman
- 1990
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Citation Context ...ive mathematics learning (Bell, 1997). When the MMTB activities are carried out in groups, students are able to construct their own knowledge and mathematical connections through social interactions (=-=Artzt & Newman, 1997-=-). The MMTB can also be used in games (Wong, 1999). Cards are designed for the same mathematics in different modes and may be played as the popular SNAP game. For the real thing mode, provide the nece... |

5 |
Visual imagery and communication in the mathematics classroom
- Dawe
- 1993
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Citation Context ...r example, a literal picture of several apples versus several dots, with each dot representing an apple. They can convey mathematical ideas in vivid ways, and constitute a crucial mode of processing (=-=Dawe, 1993-=-). Some students find colourful diagrams help them to remember mathematics results better. These diagrams may appear in textbooks, worksheets, blackboard drawings, OHP pictures, and computer screen di... |

4 |
Purpose and awareness
- Bell
- 1997
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Citation Context ...ymbolic result using some numbers? Write a story that can be solved using this diagram. This technique fosters the development of metacognition, which is important for effective mathematics learning (=-=Bell, 1997-=-). When the MMTB activities are carried out in groups, students are able to construct their own knowledge and mathematical connections through social interactions (Artzt & Newman, 1997). The MMTB can ... |

4 |
What's going on here? Problem posing in mathematics
- Rice, Mousley
- 1990
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Citation Context ...cal ideas, and examples from other disciplines. Besides solving given stories, students can exercise their creativity by generating own problems and developing a sense of ownership of their problems (=-=Rice & Mousley, 1996-=-). The stories written by students can also provide an interesting window into their value system, which is often neglected in mathematics lessons. The story above is a good example for the class to d... |

3 | Children Learning Mathematics - Dickson, M, et al. - 1984 |

2 | A mathematical think board - Haylock - 1984 |

2 |
Children’s mathematical frameworks: 8 - 13
- Johnson
- 1989
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Citation Context ...perties is also an important instructional objective in its own right, related to the psycho-motor domain. The transition from practical activities to formal abstraction, however, is not always easy (=-=Johnson, 1989-=-). Poorly designed manipulatives or improper use can hinder rather than facilitate conceptual development. Many mathematics teachers rush through or neglect practical work to focus exclusively on the ... |

2 |
Drawing diagrams and solving word problems: A study of a sample of Bruneian primary and secondary school children
- Veloo, Lopez-Real
- 1994
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Citation Context ...euristic, and many mathematicians use visual imagery when they solve problems. However, students have been found to avoid using this mode to solve problems even when specifically instructed to do so (=-=Veloo & Lopez-Real, 1994-=-; Vinner, 1989). Thus, the diagram mode has to be carefully developed in mathematics lessons. To develop visual imagery from diagrams, ask students to close their eyes and imagine the results in their... |

2 |
Multi-modal approach of teaching mathematics in a technological age.
- Wong
- 1999
(Show Context)
Citation Context ...ties are carried out in groups, students are able to construct their own knowledge and mathematical connections through social interactions (Artzt & Newman, 1997). The MMTB can also be used in games (=-=Wong, 1999-=-). Cards are designed for the same mathematics in different modes and may be played as the popular SNAP game. For the real thing mode, provide the necessary concrete materials. Students may learn more... |

2 |
Mathematics-based national education: A framework for instruction
- Wong
- 2003
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Citation Context ...hich can easily arise in many competitive situations in school and daily life. Incorporating national values into mathematics lessons is a relatively recent approach and is worth further exploration (=-=Wong, 2003-=-). Uses of the Multi-Modal Think-Board The teachers can use the MMTB to plan a series of lessons on a particular topic. They need to consider carefully whether all or only some of the six modes will b... |

1 | The mathematics of change and variation from a millennial perspective: New content, new imperatives - J - 1997 |