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Research and Development of Mathematics-Grounding Activity Modules as a Part of Curriculum in Taiwan

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Book cover School Mathematics Curricula

Part of the book series: Mathematics Education – An Asian Perspective ((MATHEDUCASPER))

Abstract

In order to develop meaningful mathematics activities for students to enjoy learning and to improve their learning, the mathematics-grounding activity (MGA) modules are developed as part of the JUST DO MATH project which has been funded by the Taiwanese Ministry of Education since 2014. The project consists of three phases: (1) research and development of the MGA modules; (2) cascading to include more teachers and designers; and (3) dissemination to students in Mathematics Camps. The evaluation of the project is still ongoing. Both student feedback and teacher feedback are collected during the MGA modules. At the current stage, data from both qualitative and quantitative results show significant positive influence.

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Author information

Authors and Affiliations

  1. National Taiwan Normal University, Taipei, Taiwan

    Fou-Lai Lin & Yu-Ping Chang

Authors
  1. Fou-Lai Lin
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  2. Yu-Ping Chang
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Corresponding author

Correspondence to Fou-Lai Lin .

Editor information

Editors and Affiliations

  1. Ateneo de Manila University, Quezon City, Philippines

    Catherine P. Vistro-Yu

  2. National Institute of Education, Nanyang Technological University, Singapore, Singapore

    Tin Lam Toh

Appendix. Examples of MGA Modules

Appendix. Examples of MGA Modules

1.1 SQUARING THE SQUARES AND RECTANGLES

  1. I.

    Materials

    • A set of several shapes of squares with areas x2 and 1, and rectangles with area x (width and length are 1 and x).

    • Record sheet (4 for each group).

    • Task sheet (4 for each group).

    • Learning feedback sheet (4 for each group).

  1. II.

    Contents of the Activity

To develop students’ mental image of the ‘method of completing the square’ through manipulating the algebraic numbers represented in ‘shapes,’ before learning the topic of factorization in school. This MGA module is suitable for 8th graders or 7th graders.

  • Students can square the given pieces (the big squares of x2, the rectangles of x, and the small squares of (1) to a new square.

  • Students can find out the number of the rest small squares in order to complete the full square through group discussion.

  1. III.

    Procedures

figure g
  1. 0.

    Observation and discussion of the shapes and areas of three different shapes.

  2. 1.

    Preparation Activities: to construct and discuss the examples and non-examples of squaring new squares, i.e., the relationship between \( x^{2} + bx + c\quad {\text{and}}\quad (x + q )^{2} \).

  3. 2.

    Exploration and Reasoning Activities: Game competitions.

  1. IV.

    Tasks and Feedback Collections

1.2 THE ISOMETRIC GEOBOARD

  1. I.

    Materials

    • An isometric geoboard for each group.

    • The rubber bands (10 for each group).

    • The game map.

    • The cards of Chance and Opportunity (9 for each).

    • Task sheet (1 for each group).

    • Learning feedback sheet (1 for each group).

  2. II.

    Contents of the Activity

To develop students’ mental image of square’s length with irrational number through manipulating the isometric geoboard before learning the topic of square root in school curriculum. The module is suitable for 7th graders or beyond.

  • Students can surround the squares of given areas in the isometric geoboard.

  • Student can surround the various squares of within a range of areas in the isometric geoboard.

  • The core notion of this MGA module is that student can surround the square of the length in irrational number through the experimental manipulation.

  1. III.

    Procedures

  1. 1.

    Preparation Activities: to surround a rotatable square on the isometric geoboard and discuss the following question:

  2. (1)

    Why the surrounded quadrangle is a square?

  3. (2)

    How to calculate its area?

  4. (3)

    Is there any other way to surround the square with the same area?

  5. 2.

    Game competition (with the given rules embedded).

  6. IV.

    Tasks and Feedback Collections

1.3 NUMBER BINGO

  1. I.

    Materials

    • A set of number cards for 2 and 4 BINGO game: 28 cards of numbers 2 and 4 each; 4 cards of the joker; 1 card of numbers 16, 18, 20, 22, 24, 26, 28, 30, and 32 each.

    • A set of number cards for 5 and 10 BINGO game: 28 cards of numbers 5 and 10 each; 4 cards of the joker; 1 card of numbers 40, 45, 50, 55, 60, 65, 70, 75, and 80 each.

    • A set of number cards for 3 and 6 BINGO game: 28 cards of numbers 3 and 6 each; 4 cards of the joker; 1 card of numbers 24, 27, 30, 33, 36, 39, 42, 45, and 48 each.

    • Task sheets for each group.

    • Learning feedback sheet for each individual.

  2. II.

    Contents of the Activity

To develop the prerequisites of solving the specific algebraic problem: a cage of chickens and rabbits for 5th graders or beyond.

  • Students can find the numerical pattern with difference 2 from 2 and 4 BINGO game.

  • Students can find the numerical pattern with difference 5 from 5 and 10 BINGO game.

  • Students can find the numerical pattern with difference 3 from 3 and 6 BINGO game.

  1. III.

    Procedures

  1. 1.

    Preparation Activities: to play with 2 and 4 BINGO game to be familiar with its rules, and to discuss how to speed up the game in the end.

  2. 2.

    Exploration Activities: to play with 5 and 10 BINGO game, and to discuss how to play with the corresponding biggest and smallest numbers of BINGO card in the end of the game.

  3. 3.

    Reasoning Activities: to play with 3 and 6 BINGO game, and to discuss in the end of game that whether it is possible the number of the BINGO card is 28 in the condition of every players get 8 cards.

  4. IV.

    Tasks and Feedback Collections

1.4 A SEVEN-PIECE PUZZLE

  1. I.

    Materials

    • A set of a seven-piece puzzle for each individual.

    • Record sheet.

    • Task and learning feedback sheets for each individual.

  2. II.

    Contents of the Activity

To develop the prerequisites of manipulating with geometric kits for benefiting the understanding of area formulae of triangles, quadrilaterals, and trapezoid for 3rd graders or beyond.

  • Students can understand the components of the seven-piece puzzle and have the preliminary understanding of its composite figures.

  • Students can apply the relationship among the components to construct new combinations of those components reasonably.

  • The core notion of this MGA module is to strengthen students’ concrete experiences in manipulating the geometric shapes and understand the area formulae of triangles, parallelograms, and trapezoids.

  1. III.

    Procedures

figure h
  1. 1.

    Preparation Activities: to practice the basic skills of movement, flip, and rotation with a seven-piece puzzle kit.

  2. 2.

    Exploration Activities: to explore the pieces of geometric shapes of the puzzle about their names, elements, and the relationship among elements (note: the trapezoid and parallelogram are not learned yet by students, it is suggested to discuss visually). The exploration is sequentially focused on:

  3. (1)

    Classification of the pieces of geometric shapes.

  4. (2)

    The base side and the height.

  5. (3)

    Practice with the given 2 or 3 pieces to compound a new composite figure.

  6. 3.

    Reasoning Activities (playing the game to compound figures).

  7. IV.

    Tasks and Feedback Collections

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Lin, FL., Chang, YP. (2019). Research and Development of Mathematics-Grounding Activity Modules as a Part of Curriculum in Taiwan. In: Vistro-Yu, C., Toh, T. (eds) School Mathematics Curricula. Mathematics Education – An Asian Perspective. Springer, Singapore. https://doi.org/10.1007/978-981-13-6312-2_8

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  • DOI: https://doi.org/10.1007/978-981-13-6312-2_8

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  • Online ISBN: 978-981-13-6312-2

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