| Summary: | 碩士 === 國立臺北教育大學 === 數學暨資訊教育學系(含數學教育碩士班) === 101 === In this study, a content analysis was used to compare and contrast the organizational plans used to teach fraction multiplication in the elementary mathematics textbooks published by the Taiwanese Ministry of Education and the Kang Hsuan Educational Publishing Group. The results are stated below.
(I)Organization plans Comparison:(1)The order in which primary educational activities are presented, as well as the corresponding target academic levels are identical.(2)The “two versions treatment” of proper fraction-integer multiplication follows the same developmental sequence, only differing in the multiplication of more advanced fraction types.(3)The presentation of integer-fraction multiplication is generally similar. However, only Kang Hsuan version explains how to address fractional remainders in integer-fraction multiplication.(4)The variation between the two versions in teaching the multiplication of fraction sets is more pronounced.
(II)Comparison of Practice Problems and Problem Solving Activities:(1)The two versions both use graphical representations and dialogue boxes to guide students through problems, only differing in what graphics are used, as well as presentation style. Furthermore, only Ministry of Education version uses the word “times” within the questions and dialogue boxes.(2)In teaching fraction-integer multiplication and fraction set multiplication, both versions include consecutive numbers in serial contexts, with the majority of practice problems following these series: all integer-fraction problems include serial contexts, discrete scenarios, and pure numeric word problems.(3)Both versions first use concrete situational word problems for students’ problem solving activities, followed by computational problems meant to balance students’ comprehension, and only Ministry of Education edition provides additional follow up problem solving activities.(4)Each version’s fraction set multiplication activities teach fraction reduction, but the fraction reduction techniques in Kang Hsuan version are more flexible and provide students with practice questions.(5)Kang Hsuan version includes related activities that allow students to verify the relationships between the multiplicand, multiplier, and product, which are not found in Ministry of Education version.(6)The mixed number problem-solving activities in both versions include mixed number reduction and distribution into improper fractions followed by calculation. Kang Hsuan version provides error identification problems for the multiplication of mixed numbers and proper fractions.
(III)Comparison of Rule Introduction and Development:(1)Within the fraction-integer multiplication activities, each version uses differing methods to present the relationship between fraction-integer multiplication and addition in fractions with like denominators. (2)Within the integer-fraction multiplication activities, Ministry of Education version uses integer multiplication to introduce column-multiplication; Kang Hsuan presents multiplication equations and answers directly, without elaboration.(3)The integer-fraction multiplication activities in both versions enable students to verify that multiplying a fraction by an integer and an integer by a fraction produce the same answer.(4)Each multiplication rule in Ministry of Education version includes one example problem that demonstrates how the rule is derived. Kang Hsuan version features many of these examples, including an additional dialogue box that more thoroughly explains the rule.(5)The mental operations are similar in both versions’ of fraction-integer multiplication, integer-fraction multiplication, and fraction-fraction multiplication activities. The fraction-integer multiplication and integer-fraction multiplication methods are the same, only varying in the method by which the fraction multiplication rules are developed into mental calculation methods.(6)In both versions, most problems first summarize the equation, and then provide an explanation of the process. After establishing the format of the rule, it is further explicated regarding usage, the only exception being the fraction-fraction multiplication activities of Ministry of Education version, in which only an explanation of the process is included.
|
|---|
