國中數學低成就學生在括號概念表現之研究
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2014
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本研究目的是為了解國中數學低成就學生在括號概念的表現，先以柯華葳(1999)基礎數學概念評量的三則運算以探討括號概念表現與正確性與流暢性的關係，再由自編括號概念評量的「數字計算題」、「代數計算題」、「數字選擇題」和「代數選擇題」四種評量方式，以蒐集學生在「括號多餘」、「去括號不變號」、「分配律去括號」及「去括號須變號」的表現，以探討數學低成就學生在不同括號概念與不同括號題型的表現。研究對象是以桃園縣某國中七年級數學低成就學生76名，並依柯華葳(1999)基礎數學概念評量三則運算的低分組分數區分為正常組、僅流暢差組和皆困難組學生。研究統計是以變異數分析數學低成就學生在括號概念表現的差異。數學低成就學生在括號概念表現分述如下：
(1)在基礎數學概念評量三則運算的正確性優於流暢性，正確性平均通過率超過七成，但流暢性平均通過率未達五成，且半數以上(44名)學生在流暢性表現有困難，而僅有16名學生在正確性表現有困難。
(2)括號概念的表現以去括號不變號最好，其次依序是括號多餘、分配律去括號及去括號須變號。不同類型學生在不同括號概念表現之穩定性有差異，正常組的括號概念答對率顯著較僅流暢差組與皆困難組高，且僅流暢差組的概念穩定性較皆困難組好。以分配律去括號和去括號須變號較能區分不同低成就學生在括號概念之表現。
(3)括號概念的表現在數字題與代數題的表現沒有顯著差異，但在選擇題的表現顯著較計算題好。正常組在不同括號題型表現未達顯著，而在僅流暢差組與皆困難組在計算題表現顯著較選擇題差，顯示括號概念發展較差的兩組在括號概念之表現受題型影響，但正常組卻不。
本研究根據研究結果及限制，對數學低成就學生在括號概念的教學實務及未來研究提出相關建議。
The purpose of this study is to identify the performance of parentheses concept of junior high students with low mathematics achievement. Two methods are conducted：(1) Implementing Ko’s “Basic Math Concept Test-Three Arithmetic Operation.” to investigate the relationships between the performance of parentheses concept and accuracy and fluency. (2) Collecting students' performance information in parentheses redundant rule, expanding expression without changing the numeral sign, distributive law,and sign-changed rule by four measurements which cover number calculation,algebra calculation, multiple choice of number, and multiple choice of algebra. There are 76 students with low mathematics achievement screened by government on-line test participating in study. They are divided into three groups, both OK, poor fluency only, both poor. The data is analyzed by ANOVA to test the difference of the performance of parentheses concept of junior high students with low mathematics achievement. The major findings of the study are as follows: (1) The students' accuracy is better than fluency in three arithmetic operation based on Ko’s Basic Math Concept Test. Most students with low mathematics achievement perform well in accuracy assessment, but more than half of students perform poor in the fluency assessment. (2) The best score of performance of parentheses concept is expanding expression without changing numeral sign, then the sequential performance is parentheses redundant rule, distributive law, and sign-changed rule. There’s difference in stability of parenthese performance for the students with different groups. The group of both OK has higher right answer rate significantly than the groups of poor fluency only and both poor. And the group of poor fluency only performs better in stability of parenthese concept than the group of both poor. (3) There's no significant difference of parentheses performance between number questions and algebra questions. However, the performance in multiple- choices is better than in calculation. The students in group of both OK perform non-significantly different among four different parentheses. However, the groups of poor fluency only and both poor perform poorer in calculation items than in multiple -choice ones. The suggestions to mathematic remediation of junior high school and further study about learning of parentheses concept are made on the basis of the study.
The purpose of this study is to identify the performance of parentheses concept of junior high students with low mathematics achievement. Two methods are conducted：(1) Implementing Ko’s “Basic Math Concept Test-Three Arithmetic Operation.” to investigate the relationships between the performance of parentheses concept and accuracy and fluency. (2) Collecting students' performance information in parentheses redundant rule, expanding expression without changing the numeral sign, distributive law,and sign-changed rule by four measurements which cover number calculation,algebra calculation, multiple choice of number, and multiple choice of algebra. There are 76 students with low mathematics achievement screened by government on-line test participating in study. They are divided into three groups, both OK, poor fluency only, both poor. The data is analyzed by ANOVA to test the difference of the performance of parentheses concept of junior high students with low mathematics achievement. The major findings of the study are as follows: (1) The students' accuracy is better than fluency in three arithmetic operation based on Ko’s Basic Math Concept Test. Most students with low mathematics achievement perform well in accuracy assessment, but more than half of students perform poor in the fluency assessment. (2) The best score of performance of parentheses concept is expanding expression without changing numeral sign, then the sequential performance is parentheses redundant rule, distributive law, and sign-changed rule. There’s difference in stability of parenthese performance for the students with different groups. The group of both OK has higher right answer rate significantly than the groups of poor fluency only and both poor. And the group of poor fluency only performs better in stability of parenthese concept than the group of both poor. (3) There's no significant difference of parentheses performance between number questions and algebra questions. However, the performance in multiple- choices is better than in calculation. The students in group of both OK perform non-significantly different among four different parentheses. However, the groups of poor fluency only and both poor perform poorer in calculation items than in multiple -choice ones. The suggestions to mathematic remediation of junior high school and further study about learning of parentheses concept are made on the basis of the study.
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正確性, 流暢性, 去括號, 括號多餘, 分配律, 括號概念, accuracy, fluency, sign-changed rule, parentheses redundant rule, distributive law, parentheses concept