數學符號知識及運算概念與學生學習化學反應式之研究

The Relationship between Students’ Knowledge of Symbols and Operations in Mathematics with Their Learning of Chemical Equations

蔡宗程

指導教授 ： 譚克平博士

國立臺灣師範大學/理學院/科學教育研究所在職進修碩士班/碩士(2003年)

摘要

本研究利用自行發展的題本，對台北縣的二所中學，共4個班級、143名國三學生進行紙筆測驗，但在施測期間，適逢國內SARS傳染病流行，使取樣困難，故本研究的樣本並非隨機抽樣，在推廣時不宜過度推論。施測的學校有實施數理等科目的分組教學，所以施測的樣本是在分組的班級中進行。在紙筆測驗之後，從這些已經作過紙筆測驗的學生中，依據測驗成績高低及任課教師們的推藨，挑選出10位學生進一步地進行排卡片的晤談測驗，用以深入瞭解學生的想法。
本研究的目的主要是探討國三學生對於化學反應式中各符號意義的瞭解情形，及學生在學習化學反應式時，受其數學符號知識及運算概念的干擾情形。本研究所探討的化學反應式的符號概念是指：箭號的方向、催化劑的位置、係數和元素右下方的數字等符號概念；至於所探討的數學符號知識及運算概念所造成的干擾是指：減法的概念、除法的概念、等量公理、次方位置的概念、等號的概念、分配律、交換律及化學式「CuSO4．5H2O」中「．」的符號概念。
研究結果發現，學生對化學反學式內符號的概念方面：學生會認為二個相反箭號方向的化學反應式是代表相同的化學反應；會把催化劑寫在反應物的位置上；對於係數和元素右下方的數字的概念不足，不瞭解二者的意義和二者在化學反應式上的關係，同時發現有些學生雖然可以利用數學的方法均衡化學反應式，但學生對於係數和元素右下方的數字的意義並不瞭解。
研究結果也顯示，學生部份的數學符號知識及運算概念會干擾其化學反應式的學習，其干擾情形如下：會把反應式中的箭號寫成等號；會受減法概念干擾，認為可以在反應式箭號的左右二邊同時減去一個相同的原子：會受到乘法或除法概念的干擾，會放大或縮小元素右下方的數字；會受分配律的概念干擾，會把要放大或縮小的數字乘以或除以每個物質的’元素右下方的數字’或’係數和元素右下方的數字’；會受到數學加法的概念干擾，會以’係數＋元素右下方的數字’的方法計算前面有係數的化學式內所含某原子的個數；會受到次方位置的概念干擾，會把’O2’寫成’O2 ’，就是把元素右下方的數字寫在元素右上方的位置，並稱呼這個數字’ 2’為’平方’。
學生在學習化學反應式時，會受到其數學符號知識及運算概念的干擾，這些干擾以等號、減法、乘法、除法及配律的概念干擾較大，教師在教學時，必須特別注意，至於其它的數學想法的干擾較小，教師在教學時可以不必擔心。

關鍵字

均衡化學反應式 ； 化學符號 ； 數學運算

並列摘要

Written tests designed in this research have been conducted on 143 9th-grade students in four classes at two high schools in Taipei County. During the period of tests, it happened to be widespread of the domestic SARS infectious disease, which made sample taking difficult. Therefore, the samples taken in this research were not random samplings, so one should not infer them excessively when in promotion. The schools being tested had practiced the group teaching in subjects of mathematics and physics & chemistry, so the test samples were taken in the class groups. After the written test, the 10 students (testees) were chosen according to their grades and recommended by the teachers and have a further interview test with cards, obtaining deeper understanding of students’ viewpoints.
This research is aimed to explore junior high school senior students’ comprehension of symbols of chemical equation, and the interference of mathematic symbols and operational concept on their learning process of the chemical equation. The symbol concept of the chemical equation in this research contains symbol concepts such as arrow direction, catalyst position, coefficients and subscripts. Interferences caused by probing knowledge of mathematic symbols and operation concepts are: subtraction, division, same quantity concept, distributive law, exchange law and the symbol concept of “．” in the chemical formula “CuSO4．5H2O “.
As the aspect of the concept of the chemical equation, the findings of the research show: students may consider opposite arrows in the chemical equation as the same chemical reaction. They would write a catalyst on the position of a reactant. They have an insufficient concept of coefficients and subscripts, not knowing the meaning of the two and their relations of the chemical equation. Meanwhile, some students may be able to utilize the method of mathematics to balance the chemical equation, yet students have poor understanding of coefficients and subscripts.
The findings of the research also reveal that students’ knowledge of partial mathematic symbols and operational concept would interfere their learning in chemical equation. They would write an arrow in equation as an equal sign; interfered by subtraction concept, considering they could take off an identical atom from the two sides of the arrow of the equation. They would also interfered by multiplication and division to enlarge or reduce the subscript; they would also interfered by distributive law to multiply or divide the enlarged figure or reduced figure by the subscript of every substance or by the coefficient and the subscript; they would also be interfered by the addition of mathematics in a way of “coefficient + the subscript” to calculate atoms in the chemical formula with coefficient in front. They would interfered by square concepts in position to write ’O2’ into ’O2’, that is to say, they write the subscript on the position of superscript, and referred the figure ’ 2’ as ’square’.
On the learning process of the chemical equation, students may be interfered by their knowledge of mathematic symbols and operational concepts. The greater interferences are such as equal sign, subtraction, multiplication, division and distributive law, which require particular attention in teaching. The rest mathematic concepts are not as much in interference, and unnecessary to feel too much concern about them on the process of teaching.

並列關鍵字

Balancing Chemical Equation ； Chemical Symbol ； Mathematical Operation

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