| Summary: | 碩士 === 國立彰化師範大學 === 科學教育研究所 === 87 === Abstract
The research explores the difficulties the first year secondary school students with bad academic performance learned from arithmetic to algebra and the remedial instructions to overcome difficulties. The research uses qualitative methodology to investigate students'''' math behaviors with constructivist teaching experiment in which ten junior high students were involved, and the questions offered will be used as the material in constructivist teaching. For this purpose, according to the textbooks used in first-half semester, homework, the usual test and discussion with the teachers, the researcher divids them into four kinds problems:(1)the letter evaluated problems(2)the simplifying expression problems(3)solving equations (4)word problems .
In order to examine the content validity, the researcher chooses two students to do the pilot study. In the formal stage, the whole procedure was undertaken three times. 8 students were interviewed at the first time, and 3 of them proceeded with the second and the third time. The first interview is to explore learning phenomena and characteristics when the students learned algebra the first time; The second one, which adds in word problems, is to explore the students'''' concept development about algebra after they have studied for a period of time; The third one is to explore whether the students can understand the mapping from the algebra representation to graphic representation .
The research information was collected by observation and deep interview,including the viedo tapes on classroom observation and on the interviews. The analysis concentrated in talk record and was supported with teaching video tapes to analyze the protocols.To show the behavior of junior high students who study algebra for the first time and to analyze how junior students understand basic algebra concepts, the researcher set up the distribution chart about students'''' wrong answers first time, their behavior when answering each classified questions and the strategies to help them. The conversation between teachers and students was used as the evidence to show the common behavior students have and the classified problems were used to describe students incorrect judgement; All of these were showing the trouble and misconception students have in common. After comparing these charts, we found that:
1. the common properties of students'''' problem solving behavior:stimulating-
reflectingness,wideness and activeness;though the direct response of students seeing
the questions was "I quit "(stimulating-reflectingness),but they didn''''t refuse to learn;
on the contrary, they were willing to accept the assistance from the
researcher(wideness) and started to learn to solve the problem(activeness).
2. The incorrect judgments made by students toward literal term were as follows:
(1) Students thought that only the terms including "x" were like terms and were
needed to be combined, and that the constant was not like terms so that no further
simplication was executed, for example,3x+4+5x+3=8x+4+3….. .Besides, students
usually combined the unlike terms in a wrong way or had no idea what 1x was That
resulted in the following situation:3x+4=7x,5x+1=6x,3x+x=3x…..
(2) The misconception about parentheses questions were as follows: (a) the coefficient
always multiplicated the first term inside the parentheses,and failed with the second
term. (b) If coefficient was negative,students always fail to change the sign of the
product.(c)Students didn''''t know which term was needed to be calculated with the
terms inside the parentheses.(d)Even though the terms inside the parentheses
couldn''''t be simplified,they still simplified them to a single term and then
multiplicated it with coefficient to remove the parentheses.(e)When there was no
confficient in front of the parentheses, students viewed it as zero.
3. Students couldn''''t map the algebraic representation and graphic representation at the same time. They could draw the diagram of a linear equation, but they didn''''t know the line represented the solution of the equation; It meant that students only have procedure knowledge and lacked conceptual understanding. Compared with signal linear equation, the meaning of two-linear equations was more understandable.
4.The researcher used the number line representing the algebraric expressing.
Visualizing the problems make students understand more the meaning of problems.
With the number line as a scaffolding,they could move from total incapability to
figurung out the correct answer.
5.The researcher neglect many necessary scaffoldings in the teaching
experiment:(1)Making the student understand understand the meaning of algebra
equations and the rules to cancel the parentheses via the principle of area of
rectangle.(2)arranging the equations with similar structures orderly and let students
find the hidden rules inside to understand how to remove the parentheses.
In fact,every student can learn math well. If teachers give them the opportunity, help them get rid of the fear, and construct their selfconfidence, students can all have a wonderful start.
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