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identifier)YP YX X \ \ Y \X \ٳ kThe analysis of high school students translative activities dealing with sequences and limits of sequences2018
Y YP!YtTŐYP YMastertǅlMaster's ThesisbThe amended curriculum of mathematics in 2015 puts emphasis on mathematical expression skills in order to create innovative and integrated individuals and the creation or transformation of mathematical expression skills such as mathematical vocabularies, symbols, tables and graphs for the development of students mathematical expression skills. The transformative activities of mathematical expression is also referred to as translation , and Janveier (1987) highlights the translation between situational/linguistic expression, tables, algebraic expressions and graphs when learning math.
Janvier(1987) especially highlights the translative activities when learning about functions, so several existing papers that analyzed students abilities to translate were about functions, and most of them dealt with students abilities to translate functions definitions and fundamentals when functions were firstly introduced. However, the translative activities of mathematical expression is one of the most basic factors of expression in the amended curriculum in 2015, and is an effective teaching and learning method to increase students skills for mathematical expression. So, those abilities should not only be dealt with when functions are firstly introduced, but also be actively applied to sequences and limit, which are the special cases of functions.
This report s aim is to analyze high school students translative skills for mathematical expressions about the sequences and the limits of sequences and types of errors that are shown during the process of translation and provide helpful materials that are needed in the teaching/learning methods to allow active translations among mathematical expressions in the chapters that deal with sequences and limits of sequences. The questions that will be dealt in the report are as follows.
Question 1. How are the translation methods of mathematical expressions about the sequences and the limits of sequences among high school students that chose to study liberal arts?
Question 2. What are the types of errors made by high school students that chose to study liberal arts in the process of translation among mathematical expressions dealing with the sequences and the limits of sequences?
In order to get the answers to the questions above, a survey that is consisted of 12 questions dealing with the translation of mathematical expressions was given to eight 2nd year high school students and twelve 3rd year high school students. This survey tests their abilities to translate mathematical expressions about sequences and limits of sequences. The retrieved papers were 20 in total, with 8 papers coming from 2nd year high school students and 12 papers coming from 3rd year high school students. Out of the 20 papers, 2 papers were exempted because the 3rd year high school students that were supposed to answer them left them completely blank. Analysis of the remaining papers regarding the frequency of answers, errors, and non-responses as well as the types of errors for questions that students got wrong were conducted. The error type the analysis of errors was created by the researchers, who referred to previous researches, and was used for the current research. The results of the research are as follows.
For question 1, the translation activities that the second and third graders in high school showed their highest abilities were the a< ctivities that translating limits of sequence s situational-linguistic expressions and equations into tables. Overall, students showed high abilities in translating different mathematical expressions into table, and the lowest capabilities in translating situational-linguistic expressions, tables, and equations into graphs. Especially, students in their second year of high school were not only poor at translating other mathematical expressions into graphs, but also in the type of translating language expressions into equations
For question 2, when listing from highest to lowest frequencies of types of errors that students showed when translating among mathematical expressions dealing with sequences and limits of sequences, it is as follows: technical errors (25.1%), omissions of the solving process and answer (26.3%), inappropriate logical deductions(22%), incorrect understanding of the problems (10.5%), inappropriate use of definitions and mathematical contents (6.1%). After interviewing the students, it was found that the reason for such high frequency of technical errors was because students did not possess sufficient experience in translating. Moreover, since 3rd year high school students usually solve problems based on the University Entrance Exams of South Korea and its mock tests, their ability to basically draw graphs and express in symbols were low.
The information on high school students skills on translating mathematical expressions about sequenses and limits of sequences and the types of errors made during the translation processes are provided by the research hopes to be helpful to understanding the level of knowledge of high school students translative activities and fixing the teaching/learning methods of sequences and limits of sequences.
On the other hand, this research only analyzed the types of errors shown by students during the translation processes, and did not provide teaching/learning methods or materials that could fix the errors. In order to increase the translation abilities of students, not only understanding high schoolers` mathematic conditions and their error types but also the development of teaching/learning methods that can fix such errors are necessary. So, further research on teaching measures that can fix the errors shown by students during translation processes is proposed. ;2015 Y P!@ =XǷ5i xǬ| 1X0 t Y XǬ %D X, YX Y XǬ %X hՑX \ )<\ Y ƴ, 08, \, X Y \D ̹p XXՔ \ٳD p\. Y \X X \ٳD (translation) t|ĳ Xp, Janvier(1987) YD Yյ` L iַŴ \, \, , tX D pX.
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