• Communications of Mathematical Education
• /
• v.20 no.3 s.27
• /
• pp.443-467
• /
• 2006

The purpose of this study was to study the 2nd grade elementary students' common thinking and differences of additive and multiplicative thinking. For meaningful discussion of the above, we have established the following research questions. 1. What are the properties of the multiplicative thinking of 2nd grade elementary students? - What are the common properties of the multiplicative thinking of 2nd grade elementary students? - What are the properties of the various multiplicative thinking levels? 2. How is multiplicative thinking presented in Korean math textbooks? The conclusions of this study were followings: First, the 2nd grade elementary students in the multiplicative thinking learnt used by translating multiplication into specific situations. And they often used different models of multiplication. Second, additive thinking developed into the multiplicative thinking. After being helped by their teachers, students who thought additively were then able to think multiplicatively. Whereas after being helped by their teachers, students who were already competent at multiplicative thinking gained a deeper understanding. Third, they learned the commutative property of multiplication after their understanding of the 'repeated addition approach' and the multiplicative approach was sufficiently reinforced. Last, students should be taught using different models based on the repeated addition approach.

• School Mathematics
• /
• v.10 no.2
• /
• pp.155-179
• /
• 2008

Multiplication problems for the 7th curriculum focus on functional realms featuring the memorization and application of the multiplication table, exposing learners only to additive thinking characterized by simple counting and drawing. A diversity of research has yet to be conducted for the transition to multiplicative thinking that highlights the capability to solve problems by using multiplication and division in the expanded number scope like 'prime numbers', 'fractional numbers', and 'ratio/rates' and to describe accurately how they solved. This research was designed to develop and utilize teaching-learning materials for the transition of fifth graders' additive thinking to advanced multiplicative one and to analyze the application results in order to identify validity in material development. The following conclusions were made. First, the development and application of teaching-learning materials for multiplicative thinking cultivation facilitated the transition from additive thinking featuring simple counting and drawing to multiplicative thinking characterized by multiplication and accurate description in a more complicated and expanded number scope. Second, the development of materials featuring 'basic'-'intermediate'-'in-depth' courses by activity enabled learners to benefit from learning by level and expansion in number scope. Third, the use of topics and materials closely connected to daily lives stimulated learners' curiosity, helping them concentrate more on given problems. Fourth, communication between teachers and students or among learners themselves was promoted by continuously encouraging them to explain and by reviewing their documents identifying rules or patterns.

• Journal of Korean Elementary Science Education
• /
• v.30 no.3
• /
• pp.271-281
• /
• 2011

The environmental education is based on the assumption that accurate knowledge and attitude could be linked to real action, but those have no effect on changing the behavior. To effect the change in behavior, we need to consider the reflective thinking which can make people change their behavior. The strategies to accelerate the reflective thinking are five steps of the reflective thinking process and the interaction through the discussion of students. And also, it is more proper if the contents are based on the real experiences of the students. Thus, this study tried to know whether the improvement of reflective thinking was able to affect to the environmental behavior. The environment education program was applied to the 60 elementary school 6th grade students in Gyeonggi-do and the survey methods were presented in the general experimental curriculum. To study 6th subjects (energy, harmful chemical material, heavy metal and agricultural chemicals, food additive, environmental friendly consumption, and recycle) was developed. This study shows the effect of the program on the environment knowledge, the environment behavior, the level of reflective-thinking and communication ability.

• Journal of Educational Research in Mathematics
• /
• v.23 no.1
• /
• pp.1-16
• /
• 2013

The primary purpose of this study is to survey multiplicative thinking levels and its characteristics of third graders in elementary school and to analyze how to use it when they solve the proportional problems. As results, the transition thinking ranked the highest among the four kinds of thinking levels when the $3^{rd}$ graders solved the multiplication problems. It means that the largest numbers of students still can not distinguish the additive and multiplicative situations completely and remain in the transition thinking, which thinks both additively and multiplicatively. In addition, the performance of solving proportional problems was distinguished from the levels of thinking. Through this study, we can give some implications of the importance of multiplicative thinking and instructional methods related to multiplication.

• Journal of Elementary Mathematics Education in Korea
• /
• v.21 no.2
• /
• pp.343-364
• /
• 2017

Despite the significance of functional thinking at the elementary school level there has been lack of research on teachers who play a major role in making students be engaged in functional thinking. This study surveyed 119 elementary school teachers to investigate their knowledge of functional thinking for teaching. A written assessment for this study was developed with a focus on the knowledge of mathematical tasks and instructional strategies to teach functional thinking. The results of this study showed that many teachers were able to design tasks corresponding to both the additive relationship and the multiplicative relationship, and to justify some strategies to promote functional thinking. However, some teachers had lack of understanding with regard to the core ideas of functional thinking. Based on these results this study is expected to suggest implications on what aspects of knowledge are further needed for elementary school teachers to promote students' functional thinking.

• Journal of The Korean Association For Science Education
• /
• v.22 no.3
• /
• pp.604-616
• /
• 2002

The purpose of this study was to analyze the development of the compensational thinking by the compensation activities of 'Thinking Science' program. The 138 students were sampled in elementary schools and were divided into two groups, the experimental group of 74 students and the control group of 64 students. Both the compensation activities of the 'Thinking Science' program and a regular science curriculum were implemented to the experimental group, while only a regular science curriculum to the control group. Both experimental and control group were pre-tested with Science Reasoning Task II and compensational thinking test I and were post-tested with compensational thinking test II. This study revealed that the types of strategies used in compensation problem solving were categorized as illogical explanation, rule automation, proportionality, explanation in qualitative terms, additive quantification, inverse proportionality and were related to the context of the items. It was found that compensation activities of the 'Thinking Science' program were effective on the development of the compensational thinking.

• School Mathematics
• /
• v.14 no.3
• /
• pp.275-296
• /
• 2012

This study investigated elementary school students' understanding of basic functional relationships. It analyzed the written responses from a total of 2087 students of second, fourth, and sixth graders using tests that examined their understanding of five types of functional relationships. The results of this study showed that students tended to be more successful as their grades went up with regard to all the problem types. There were statistically differences among the three grade levels. Even lower graders were quite successful in dealing with additive relation, direct proportion, and inverse proportion. However the items dealing with square relation and linear relation were difficult even to sixth graders. It was common that students were good at completing the table by looking for a pattern from the given numbers but that they had difficulties in anticipating the value of 'y' when the value of 'x' is given either as a big number or as a symbol. Given these results, this paper includes issues and implications on how to foster functional thinking ability at the elementary school.

• Journal of Educational Research in Mathematics
• /
• v.17 no.1
• /
• pp.1-31
• /
• 2007

Negative numbers have been one of the most difficult mathematical concepts, and it was only 200 years ago that they were recognized as a real object of mathematics by mathematicians. It was because it took more than 1500 years for human beings to overcome the quantitative notion of numbers and recognize the formality in negative numbers. Understanding negative numbers as formal ones resulted from the Copernican conversion in mathematical way of thinking. we first investigated the historic and the genetic process of the concept of negative numbers. Second, we analyzed the conceptual fields of negative numbers in the aspect of the additive and multiplicative structure. Third, we inquired into the levels of thinking on the concept of negative numbers on the basis of the historical and the psychological analysis in order to understand the formal concept of negative numbers. Fourth, we analyzed Korean mathematics textbooks on the basis of the thinking levels of the concept of negative numbers. Fifth, we investigated and analysed the levels of students' understanding of the concept of negative numbers. Sixth, we analyzed the symbolizing process in the development of mathematical concept. Futhermore, we tried to show a concrete way to teach the formality of the negative numbers concepts on the basis of such theoretical analyses.

• Journal of Korean Society of Transportation
• /
• v.21 no.1
• /
• pp.103-113
• /
• 2003

This paper shows alternative route search and preference route search for the traffic route search, and proposes the use of the fuzzy non-additive controller by the application of AHP(analytic hierarchy process). It is different from classical route search and notices thinking method of human. Appraisal element, weight of route is extracted from basic of the opinion gathering for the driving expert and example of route model was used for the finding of practice utility. Model evaluation was performed attribute membership function making of estimate element, estimate value setting, weight define by the AHP, non additive presentation of weight according to $\lambda$-fuzzy measure and Choquet fuzzy integral. Finally, alternative route search was possible to real time traffic route search for the well variable traffic environment, and preference route search showed reflection of traffic route search disposition for the driver individual. This paper has five important meaning. (1)The approach is similar to the driver's route selection decision process. (2)The approach is able to control of route appraisal criteria for the multiple attribute. (3)The approach makes subjective judgement objective by a non additive. (4)The approach shows dynamic route search for the alternative route search. (5)The approach is able to consider characteristics of individual drivers attributed for the preference route search.

• Research in Mathematical Education
• /
• v.11 no.4
• /
• pp.247-263
• /
• 2007

Problem solving takes place not only in mathematics classes but also in real-world. For this reason, a problem and the structure of problem solving, and the enhancing of success in problem solving is a subject which has been studied by any educators. In this direction, the aim of this study is that the strategy used by students in Turkey when solving oral problems and their achievements of choosing operations when solving oral problems has been researched. In the research, the students have been asked three types of questions made up groups of 5. In the first category, S-problems (standard problems not requiring to determine any strategy but can be easily solved with only the applications of arithmetical operations), in the second category, AS-SA problems (problems that can be solved with the key word of additive operation despite to its being a subtractive operation, and containing the key word of subtractive operation despite to its being an additive operation), and in the third category P-problems (problematic problem) take place. It is seen that students did not have so much difficulty in S-problems, mistakes were made in determining operations for problem solving because of memorizing certain essential concepts, and the succession rate of students is very low in P-problems. The reasons of these mistakes as a summary are given below: $\cdot$ Because of memorizing some certain key concepts about operations mistakes have been done in choosing operations. $\cdot$ Not giving place to problems which has no solution and with incomplete information in mathematics. $\cdot$ Thinking of students that every problem has a solution since they don't encounter every type of problems in mathematics classes and course books.