• Journal of the Korean School Mathematics Society
• /
• v.10 no.1
• /
• pp.91-111
• /
• 2007

This study investigated how high school students predict the rule, the sum of sequence for the concept of sequence, for the given patterns based on inductive approach using computers that provide dynamic functions and materials that are visual. Students for themselves were able to induce the formula without using the given formula in the textbook. Furthermore, this study examined how these technology and materials affect students' understanding of the concept of actual infinity for those who have the concept of the potential infinity which is the misconception of infinity in a infinity series. This study shows that students made a progress from the concept of potential infinity to that of actual infinity with technology and materials used I this study. Students also became interested in the use of computer and the visualized materials, further there was a change in their attitude toward mathematics.

• Journal of Gifted/Talented Education
• /
• v.13 no.3
• /
• pp.1-17
• /
• 2003

Development and evaluation of distance learning for the gifted students in science and mathematics In this study, we developed and administrated the distance learning for the gifted students in science and mathematics, and analysed their responses. To do this, four types of teaching programs - lectures using program for distance learning, practice activities using simulation program, tasks solving programs based on discussions, and problem solving activities - were developed and students responses were analysed in eight area - stimulus, difficulties, structure, learning circumstances, involvement, interaction, learning outcomes, comparison with other learning -. As results, it was found that many students responded positively and thought programs helped their creativity, logical thinking, intelligent ability, and information searching ability. Students preferred practice activities based on appropriate guidances to lectures providing detailed explanations. And interaction could be stimulated by inducing discussion.

• School Mathematics
• /
• v.17 no.3
• /
• pp.391-405
• /
• 2015

This study was aimed to investigate how students' relational thinking about equations could be formed by exploring web-based balance. The researchers developed 3 groups of 4 typed 12 equation problems of (a+b+c = d+ _ ) to test 24 4th graders. Pretest and post-test were conducted using Eye-tracker for investigating their eye movements. The researchers interviewed students who were not having distinct strategies to look into their cognitive process. As a result, we can conclude web-based balance helped students to get the concept of the equal sign and to form the relational thinking by the process of comparing both sides, right and left on the basis of fulcrum on balance.

• Education of Primary School Mathematics
• /
• v.20 no.4
• /
• pp.305-319
• /
• 2017

In the process of finding the triangle height, 26 students in the 6th grade were surveyed to understand the students' triangle height through the eye movement data and to investigate the cognitive load of the students. As a result, the correctness rate of the pre-test was significantly increased in the post-test, and the frequency and retention of gaze data were smaller in the post-test than in the AOI of each question. The Participants's subjective cognitive load indicated that it was more difficult to understand the concept of rotated triangles compared with upright triangles that were parallel to the ground. More frequent and more retentions in the eye-tracking data were detected in the right triangles and acute triangles by rotating configuration. Eye movement data show that eye tracking technology can provide an objective measure of students' cognitive load for feedback on instructional design.

• Journal of Educational Research in Mathematics
• /
• v.21 no.4
• /
• pp.399-422
• /
• 2011

There has been an agreement on the necessity for each citizen is to be educated, so called, to develop quantitative literacy or statistical literacy, dealing with real world data. For this reason, it is highly demanded to improve traditional statistics education. In particular, critical thought and statistical communication competency cultivation is becoming more crucial in statistics classes. In line with this reform movement in statistics education, we developed tasks facilitating statistical debate among students through inducing cognitive conflict. The tasks employed for this study resulted in playing crucial role to activate statistical debate. Including aforementioned feature about the tasks for this study, we obtained several positive results such as promoting critical thought and conceptual extension by designed teaching experiment focusing on statistical debate.

• School Mathematics
• /
• v.11 no.1
• /
• pp.131-145
• /
• 2009

This research was designed to investigate the possibility to teach function concept and graph representation of functions in explicit manner toward at elementary level. Eight class-hours instruction was given to four Grade 5(age 11) students, and dynamic geometry software GSP was partially used in the class. Results indicate that the students could conceptualize the function relation, interpret linear function graphs, recognize the meaning of their slopes, and discuss the relationships among linear graphs and real life situation. Results also indicate that GSP helped students to recognize the relation between dots and the linear graph clearly and that GSP-line graph did decisive role for children to understand the meaning of graph representation of function.

• School Mathematics
• /
• v.8 no.4
• /
• pp.441-463
• /
• 2006

The purpose of this research is to investigate how elementary school students execute sampling with what designs in order to gather information under a situation that requires collecting data and information about their household and everyday life, and to examine how they use tools, including table or graph, etc., in order to perform efficient analysis of data and information they surveyed, also what results they acquire. To test this, the researcher set up a situation in advance that requires collecting data, and, under this circumstance, the researcher instructed and guided school students to look for methods how to design and survey in order to gather data by having them discuss tasks, involving small groups or entire class, and seek its solutions by themselves through trial and errors. The results from surveys revealed that a lesson, which will have students do sampling and arrange statistical data and analyze the results, was possible to carry out in the class of 6th grade of elementary school.

• School Mathematics
• /
• v.1 no.2
• /
• pp.637-660
• /
• 1999

Although ‘to understand mathematics’ is an important educational purpose, most student do not have a relational understanding of the basic concept of mathematics but have a instrumental understanding. This paper will investigate the possibility of using computers for enhancing relational understanding. In the ‘Qualitative case study’, three students who are in the first grade at E-High school took part in 7 activities during four weeks, and were later interviewed and engaged in informal discussion and were observed. This is the result of this study. 1. The three students were passive participants in mathematics problem solving situation at school. Therefore, student B just applied formulas which she had memorized, and student C would forgot the formulas occasionally. These common students needed to participate actively in doing mathematics. 2. The activities utilized two software healing with connection between graphs and function, giving the students the opportunity to plan, practice, and test by themselves. As a result, they understood the mathematical formulas and rules more deeply through their own trial and error, and then they gained thinking abilities necessary for doing mathematics. In addition, the activities boosted their confidence. 3. The understanding type of students was slightly different. Student A who received a high score, understood the most relationally, but student B who received a very high score, understood instrumentally and so couldn't app1y her knowledge to solving problems related to function concept. Student C who received a middle score lacked knowledge of mathematics but thought more creatively. The result is that students need an opportunity to think rotationally regardless of score. Therefore, this study concludes that using computer software will provide a positive effect for relational understanding in loaming function concept.

• School Mathematics
• /
• v.14 no.3
• /
• pp.297-313
• /
• 2012

The purpose of this paper is to discuss the potential and to examine the effect of narrative, as an alternative approach to teach formal proof in more easier and comprehensible way. Identifying the key elements of narrative in proof, we constructed a narrative that derives the equation of function translation. We examined the effect of teaching through the narrative, in comparison with teaching the corresponding proof, on low-achieving students' instrumental understanding and relational understanding of function translation. Since we found no statistically significant differences between the experimental and the comparison group, this study could not conclude that teaching through the narrative was more effective than teaching the corresponding proof. But there were some qualitative differences in the relational understanding responses and the evaluation of the teaching between two groups. These findings suggested some potential of narratives that complement the formal proof.

• Journal of Educational Research in Mathematics
• /
• v.18 no.1
• /
• pp.25-50
• /
• 2008

Several previous studies suggested that simulation could be a main didactic instrument in overcoming misconception and probability modeling. However, they have not described enough how to reorganize probability knowledge as knowledge to be taught in a curriculum using simulation. The purpose of this study is to identify the theoretical knowledge needed in developing a didactic transposition method of probability knowledge using simulation. The theoretical knowledge needed to develop this method was specified as follows : pseudo-contextualization/pseudo-personalization, and pseudo-decontextualization/pseudo-deper-sonalization according to the introductory purposes of simulation. As a result, this study developed a local instruction theory and an hypothetical learning trajectory for overcoming misconceptions and modeling situations respectively. This study summed up educational intention, which was designed to transform probability knowledge into didactic according to the introductory purposes of simulation, into curriculum, lesson plans, and experimental teaching materials to present didactic ideas for new probability education programs in the high school probability curriculum.