• School Mathematics
• /
• v.14 no.1
• /
• pp.1-28
• /
• 2012

The purpose of the study are to identify factors of mathematical visualization through the thirty students of highschool 2nd year and to investigate how each visualization factor is used in mathematics problem solving process. Specially, this study performed the qualitative case study in terms of the five of thirty students to obtain the high grade in visuality assessment. As a result of the analysis, visualization factors were categorized into mental images, external representation, transformation or operation of images, and spacial visualization abilities. Also, external representation, transformation or operation of images, and spacial visualization abilities were subdivided more specifically.

• Communications of Mathematical Education
• /
• v.27 no.3
• /
• pp.221-248
• /
• 2013

Among five types of the model textbook based on storytelling, the type of 'Inquiry into history of Mathematics' focuses on adapting the logic of mathematical discovery to the organization of mathematical contents. It enables students to recognize that mathematics has been developed by human needs and creativity while they are engaged in the story about knowledge formation. Moreover the textbook offers the context in which students are able to understand mathematical insights and logics hidden in the subject matter, so that they can reinvent and develop mathematical knowledge. In this study, we found the principles for development of the textbook based on storytelling for 'Inquiry into History of Mathematics' by analyzing the chapter about 'Complex number and Quadratic Equations' of the model textbook. The chapter was implemented in classroom environment and students' understanding of the subject matter and their perception on the textbook based on storytelling were surveyed before and after the implementation. The results showed the possibilities of adapting the textbook based on storytelling and we suggested some implications for further development.

• Journal of the Korea Society of Computer and Information
• /
• v.25 no.2
• /
• pp.241-250
• /
• 2020

In this paper, we propose a direction of teaching method for future generations. In order to suggest such the direction, teaching and learning materials that integrate coding activities and mathematical modeling were developed through top-down and bottom-up processes. Coding and engineering experts and mathematics education experts developed teaching and learning materials through councils (top-down courses) and applied them to 24 high school first graders based on student responses (bottom-up courses). Additionally, the developed curriculum helped students increase interest and motivation and realize conceptual understanding, problem posing, and problem solving in mathematics. On the basis of these results, it provided an idea about how to develop curriculum combining mathematical modeling with coding activities, needed for the fourth industrial revolution.

• School Mathematics
• /
• v.13 no.3
• /
• pp.363-384
• /
• 2011

This study is based on the recognition that the school mathematics education should reinforce the heuristic and constructional aspects related with discoveries of mathematical rules and understanding of mathematical concepts from real world situations as well as the deductive and formal aspects emphasizing on mathematical contents precisely. The 11th grade students of one class from a city high school with average were chosen. They were given time to learn various functions of Excel in regular classes of "Information Society and Computer" subject. They don't have difficulty using cells, mathematical functions and statistical functions in spreadsheet. Experiment was performed for six weeks and there were two hours of classes in a week. Considering the results of this research, teaching materials using spreadsheets play an important role in helping students to experience probabilistic and statistical reasoning and construct mathematical thinking. This implies that teaching materials using spreadsheet provide students with an opportunity to interact with probabilistic and statistical situations by adopting engineering which can encourage students to observe and experience various aspects of real world in authentic situations.

• Journal of the Korean School Mathematics Society
• /
• v.23 no.1
• /
• pp.67-88
• /
• 2020

This study analyzed the characteristics of prospective teachers' Horizon Content Knowledge(HCK) related to understandings of an inverse function symbol. This study aimed to deduce implications of developing HCK in terms of the means which would enhance mathematics teachers' professional development. In order to achieve the aim, this study identified features of HCK by examining the previous literature on HCK, which has conformed Ball & Bass(2009) and exploring the research in AMT, including Zazkis & Leikin(2010) which has emphasized cultivating AMT through university mathematics education. In addition, a questionnaire was developed regarding the features of HCK and taken by 57 prospective teachers. By analyzing the data obtained from the written responses the participants presented, this study delineated the specific characteristics of the teachers' HCK with regard to an inverse function symbol. Additionally, several issues in the teacher education for improving HCK were discussed, and the results of this research could inspire designing and implementing a teacher education program relevant to HCK.

• Communications of Mathematical Education
• /
• v.36 no.4
• /
• pp.487-509
• /
• 2022

The purpose of this study is to analyze classroom discourse in the math classroom of middle school in China, which has a unique math classroom background of entrance examination for high school. To this end, this study analyzed teacher question statistics and episodes by teacher question type as starting speech in mathematics classroom discourse, and five IRF subtypes were especially identified by class discourse structure analysis. The data were analyzed focusing on a total of 15 transcripts of math classes recorded by three math teachers at H School in Guiyang, Guizhou Province, China, and written interviews of teachers. According to the results of this study, an average of 20 teacher questions were observed for each class, and the teacher question type was classified into confirmation question (understanding confirmation question, explanation request question, and double check question) and information question (information presentation question). In addition, according to classroom discourse analysis, the IRF discourse structure was divided into fragmentary evaluation, evaluation+reason, evidence of explanation, evaluation+student response re-statement, guidance on other thoughts or solutions, and student answer correction or teacher opinion presentation.

• Journal of The Korean Association of Information Education
• /
• v.14 no.3
• /
• pp.319-328
• /
• 2010

Computer programming education gives students a chance to use computers independently and actively. This plays a very positive role in acquiring higher cognitive skills such as mathematical skills and creative logical thinking. Thus the purpose of this study is to measure the degrees of students' problem-solving abilities using MCU programming kits based on the ICT Education Guide. The experiment confirms that programming classes using MCU kits have a more positive effect on the students problem-solving abilities than do those using the existing computer textbooks. The sub-constituents of problem-solving abilities - problem recognition, information gathering, analysis, diffuse thinking, decision-making, planning, execution, evaluation and feedback - also show significant statistical differences. Therefore, we can conclude that programming classes using MCU kits are very effective in advancing problem-solving abilities.

• Journal of Educational Research in Mathematics
• /
• v.23 no.4
• /
• pp.467-490
• /
• 2013

Correlation is a basic statistical concept which is necessary for understanding the relationship between two variables when they change values. In the middle school curriculum of Korea, only informal definition of correlation is taught with two-way data representations such as scatter plots and contingency tables. In this study, we investigated Korean high school students' understanding of correlation using a test consisting of 35 items about interpretation of scatter plot, contingency table, and text in realistic situation. 216 students from a high school in Seoul took the test for 20 minutes. From the results, we could observe the following: First, students did not have right criteria for determining the strength of correlation presented in scatter plots. Most of students could determine if there is correlation/no correlation and if the correlation is positive/negative by seeing the data presented in scatter plots. However, they did not judge by the closeness to the regression line but rather judged by the closeness between data points. Second, when statements about comparing the strength of correlation in the context of real life situation were given in text, the students had difficulty in understanding the distribution-related characteristic of the bi-variate data. Students had difficulty in figuring out the local distribution characteristic of data, which cannot be guessed merely based on the expression 'The correlation is strong' without statistical knowledge of correlation. Third, a large number of students could not judge the association between two variabels using conditional proportions when qualitative data are given in 2-by-2 tables. They made judgement by the absolute cell count and when the marginal sum of two categories are different for explanatory variable they thought the association could not be determined. From these results, we concluded that educational measures are required in order to remove such misconceptions and to improve understanding of correlation. Considering that the current mathematics curriculum does not cover the concept of correlation, we need to improve the curriculum as well.

• Journal of Educational Research in Mathematics
• /
• v.21 no.4
• /
• pp.327-344
• /
• 2011

This study is the first step for us toward improving high school students' capability of statistical inferences, such as obtaining and interpreting the confidence interval on the population mean that is currently learned in high school. We suggest 5 underlying concepts of 'discretion of contingency and inevitability', 'discretion of induction and deduction', 'likelihood principle', 'variability of a statistic' and 'statistical model', those are necessary to appreciate statistical inferences as a reliable arguing tools in spite of its occasional erroneous conclusions. We assume those 5 concepts above are to be gradually developing in their school periods and Korean mathematics textbooks of grades 1-12 were analyzed. Followings were found. For the right choice of solving methodology of the given problem, no elementary textbook but a few high school textbooks describe its difference between the contingent circumstance and the inevitable one. Formal definitions of population and sample are not introduced until high school grades, so that the developments of critical thoughts on the reliability of inductive reasoning could not be observed. On the contrary of it, strong emphasis lies on the calculation stuff of the sample data without any inference on the population prospective based upon the sample. Instead of the representative properties of a random sample, more emphasis lies on how to get a random sample. As a result of it, the fact that 'the random variability of the value of a statistic which is calculated from the sample ought to be inherited from the randomness of the sample' could neither be noticed nor be explained as well. No comparative descriptions on the statistical inferences against the mathematical(deductive) reasoning were found. Few explanations on the likelihood principle and its probabilistic applications in accordance with students' cognitive developmental growth were found. It was hard to find the explanation of a random variability of statistics and on the existence of its sampling distribution. It is worthwhile to explain it because, nevertheless obtaining the sampling distribution of a particular statistic, like a sample mean, is a very difficult job, mere noticing its existence may cause a drastic change of understanding in a statistical inference.

• The Mathematical Education
• /
• v.63 no.1
• /
• pp.1-18
• /
• 2024

This study aims to analyze low-performing high school students' difficulties in constructed response (CR) mathematics assessments and explore ways to use writing activities to support student learning. The participants took CR assessments, engaged in guided writing activities across 15 lessons, and provided responses to our interviews. The study identified 20 types of student difficulties, which were sorted into two main categories: "mathematical difficulties" and "CR difficulties." The difficult nature of mathematics as a school subject included a lack of understanding of mathematical concepts, students' difficulty with mathematical symbols and notations, and struggles with word problems. Challenges specific to CR assessments included students' difficulties arising from the testing conditions unlike those of multiple-choice items, and included issues related to constructing appropriate responses and psychological barriers. To address these challenges in CR assessments, the study conducted guided writing activities as an intervention, through which six themes were identified: (1) internalization of mathematical concepts, (2) mathematical thinking through relational understanding, (3) diverse problem-solving methods, (4) use of mathematical symbols, (5) reflective thinking, and (6) strategies to overcome psychological barriers.