• The Mathematical Education
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• v.58 no.3
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• pp.403-422
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• 2019

As the informal graph was introduced newly in the area of function in middle school mathematics curriculum revised in 2015, ten publishing company became to have a concern on how to represent the graph content uniquely and newly. At this time, it may be meaningful and useful to compare and analyze the content of the graph unit shown on each textbook published by publishing companies. To accomplish this, on fundamentally the basis of diverse prior researches this study tried to select the elements of expression and interpretation of the graph and establish an analytic frameworks of expression and interpretation of the graph respectively. This study executed the frequency analysis and cross analysis by textbook system, textbook, and the number of the graph drawn on a coordinate plane on the representation and interpretation of the graph. As a result, the textbook contains more items on interpretation than the representation of the graph, and students showed a learning effect on the graph unit but showed a neutral response to the impact of learning. This basic and essential paper shed light on developing the practical and more creative textbook which has diversity and characteristic respectively, while adjusting the scope of the elements of the graph's representations and interpretations and providing proper level and quality content.

• Education of Primary School Mathematics
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• v.27 no.2
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• pp.155-171
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• 2024

This study compared and analyzed students' reasoning processes and justification methods when introducing the concept of "the sum of angles in a triangle" in mathematics classes with a focus on both measurement and geometric aspects. To confirm this, the research was conducted in a 4th-grade class at H Elementary School in Suwon, Gyeonggi-do, South Korea. The conclusions drawn from this study are as follows. First, there is a significant difference when introducing "the sum of angles in a triangle" in mathematics classes from a measurement perspective compared to a geometric perspective. Second, justifying the statement "the sum of angles in a triangle is 180°" is more effective when explained through a measurement approach, such as "adding the sizes of the three angles gives 180°," rather than a geometric approach, such as "the sum of the angles forms a straight angle." Since elementary students understand mathematical knowledge through manipulative activities, the level of activity is connected to the quality of mathematics learning. Research on this reasoning process will serve as foundational material for approaching the concept of "the sum of angles in a triangle" within the "Geometry and Measurement" domain of the Revised 2022 curriculum.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.635-652
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• 2023

This study conducts a comprehensive analysis of the curricular progression of the concepts and learning sequences of 'lines', specifically, 'line segments', 'straight lines', and 'rays', at the elementary school level. By examining mathematics curricula and textbooks, spanning from 2nd to 7th and 2007, 2009, 2015, and up to 2022 revised version, the study investigates the timing and methods of introducing these essential geometric concepts. It also explores the sequential delivery of instruction and the key focal points of pedagogy. Through the analysis of shifts in the timing and definitions, it becomes evident that these concepts of lines have predominantly been integrated as integral components of two-dimensional plane figures. This includes their role in defining the sides of polygons and the angles formed by lines. This perspective underscores the importance of providing ample opportunities for students to explore these basic geometric entities. Furthermore, the definitions of line segments, straight lines, and rays, their interrelations with points, and the relationships established between different types of lines significantly influence the development of these core concepts. Lastly, the study emphasizes the significance of introducing fundamental mathematical concepts, such as the notion of straight lines as the shortest distance in line segments and the concept of lines extending infinitely (infiniteness) in straight lines and rays. These ideas serve as foundational elements of mathematical thinking, emphasizing the necessity for students to grasp concretely these concepts through visualization and experiences in their daily surroundings. This progression aligns with a shift towards the comprehension of Euclidean geometry. This research suggests a comprehensive reassessment of how line concepts are introduced and taught, with a particular focus on connecting real-life exploratory experiences to the foundational principles of geometry, thereby enhancing the quality of mathematics education.

• Journal of the Korean School Mathematics Society
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• v.22 no.4
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• pp.369-393
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• 2019

The purpose of this study is to find the commonality between process-focused assessment and existing performance evaluation and to find out whether the process-focused assessment is effective for the development of the character of school mathematics. By analyzing the previous research, this study defined the meaning of process-focused assessment as an evaluation that can improve students' growth and quality of class through immediate feedback by introducing various performance tasks and evaluation methods. The character of school mathematics refers to personality factors that are easily expressed and cultivated during math classes. Therefore, this study presented examples of the feasibility of process-focused assessment focusing on geometry and vector subjects and examined the effectiveness of mathematics and character development through process-based evaluation. Four course-based assessments (math experiments, logic, proof, and communication) aimed at cultivating the character of school mathematics were conducted from March to June 2019 for the third year of high school. The index was measured. Analysis of the results using the corresponding variable t-test showed that the process-based evaluation in this study had a significant effect on the character of school mathematics development.

• School Mathematics
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• v.19 no.3
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• pp.423-441
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• 2017

New Zealand had reformed their national curriculum with competence and are applying the revised curriculum. As the 2015 revised national curriculum is clothed with competency-based curriculum, New Zealand may have important implications for the study of the Korean revised curriculum. In this study, we examine characteristics of the education system and the national curriculum in New Zealand. In addition, we analyze the standards into the New Zealand national curriculum in terms of 'curriculum connectivity' that is one of important curriculum criteria for improving the quality of education. For this, we look an overview of the relation between the New Zealand curriculum and NCEA, which is the core of the student-centered education system in New Zealand, and analyze the correspondence between the New Zealand curriculum and the Korean curriculum. And we establish analysis framework of curriculum connectivity based on these comparison analysis contents, and analyze Korean mathematics standards with corresponding levels from among the New Zealand mathematics curriculum. According to the results of this study, the New Zealand curriculum includes the most of standards which Korean high school students who want to enter university of natural sciences of engineering need to require. In addition, the New Zealand curriculum highlights statistical research activities for developing problem-solving ability in real life. From perspective of curriculum connectivity, 'in-depth contents' adding on to repeating mathematical concepts or contents are included in the New Zealand curriculum.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.273-289
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• 2001

Given that the culture of the mathematics classroom has been perceived as an important topic in mathematics education research, this paper deals with the construct of sociomathematical norms which can be used as an analytical tool in understanding classroom mathematical culture. This paper first reviews the theoretical foundations of the construct such as symbolic interactionism and ethnomethodology, and describes the actual classroom contexts in which social and sociomathematical norms were originally identified. This paper then provides a critical analysis of the previous studies with regard to sociomathematical norms. Whereas such studies analyze how sociomathematical norms become constituted and stabilized in the specific classroom contexts, they tend to briefly document sociomathematical norms mainly as a precursor to the detailed analysis of classroom mathematical practice. This paper reveals that the trend stems from the following two facts. First, the construct of sociomathematical norms evolved out of a classroom teaching experiment in which Cobb and his colleagues attempted to account for students' conceptual loaming as it occurred in the social context of an inquiry mathematics classroom. Second, the researchers' main role was to design instructional devices and sequences of specific mathematical content and to support the classroom teacher to foster students' mathematical learning using those sequences Given the limitations in terms of the utility of sociomathematical norms, this paper suggests the possibility of positioning the sociomathematical norms construct as more centrally reflecting the quality of students' mathematical engagement in collective classroom processes and predicting their conceptual teaming opportunities. This notion reflects the fact that the construct of sociomathematical norms is intended to capture the essence of the mathematical microculture established in a classroom community rather than its general social structure. The notion also allows us to see a teacher as promoting sociomathematical norms to the extent that she or he attends to concordance between the social processes of the classroom, and the characteristically mathematical ways of engaging. In this way, the construct of sociomathematical norms include, but in no ways needs to be limited to, teacher's mediation of mathematics discussions.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.5
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• pp.2101-2121
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• 2020

The rapid growth of instructional videos repositories and their widespread use as a tool to support education have raised the need of studies to assess the quality of those educational resources and their impact on the quality of learning process that depends on them. Khan Academy (KA) repository is one of the prominent educational videos' repositories. It is famous and widely used by different types of learners, students and teachers. To better understand its characteristics and the impact of such repositories on education, we gathered a huge amount of KA data using its API and different web scraping techniques, then we analyzed them. This paper reports the first quantitative and descriptive analysis of Khan Academy repository (KA repository) of open video lessons. First, we described the structure of repository. Then, we demonstrated some analyses highlighting content-based growth and evolution. Those descriptive analyses spotted the main important findings in KA repository. Finally, we focused on users' interactions with video lessons. Those interactions consisted of questions and answers posted on videos. We developed interaction profiles for those videos based on the number of users' interactions. We conducted regression analysis and statistical tests to mine the relation between those profiles and some quality related proposed metrics. The results of analysis showed that all interaction profiles are highly affected by video length and reuse rate in different subjects. We believe that our study demonstrated in this paper provides valuable information in understanding the logic and the learning mechanism inside learning repositories, which can have major impacts on the education field in general, and particularly on the informal learning process and the instructional design process. This study can be considered as one of the first quantitative studies to shed the light on Khan Academy as an open educational resources (OER) repository. The results presented in this paper are crucial in understanding KA videos repository, its characteristics and its impact on education.

• Education of Primary School Mathematics
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• v.26 no.1
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• pp.29-43
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• 2023

The purpose of this study was to synthesize intervention studies, which utilized single case experimental design, on teaching mathematical word problems for elementary school students with disabilities and evaluate each of their methodological rigor. The researchers reviewed all studies from 2000 to 2022 that involved teaching mathematical word problems to individuals with disabilities. A total of 12 studies was included for a final analysis. Most of the interventions were delivered by researchers for about 30-40 minutes per session to elementary school students with disabilities. Schema-based instruction, cognitive-metacognitive strategy, and technology-based instruction were used as intervention methods, and explicit instruction was mostly used in conjunction with them. On the other hand, the researchers found that none of research articles met quality indicators for single case experimental design according to Cook et al. (2015). Limitation and directions for future research were also discussed.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.75-90
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• 2024

This study analyzed the vocabularies presented in the 1st to 2nd grade elementary school mathematics field review textbook according to the 2022 revised curriculum using a 9th grade vocabulary system and improved them. The result of the analysis shows that the frequency of vocabulary that was not appropriate for the students' level was found to be 6.67% in the first semester of the first year and 12.17% in the second semester of the first year. For the first semester of the second year, it was 11.73%, and for the second semester of the second year, it was 14.19%. This shows that the frequency of vocabulary that may be difficult for students gradually increases. Based on the analysis results, vocabulary that had a high difficulty level but was not essential in the textbook was deleted, and essential vocabulary or vocabulary that was difficult for students was presented with pictures added or revised in more detail. In addition, words that can be modified with similar words with low lexical difficulty were replaced and presented. In this way, research on vocabulary difficulty can identify aspects of vocabulary used in textbooks and can help develop high-quality textbooks by appropriately modifying vocabulary for effective mathematics learning.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.121-141
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• 2016

In Korea where there is the national curriculum and teachers depend highly on textbooks, the school mathematics is based on curriculum and textbooks. Especially considering responsibility that textbooks should reflect the curriculum properly, it is necessary to analyze the connection of mathematics curriculum and textbooks in order to review and improve the quality of our mathematics education. This research analyzes the connection of curriculum and textbooks for 5~6 grades and aims to have some implications for revision of the textbooks when application of elementary mathematics textbooks based on the 2009 revised national curriculum is completed to all grades. Following the preceding research for 1~2 and 3~4 grades, this research sets 5~6 grades as a subject of analysis and has four contents of analysis; analysis of textbooks based on restructured achievement criteria, analysis of connections between unit objectives of textbooks and the reconstructed achievement criteria, analysis of textbooks related to mathematical terms and symbols, and analysis of textbooks related to mathematical process. The result of analysis has some implications to develop textbooks based on the 2015 revised national curriculum.