Middle School Geometry Research Articles

Strengthening Mathematical Connections in Middle School Geometry: The Role of Means-Ends Analysis in Learning Cubes and Rectangular Prisms

The mathematical connection abilities of middle school children are the primary subject of this study, which aims to understand how means-end analysis (MEA) policies and procedures might assist. Students need to build mathematical connection abilities that enable them to comprehend and associate various mathematical concepts to improve their ability to comprehend and apply mathematics in real-world contexts. This is an essential component of the learning process. The research uses a quasi-experimental methodology by administering tests to the control and experimental groups before and after the intervention. One group utilised the MEA tactics in the mathematics lesson, while the other group remained committed to the tried-and-true method. Data was collected through mathematical connection tests, and then statistical analysis was performed on it to determine whether or not the intervention was effective. According to the findings, students whose courses contained MEA strategies showed a considerable improvement in their mathematical connection abilities compared to the control group. This study validates that incorporating MEA approaches into the mathematics curriculum is a viable alternative for increasing students' mathematical literacy and competence. The findings of this study provide more evidence to support this idea.

Development of Middle School Geometry Teaching Materialsby Utilizing Learning Resources in the Neighborhood

Development of Middle School Geometry Teaching Materialsby Utilizing Learning Resources in the Neighborhood

Integrating Art and Dynamic Geometry Software into the Teaching and Learning of Middle School Geometry

Abstract This study focuses on understanding the ways in which integration of art and dynamic geometry software (DGS) into geometry influenced middle school teachers’ understanding of geometric concepts that are difficult to teach, and their perceptions of teaching these topics. The study indicated that art materials combined with DGS played different roles in teachers’ understanding of geometry: in some cases, they helped acquisition of new knowledge and development of deeper conceptual knowledge while addressing misconceptions; in other cases, they helped the retention of knowledge by association with the activity; and in some cases, they facilitated the transfer of knowledge and development of strategic knowledge. Study results also indicated that integration of art combined with DGS led to a higher level of creative engagement that supported productive struggle and helped teachers appreciate and understand pedagogy differently. Lastly, the teachers made connections from learning mathematics content to the pedagogy of teaching that same content.

우리나라, 일본, IB 중학교 수학 교육과정과 교과서의 증명 내용 분석1)

Korea has not dealt with proof in middle school geometry since the 2009 revision of the curriculum. In this study, we propose to reintroduce proof in the new curriculum in Korea, and examine the contents and methods of proof education in the geometry domain of the Japanese and IB (International Baccalaureate) middle school mathematics curriculum, and based on this, we would like to suggest implications for proof education. To this end, in order to diagnose the current status of proof education in Korea, the introduction period of proof and related terms were analyzed by curriculum period. Next, we looked at the 2017 revised middle school mathematics curriculum in Japan, which has a similar academic system, curriculum, and educational environment to Korea, and the proof of the middle school mathematics textbook first published in 2021 based on this curriculum. In addition, we looked at how proof is handled in the IB (International Baccalaureate) mathematics curriculum and textbook, which is an internationally accredited curriculum. By summarizing these, implications for how to develop proof education in Korea

Authentic Integration of Physical Education and Mathematics: The Geometry Racket

This article offers a blueprint for how middle-school geometry and physical education units naturally intersect for authentic integration of both subjects. This disciplinary intersection is called the “Geometry Racket” and illustrates how mathematics knowledge provides and almost unfair advantage (i.e. racketeering) in net/wall games.

2015 Revised Curriculum Mathematics textbook core copetencies analysis: Focused on the 3rd grade middle school geometry unit

2015 Revised Curriculum Mathematics textbook core copetencies analysis: Focused on the 3rd grade middle school geometry unit

A Comparative Analysis of Mathematical Tasks in Middle-School Geometry of Korea and the US

A Comparative Analysis of Mathematical Tasks in Middle-School Geometry of Korea and the US

Impact of augmented reality technology on academic achievement and motivation of students from public and private Mexican schools. A case study in a middle-school geometry course

In this paper, the authors show that augmented reality technology has a positive impact on learning-related outcomes of middle-school Mexican students. However, the impact varies depending on whether students were enrolled in public or private schools.The authors designed an augmented reality application for students to practice the basic principles of geometry, and a similar application which encompasses identical learning objectives and content deployed in a Web-based learning environment. A 2 × 2 × 2 factorial design was employed with 93 participants to investigate the effect of type of technology (web, augmented reality), type of school (private, public), and time of assessment (pre, post) on motivation, and declarative learning. The results show that: (1) there is an interactive effect of type of technology, type of school, and time of assessment when students' achievement scores are measured; (2) students using the augmented reality-based learning environments scored higher in post-test than those using the web-based application; (3) the augmented reality learning environment was more learning effective compared with the web-based learning environment in public schools, but not in private schools; (4) there is not an interactive effect of type of technology, type of school and time of assessment when students' motivation is measured; (5) students from private schools reported higher levels of motivation compared with those from public schools when using the augmented reality learning environment. The research findings imply that in Mexico, augmented reality technology can be exploited as an effective learning environment for helping middle-school students from public and private schools to practice the basic principles of Geometry.

Transforming Middle School Geometry Instruction

Students move from slides, flips, and turns into reasoning about the characteristics of rigid transformations.

Designing Digital Badges for Educational Games

Findings from two studies on the design of digital badges for a middle school geometry game and their impact on motivational and cognitive learning outcomes are reported. Study 1 compared the effect of badges in the game to a group with no badges. Badges did not increase posttest performance for all. Learners with high situational interest performed better with badges, learners with low situational interest performed worse with badges. Study 2 compared mastery goal orientation badges with performance goal orientation badges. The interaction of condition and situational interest from Study 1 was replicated. Furthermore, students receiving performance badges performed better on the posttest than students in the mastery badges condition; the no-badges condition was not different from either of the other conditions. Results suggest badges do not always help in educational video games: Types of badges interact with students' interest and motivation to affect learning outcomes.

예비수학교사의 MKT에 관한 연구

본 연구에서는 내용 지식 교육의 측면에서 예비수학교사 교육의 방향을 탐색하고자 예비수학교사들의 MKT에 대한 인식 조사와 더불어 실제 과제 수행 과정에서 드러나는 MKT에 대한 분석을 실시하였다. 26명의 예비수학교사가 MKT에 대한 인식 설문 조사와 중학교 수준의 기하 영역에 해당되는 2개의 MKT 과제의 수행에 참여하였다. 본 연구에 참여한 예비교사들은 KCT-2 범주를 제외한 MKT 하위 범주 각각에 대한 지식이 충분하다고 인식하는 것으로 나타났고, 예비교사교육에서 MKT의 각각의 하위 범주에 대한 교육은 중요하게 생각하고 있었다. 그러나 MKT 과제 수행 분석으로부터 본 연구에 참여한 예비수학교사들은 SCK, KCS, KCT를 요구하는 문항에 어려움을 겪고 있는 것을 알 수 있었고, 특히, SCK와 KCT를 요구하는 문항에 적절한 응답을 준 예비교사의 비율이 50% 이하로 나타나 MKT에 대한 예비교사들의 일반적인 인식과 실제적인 지식 발현 과정 사이에는 불일치되는 부분이 있음을 확인할 수 있었다. The purposes of the study were to analyze pre-service mathematics teachers' MKT and to examine the perceptions of MKT to find implications for the improvement of pre-service mathematics teacher education program in the aspect of teachers' content knowledge. Twenty-six pre-service mathematics teachers participated in the survey to examine the perceptions of MKT and they also finished two MKT tasks which focused on a specific area of middle school geometry. According to the survey results, the participants thought that they have enough knowledge in all categories of MKT except KCT-2 and they appreciated the importance of MKT education in pre-service mathematics teacher education program. However, the participants showed difficulties in MKT task items which required SCK, KCS, KCT, especially, the proportions of those who showed appropriate knowledge on the items required SCK and KCT was less than 50%. These results show disagreement between the perceptions of pre-service mathematics teachers' MKT and practice of MKT.

스토리텔링을 활용한 중학교 기하영역 자료 개발 연구

스토리텔링을 활용한 중학교 기하영역 자료 개발 연구

중학교 기하영역 등분할 개념에 대한 수학사적 분석 및 확장에 대한 연구

본 연구에서는 중학교 기하영역에서 다루어지는 등분할 개념을 조사하고, 이를 바탕으로 수학사적 분석을 통해 등분할 개념에 대한 확장 가능성을 탐구한 문헌연구이다. 중학교 기하영역에 대한 조사를 통해 선분의 등분할, 각의 등분할, 호의 등분할, 넓이의 등분할 개념이 다루어지고 있음을 발견하였다. 이들 네 개의 등분할 개념에 대한 수학사적 분석을 통해 역사적으로 등분할 개념이 다양한 측면에서 다루어졌음을 확인할 수 있었다. 최종적으로 선분의 등분할 개념과 각(호)의 등분할 개념은 방법적 측면에서의 확장에 대해 고찰하였고, 넓이의 등분할 개념은 개념적 측면에서의 확장에 대해 탐색하였다. 본 연구에서 제시한 등분할에 대한 수학사적 분석 및 확장에 대한 분석 결과를 통해 중등학교에서 수학사의 효과적 활용에 대한 방향 설정이 기대된다. This is a literature study about the concept of 'Division into Equal Parts' in middle school geometry. First, we notice that the concept of the division into equal parts in middle school geometry is given in four themes, which are those of line segments, angles, arches and areas. Second, we investigate and analyse the historical backgrounds of these four kinds of divisions into equal parts. Third, the possibility of extension in terms of method and concept was researched. Through the result of this study, we suggest that it is desirable to use effective utility of history in mathematical teaching and learning in middle school.

A changing trajectory of proof learning in the geometry inquiry classroom

The purpose of this study is to explore how students changes through learning to construct mathematical proofs in an inquiry-based middle school geometry class in Korea. Although proof has long been considered as one of the most important aspects of mathematics education, it is well-known that it is one of the most difficult areas of school mathematics for students. The geometry inquiry classroom (GIC) is an experimental class designed to teach geometry, especially focusing on teaching proof, based on students’ own inquiry. Based on a 2-year participant observation in the GIC, this study was conducted to address the following research question: how has students’ practice of mathematical proof been changed through their participation in the GIC? The in-depth analysis of the classroom discourse identified three stages through which the students’ practice of mathematical proof was transformed in the GIC: ‘emergent understanding of proof’, ‘proof learning as a goal-oriented activity’, ‘experiencing proof as the practice of mathematics’. The study found that as learning evolved through these stages, so the mathematics teacher’s role shifted from being an instructor to a mediator of communication. Most importantly, this research showed that the GIC has created a learning environment where students develop their competence in constructing meaningful mathematical proof and grow to be ‘a human who proves’, ultimately ‘a person who playfully engages with mathematics’.

일상적 정의에서 수학적 정의로의 이행 - 영재 중학생들의 점과 선의 정의 인식 -

This paper analysed gifted middle students' conception of the definitions of point and line and the uses of definitions in proving. The findings of this paper suggest that the concept of mathematical definitions is very unnatural to students, therefore teachers and textbooks need to explain explicitly the characteristics of mathematical definitions which are different from dictionary definitions using common sense. Also introducing undefined terms in middle school geometry would give students a critical chance to deal with the transition from dictionary definitions to mathematical definitions.

Using Delphi methodology to design assessments of teachers’ pedagogical content knowledge

Descriptions of methodologies that can be used to create items for assessing teachers’ professionally situated knowledge are lacking in mathematics education research literature. In this study, researchers described and used the Delphi method to design an instrument to measure teachers’ pedagogical content knowledge. The instrument focused on a specific area of middle school geometry and measurement, decomposing and recomposing figures in 1-D and 2-D. The Delphi methodology used included three rounds of surveys of a diverse panel of 20 experts. The data analysis and data collection were done reflectively. Initial items were developed based on the research literature in the field of geometry education and teacher knowledge. New categories for the analysis emerged from the data and were used to complete the analysis. Consensus among the experts was reached after the third round of surveys, producing the assessment instrument. The researchers described strengths and limitations of this methodology for designing assessment tools of teachers’ knowledge. The researchers suggested that Delphi methodology could also be used to design and validate broader instruments related to other types of professional knowledge of teachers in different fields.

Performance on Middle School Geometry Problems With Geometry Clues Matched to Three Different Cognitive Styles

ABSTRACT— This study investigated the relationship between 3 ability‐based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems provided clues compatible with their cognitive style. Students were identified as having a particular cognitive style when they scored equal to or above the median on the measure assessing this ability. A geometry test was developed in which each problem could be solved on the basis of verbal reasoning clues (matching verbal deductive cognitive style), mental rotation clues (matching spatial imagery cognitive style), or shape memory clues (matching object imagery cognitive style). Straightforward cognitive style–clue‐compatibility relationships were not supported. Instead, for the geometry problems with either mental rotation or shape memory clues, students with a combination of both verbal and spatial cognitive styles tended to do the best. For the problems with verbal reasoning clues, students with either a verbal or a spatial cognitive style did well, with each cognitive style contributing separately to success. Thus, both spatial imagery and verbal deductive cognitive styles were important for solving geometry problems, whereas object imagery was not. For girls, a spatial imagery cognitive style was advantageous for geometry problem solving, regardless of type of clues provided.

A virtual reality application for geometry classes

Abstract In communicating information about geometric figures, one drawing may be worth many hundreds of words and, therefore, visualisation aids for complicated three‐dimensional (3‐D) solid objects are very helpful for both teacher and students. This paper describes the use of the Virtual Reality Modelling Language (VRML) to visualise 3‐D objects for middle school geometry classes in a networked environment and shows its usefulness for both teacher and students. In class, the teachers use VRML objects retrieved from their server and students are allowed to explore these objects accessing the teachers' server via the world‐wide web. A comparison of the test results from VRML‐based geometry classes and traditional classes, that solely depend on verbal explanation with paper and pencil, show that the application of VRML‐based 3‐D objects has a positive affect on students' learning of geometric topics.