Academic literature on the topic 'Geometry – Textbooks'

This paper is a product of a research that investigates the presence of Geometry in textbooks, that is part of project of a Theorem – Reflection on Geometry and Mathematics Education research group. The focus here is to present results of the international study: how textbooks present the concept of similarity? For this, a qualitative research were developed and textbooks of three collections from Brazil and three from United States were examined. A synthesis of the literature related to the search for textbooks and the teaching and learning of the concept of similarity is presented, and the theoretical framework explores similarity as positioned at the crossroads of geometry and number to describe the ways in which different textbooks approach it. Sequence of topics and tasks presented in each textbook are described and then comparisons are made. There were theorems and problem types that were presented consistently across all textbooks, but differences in expectations related to proof and the use of coordinates and geometric transformations were identified. Only textbooks in the US included the use of transformations and coordinates and placed more emphasis on formal proof. Implications for the teaching and learning of similarity are provided

Starting with 2018/2019 school year in Bulgaria, the math education in the third grade is implemented through new training kits. They were developed on the basis of the new third-grade mathematics curriculum, approved by Order No. РД 09-1093 / 25.01.2017 of the Minister of Education and Science, Annex No. 8, supplemented by Order No. РД 09-2555 / 15.06.2018 of the Minister of Education and Science. Training kits are approved by the Ministry of Education and Science and are 7 in total. Geometric learning content in new math textbooks is the second most important element after arithmetic content. It is combined with the arithmetic learning content, and by this the foundation of the successful study of geometry in the next school grades is laid. The new geometry knowledge that is included in the third grade curriculum is the following: straight line, curve, beam, angle, right angle, obtuse angle, acute angle, right triangle, acute triangle, obtuse triangle; naming geometric figures with Latin alphabet letters [11]78. It is important in a modern mathematics textbook to have a rich and varied geometric content. It is important that the new types of geometry tasks are introduced with rich visualization using a specific-inductive approach. The relative number of tasks of a given type is an important prerequisite for the successful formation and improvement of skills for solving geometric problems in pupils at the age of 9-10. This article will present a comparative analysis of the geometric content in the seven approved Bulgarian third-grade mathematics textbooks, which are used in the mass practice of this school year. For the purpose of the study, a classification of all types of tasks and exercises with geometric content has been developed. Then the tasks in the seven textbooks are systematized by the so chosen classification. The data are statistically processed taking into account the relative share of tasks of each type within a textbook, as well as a comparison between the relative shares of the geometric tasks in the different textbooks. The established differences in the number and relative share of different types of geometric tasks make it possible for the analyzed textbooks to be ranked. Such a study has not been published so far. It has a relation to the assessment of the quality of the textbooks offered. The conclusions formulated in this article can help primary teachers in their choice of textbooks to teach to their third grade students.

We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that instructional tasks were drawn from multiple sources, including textbooks, tests, supplemental materials, and the teacher. Our analysis of cognitive complexity indicated that the instructional tasks frequently involved both diagram complexity and problem-solving complexity. Moreover, the geometric calculation with number tasks from nontextbook sources tended to be more cognitively demanding than those found in the textbooks. Implications of task analysis on geometry domain and textbook analysis studies are discussed.

The study focuses on improving higher-order thinking skills (HOTS) in mathematics students using a Desmos-assisted planar analytic geometry course. Analytic geometry, which is essential for understanding geometric properties using analytic methods, requires students to develop problem-solving, analysis, assessment, and creativity abilities. However, current educational practices fall short of acquiring these abilities due to insufficient instructional techniques, textbooks, and a lack of integration with information and communication technologies. To address these shortcomings, the study proposes a Desmos-assisted textbook meant to increase students' HOTS through the use of interactive Desmos platform tools such as graphic depiction, experimentation, simulation, and collaborative learning. The textbook development followed the PLOMP model, which included preliminary research, prototyping, and assessment phases, ensuring the textbook's validity and practicality through reiterated evaluations. The findings show that the textbook is highly valid and practical for instructional purposes, improving students' knowledge of mathematical concepts and ability to engage in HOTS processes. Despite some difficulties with HOTS-related practice questions, generally student feedback was positive, emphasizing the textbook's function in supporting a deeper understanding of analytic geometry and encouraging problem-solving skills. The study indicates that integrating technology such as Desmos into mathematics education can greatly contribute to the development of students' HOTS, and recommends its use in teaching techniques as well as additional research on its implementation in educational contexts.

This study examined the differences in the presentation of geometry concepts and characteristics of geometry questions among elementary mathematics textbooks in Finland, Singapore, and Taiwan. Horizontal and vertical analysis methods were used to collect and analyze the data. A popular Mathematics textbook from a dominant publisher in each country were selected: Laskutaito from Finland, My Pals are Here! Maths from Singapore, and Kang Hsuan from Taiwan. The results indicated differences in the presentation of geometry concepts among the three textbook series. In addition, the questions in these textbooks were determined to demonstrate different characteristics. Moreover, these findings highlight the importance of cross-national textbook comparison to enhance the understanding of differences in learning opportunities across different countries.

The topic of similarity plays an essential role in developing students’ deductive reasoning. However, knowing how to teach similarity and understanding how to incorporate deductive reasoning and proof along with plane geometry remain a challenge to both school curriculum creators and teachers. This study identified the problems and characteristics regarding how similarity is treated in secondary mathematics textbooks in Hong Kong in the past half century. The content analysis method was used to analyze six secondary mathematics textbook series published in different periods. From the epistemological perspective of the textbook contents, our analysis shows the historical context and learning trajectories of how similarity was treated in school curriculum. The natural axiomatic geometry paradigm is not emphasized too much at different stages and most of the textbooks did not provide formal proofs of similarity. The intuitive idea was gradually consolidated into a formal definition of similarity. Furthermore, the way that rigorous geometric deduction can be performed from intuitive concepts and experimental geometry to the idea of proofs and formal proofs is also discussed.

The purpose of this study is to analyze tasks reflected in Korean and US textbooks according to the mathematical modeling perspectives, and then to compare the diversity of learning opportunities given to students from both countries. For this, we analyzed mathematical modeling tasks of textbooks based on three aspects: mathematical modeling process, data, and expression. Results are as follows. First, with respect to modeling process, Korean textbook provides a high percentage of the task at all stages of modeling than US textbook. Second, with respect to data, both countries’ textbooks have the highest percentage of matching task. Korean textbooks have a large gap in data characteristics by textbook. Third, with respect to expression, both countries’ textbooks have the highest percentage of text and picture. Korean textbooks have a large gap in the type of expression than US textbooks, and some textbooks have no other expression except for text and picture. Fourth, tasks were analyzed by integrating the three features. The three features were not combined in various ways. It is necessary to diversify the integration of the three features.

This study compares Malaysian and Korean geometry content in mathematics textbooks to help explain the differences that have been found consistently between the achievement levels of Malaysian and South Korean students in the Trends in International Mathematics and Science Study (TIMSS). Studies have shown that the use of textbooks can affect students’ mathematics achievements, especially in the field of geometry. Furthermore, to date, there has been no comparison of geometry content in Malaysian and Korean textbooks. Two textbooks used in the lower secondary education system in Malaysia and South Korea were referred. The topic of quadrilaterals was chosen for comparison, and the topic’s chapter in the South Korean textbook has been translated into English. The findings show four main aspects that distinguish how quadrilaterals are taught between the two countries. These aspects include the composition of quadrilaterals topics, the depth of concept exploration activities, the integration of deductive reasoning in the learning content and the difficulty level of mathematics problems given at the end of the chapter. In this regard, we recommend the Division of Curriculum Development of the Malaysian Ministry of Education reviews the geometry content of mathematics textbook used today to suit the curriculum proven to produce students who excel in international assessments.

Textbooks have always played an important role in mathematics education. Textbook tasks are widely used by students, so it is important to examine their requirements in order to identify the opportunities students have to learn mathematics. Publishers now produce both printed and digital versions of textbooks. While the requirements of the tasks in printed textbooks have been well examined all over the world, the tasks in digital textbooks are yet to be analysed and systematically developed. The research presented in this paper encompasses the analysis and comparison of the tasks in the printed and digital versions of the same mathematics textbook set. The examined set covers Grades 1 to 4 of primary education in Croatia. The aim was to find what task requirements are predominant in the printed and the digital textbooks, and to determine whether these textbook versions provide a wide variety of task features. In addition, the features and capacities typical of digital tasks, such as interactivity and dynamics, are examined. These task features are particularly important in geometry education for comprehending visual and dynamic geometrical objects and relations. The results show that both the printed and the digital textbook tasks have traditional requirements, with an emphasis on closed answer forms. Moreover, the new opportunities afforded by digital tasks are not realised. These findings reveal the potential of digital tasks as a new area to be explored and developed.

To make geometry meaningful, fun, and applicable to the lives of our students, we adapted the game of miniature golf as a way to teach transformatiOnal geometry. Geometry textbooks often feature twodimensional pictures of miniature-golf holes to illustrate transformational geometry. Geometry students in this project actually brought the golf holes out of the textbook by constructing a life-sized miniature golf course.