The Dutch reform movement towards Realistic Mathematics Education (RME) started at the end of the 1960s. As an alternative for the then prevailing mechanistic approach, tasks, lessons and longitudinal teaching sequences were developed together with suggestions for helpful contexts and didactical models. Over the years, RME ideas were laid down in many studies, covering both general ideas on...
This paper presents an examination about mathematical textbooks for high school students from China, Japan and the United States at both macro and micro levels, paritcularly with respect to general features, the trigonometric content included, the sequencing of trigonometric content, the structure of trigonometric content, presentation features and the requirement of problems. We have found...
We utilize four sampling methods (simple random sampling, systematic sampling, stratified random sampling, and cluster sampling) to select pages from ten textbooks, resulting in forty samples of pages. For each sample, we estimate the proportion of pages containing statistics tasks and the number of statistics tasks within each textbook. These estimates are compared with the actual values...
Textbooks play an important part in the design of instruction and for students’ mathematics learning as well. This study compared the cognitive complexity of Geometry textbooks at junior secondary school level in China, Singapore, and the UK. A comparison framework was developed specifically which includes the two aspects: 1) the width of cognitive complexity; and 2) the depth of cognitive...
A significant number of mathematics textbooks for secondary and high school levels in Mexico presumably contain authentic mathematical tasks. However, after we analyzed some of them through several aspects involved in Palm’s Theory, we found that authenticity degree of mentioned tasks is low or, practically non-existent. It has motivated us to propose a Model for Authentic Task Design. In a...
In this paper, the contents of Korean elementary school math textbooks before and after the revision were analyzed in order to present the trend of teaching method of ‘division of fractions’ in South Korea. Fraction division can be easily solved by using 'invert and multiplying' algorithm, It is easy for students to perform calculation mechanically without understanding. But in fact, it is...
In this article, we examine and compare how the procedures for solving one-variable linear equations and inequalities are presented in the narrative of Brazilian, Portuguese and Spanish textbooks. We analyze the main resources used, the relationships between the procedures of solving equations and inequalities, and the presence of reasoning-and-proving in the exposition of content. Results...
In the Undergraduate Teaching and Learning in Mathematics with Open Software and Textbooks (UTMOST, Beezer et al., 2018) project we study the use of open source computational resources in the teaching and learning of mathematics at undergraduate level. The project gathers (a) real-time, individualized viewing data from three dynamic undergraduate textbooks authored in textbooks authored in...
Computational thinking is a series of thinking activities that use the basic concepts of computer science to solve problems, design systems and understand human behaviors. It is considered as important as 3R (Reading, wRiting, and aRithmetic ). Because of the close relationship between mathematics and the basic concepts and principles of computer science, computational thinking is also...
Textbooks are different in many ways. Not only the mathematical content differs even more the presentation and handling of mathematics show great varieties.
To explore the field and to identify the differences with statistical methods, an instrument for analysing textbooks was developed. This instrument focuses on the three main structural elements of textbooks: tasks, pictures and...
Curricula around the world make more and more use of goals trying to capture different
kind of processes for the students to master. For mathematics education in Denmark,
these ambitions have been described in terms of a set of mathematical competencies.
However, bringing such competencies into the actual teaching practices has proved
challenging. Matematrix is a Danish mathematics textbook...
Procedural fluency is the ability to use skills flexibly, accurately, effectively and appropriately to perform mathematical processes. Based on literatures, a learning trajectory (LT) with five computational strategies (CSs: Concrete counting in Level 1, Concrete counting in Level 2, Abstract counting, Deriving, and Retrieving) for developing procedural fluency of addition and subtraction with...
Problem solving has been a major theme in mathematics education for nearly 50 years, and numerous teacher reference books and lesson plans have been published on the topic. However, despite this emphasis on problem solving, classrooms which effectively focus on nurturing students to become independent problem solvers are far from the norm. One of the major obstacles is that while many teachers...
Present setcentric and pre-setcentric math are challenged by
post-setcentric math seeing math, not as a goal, but as a means to develop
the mastery of Many children bring to school.
Asked “How old next time?”, a 3year old says “Four” showing 4 fingers; but
protests if held together 2 by 2: “That is not four, that is two 2s”, thus
describing what exists, and with units: the total is bundles of...
The aim of this paper is to discuss the development of task designs by Mathematics teachers, which involved the articulation between the official textbook of the State of Sao Paulo, Brazil, with the GeoGebra dynamic software. This occurred in two university extension courses offered to Mathematics teachers of the public schools of the State of Sao Paulo, specifically in the cities of Bauru and...
In Germany, primary school children should learn to not only execute the subtraction algorithm. They should also understand why the algorithm works. But this understanding is hard to achieve because the description of these processes is dominated by many technical terms and phrases like: “Unbundle one ten to ten ones. Reduce the number of tens…” – in this case for the subtraction algorithm...
Proportional reasoning is an important skill that requires a long process of development and is a cornerstone at the middle school level. One of the reasons why students cannot demonstrate this skill at the desired level is the learning opportunities provided by the textbooks. The aim of this study examines the extent to which selected Turkish, Singaporean and Canadian middle school...
The integer numbers structure and the idea of equivalence are elementary in the mathematical construction of the ordered field of the rational numbers. Hence, the concept of equivalence should not be absent in the Elementary School´s classrooms and textbooks, and it should be well constructed with the students in the sense that they are able to answer the question ‘How can one decide if two...
It is widely recognized that textbooks play an important role in teaching and learning of mathematics. Therefore, the way in which textbooks address gender equity is expected to have a significant influence on learning outcomes. However, when gender stereotyping is often investigated by textbook researchers, gender equity is rarely a concern when selecting and organizing teaching contents...
Interactions between teachers and textbooks are an active process and have an impact on mathematical lessons. International studies show that historical snippets are one way to including the history of mathematics in textbooks. Teachers must handle these tasks, but in which way they use these historical snippets? The aim of this explorative survey is to identify teachers’ language about tasks...
“Kyozai-Kenkyu” is an essential part of Japanese lesson study and involves task design for classroom lessons. Most of Japanese teachers often refer to textbooks as a main resource in doing “Kyozai-Kenkyu”. However, there are different kinds of use with regard to different approaches to knowledge at stake. In this study, we aim to examine teachers’ paradidactic activities related to...
*Integrating history of mathematics into mathematics textbooks is a commonly accepted idea and practice in modern textbook development in China, and mathematicians are an integral part of mathematical history. So how do Chinese mathematics textbooks fare in this particular aspect? In this study, we investigate how mathematicians are represented in two series of primary and junior secondary...
To be used in Mexican public schools, all mathematics textbooks have to pass an allegedly rigorous review process by Ministry of Public Education (Secretaría de Educación Pública). Nevertheless, various revisions of approved mathematics textbooks reveal many deficient features, going from orthographical, mathematical and contextual errors to inadequate learning sequences. The aim of this...
The limit is a key concept for students to understand as they move on to more advanced mathematics courses. Research related to student understanding of calculus concepts has detailed misconceptions that students have related to the concept of limit, a common one being that a function’s limit cannot be reached. To narrow the scope of this misconception, I focus on how three different calculus...
In this paper, we aim at identifying inclusive practises in inclusive maths lessons. Based on the textbook “Das Zahlenbuch” and the accompanying artefacts, the lessons should offer occasions for all children to participate in and benefit from the learning situation. In our study, we analyse videographed lessons, considering the ideas of sensitivity of differences, language and materials and...
Mathematical and linguistic features of word problems have been investigated with respect to their potential difficulties in various studies. In the current study, the transition of grade 4 (primary school) to grade 5 (secondary school) is studied for identifying changing demands in these features. For this, the study focuses word problems using the basic rules of arithmetic in different...
In the United States, teaching mathematics for social justice has the potential to make studying advanced mathematics more accessible to students coming from low income and historically underrepresented ethnic groups. Gutstein’s (2005) work on teaching students to “read” and “write” the world with mathematics laid the foundation for the framework that will be used in this middle school...
The OECD Education 2030 project has been examining many curriculum aspects through the lens of what will be desired for students to know and be able to do upon completion of their pre-university education in 2030. Representatives from key economic sectors—health, manufacturing, finance, and business—advised mathematicians about the mathematics and ancillary competencies needed in their...
Mathigon is a digital textbook for secondary Mathematics, developed in partnership with the EDUCATE project at University College London. The goals is to create a completely new format for digital textbooks, and to push the technical boundaries of interactivity and personalisation.
Mathigon’s unique platform combines elements for printed textbooks, videos, software environments, and physical...
In this contribution, we present a praxeological analysis of (introductory) tasks on vectors in German textbooks for secondary schools in the state North Rhine-Westphalia. We motivate our research concern from our interest in transition research from school to university and found a lack of research on vectors in this area. The Anthropological Theory of the Didactic (ATD) has already proven to...
This paper focuses on troubling the distribution and market strategies of school mathematics textbooks in a context embedded in neoliberal policies and assumptions about education. And so, it raises a set of questions about the dynamic of the production, distribution, and selection of the official mathematics textbooks for Chilean schools and the market that unfolds simultaneously of...
The capacity needed for using existing resources was explored and its potential components were identified previously in the context of elementary teachers using various curriculum programs in the United States. This study further explored the capacity needed for productive resource use in a mathematics methods course, focusing on preservice teachers’ learning to use existing resources...
Ratio, rate and proportional relationships are arguably the most important topics in middle grades mathematics curriculum before algebra. However, many teachers find these topics challenging to teach and students find them difficult to learn.
We examined the Japanese national course of study published by the Ministry of Education and one of the most widely used elementary and lower secondary...
This article presents a deeper theoretical understanding from the concept of "reading geometrically", proposed by Dietiker and Brakoniecki (2014), which is characterized as a reader’s negotiation of meaning with what is, what it is not, and may be misleading in a given diagram. They propose that from the reading geometrically is a new drawing of the diagram in the reader's mind, taking into...
Report on the main ideas, the design, the practical and theoretical components and the realisations of the workshop ‘Writing Maths Textbooks’ which the author developed on behalf of the GIZ (Deutsche Gesellschaft für Internationale Zusammenarbeit) for the Republic of Yemen to teach future textbook writers how to write Maths Textbooks. Because of acts of war the workshop was delivered in 2016...
The concept of vector is a central part of mathematics and physics at school. Three approaches to the concept of vector can be distinguished: arrow classes, n-tuples and vector space axioms. In order to develop adequate conceptions of vectors, different facets of the concept should be presented to the students and the representation in the subjects mathematics and physics should be...
To understand current state of the research on the representation of textbooks, 170 articles on mathematical representation are randomly selected to explore the research objects in recent decades, with the result of only 10.6% papers focusing on mathematics textbooks. Then, those papers are analyzed in terms of research questions, theoretical frameworks and research methods. Results show that...
This paper summarized domestic main models of degree of difficulty of curriculum and textbook from two aspects：the quantification of the component factors and the proportion of the component factors. Based on this, we propose five points the future research on models of degree of difficulty of curriculum and textbook needs to focus on: the concept definition in the study of models of degree of...
The utilization of textbooks by mathematics teachers has been the subject of many recent studies; students’ opinions, however, have not received such attention. The study presented in this paper aims to investigate both students’ and their teacher’s ways of and reasons for using the textbook, with an emphasis on the vertices of the Socio-Didactical Tetrahedron. The findings indicate that the...
The aim of this research is to design age-appropriate curriculum to nurture children’s mental operations ability and to clarify these effects through concrete classroom-based lessons.
I designed two lesson plans for grade4 students that nurtured children’s mental operations, and taught these in two classes. Two of the lesson plans were as follows.
1. The group 1 lesson was the same order in...
More teachers from Shanghai and other provinces are taking self-learning seriously. It is all a question of the textbook’s readability. “Inverted classroom” represent major shift in this process, which require students to read the textbook by themselves. However, there are growing doubts about whether textbooks are prepared for such a big shift. Without teacher guidance, can students learn...
In the arena of mathematics teaching and learning at undergraduate level, we strive to assess and evaluate the use of dynamics textbooks authored in PreTeXt. We seek to investigate how mathematical content in a textbook is taken up by instructors as they plan and teach their lessons, and by students who participate in those lessons. We analyze textbook raw content to identify competencies...
We present a work in progress of a new method for textbook research based on the Anthropological Theory of Didactics (ATD). Representation of the concept of function is chosen as a particular example to validate how the praxeology and levels of didactic co-determination of ATD can be used for textbook research. Two different Norwegian textbooks published at different times are selected. The...
In the field of mathematics textbook research, researchers have argued that there has been a lack of research focusing on the issues concerning the mathematics textbook development, and called for more research in this area. In part to address this concern, in this paper I propose a model of mathematics textbook development for examining and analysing issues about a special practice, which I...
Our work is part of a thesis that deals with university teachers’ practices, particularly the relation between research and teaching practices of university professors. We study this issue from the lens of interactions with resources (including textbooks). We choose graph theory as an object of study. Graph theory is a contemporary mathematical field, taught in several academic paths (computer...
The textbooks of mathematics of the Mexican National Commission of Free Textbooks are analysed for secondary education considering the temperature context in order to observe if these materials are in accordance with the pedagogical focus of the mathematics curriculum of the New Educational Reform of the Secretariat of Public Education. This pedagogical model emphasizes that authenticity of...
Semiotics raises an increasing interest in Mathematical
Education since Semiotics provides an array of methods and concepts to understand
the nature of mathematical discourse. Signs are carriers of cultural conventions and
Semiotics helps to understand the way in which individuals think and communicate
with signs in a cultural context. Duval's theory of semiotic representations...
Taking the current mathematics textbooks of primary schools in China as the analysis medium, through the systematic analysis of the content of "pattern finding" in the teaching material, the educational value of "pattern finding" content is grasped. In this study, we took the most widely used elementary school mathematics textbooks in China edited by People's Education Edition and Beijing...
In mathematics teaching and learning, it is important for students to learn not only mathematical contents but also roles and functions of the contents. Functions of a hierarchical classifications are particularly related to mathematical definition and defining. The purpose of this paper is to clarify functions of a hierarchical classification of quadrilaterals in Japanese textbook. From the...
Textbooks, which still are one of the most used tools in the mathematics classroom worldwide have a substantial impact on the production of students’ subjectivities. In this sense, despite research showing that there is a need in eliminating gender bias in mathematics textbooks, they still reproduce the portrayal of what it means to be a girl/woman or a boy/man in our current society....
A challenging task when doing research about the use of mathematics textbooks is the comprehensible description of activity shown by students and their construction of knowledge when using the textbook. As argues Kadunz (2016), the semiotics of Charles S. Peirce seems to be a promising tool for fulfilling this task.
In this paper, we turn our attention to student’s inscriptions (e.g., their...
Teachers are central actors in the interpretation and implementation processes of curricular resources. Holding this central position in the teaching and learning process of mathematics, teacher's interactions with curriculum resources are often studied in different stages and forms of interactions. In this study we focus on means of communication that teachers use to describe the narrative,...
This paper seeks to explore the value given to technology in the Chilean school mathematics textbooks. In recent years, digital media has been incorporated as an important part of the school mathematics textbook. This phenomenon has unfolded forms of producing a particular reality, as well as, conducting—and sometimes delineating and shaping—students’ and teachers’ ways of thinking and acting....
As already known well, for learning geometry, students start from their own experience and concrete shapes; on the other hand, students have to leave from them for developing their geometric thinking (cf. van Hiele, 1958).
When we seen textbooks as (implemented) curriculum, textbook must help students’ this process.
For this background, our research question is: Are Japanese elementary school...
Currently, too few students, including those in underrepresented groups, are engaged in making sense of mathematics. Our curriculum and development research goals are to enhance student productive disciplinary engagement and learning through four design principles: problematizing, authority, accountability, and resources (Engle, 2011). Examining student behaviors, participations, and...
Results from earlier research found that textbook use by teachers of mathematics was largely tacit and not deliberate, making for un-intimate teacher-textbook relationships, and therefore low levels of teacher capacity for pedagogic design. The change from textbooks as primary curricular resources for teaching to daily scripted lesson plans begs a question about the kinds of relationships...
The realization of principles and goals of curriculum reform is affected by many factors, among which degree of teacher recognition and understanding directly influences result of curriculum reform (e.g. New Math). Meanwhile, as representation form of curriculum standard and original base of teacher instruction, textbooks have been the bond to connect curriculum and teacher instruction.
...
In primary schools around the world, mathematics textbooks are the most relevant medium for lesson preparation for the vast majority of teachers. Though the field of textbook research is constantly growing, our knowledge about textbook effects on students learning is still rather constrained. In this contribution, three studies are presented, which address that research gap for the field of...