Mathematics Textbook Series Research Articles

A Content Analysis of the Algebra Strand of Six Commercially Available U.S. High School Textbook Series

Algebra as a school subject is ill defined. Students experience algebra quite differently depending on the perspective of algebra taken by authors of the textbooks from which they learn. Through a content analysis of problems (n = 63,174) in the narrative and homework sections of six high school mathematics textbook series published in the U.S., we acquired systematic and reliable information about the algebra strand (i.e., symbolic algebra and functions) of each textbook series. We introduce plots to show the density, distribution, and sequencing of content, and present analyses of data for cognitive behavior, real-world context, technology, and manipulatives. Feedback on this study from an author of each textbook series is shared, and findings are discussed in terms of students’ opportunities to learn.

Revitalizing Sustainability in Mathematics Education: The Case of the New Norwegian Curriculum

This paper aims to discuss the revitalization of education for sustainable development (ESD) in mathematics education, particularly in relation to mathematics curricula for grades 1–10, using the example of the new Norwegian curriculum, LK20, which came into effect at the beginning of the 2020 school year. Several studies in the past two decades have identified disengagement of sustainability learning (SL) within mathematics education and called for a change in the philosophy of mathematics education to integrate sustainability into the teaching and learning of mathematics. Using the qualitative content analysis method, we examined three types of documents: the core curriculum, the mathematics curriculum, and one Norwegian mathematics textbook series called Matemagisk. We find that sustainable development (SD) is one of the interdisciplinary issues addressed in LK20. Even though the mathematics curriculum does not explicitly incorporate terms such as ‘sustainability’ or ‘sustainable development’, indicating that mathematics and sustainability are unconnected, its six core elements—exploration and problem-solving, modeling and applications, reasoning and argumentation, representation and communication, abstraction and generalization, and mathematical fields of knowledge—provide opportunities for integrating sustainability learning (SL). On the other hand, looking at one of the mathematics textbook series, Matemagisk, for grades 4, 7, and 10, it appears that tasks that use sustainability contexts were included implicitly or explicitly, indicating another opportunity to facilitate sustainable learning. By including sustainability contexts in tasks and mathematical activities, it is possible to boost the process of embedding ESD in mathematics education without compromising content.

Some Conceptual Metaphors for Rational Numbers as Fractions in Swedish Mathematics Textbooks for Elementary Education

ABSTRACT This study examines the presence of three conceptual metaphors for fractions – The measuring stick metaphor, Arithmetic is motion along a path, and Arithmetic is object construction – in four common and popular Swedish mathematics textbook series for years 1–3. I analyse the introduction of fractions and the kinds of tasks students are given in these books. The results show an abundance of labelling exercises related to Arithmetic is object construction, with representations of geometric shapes, in three of the book series. One book series reversely introduces fractions with The measuring stick metaphor and Arithmetic is motion along a path, with a focus on number line representations. The consequences of these variations in fraction introduction and treatment are discussed in relation to previous research and to process-object theories.

What do we mean by mean?

In order to be successful with a certain concept at school, it is often sufficient to master some types of tasks, without having to be aware of the different perspectives that a concept can be viewed from. It is, however, definitely not enough when the goal is to understand mathematics and become flexible and creative in solving mathematical tasks. Not only school students, but also prospective teachers should be encouraged to reflect on what particular concepts actually mean and how they can be thought of.
 In this article we focus our attention on the concept of mean. In the introduction we outline the gaps that our paper partially fills. Then we provide a brief review of how the Polish core curriculum and two very popular mathematics textbook series (one each for primary and secondary school) treat the topic of means. Next, we present results from a study conducted on a group of first-year students of mathematics and a group of teachers undertaking postgraduate studies qualifying for teaching mathematics as a second subject. We show the results obtained in two tasks concerning the arithmetic and geometric mean. The paper ends with several teaching suggestions and recommendations for mathematics teachers’ educators.

The Learning Trajectories of Similarity in Mathematics Curriculum: An Epistemological Analysis of Hong Kong Secondary Mathematics Textbooks in the Past Half Century

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.

Opportunities to Learn Three-Dimensional Shapes in Primary Mathematics: The Case of Content Analysis of Primary Mathematics Textbooks in Hong Kong

Textbooks play an important part in teaching and learning mathematics. However, textbook research on spatial ability has so far received little attention. In this study, we investigated whether school mathematics textbooks provide enough opportunities for primary students to learn three-dimensional shapes and help them acquire spatial ability. Three mathematics textbook series used in Hong Kong were analysed through content analysis. Findings showed each series of textbooks contained five domains for introducing solid figures, which included real-life examples, understanding concepts, measurement, finding laws, and developing spatial ability. The development of spatial abilities was mainly shown in the production of three-dimensional graphics. What students experienced in the learning of 3-D shapes was relatively narrow. Geometric graphics were mainly limited to the conventional shapes at the early stage. Activities to explore three-dimensional graphics were insufficient. It was suggested that combining the surrounding world of children with geometry in the classroom was not just a criterion for textbooks but also the focus of classroom teaching. The flexibility of teachers’ adoptions of textbooks is also worthy of further investigation.

Kako su matematičari kao deo istorije matematike predstavljeni u savremenim kineskim udžbenicima matematike?

As part of our efforts to understand how history and culture are manifested in mathematics textbooks, we investigated particularly in this study how mathematicians are represented across three different series of contemporary school mathematics textbooks used in primary and junior secondary schools in China. The study intends to document the ways of representation of mathematicians in the three series of textbooks, compare the similarities and differences, and explore the reasons and implications of the findings concerning mathematics textbook research and development. Our findings show that each series of mathematics textbooks introduced both Chinese and non-Chinese mathematicians in a commendable way, though most of the mathematicians introduced were ancient mathematicians, and all the three series introduced mathematicians each year from Grade 2 to Grade 9. There is also a high level of consistency in the distribution of the introduction of mathematicians in the three series in terms of mathematics contents and the structures of the chapters. In comparison, we found the mathematics textbook series by the PEP presented a more balanced distribution of the introductions of mathematicians in terms of grade levels, ethnic origins and the history timeline. The explanations and implications of the findings are discussed at the end of the paper.

THE CONTEXTUALIZED SITUATIONS CONSTRUCTED FOR THE USE OF STATISTICS BY SCHOOL MATHEMATICS TEXTBOOKS

The consideration of context is crucial in the discipline of statistics. In this paper, I present a Foucauldian discourse analysis (FDA) of two popular high school mathematics textbook series in the United States investigating what contextual situations they construct for the (re)use of statistics. As FDA is a novel approach in statistics education,an extended discussion is provided to help show a rationale for its use and to provide a foundation for others. An important finding is that the contextualized situations presented in both textbook series are predominantly fictional, neutral, and providelimited raw data. The findings have implications for the teaching and learning of statistics in view ofrecent calls for more focus on data and statistical literacy in schools.
 First published November 2019 at Statistics Eduation Research Journal Archives

한국과 일본의 초등학교 수학 교과서에 제시된 분수 곱셈에 관한 비교 분석: 양적 추론을 중심으로

This study explored fraction multiplication of Korean and Japanese elementary mathematics textbook series based on a content-specific analytic framework that put an emphasis on quantities with referent units along with the meanings of fraction multiplication and visual representations. The results of this study illuminated noticeable differences in the textbooks, even though they were similar in addressing the main topics. Whereas multiple meanings of fraction multiplication were presented in the Korean textbook, the meaning of scaling was mainly emphasized in the Japanese textbooks. Whereas quantities with referent units were explicit in the Japanese textbook, those were implicit in the Korean counterpart. Whereas a visual representation was systematically employed in the Korean textbook mainly to demonstrate the results of fraction multiplication, various representations were used in the Japanese textbook to explain the algorithms for fraction multiplication. Based on these differences emergent through the content-specific framework, this study provides mathematics education researchers, curriculum developers, and teachers with specific implications for teaching and learning of fraction multiplication.

Investigating a Singapore-Based Mathematics Textbook and Teaching Approach in Classrooms in England

The high mathematics performance of pupils in Singapore on international assessments has prompted educational initiatives in other countries – such as the UK and the USA – to adopt Singapore-based approaches in an attempt to raise mathematics achievement. Empirical evidence to support the transferability of such approaches beyond the Singaporean context, however, is limited. This article reports findings from a mixed methods Cluster Randomized Controlled Trial (mmCRCT) evaluating the use of a primary mathematics textbook series and teaching approach in England based on a textbook and teaching approach from Singapore. Main features of the intervention included textbook use, mixed-ability groups, use of manipulatives, and emphasis on mastery (i.e. ensuring all pupils grasp core concepts before proceeding to new topics). A delayed treatment experimental design was used within the mmCRCT, with 12 schools randomly allocated into two groups. The experimental group used the textbooks and teaching approach from September 2015. The delayed treatment control group proceeded with “business as usual” until January 2016, then started using the textbooks and teaching approach. Data were collected (in the first, second and third terms of one school year) on pupils’ mathematics knowledge and skills, pupils’ attitudes towards mathematics, classroom practice (based on structured observation schedules and qualitative field notes), teacher perspectives (from semi-structured interviews), and intervention-specific professional development (in July 2015 for the experimental group, December 2015 for the delayed treatment control group, observed by researchers and followed by focus-group interviews). Results showed a small but significant positive effect by Term 3 of using the mastery-oriented materials and approach from September on pupils’ subsequent mathematics knowledge and skills, but no persistent difference between groups across terms on their attitudes. Differences in classroom practice between the two groups were observed in the first term but insignificant by the third term. Qualitative findings elaborate on and illustrate these first-term differences, teachers’ perspectives on their practice, variations in textbook use and teaching approach implementation, and considerations of fidelity to intervention. Implications are drawn for policy and practice in mathematics teaching and for research using mixed methods experimental designs to evaluate a combination of processes, perspectives and outcomes.

History of Mathematics in the Turkish Middle School Mathematics Curriculum and Textbooks

The purpose of this study was to analyze how the history of mathematics incorporated into Turkish middle school mathematics curriculum (5 th -8 th grades) and textbooks. The data were collected through document analysis from the Turkish middle school mathematics curriculum guide (5 th -8 th grades) and six Turkish middle school mathematics textbook series approved by the National Board of Education. According to the results gathered from the math curriculum, only one reference of the history of mathematics was found in the sixth-grade learning objectives and a few suggestions acknowledging the use of the history of mathematics in the learning and teaching process. No trace of the history of mathematics found in the content and assessment aspects of the curriculum. Further, the total number of the instances of the history of mathematics found in the six Turkish middle school mathematics textbooks for 5 th -8 th grade is only twenty-seven. Most of the references found in the math textbooks were placed in the introduction part of the topic. Based on the findings, it is obvious that the history of mathematics was used like a rarely-found appetizer both in the curriculum and the textbooks.

Study of fractions in elementary mathematics textbooks from Finland and Taiwan

This study examines the different ways in which fractions are dealt with in two elementary mathematics textbook series: Kang Hsuan (KH) in Taiwan and Laskutaito in Finland. The results showed that the total number of fraction questions in Laskutaito is higher than that in KH and that Laskutaito highlights the basic definition of fractions to help children develop higher levels of reasoning. Fraction questions in Laskutaito were presented with a number of pictorial representations to clarify the concepts. Laskutaito includes more symbolic representation of questions. Moreover, the questions posed in the Laskutaito reflect real-life situations, whereas the questions posed in KH do not connect with real life. The implications of this study are discussed and suggestions for future studies are made in this paper.

A Comparison of Geometry Problems in Middle-Grade Mathematics Textbooks from Taiwan, Singapore, Finland, and the United States

Background:This study analyzed geometry problems in four middle-grade mathematics textbook series from Taiwan, Singapore, Finland, and the United States, while exploring the expectations for students’ learning experiences with these problems.Material and methods:An analytical framework developed for mathematics textbook problem analysis had three dimensions: representation forms, contextual features, and response types.Results:The results showed that Taiwanese and Singaporean textbooks contained more problems in combined form, whereas Finnish and the American textbooks contained more problems in verbal and visual forms. The problem distribution across various representation forms was more balanced in the Finnish and Singaporean textbooks than in the Taiwanese and American textbooks. Most problems were non-application and close-ended problems compared to other application and open-ended problems. The Taiwanese textbooks contained the lowest proportion of real-world problems, whereas the American textbooks contained the highest proportion of open-ended problems.Conclusions:Implications of this study’s findings for textbook developers and future research directions are discussed.

An Analysis of Problem-Posing Tasks in Chinese and US Elementary Mathematics Textbooks

This paper reports on 2 studies that examine how mathematical problem posing is integrated in Chinese and US elementary mathematics textbooks. Study 1 involved a historical analysis of the problem-posing (PP) tasks in 3 editions of the most widely used elementary mathematics textbook series published by People’s Education Press in China over 3 decades. Study 2 compared the PP tasks in Chinese and US elementary mathematics textbooks. This allows for the examination of PP tasks from an international comparative perspective, which provides one point of view about the kinds of learning opportunities that are available to students in China and the USA. We found evidence that the inclusion of PP tasks in the Chinese textbook series reflected, to some degree, changes in the curricular frameworks in China. However, the distribution of PP tasks across grade levels and content areas, as well as the variety of types of PP tasks included, suggest a need for greater intentionality in the design and placement of PP tasks in both the Chinese and US textbook series. Findings from the 2 studies reported in this paper not only contribute to our understanding about the inclusion of PP tasks in curriculum both historically and internationally, but also suggest a great need to systematically integrate PP activities into curriculum and instruction. The fact that both Chinese and US curriculum standards have heavily emphasized PP in school mathematics, despite there being only a small proportion of PP activities in both Chinese and US elementary mathematics curricula, suggests the existence of challenges that are delaying the implementation of reform ideas such as problem posing in school mathematics.

Research Findings' Impact on the Representation of Proportional Reasoning in Swedish Mathematics Textbooks

This article investigates the impact of research findings on the representation of proportional reasoning in two commonly used Swedish mathematics textbook series for grades 7-9. A research-based framework that identifies five learning goals for understanding of proportional reasoning was used to analyse the textbooks. The results brought to surface a gap between research findings of important issues to address and the actual design of mathematics textbooks. Both textbook series make use of an effective range of representations. Besides that, the analysis shows low impact from research findings concerning the importance of given opportunities to compare and contrast additive and multiplicative situations, identify multiplicative structures and proportional thinking, make use of meaningful symbolic representations, and connect and relate fraction knowledge. The main conclusion is that there are possibilities for improvement in textbook design in relation to understanding proportional reasoning.

Recent Trends in Japanese Mathematics Textbooks for Elementary Grades: Supporting Teachers to Teach Mathematics through Problem Solving

Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over the years. As a result, almost every chapter in Japanese mathematics textbooks for elementary grades begins with problem solving as a way to introduce students to new concepts and to introduce new procedures. But a large wave of teacher retirement in recent years has left newly hired teachers without the collegial support they need to develop the expertise to teach through problem solving. In order to overcome this challenge, the latest edition of a major mathematics textbook series in Japan includes more resources to help teachers teach through problem solving and to help students learn through problem solving. The book contains more alternative approaches to a problem, provides diagrams meant to help students solve problems independently, and includes pages that teach students how to take notes effectively. By comparing the latest two editions of this textbook series, the author will highlight how the text has increased its support of problem solving, and will relate the changes to recent trends of Japanese mathematics textbook designs.

초등학교 수학 교과서에 제시된 패턴 지도방안에 대한 분석

패턴을 다루는 여러 가지 활동은 초등학생들의 대수적 사고를 신장하는데 매우 효과적이다. 이에 본 연구는 초기 대수(early algebra)적 관점에서 패턴을 지도하는 세 가지 주요 활동인 패턴의 구조를 분석하는 활동, 패턴에서 두 변수 사이의 관계를 탐색하는 활동, 패턴의 일반화된 규칙을 추론하고 표현하는 활동을 중심으로 현행 초등학교 수학 교과서에 제시된 패턴 지도방안을 분석하였다. 분석결과 패턴의 구조를 분석하는 활동은 교과서 상에서 명시적으로 고려되지 않았다. 반면 패턴에서 두 변수 사이의 관계를 탐색하는 활동은 주로 대응표를 활용하여 전 학년에서 다루어졌고, 패턴의 일반화된 규칙을 추론하고 표현하는 활동은 저학년에서는 패턴의 규칙을 비형식적으로 표현하는 활동을 통하여, 고학년에서는 패턴의 규칙을 수식이나 기호를 사용하여 형식적으로 표현하는 활동을 통하여 다루어졌다. 한편 다른 수학 내용과의 연계성 측면에서 패턴의 지도방안을 분석한 결과, 현행 초등학교 수학 교과서에서는 패턴 활동이 규칙성 영역에 해당하는 일부 단원에서만 한정적으로 다루어지고 있었다. 이와 같은 연구결과를 토대로 본 연구는 초등학생들의 대수적 사고를 신장하기 위한 패턴 지도방안과 관련하여 구체적인 시사점을 제공하고자 한다. Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.

Teachers’ views of mathematics textbook series in Flanders: Does it (not) matter which mathematics textbook series schools choose?

The debate on the differential effects of mathematics textbook series is a recurrent topic in the research literature. Research results remain inconclusive, pointing to a lack of evidence to decide on the relevance of the selection by schools of a mathematics textbook series. Studies also point to difficulties in comparing textbooks. Recently, in order to examine the influence of mathematics textbook series on student learning, the need to take into account mediating variables between the mathematics textbook series and the enacted curriculum is stressed. This paper focuses on one such mediating variable: teachers’ views of mathematics textbook series. Views of a mathematics textbook series of 814 teachers and mathematics performance results of 1579 students were analysed. The results point out that, with regard to teachers’ views of mathematics textbook series, the question ‘Does it really matter which mathematics textbook series schools choose’ has to be answered positively. Implications of the findings are discussed.

A Cross-Cultural Lesson Comparison on Teaching the Connection Between Multiplication and Division

This study compared one lesson across four U.S. “traditional” textbook series, two U.S. reform-based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of the lesson across three dimensions (i.e., problem schemata, response requirement, and algebra readiness). In particular, the Chinese lesson's penetrating analysis or explanation of the topic is reflected in its deliberately constructed examples and wide range of problems (pertaining to problem types and difficulty levels) present in the teaching and practice sections of the lesson. None of analyzed U.S. lessons are comparable with the Chinese lesson with respect to the breadth and depth in teaching the topic. A deliberate emphasis, both arithmetically and algebraically, on problem schema acquisition as found in the Chinese lesson represents a promotion of symbolic or higher order of conceptual understanding. The findings are discussed within the context of teaching big ideas through problem schemata acquisition and the importance of symbolic level of conceptual understanding.

Reasoning-and-Proving in School Mathematics Textbooks

Despite widespread agreement that the activity of reasoning-and-proving should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that teachers make about what tasks to implement in their classrooms and when and how to implement them are mediated by the textbooks they use. Yet, little is known about how reasoning-and-proving is promoted in school mathematics textbooks. In this article, I present an analytic/methodological approach for the examination of the opportunities designed in mathematics textbooks for students to engage in reasoning-and-proving. In addition, I exemplify the utility of the approach in an examination of a strategically selected American mathematics textbook series. I use the findings from this examination as a context to discuss issues of textbook design in the domain of reasoning-and-proving that pertain to any textbook series.