Thesis (Ed.M.)--Boston University

This study was a qualitative research study dedicated to the deep investigation of a regular and advanced seventh grade mathematics textbook used in Florida and the United Kingdom. A questionnaire was created for a teacher in both locations, along with the researcher, to rate the textbooks according to different characteristics. The two research questions that were answered through the research include: 1. In what ways, if any, is diversity represented in the pages of each seventh grade mathematics textbooks examined? a. In what ways is the diversity of each textbook comparable to the observed diversity of the country in which it is used? 2. How do the seventh grade mathematics textbooks in the United States and the United Kingdom compare with aspects of appearance, readability, illustrations, content, the teacher's guide/resources, and EL accommodations? These research questions were answered through the questionnaire, follow up interview, as well as the observed environment. The conclusion to the research was that although these textbooks are from two different countries, they have qualities each teacher liked and disliked. When I completed the questionnaire I was only able to rate the textbooks according to visual perspectives, while the teachers in each location were able to base their ratings on tangible classroom experiences. To further my research, I would enjoy being able to teach for a year in each location and then complete the questionnaire again to compare the differences between my first time completing it and the second time.

The aim of this study is to analyse how mathematical problem solving (MPS) is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering a) the quantity of tasks that are actually mathematical problems (MPs), b) their location in the chapter, c) their difficulty level, and d) their context. Based on an analysis of 5,722 tasks from the area of calculus, it is concluded that the textbooks themselves contain very few tasks that can be defined as MPs, and that those that are MPs are found at the end of a chapter at the most difficult level, and are presented in a pure mathematical context. Implications are discussed.

Thesis (M. Ed.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 144-151).

Thesis (M.Ed.)--University of Hong Kong, 1996. / Includes bibliographical references (leaves 144-151). Also available in print.

The purpose of this study was to prepare a rating scale to be applied as an objective basis in the selection of business arithmetic textbooks. After the rating scale was developed, it was then applied to a number of recently published texts to demonstrate its use and practical value.

Mathematical connection has received increasing attention and become one major goal in mathematics education. Two types of connections are distinguished: (a) between-concept connection, which cuts across two concepts; and (b) within-concept connection, which links two representations of one concept. For example, from the theoretical probability to experimental probability is a between-concept connection; generate a graph of a circle from its equation is a within-concept connection. Based on the directionality, unidirectional and bidirectional connections are discerned. Bidirectional connection portrays a pair of a typical and a reverse connection. The benefits of connections, especially bidirectional connections, are widely endorsed. However, researchers indicated that students and even teachers usually make unidirectional connections, and underlying reasons may be the curriculum and cognitive aspects. Previous studies have reported differences in learning opportunities for bidirectional connections in U.S. and Chinese textbook problems, but few have explored the high school level. This study addressed this issue by comparing the directionality of mathematical connections and textbook-problem features in popular U.S. (the UCSMP series) and Chinese (the PEP-A series) high school mathematics textbook problems. The results indicated that the between-concept condition and unidirectional connections dominated textbook problems. Mathematical topic, contextual feature, and visual feature were most likely to contribute to different conditions of connections. Overall, problems dealing with quadratic relations from Chinese textbooks presented a vigorous network of more unique and total between-concept connections with balanced typical and reverse directions than the U.S. counterparts. Problems from U.S. textbooks showed a denser network of (a) within-concept connections in two topics and (b) between-concept connections in probability and combinatorics than the Chinese counterparts, but still exhibited an emphasis on specific concepts, representations, and directionality. The study reached a generalized statement that the new-to-prior knowledge direction was largely overlooked in textbook problems. The results have implications for adopting graph theory and Social Network Analysis to visualize and evaluate mathematical connections and informing mathematics teachers and textbook authors to pay attention to the new-to-prior knowledge connection.

Research on the relationship between mathematics education and society has established that societal change can have a direct effect on mathematics education. Qatar experienced a large amount of societal change since its leadership change in 1995. The literature would suggest that changes in mathematics education in Qatar would follow. The purpose of this study was to investigate the changes in mathematics education in Qatar from 1995 until 2018 and to understand the reasons for these changes. This study applied historic research methods in the form of primary source analysis. The primary sources consisted of text analysis and in-depth interviews. The texts included published reports from the Ministry of Education in Qatar and Qatari mathematics textbooks. Seven in-depth, semi-flexible interviews were conducted with educators involved with Qatar’s mathematics education system within the timeframe of interest. The findings revealed that there were significant changes in mathematics education in Qatar during this timeframe. Specifically, changes were made to the mathematics standards and curriculum, the mathematics language of instruction, mathematics assessments, and mathematics teachers’ preparation. New mathematics standards were created, and government-issued textbooks were abandoned for many years to encourage autonomy and creativity. The language of instruction in the mathematics classroom was transitioned from Arabic to English, and then back to Arabic again. New, national mathematics assessments were created to track the new mathematics reform project. They were later abandoned. The reasons for these many changes, and the challenges they created, touched on many different areas of research in mathematics education and sociology. These included policy borrowing, the language of instruction, knowledge societies, rentier societies, and the relationship between mathematics and society. The findings from this study confirmed that the rapid societal changes that occurred in Qatari society during this timeframe were mirrored by rapid changes in mathematics education within the country.

Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for students’ poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with certain types of problems almost never presented (Braithwaite et al., 2017). As a result, students often err when they attempt to solve those rare types of problems (Siegler & Pyke, 2013). Two experiments, a pilot study (n = 40 students in grades 5 through 7) and a larger study (n = 127 students in grades 6 and 7), were conducted. These experiments utilized a pretest-intervention-posttest design to empirically test the benefits of providing either a complement of the typical textbook distribution of problems (hyperbalanced practice) or an equal distribution of problems (balanced practice) compared to the benefits of providing a practice set that followed the typical distribution found in math textbooks. A MANCOVA and follow-up ANCOVAs revealed significant differences between students in the textbook condition and students in the balanced and hyperbalanced conditions.For items involving adding fractions with unequal denominators, students who received typical textbook practice showed greater improvement and made fewer strategy errors than students who received hyperbalanced practice. For items involving multiplying two fractions with equal denominators, the opposite was true. Students who received hyperbalanced practice showed greater improvement and made fewer strategy errors than students who received typical textbook practice on items involving multiplying two fractions with equal denominators. Finally, students who received fully balanced practice showed greater improvement and made fewer strategy errors than students who received typical textbook practice on problems involving multiplying one whole number and one fraction. This last finding was of particular interest since none of the practice conditions included practice with that item type. The results of this study demonstrate that even a brief intervention in which students received extra practice with rare item types could improve performance. It also showed that gains in one type of item often resulted in decrements in others, which must be considered when making recommendations to textbook publishers and educators. In sum, this dissertation seeks to make a scholarly contribution to the field by discussing the role that textbooks play in student performance and by analyzing the benefits of supplementing typical textbook instruction with differently balanced fraction arithmetic practice.

Läroboken styr till stor del vilket innehåll som behandlas i matematikundervisningen. Med detta i åtanke har fem svenska läroboksserier har utsatts för en latent och manifest innehållsanalys av hur de presenterar de aritmetiska räknelagarna och räknereglerna. I studien framkommer både kvantitativ och kvalitativ data. Den kvantitativa datan indikerar att få läroboksserier tar upp associativa och distributiva lagen explicit. Den kvalitativa datan pekar på att räknelagarna ofta beskrivs i andra sammanhang. Flera exempel i läroböckerna gör generaliseringar som riskerar leda till begränsad förståelse för räknelagarna och räknereglerna. / In mathematics education textbooks to a large extent determine what is offered for students to be learnt. With this in mind, in this study, five Swedish textbooks series is reviewed in a latent and manifest content analysis approach where both quantitative and qualitative data is presented. The result of the quantitative data indicate that only a few textbooks series mentions the associative and distributive law in explicit manners. The result of the qualitative data shows that the basic laws of arithmetic is often described in other contexts. Many examples in the textbooks makes generalizations that may lead to limited understanding of the basic laws and rules of arithmetic.