This study is an attempt to determine how a course in general mathematics can satisfy some of the needs of youth. The purpose of this study is to find out how the course in general mathematics can be made to contribute effectively to pupil growth, and how well the present course is contributing to pupil growth.

This study concentrated on word problems in Grades Kindergarten-3 and the application of the Standards for Mathematical Practice and the Content Standards. The study also included an analysis of focus, coherence, and rigor in the materials. The textbooks used were among the first editions to be published after the acceptance of the Common Core State Standards in more than 40 states. The study analyzed the presence of the Common Core Standards in each series and how the three textbook series compared to each other in their word problem solving. The correlation of materials in the three textbook series relied on publishers’ descriptions in the Lesson Openers where the usages of the Standards for Mathematical Practice and the Content Standards and the principles of focus, coherence, and rigor are listed. The publishers’ descriptions were analyzed and compared to the individual evaluation criteria. Using an evaluation criterion, the study examined how Standards for Mathematical Practice were implemented in the textbooks. With the exception of a few grades in two textbook series, the texts displayed low percentages in their adherence to the Standards. The textbook series were similar in their development of word problems labeled with Standards for Mathematical Practice and word problems not labeled with the Standards. In this comparison, the only difference between the two types of word problems was in the verbiage. The Content Standards were used to determine the textbook series alignment with the Standards. The three textbook series showed low implementation of word problem Content Standards when compared to the total number of Standards. In two series, only one Content Standard was listed multiple times rather than a combination of comparable Standards. Relying on the publishers’ descriptions, the study showed how publishers implemented focus, coherence, and rigor in their materials. Of the three publishers, one publisher did not list coherence and rigor in its materials. The other two publishers adhered to focus and coherence in most or all of their materials. All of the publishers fell short in the application of rigor in their textbook series.

I conducted a content analysis to examine the treatment of the surface area and volume concepts within four published middle-grades mathematics textbook series. In particular, I examined the treatment of the surface area and volume concepts in terms of the location of surface area and volume lessons in the textbook and the number of pages and lessons devoted to these concepts. I also investigated the sequence of the instructional blocks of surface area and volume lessons. In addition, I evaluated the tasks included in these lessons in regards to the performance expectations of students, the types of visual representations of 3D objects, and the level of mathematical complexity. At last, I examined the extent to which the content of surface area and volume lessons address the Common Core Content Standards (CCCS) for 6-8 geometry that are aligned with these topics. I used content analysis to analyze relevant content in a total of twelve middle-grades student edition mathematics textbooks from two popular textbook series, Go Math!(GM) and Glencoe Math (GMC); and two alternative textbook series, Connected Mathematics 3 (CM) and University of Chicago School Project (UCSMP). First, I used Flanders’ (1994) counting method to examine the physical characteristics of textbooks, such as the location of the surface area and volume lessons in the textbook, the number of pages and lessons devoted to these concepts. Second, I analyzed the sequence of the instructional blocks of surface area and volume lessons by using content analysis. Third, I adapted the Trends in International Mathematics and Science Study [TIMSS] (2002) Performance Expectations for Mathematics Framework to examine the performance expectations of students within tasks. Fourth, I developed and used the Visual Representations of 3D Objects Framework to examine the types of visual representations of 3D objects included in the tasks. Fifth, I employed the Mathematics Framework for the 2007 National Assessment of Educational Progress (NAEP) to examine the level of mathematical complexity of tasks. Finally, I created the CCCS for 6-8 Geometry Components guideline to examine to what extend the surface area and volume lessons address the geometry content standards. Results indicated that the majority of textbooks place the concepts of surface area and volume towards the end of the textbook. Small percentages of instructional pages and lessons are devoted to these concepts in all textbooks. Findings also revealed great similarities among the instructional blocks of lessons within three textbook series (GM, GMC, and UCSMP). The majority of tasks within all textbook series contain miniscule amounts of important performance expectations such as justifying and proving and visual representations of 3D objects such as nets and pictures. A significant amount of tasks are of moderate complexity across all textbook series. Analysis also showed that the CM textbook series offers the greatest opportunity for students to generate visual representations of 3D objects and contains the largest amount of high complexity tasks. At last, nearly all lessons address the appropriate geometry content standard among all textbook series. Limitations of the study, implications for mathematics education, as well as recommendations for future research are also presented.

Abstract This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum project textbook series, Connected Mathematics 2; and one non-NSF funded curriculum project, the University of Chicago School Mathematics Project (UCSMP). A framework was developed to distinguish the characteristics in the treatment of geometric transformations and to determine the potential opportunity to learn transformation concepts as measured by textbook physical characteristics, lesson narratives, and analysis of student exercises with level of cognitive demand. Results indicated no consistency found in order, frequency, or location of transformation topics within textbooks by publisher or grade level. The structure of transformation lessons in three series (Prentice Hall, Glencoe, and UCSMP) was similar, with transformation lesson content at a simplified level and student low level of cognitive demand in transformation tasks. The types of exercises found predominately focused on students applying content studied in the narrative of lessons. The typical problems and issues experienced by students when working with transformations, as identified in the literature, received little support or attention in the lessons. The types of tasks that seem to embody the ideals in the process standards, such as working a problem backwards, were found on few occurrences across all textbooks examined. The level of cognitive demand required for student exercises predominately occurred in the Lower-Level, and Lower-Middle categories. Research indicates approximately the last fourth of textbook pages are not likely to be studied during a school year; hence topics located in the final fourth of textbook pages might not provide students the opportunity to experience geometric transformations in that year. This was found to be the case in some of the textbooks examined, therefore students might not have the opportunity to study geometric transformations during some middle grades, as was the case for the Glencoe (6, 7), and the UCSMP (6) textbooks, or possibly during their entire middle grades career as was found with the Prentice Hall (6, 7, Prealgebra) textbook series.

published_or_final_version / Education / Master / Master of Education

Syftet med denna studie var att kartlägga 13 gymnasieelevers uppfattningar om problemlösningsuppgifter i matematik. I studien användes individuella intervjuer som datainsamlingsmetod. Frågorna rörde elevernas syn på matematiska problem i stort samt deras syn på om uppgifterna i deras läromedel var problem eller ej. Detta ledde till användandet av två analysmetoder, den ena för att studera vilka uppgifter i läromedlen som var problemlösning, den andra för att kartlägga och kategorisera elevernas uppfattningar. Resultaten visar att eleverna hade vissa uppfattningar som överensstämmer med hur forskningslitteraturen definierar problemlösningsuppgifter, men det framkom även uppfattningar som inte tas upp av litteraturen. Studien visar därmed på vilka som kan vara elevernas missuppfattningar kring problemlösningsuppgifter. Detta kan vara till nytta för både lärare, elever och forskare, då denna studie har kartlagt eleverna missuppfattningar kring problemlösnings uppgifter. Där läraren kan rätta elevernas missuppfattningar kring problemlösningsuppgifter, detta innebär att eleverna får en mer korrekt uppfattning kring problemlösningsuppgifter som är mer nära forskning.

Covariational reasoning is a cognitive activity that attends to two or more varying quantities and how their changes are related to each other. Previous studies indicate that covariational reasoning seems to have levels. Content analysis was used to examine the pedagogy and development of covariational reasoning levels in the sections that conceptually introduce derivatives in four calculus textbooks. One widely used calculus textbook was selected for the study in each of the four categories: U.S. college, U.S. high school, China college, and China high school. Two qualified investigators and I conducted the study. We used a framework of five developmental levels for covariational reasoning. The conceptual analysis of four calculus textbooks found that the U.S. college and the U.S. high school textbooks emphasize the average and instantaneous rate of change. However, both lack development of the direction and magnitude of change. On the other hand, this study's Chinese high school calculus textbook has a greater degree of development in the direction and magnitude of change while having a deficit in the average rate of change. This study's Chinese college calculus textbook does not have any meaningful development regarding covariational reasoning pedagogy. The relational analysis of the concepts previously identified in the conceptual analysis phase revealed that this study's U.S. college calculus textbooks provide abundant examples and exercises to transition between the average and instantaneous rate of change. On the other hand, all other calculus textbooks in this study lack any significant transition among passages that stimulate covariational reasoning. The textbook analysis in this study provides insights into the current focus of calculus textbooks in both the U.S. and China. In addition, the study has implications for learning and teaching calculus at both high school and college, as well as future editions of calculus textbooks. Finally, limitations and recommendations are discussed.

No description available.

The purpose of this study was to identify and compare specific writing assignments provided in the four basal mathematics textbook series, grades six through eight, accepted by the state of Texas in 1990. The student and teachers' editions by each publisher were analyzed (1) for the total number and types of writing assignments provided, (2) to compare how the writing assignments compared with the four purposes of writing mandated in the English Language Arts Framework, Kindergarten through Grade 12 for the state of Texas, (3) to compare how the writing assignments compared with the recommendations for communication opportunities stated in the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards for School Mathematics for grades five through eight, and (4) to compare the number and types of writing assignments among the four publishers. The total number of writing assignments varied among publishers ranging from 151 to 316 in the student editions and from 147 to 523 in the teacher's editions. The findings of this study indicate that from 80 to 98 percent of the writing assignments in the student editions and from 72 to 96 percent of the writing assignments in the teacher's editions corresponded to the Informative purpose of writing. Very few writing assignments were provided corresponding to the Literary, Expressive, and Persuasive purposes of writing. The writing assignments corresponding to the NCTM recommendations varied among publishers. Writing assignments dealing with modeling mathematical situations ranged from 14 to 66 percent in the student editions and from 24 to 39 percent in the teacher's editions. Writing assignments focusing on understanding and definitions ranged 15 to 61 percent in the student editions and from 31 to 53 percent in the teacher's editions. Writing assignments focusing on interpretation and application ranged from 5 to 29 percent in the student editions and from 10 to 15 percent in the teacher's editions.

The aim of this thesis is to identify differences among Mathematics textbooks and to find out how they work in real education process. This research will provide information whether such textbooks are actually used by Maths teachers, and if so, then in what manner and how effectively. This will be viewed from the perspective of a teacher-beginner who searches for the most appropriate textbook for Mathematics lessons. Another goal is to introduce the offer of various Maths textbooks for the 2nd stage of basic schools. Also, there is a research performed that could compare these books, especially books published by Prometheus, Fraus and H-mat. Results of the research will be then used for lesson plans of a beginning teacher.