Edited by: Douglas F. Kauffman, Medical University of the Americas – Nevis, United States
Reviewed by: Radman Mohamed Saeed, Sana’a University, Yemen; Ibrahim Hassan Assaf, Tanta University, Egypt
This article was submitted to Educational Psychology, a section of the journal Frontiers in Psychology
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
This study analyzes the content of 12th-grade mathematics textbooks and workbooks, based on their inclusion of mathematical discourse components. The mathematics textbooks and workbooks were used in a Saudi Arabian school, where students are transitioning from secondary education to university. The results revealed that Saudi Arabian school textbooks and workbooks did not appropriately include discourse components or discourse skills to help facilitate mathematical learning among students. Furthermore, these textbooks did not exceed level two of the four levels of inclusion. As a result, the inclusion was insufficient in helping students meaningfully understand mathematical concepts, become active students, and develop successful community leadership. This implies that mathematics textbooks and workbooks should be revised to include mathematical discourse so that this inclusion is more student directed than teacher directed.
Mathematics is a vital discipline in facilitating the mastery of science and technology. However, research has indicated that mathematics is a difficult field of study (
The
Previous research on mathematical discourse gained its importance from its ability of improving students’ conceptual understanding of mathematics concepts and mathematical reasoning (
Mathematical discourse inclusion in mathematics textbooks is worth studying, because it is highly important in support of mathematics learning, as well as the advancement of science and technology.
Therefore, discourse should be given a major role in the objectives of teaching and learning mathematics in order to ease the difficulty of learning and teaching mathematics. As such, discourse should have been stressed as an important skill in school for students to develop (
Multiple studies (
Most current mathematics textbooks do not ensure the inclusion of student-cantered mathematical discourse components; rather, they stress on the inclusion of procedural components (
Several studies have focused on textbooks analysis in the areas of science and mathematics. For example,
Several studies have dealt with the analysis of textbooks regarding the inclusion of some constructs and components that are associated with discourse. Many studies (
This study explores textbooks’ inclusion of discourse, which aids students’ acquisition of thinking components, habits of persistence, and curiosity. Furthermore, it equips them with self-esteem by instilling confidence in their abilities to succeed in mathematics. Discourse employs scientific dialogue in the development of students’ scientific knowledge (
The inclusion of mathematical discourse skills in the textbooks, such as the logical use of words, symbols, diagrams, physical models, and technology, may help students in communicating their ideas and in the development of their meaningful learning, as well as their thinking skill. These procedures may help teachers to structure lessons in such a way to encourage student interaction and assess their students’ mathematical understanding and help students’ present mathematical concepts more precisely, which may develop their thinking skills. Mathematical discourse would also direct students’ conversation during mathematical discussion to ensure the occurrence of meaningful mathematics learning (
This study aims to investigate the extent, as well as level, of inclusion of mathematical discourse components in 12th-grade mathematics textbooks and workbooks in Saudi Arabia for the academic year 2019–2020. Through this, the study attempts to find answers to the following questions and subquestions:
Primary Question
To what extent are mathematical discourse components represented in the 12th-grade mathematics textbooks and workbooks in Saudi Arabia for the academic year 2019–2020?
Subquestions
What levels of the included mathematical discourse components are represented in the 12th-grade mathematics textbooks and workbooks in Saudi Arabia?
Which types of activities could contribute most to the promotion of mathematical discourse components in the 12th-grade mathematics textbooks and workbooks in Saudi Arabia?
Content analysis was employed as a research methodology. In this study, data sources were described, and an analytical framework was then used to explore the representation of mathematical discourse components in the Saudi Arabian 12th-grade mathematics textbooks and workbooks.
The Mathematical Discourse Analytic Rubric was developed to analyze the targeted mathematics contents. The rubric consisted of five discourse components, as well as the variations of their four levels, depending on the overall number of students or the teacher’s involvement in their learning (
Hufford–Ackles mathematical discourse rubric (
Level | Engagement | Questioning | Explaining mathematical thinking | Mathematical representations | Building student responsibility within the community |
1 | Content stressing that the teacher dominates the conversation. | Content stressing that the teacher is the only questioner and that questions serve to keep students listening. Content requires the students to give short answers and to respond to the teacher only. | Content questions are focusing on correctness. Students provide short, answer-focused responses. Teacher may give answers as well. | Representations are missing, or the content includes the representations for the students. | Contents encourage students to keep ideas to themselves or to merely provide answers when asked. |
2 | Content asks the teacher to encourage the sharing of math ideas and directs speakers to talk to the class, not to the teacher only. | Content questions begin to focus on student thinking and less on answers. Only the teacher asks questions. | Content probes student thinking. One or two strategies may be elicited. Content may fill in an explanation and encourages students to provide brief descriptions of their thinking in response to teacher probing. | Content asks students to create math drawings to depict their mathematical thinking. | Content encourages the students to believe that their ideas are accepted by the classroom community. They begin to listen to one another supportively and are now able to restate in their own words what another student has said. |
3 | Content instructs teachers to facilitate the conversation between students and encourages students to ask questions among one another. | Content asks probing questions and facilitates student-to-student conversation. Students ask each other questions after prompting from the teacher. | Content probes teachers to more deeply learn about student thinking and elicit multiple strategies. Content encourages students to respond to probing, to share their views, and to defend their answers. | Content asks students to label their math drawings so that others are able to follow their mathematical thinking. | Content encourages students to believe that they are math learners and that their, as well as their classmates’, ideas are important. They listen actively so that they can contribute significantly to the discussion. |
4 | Content encourages students to carry the conversation by themselves. They should only ask teachers to guide students from the periphery of the conversation and to clarify the ideas of others. | Content encourages students to initiate student-to-student conversation. It encourages students to ask questions and to listen to the responses of other students. Many questions begin with “why” and call for justification. It instructs the teacher to ask questions that guide the discourse. | The teacher follows student explanations closely. The teacher asks students to contrast strategies. Students defend and justify their answers with little prompting from the teacher. | Content asks students to follow and help shape the descriptions of others’ mathematical thinking through math drawings. They may suggest edits in others’ math drawings. | Content encourages students to believe that they are math leaders and can help shape the thinking of others. They help shape others’ math thinking in supportive and collegial ways and accept the same support from others. |
The sample for the content analysis included 12th-grade mathematics textbooks and workbooks (Arabic Edition) adapted from the McGraw-Hill series. These were recently applied in Saudi Arabia in light of the level and the extent of their inclusion of mathematical discourse components. Mathematics documents analyzed in this study included two textbooks and two workbooks for the first and the second terms in the academic year 2019–2020. The mathematics textbooks were 404 pages long (214 for the first term and 190 for the second term) and have eight main chapters altogether. The workbooks were 48 pages long (25 for the first term and 23 for the second term) with eight main sections corresponding to the textbooks’ chapters. Each chapter contained three to seven lessons. There were 42 lessons across the eight chapters. We intentionally selected and analyzed four lessons from each of the textbooks and associated parts of the workbooks—one lesson from each chapter in order to represent a different variety of lessons. Where some lessons included discovery activities such as an introduction to each lesson, others include thinking skills activities or expanded activities as enrichments of the lessons. Many of the activities incorporated a set of problems with the same characteristics. Therefore, we dealt with each of them as one activity. Some activities that included several problems with different characteristics were grouped into sets of activities that have similar characteristics. Many activities have only one problem, and these were dealt with as a single entity. We analyzed the entire selected lesson in each chapter and the related set of activities or problems in the workbook. Each lesson includes an introduction, the concept being studied, examples, and problems.
The main target of the analysis was the conceptual framework used to guide mathematical discourse components. Studies presented a variety of conceptual frameworks for the analysis of printed material from a particular perspective (
In this study, the mathematics textbooks and associated workbooks were analyzed using the following mathematical discourse components identified by
Component 1: engagement
Component 2: questioning
Component 3: mathematical thinking
Component 4: mathematical representations
Component 5: building student responsibility within the community.
There are four levels assigned for each component (ranging from 4, “more student directed,” to 1, “more teacher directed”). The rubric includes five main components and 20 subcomponents, each of which represents a math discourse component and levels to be included in the mathematics curriculum (
The rubric was redesigned to fit the analysis of mathematics learning content for the 12th grade (third year of secondary school) in Saudi Arabia. The English version of the rubric was translated and then back-translated to ensure that the evaluators clearly understand the content of the instrument.
The following steps were followed in the content analysis of the mathematics learning sources used in this study. First, we identified the analysis categories, which are the discourse components and subcomponents specified in the instruments’ rubric. Thereafter, the mathematics lessons in the textbooks and the related sections in the workbooks were specified as the analysis units. All parts of the lessons were coded by marking the appropriate column cell in the analytical framework. We marked more than one for each analysis unit if necessary. The marks for each component were then counted, organized, and tabulated. Finally, the obtained number was divided by the total number of mathematical discourse components found in each lesson, and the percentages of the frequencies were calculated for each book.
In order to ensure the reliability of the data collected for this study, the analyses of the sample content of the 12th-grade mathematics textbooks and workbooks used in Saudi Arabia were assigned to two university math educators. These assigned university math educators served as its raters. The results of their coding of each unit of analysis of the five mathematical discourse components were assessed to ensure that the degree of agreement was reached. The reliability of the analysis value was determined by using the following κ formula developed by
where po represents the proportion of the analysis on which the two raters agree, and pc represents the proportion of ratings for which agreement is reached by chance. We used this formula because it corrects for both the number of categories and the probable frequency with which each is used by the coder; it also considers chance agreement. The percentage agreement between the two raters for activities included in the analyzed secondary school textbooks and workbooks ranged from 73 to 92%, with a corresponding range of κ values from 0.66 to 0.87. According to these values, there is a high degree of agreement between the two raters (
To establish the rating rubric’s content validity as well as fine-tune the rating rubric, a pilot study was conducted ahead of the content analysis. This helped determine the various levels of mathematical discourse components for a small sample of lessons. This step helped us make necessary revisions of the instrument’s rating rubric prior to its implementation, as well as to determine if the rating rubric accurately measured the content (
We calculated the weighted means as well as the weighted percentages in order to explain the results. These weighted means of responses to the items, which are the measure of central tendency, were calculated based on the number of levels in the rubric (four levels). The range is three, and the length of the category is 3/4, or 0.75. Thereafter, the weighted mean intervals for each level of the rubric, or each level of the inclusion of the mathematical discourse, are as follows: level 1, from 1 to 1.75; level 2, from 1.76 to 2.51; level 3, from 2.52 to 3.08; and level 4, from 3.28 to 4.
In this part, we presented the data regarding discourse components included in the 12th-grade mathematics textbooks and workbooks and discussed the nature of the results achieved from those data.
Frequencies, means, and percentages for discourse components included in the 12th-grade mathematics textbooks and workbooks.
Components of discourse | Freq. (f%) | Total | Weighted means | % | Level | |||
1 | 2 | 3 | 4 | |||||
Component 1: engagement | 45 | 0 | 0 | 0 | 45 | 1 | 25 | 1 |
Component 2: questioning | 41 | 190 | 21 | 0 | 252 | 1.92 | 48 | 2 |
Component 3: explaining mathematical thinking | 45 | 116 | 92 | 2 | 255 | 2.2 | 55 | 2 |
Component 4: mathematical representations | 82 | 10 | 29 | 0 | 121 | 1.56 | 39 | 1 |
Component 5: building student responsibility within the community | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Frequencies and percentages of inclusion of each level of discourse components in both students’ textbooks and the workbooks for the 12th-grade mathematics textbooks and workbooks.
Book type | Level | Freq. | Total | ||||
Component 1 | Component 2 | Component 3 | Component 4 | Component 5 | |||
Textbooks | 1 | 45 | 41 | 45 | 79 | 0 | 210 |
2 | 0 | 159 | 95 | 8 | 0 | 262 | |
3 | 0 | 19 | 79 | 22 | 0 | 120 | |
4 | 0 | 0 | 2 | 0 | 0 | 2 | |
Total | 45 | 219 | 221 | 109 | o | 594 | |
Weighted means | 1 | 1.90 | 2.17 | 1.48 | 0 | ||
Inclusion Level | 1 | 2 | 2 | 1 | 0 | ||
Workbooks | 1 | 0 | 0 | 0 | 3 | 0 | 3 |
2 | 0 | 31 | 21 | 2 | 0 | 54 | |
3 | 0 | 2 | 13 | 7 | 0 | 22 | |
4 | 0 | 0 | 0 | 0 | 0 | 0 | |
Total | 0 | 33 | 34 | 12 | 0 | 79 | |
Weighted means | 1 | 2.06 | 2.38 | 2.33 | 0 | ||
Inclusion level | 1 | 2 | 2 | 2 | 0 |
The results of the analysis indicated that the inclusion of almost all components of the mathematical discourse fluctuated between levels one and two. These results indicate that the inclusion of the discourse component in the textbooks and workbooks is teacher-directed rather than student-directed as specified by the
Regarding the inclusion of component 3, “Explaining mathematical thinking,” the inclusion did not exceed that of level 2, because none of the activities probed teachers to learn more deeply about students’ thinking or to elicit multiple strategies. The content did not encourage students to respond to probing, share their views, or to defend their answers. For example, high-thinking problems in the textbook for term 1 (p. 179) asked students to interpret their justification but did not ask them to express their opinion to their peers. Most of the mathematical representations were included at level 1. None of these asked students to label their math drawings so that others are able to follow their mathematical thinking, or to follow and help shape the descriptions of others’ math thinking through math drawings and suggest edits to others’ math drawings (
The results showed that both Arabic mathematics textbooks and workbooks used in Saudi Arabia did not include appropriate discourse components or skills. Both failed to exceed the second level of inclusion, which will not help learners meaningfully understand mathematical concepts or become active, successful leaders of their community. None of the activities in the 12th-grade mathematics textbooks and workbooks in Saudi Arabia contributed to the promotion of mathematical discourse components. This implies that mathematics textbooks and workbooks should be revised to include mathematical discourse so that this inclusion is more student directed than teacher directed. The inclusion of mathematical discourse skills in the mathematics textbooks would help facilitate mathematical learning among students. This implies also that teachers should be trained to use mathematical discourse in their teaching and strive to develop this discourse among students, even if textbooks and workbooks do not include these skills. The instrument used in this study must be used to conduct studies examining the inclusion of mathematical discourse in mathematics curricula for elementary and middle schools, to widen the literature.
The datasets generated for this study are available on request to the corresponding author.
Both authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.