Secondary Mathematics Courses Research Articles

Influences on student decisions to enrol in higher-level mathematics courses

AbstractAddressing the participation rates in senior secondary mathematics courses in Australian schools remains a critically important issue. In this paper, the authors report on quantitative findings from a study in which all year 11 and year 12 (aged 17–18 years) Australian Tertiary Admissions Ranking (ATAR) students in Western Australia were invited to participate. The aim was to explore the perceptions of these students regarding their enrolment in higher-level mathematics courses. Data from 1633 students were collected using a survey instrument comprised of 12, 5-point, Likert-scale items. Data were analysed by applying two statistical procedures: calculating frequencies of the 12 items in the scale and examining associations with demographic characteristics and individual items through generalised linear modelling. Analyses indicated most students agreed that other courses of study were more attractive, with almost half indicating that they did not like mathematics. In addition, approximately half of the students said that they did not need to enrol in any mathematics course for ATAR or for university entrance. Significant findings were also identified for gender, school type, and school gender. The knowledge gained from this research is valuable in understanding students’ reasons for choosing not to enrol in higher-level mathematics courses when they have the option to do so and, more broadly, to address persistently low or declining participation rates in these areas of study.

Teaching Fraction-to-Decimal Translation Using the Number Line

Rational number proficiency is predictive of later mathematics achievement, especially for rigorous mathematics courses, such as Algebra I. Students with learning disabilities (LD) in mathematics struggle to make adequate progress on rational number concepts and skills that lay the foundation for successfully completing secondary mathematics courses. However, recent research has demonstrated that utilizing effective instructional design, such as the use of a number line with systematic and explicit instruction, can result in academic progress for students with LD in mathematics. This article presents teachers with a four-step teaching sequence utilizing the number line and effective strategies for teaching students with LD in mathematics to introduce fraction-to-decimal relationships in upper elementary, a prerequisite for middle school mathematics.

Incentivising student enrolments in secondary mathematics courses: is a 10% bonus enough?

This replicated research project [see Hine, G. S. C. (2019). Reasons why I didn’t enrol in a higher-level mathematics course: Listening to the voice of Australian senior secondary students. Research in Mathematics Education, 21(3), 295–313. https://doi.org/10.1080/14794802.2019.15999982019] explored the reasons why senior secondary (i.e. Year 11 and Year 12) students elected not to enrol in a higher-level mathematics course. For this project, all senior secondary Australian Tertiary Admissions Ranking (ATAR) students within Western Australian schools (aged 17–18 years) were invited to participate in an anonymous, online survey comprised predominantly of qualitative items. The researcher analysed 1633 ATAR students’ perspectives of enrolments in mathematics courses, according to a symbolic interactionist paradigm. Reasons included the extent to which students feel higher-level courses are too challenging, time-consuming, not required for university nor future life, and requiring more effort and stress to complete than lower-level mathematics courses. Especially outlined is the extent to which participants feel a 10% bonus is a sufficient incentive to increase higher-level course enrolments, an extension of the original project. Participants indicated a range of responses either supporting or opposing this incentive. While approximately 47% of participants agree that the incentive is sufficient, a small proportion of these supporters offer their agreement conditionally. Within the proportion asserting the incentive is insufficient, a majority of participants suggested that a higher percentage bonus should be offered to students enrolled in Mathematics Specialist.

Solving for X: Constructing Algebra and Algebra Policy During a Time of Change

The year students take Algebra I historically determines how far they progress in secondary mathematics, creating complex equity issues around access to this course. By examining a case study of one large, urban school district adjusting to the Common Core State Standards in Mathematics (CCSS-M), we demonstrate how district leaders’ interactions, in combination with their organizational and institutional environments, led to an overhaul of the secondary mathematics course pathway, ending in detracked middle school mathematics. We find that district leaders’ deliberations of mathematics policy were constrained by organizational concerns around pedagogy, equity, logistics, and politics. In other words, the disruption created by the CCSS-M was limited by extant organizational priorities. This study has potential implications for theorizing disruptions and for better understanding equity-oriented mathematics policy and practice.

Alternative Assessment Strategies and the Obstacles of their Application in Intermediate and Secondary Mathematics Courses in Hail City

The present study aimed at exposing the level of activation of alternative assessment strategies in teaching mathematics courses in the intermediate and secondary levels in Hail, and even to identify the obstacles that prevent their application. The study tool (the questionnaire) was designed after formulating the most important teaching practices related to the use of alternative evaluation and its skills in math’s curricula. The most important obstacles that may reduce the adoption of alternative evaluation strategies in teaching mathematical content were also formulated, and hence identifying teachers’ assessment of their reality. The sample of the study consisted of (70) mathematics teachers in the intermediate and secondary levels, during the second semester of the academic year 1441 AH. The results unfolded that the paper-and-pencil evaluation method (tests, worksheets) is regarded the most popular with 84%. Consequently, the two teaching practices are applied in a high way; urging students to progress in acquiring mathematical concepts and skills by varying assessment tools, and the teacher provides his students with several tasks that raise the value of mathematical understanding and apply what they have learned in similar contexts. Also, the most important hindrance facing teachers is the requirement of alternative assessment tools to be high dominated towards the levels of student acquisition and learning opportunities for mathematical concepts. Thus, the study recommended an increasing interest in alternative evaluation strategies, and activating its patterns and skills that can increase understanding and application of the components of mathematical content.

Reasons why I didn’t enrol in a higher-level mathematics course: Listening to the voice of Australian senior secondary students

ABSTRACTThis research project investigated the reasons why senior secondary school students elect not to enrol in a higher mathematics course. All Year 11 and Year 12 mathematics students within Western Australian schools (aged 17–18 years) were invited to participate in a single, anonymous, online survey comprised predominantly of qualitative items. In line with a symbolic interactionist theoretical perspective, participant responses (n = 1351) were analysed to determine the meaning students conferred upon decisions to enrol in mathematics courses. In particular, responses indicated that students are dissatisfied with mathematics, there are other more viable courses of study to undertake, and that the Australian Tertiary Admissions Ranking (ATAR) score can be maximised by taking a lower mathematics course. Additional testimony suggests that there are few incentives offered to students undertaking a higher mathematics course, and that such courses are not needed for university entrance nor in later life. In light of these findings, a discussion synthesises student-led suggestions with current literature which could lead to higher future enrolments in secondary mathematics courses.

Readability of Texts in Secondary School Mathematics Course Books

This study aimed to investigate the readability of the fifth-, sixth, seventh and eighth-grade mathematics course books prepared in deference to the 2017 curriculum and distributed to schools by MEB. This study utilized the descriptive document analysis which is a qualitative research method. Readability of the mathematics course books were subjected to a quantitative analysis by Cetinkaya-Uzun Readability Formula. Addressing the readability levels of the texts in secondary mathematics course books, this study performed analyses of average word and average sentence lengths of the texts in secondary school course books. These analyses showed that there is no linear correlation between grade level and word and sentence length averages. Readability scores and levels of the text in the analyzed secondary school mathematics course books are not in parallel with the grade level. Accordingly, readability scores of information and solution texts in the fifth-grade course book were lower than the scores in other grades' course books whereas readability scores of question texts were lower than the scores in all grades' course books but the eighth-grade course book. Readability levels of the text in the analyzed secondary school mathematics course book were found to be on frustration level and educational level. Course books should also include independent texts with readability scores and levels.

Polynomial calculus: rethinking the role of calculus in high schools

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in their definition and exposition. We develop the beginning concepts of differential and integral calculus using only concepts and skills found in secondary algebra and geometry. It is our underlining objective to strengthen students' knowledge of these topics in an effort to prepare them for advanced mathematics study. The purpose of this reconstruction is not to alter the teaching of limit-based calculus but rather to affect students' learning and understanding of mathematics in general by introducing key concepts during secondary mathematics courses. This approach holds the promise of strengthening more students' understanding of limit-based calculus and enhancing their potential for success in post-secondary mathematics.

“I am [not always] a maths hater”: Shifting students’ identity narratives in context

In this study, individual students’ engagement in learning mathematics in different contexts was explored. The students’ narrated identities during their first compulsory upper secondary mathematics course provided a way to understand students’ shifts in participation and why these shifts occurred in different contexts at particular times. Identity narratives such as that of being a “maths hater” were linked to the learning opportunities. The connections between identity narratives and contexts suggest that how students are categorised in mathematics education needs to be queried, as these categorisations have an impact on students’ learning of mathematics.

This Mattered to Me

A Survey of the Current Status of Visually Impaired Students in Secondary Mathematics, by Donald W. Rapp and Audrey J. Rapp, originally published in the February 1992 issue of the Journal of Visual Impairment & Blindness, Volume 86, pp. 115-117. When I was asked to take on this project and pick one single article that mattered to me, I found it to be very difficult. I have read The series editor of This Mattered to Me is Stuart H. Wittenstein, Ed.D., superintendent of the California School for the Blind. hundreds of articles from the Journal of Visual Impairment & Blindness (JVIB) that have had an impact on my professional career. Like many in the field of visual impairment, I have an array of professional teaching and research interests. Thus, picking just one article on one area of was quite difficult. After much thought, I decided to go back to my roots as an educator: secondary mathematics. My first job was at the Alabama School for the Blind as its secondary mathematics teacher, and it was during my time there that I began a never-ending search for any and all information related to teaching mathematics to students with visual impairments. During this search, I discovered the JVIB article, A Survey of the Current Status of Visually Impaired Students in Secondary Mathematics, by Donald W. Rapp and Audrey J. Rapp, which included the findings of a questionnaire that was answered by teachers of students with visual impairments. Timeless research When I first read the Rapp and Rapp article, it was already eight years old, but it was the only data that existed at that time that discussed the types of mathematics that were being taught to secondary students with visual impairments. The authors conducted a simple survey of teachers of students with visual impairments in six New England states. The survey included questions on which secondary mathematics courses the teachers' students were taking, how the students were aided in their general education mathematics courses, and what tools they utilized. The most profound aspect of the article was the finding that of the 40 students who were reported as using braille as their primary literacy medium, only 19 (over half) were not enrolled in typical secondary mathematics courses. From this finding, one can surmise that either a large proportion of the students studied had cognitive disabilities in addition to their visual impairment that inhibited their abilities to take secondary mathematics courses or that their IEP (Individualized Education Program) teams did not push them to enroll in higher mathematics courses. Although cognitive disabilities may have ruled out higher mathematics for a number of these students, I suspect the latter is true. In my experience in the field of visual impairment, unfortunately, I do not believe that conditions have improved since this article was published. Let this study serve as a reminder that students who are blind need to be encouraged to enroll in higher mathematics courses. The article also highlighted the need for increased teacher training in braille. I was moved by the fact that 73% of the teachers who responded to the survey expressed interest in a workshop to review concepts of algebra, geometry and algebra II, with application of the Nemeth Code (p. …

Secondary Mathematics Course Trajectories: Understanding Accumulated Disadvantages in Mathematics in Grades 9–12

Schools are institutions in which students’ course taking creates series of linked learning opportunities continually shaped by not only curricular structures but demographic and academic backgrounds. In contrast to a seven-step normative course sequence reflecting the conventional hierarchical structure of mathematics, analysis of more than 17,000 high school transcripts indicates that students followed remarkably diverse pathways through high school mathematics. Students from less socially and academically advantaged backgrounds were more likely to deviate from common course sequences, thus contributing to their not progressing as far through the mathematics curriculum by the end of high school. Modeling course enrollments as growth trajectories indicates that gaps in mathematics progress related to demographic and earlier educational differences widen most rapidly in the later years of high school. The implications of our findings for schools’ course scheduling and monitoring of students’ progress are discussed.

"Guide on the side": An instructional approach to meet mathematics standards

The ultimate goal of high school mathematics teachers is to create a meaningful learning environment that is conducive to teaching students the necessary concepts for academic achievement. Unfortunately, evidence suggests that many secondary educators still teach in a rote lecture style that focuses on the teacher providing information to passive, uninvolved students. Current mathematics reform movements endorse inquiry-based, "guide on the side" instruction grounded in constructivist pedagogy. The authors' research examines the effects of constructivist teaching and learning in pre-service secondary mathematics courses. The applicability of constructivism to teach secondary mathematical concepts, using practical instructional ideas, will conclude the article.

Data-Driven Mathematics Investigations on Curved Data

Investigations of real–world data begin in elementary school. Students often produce scatter plots, leading to trend lines. In the middle grades, lines of best fit are often investigated through median–median lines and double–centroid lines (Shawer et al. 2002). In the secondary grades, linear regression is produced by the least squares line. While these techniques are adequate for data that is more or less linear, teachers and students often encounter data that produce a “curved” scatter plot. In these cases additional techniques are required. This article demonstrates three techniques to determine the equation of a polynomial function through two or more points that model the graph of “good fit” for a set of data. Using these techniques, students can develop functions through which they can evaluate mathematical behavior and make predictions. Secondary mathematics teachers will find these techniques particularly valuable. Each technique can be applied within various secondary mathematics courses such as algebra 2, statistics, or precalculus.

Developing a diagnostic framework for evaluating student approaches to applied mathematics problems

In the development of innovative programmes to enhance the application skills of students a neglected population tends to be those students who have difficulty in addressing quite basic problems, but whose educational setting is prescribed by school policies such that more innovative teaching and learning environments are not available to them. This research sets out to develop a diagnostic framework that supports teaching and learning in such situations. Based on empirical research studies and on theoretical constructs of human learning a script analysis framework was developed encompassing criteria across categories of planning, monitoring, heuristic strategies, verification, knowledge resources, and beliefs. The framework represents a synthesis and extension of previous work. Two teachers worked with 47 students throughout a year in a senior secondary mathematics course geared to students intending to study mathematics at tertiary level. Data collection was limited to the type of information available to teachers working under restrictive policies—written protocols of student problems solving together with student comments on their own problem solving processes. Characteristic patterns were identified, confirmed, and used to generate a response quality hierachy within the framework. The resulting structure contained 23 cells and fulfils three purposes: 1. as a self‐assessment aid to assist students to evaluate and enhance their application skills; 2. as a format for the provision of detailed formative feedback by teachers; 3. as a set of explicit targets for achieving summative quality in mathematical applications.

Relationships Between Technically-oriented Secondary School Courses And A College Private Pilot Ground School

This study was undertaken to determine if there is a relationship between final grades received in secondary school technically-oriented courses and the final grade received in a college private pilot ground school course. Ninety-six first-year students enrolled in the ground school course comprised the sample, with data for 51 aviation pre-major students and 45 non-aviation pre-major students examined both as two separate samples and as a single sample. Final grades earned by these students in secondary school elementary algebra, geometry and advanced algebra, the mean of the three mathematics final grades, the mean of the secondary science final grades and the mean of the secondary English final grades were used as independent variables. The final grades earned in Technology 101, Private Pilot Ground School, were used as the dependent variable. From the analysis, it may be concluded that, when grades earned by aviation pre-major students and non-aviation pre-major students were analyzed as one sample, there was a relationship for all students between the private pilot ground school course and all of the secondary school technically-related courses. When the grades earned by aviation pre-majors were analyzed alone, there were relationships between only the ground school course and geometry and the mean of the final grades earned in secondary mathematics courses. The analysis of the grades earned by non-aviation pre-majors revealed relationships between the ground school course and all of the secondary school technically-related courses. There was no relationship between the ground school course and the mean of the final grades earned in secondary English courses for any of the three samples studied. This study suggests that secondary school mathematics plays a role in preparing all students for a college private pilot ground school course. Secondary school geometry appears to playa particularly Significant role in preparing pre-aviation majors who are taking a private pilot ground school course as an initial professional course.

Attitudes to mathematics of beginning undergraduates and prospective teachers: Some implications for education

An acute shortage of mathematics teachers has emerged in the Western world. This article describes a study of the influence of tertiary education experiences on the attitudes of potential mathematics teachers towards their subject. Parallel questionnaires were given to groups of students who were respectively entering university mathematics courses as new undergraduates, and entering postgraduate teacher training courses. Both groups of students answered items pertaining to their experiences within secondary mathematics courses. The undergraduate students were also asked a series of questions about their expectations of tertiary mathematics courses. For the postgraduates a parallel set of questions was provided that required them to rate their actual tertiary experiences. An analysis of responses indicated that the postgraduate students were more positive about their recollection of secondary mathematics than were the undergraduate students with their more recent experience of it. They were also less positive about the reality of their tertiary courses than were the undergraduates about their expectations. Responses of the postgraduates suggested that tertiary mathematics is not merely an extension of secondary mathematics, but a subject with which distinctive and, in general, more negative reactions are associated. Mathematics emerges as a subject which progressively loses its appeal with further study and implications are drawn for both tertiary education and teacher supply.

The Prediction of Success in Each of Six Four‐Year Selections of Secondary Mathematics Courses

School Science and MathematicsVolume 71, Issue 8 p. 693-696 The Prediction of Success in Each of Six Four-Year Selections of Secondary Mathematics Courses Lucien T. Hall Jr., Lucien T. Hall Jr. Supervisor of Mathematics, Richmond Public Schools, Richmond, Virginia, 23219Search for more papers by this author Lucien T. Hall Jr., Lucien T. Hall Jr. Supervisor of Mathematics, Richmond Public Schools, Richmond, Virginia, 23219Search for more papers by this author First published: November 1971 https://doi.org/10.1111/j.1949-8594.1971.tb08817.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume71, Issue8November 1971Pages 693-696 RelatedInformation