Entry-level Mathematics Research Articles

The Challenges Entry-Level Mathematics Teachers Face in Conducting Blended Teaching

In recent years, there has been an increasing amount of literature on online teaching and learning. Teaching mathematics in the fourth industrial revolution offers entry-level mathematics teachers formidable challenges. Despite using various teaching aids in explaining the learning area, entry-level mathematics teachers, those with zero to three years of teaching experience, have experienced challenges in blended teaching during the COVID-19 pandemic. Such challenges could support the preconceived notion identified by others that the field of learning (mathematics) is difficult. This paper hinged on constructivist epistemology and investigated the challenges that entry-level mathematics teachers face in conducting blended teaching in the Sedibeng West District of Gauteng Province in the Republic of South Africa. Eight entry-level mathematics teachers were purposely sampled from four selected schools that participated in the article. This article adopted a case study design and responses were analysed thematically. The focus group interviews were used as tools to collect data in this study. The study revealed a variety of perceptions that entry-level mathematics teachers shared about the impact of blended teaching in mathematics learning. These included, but were not limited to, the use of teaching programs or software, the effects of load shedding and blended teaching challenges related to learners' performance and behaviour. The results of this study could provide program developers, subject advisors, school principals with other members of the management team, and mathematics teachers to support the entry-level mathematics teacher's confidence, sense of future and communication skills, as well as foster multigenerational connections in blended teaching.

Language demands in undergraduate mathematics courses

This study examines language demands in undergraduate university mathematics classes with a view to better preparing and supporting international and other culturally and linguistically diverse (CLD) students in the United States universities. We observed and analyzed the language demands of 13 entry-level mathematics classes across two large universities. Findings showed that mathematics instruction required extensive and varied listening skills requiring students to listen to long and uninterrupted stretches of sometimes fast paced speech. Technical vocabulary contributed to the language demands, but instructors used both academic and colloquial varieties of language in instruction, interweaving mathematical nouns with phrasal verbs to explain mathematical processes. We suggest a greater focus on development of academic listening skills in English language classes as well as potential collaboration with mathematics campus resources and faculty for additional student support for preparing CLD students for potential future discourse practices.

Access to senior secondary science and mathematics: examining the evidence for stratification in an Australian school system

This research investigates access to senior school science and mathematics subjects offered in the final year of secondary schooling. Using data from the most populous Australian state of New South Wales, we examine whether stratification occurs in access to science and mathematics curricula. We find that the opportunity to study these subjects differs by key school characteristics, including location, socioeconomic composition and school sector. We find that while some science subjects and entry level mathematics are offered in most schools, substantial inequalities exist in access to the most advanced level of mathematics and chemistry. School location, socioeconomic composition, enrolment size and the availability of teachers predict the probability of whether a school offers the least and most advanced science and mathematics subjects. The findings highlight that stratification in curricula offerings occurs systemically and may intensify educational inequalities.

A Mathematics Educator Walks into a Physics Class: Identifying Math Skills in Students’ Physics Problem-Solving Practices

AbstractOne of the main goals of lower division “service” mathematics courses is to provide STEM-intending students with opportunities to engage in activities and contexts that can support their efforts to apply the mathematical ideas they are learning to successive major courses. The Mathematics Association of America has supported many mathematicians’ efforts to ask partner discipline faculty what topics and habits of mind they feel should be covered in mathematics classes to prepare them for their subsequent classes. We add to this work with a twist: Instead of asking physics faculty what they want students to know, we analyzed videos that students in an introductory physics class created so that we could ask ourselves what mathematical practices were most and least prevalent in the students’ physics problem-solving efforts. A qualitative analysis of the results, which we present here, indicated that most students were proficient in math practices involving problem setup and that the majority were able to apply mathematical concepts such as trigonometry and the solving of algebraic equations. However, only 44% of the student groups concluded their explanations by discussing answer reasonability and only 18% conducted a unit analysis to determine if their answers were applicable to the context of the problems assigned, even though both of these elements are important components of the overall sensemaking process. This report presents examples that illustrate these results and concludes with implications for teaching both entry-level mathematics and physics courses by modeling productive problem-solving and sensemaking practices.

Use of variables in calculus class: focusing on Teaching Assistants’ discussion of variables

Given the importance of the ability to use variables flexibly in Calculus and students’ difficulties related to various uses of variables, this study examined how variables are treated in calculus class. Data for this study came from graduate teaching assistants’ (TAs’) classroom teaching, which plays a crucial role in undergraduate students’ learning of entry-level mathematics, but of which we still have a limited understanding. We analyzed TAs’ uses of variables in terms of prior literature examining how students use variables and what uses of variables cause difficulties for students. Our results show that the uses of variables by the TAs in this study typically aligned with students’ dominant conception of variables as symbols to be manipulated and did not give students many opportunities to consider the uses of variables that commonly cause difficulties for students.

On the Use of Writing Prompts in Entry-Level Mathematics Courses

In introductory level math classes, writing prompts can be used as part of weekly homework assignments to encourage students to think more deeply about the subject at hand. These writing prompts present scenarios related to recently learned material in a new context and require students to submit a short written response online. Writing prompts complement more computational exercise-based homework, as they allow students to develop their communication and logical reasoning skills while providing additional motivation for the concepts being discussed. By creating a detailed rubric and providing it to students ahead of time, student responses can also be graded without a significant time commitment on the part of the instructor. A sample rubric is provided, along with examples of some writing prompts and evaluated student responses.

Item efficiency: an item response theory parameter with applications for improving the reliability of mathematics assessment

ABSTRACTMany large universities, community colleges and some smaller four-year colleges are turning to hybrid or online instruction for remedial and entry level mathematics courses, often assessed using online exams in a proctored computer lab environment. Faculty face the task of choosing questions from a publisher's text bank with very little, if any, background in test theory and design. We present a new item parameter, item efficiency, that is calculated from the results of an item response theory analysis of a comprehensive college algebra final examination and show that this new parameter may be used to identify items better suited for similar comprehensive final assessments. Further, by relating Item Efficiency to classical test theory item statistics, we propose guidelines that can be used to identify suitable items prior to testing with little or no background in psychometric theory.

The influence of entry route to teaching on Irish pre-service primary teachers’ attitudes towards mathematics

Research examining the characteristics of both qualified and pre-service teachers focuses on traits including gender, socio-economic and socio-demographic background, knowledge and a variety of relevant affective constructs. Studies also investigate such traits among entrants to initial teacher education (ITE). The desire for more diversity within the teaching profession has led to alternative entry routes to the teaching profession (consecutive model for post-graduates) for those who may be unable to gain entry via the traditional concurrent (undergraduate) route. Internationally, there are divergent viewpoints and practices in relation to the value and use of the respective routes. This paper presents a comparative study within the Irish context, examining whether the consecutive model route to ITE promotes diversity in terms of entrants’ attitudes to mathematics. The study examines the entry-level mathematics attitudes of two distinctive groups of ITE entrants, namely 419 concurrent and 59 consecutive elementary pre-service teachers, in one Irish ITE institution prior to engagement with their ITE mathematics education programme. It compares their enjoyment of mathematics as well as their beliefs regarding the value of mathematics and examines the extent to which any distinguishing differences are apparent among the respective cohorts using the Aiken’s Revised Mathematics Attitude Scale. Analyses indicate generally positive attitudes among both cohorts; however, differences are evident between the cohorts with the consecutive route cohort demonstrating particularly apposite attitudes. The findings support the belief that the consecutive ITE route holds merit and prompts further investigation regarding the unique dispositions that these entrants possess.

Exploring the Impact of Reform Mathematics on Entry-Level Pre-service Primary Teachers Attitudes Towards Mathematics

This study reports entry-level mathematics attitudes of pre-service primary teachers entering an initial teacher education (ITE) program one decade apart. Attitudes of 360 pre-service primary teachers were compared to 419 pre-service teachers entering the same college of education almost one decade later. The latter experienced reform school mathematics curricula compared to the earlier cohort who experienced traditional curricula. Attitudes were determined by administering Aiken’s Revised Mathematics Attitude Scale (Aiken, 1974). Analyses indicate generally positive attitudes on entry to ITE. The earlier cohort demonstrated greater Enjoyment of Mathematics while the later cohort exhibited higher scores on the Value of Mathematics scale.

A quantitative analysis of the relationship between an online homework system and student achievement in pre-calculus

Supporting student success in entry-level mathematics courses at the undergraduate level has and continues to be a challenge. Recently we have seen an increased reliance on technological supports including software to supplement more traditional in-class instruction. In this paper, we explore the effects on student performance of the use of a computer software program to supplement instruction in an entry-level mathematics course at the undergraduate level, specifically, a pre-calculus course. Relying on data from multiple sections of the course over various semesters, we compare student performance in those classes utilizing the software against those in which it was not used. Quantitative analysis of the data then leads us to conclusions about the effectiveness of the software as well as recommendations for future iterations of the course and others like it.

Comparative Study of the Numeracy Education and Writing Across the Curriculum Movements: Ideas for Future Growth

The percentage of American institutions with a Writing Across the Curriculum (WAC) program grew from 38% to 54% over the 20-year period from 1987 to 2008. Meanwhile the trajectory of the numeracy movement from publication of the popular book Innumeracy in 1988 to the appearance of Numeracy in 2008 was similar to the trajectory of the WAC movement from the publication of “Why Johnny Can’t Read” (1975) to the appearance of the first WAC journal in 1994. Review of the WAC literature shows that the growth of WAC occurred despite numerous challenges: the need for institutional buy-in; assessment; orthodoxy of English departments; the notion that writing is a pre-college skill; recognition of WAC scholarship; the workload of grading; student resistance; and difficulties of getting external funding. Similar challenges face the numeracy movement today. The WAC literature reveals four major contributors to its successful growth: (1) a paradigm shift in thinking about writing pedagogy (exemplified by WTL, “writing to learn” rather than just “learning to write”; WID, writing in the disciplines; a rethinking of first-year writing courses; and writing across the curriculum); (2) campus-level faculty and student support for writing; (3) professional networks and scholarship around WAC; and (4) framing WAC within institutional movements. How can the numeracy movement apply these “lessons learned” from WAC? I conclude with five suggestions: (1) document that numeracy education increases students’ critical thinking and decision-making skills; (2) compile electronic resources for faculty to integrate numeracy education into their disciplines; (3) expand our research methodologies and scholarly output so that numeracy education can be seen as its own field of study; (4) work with math departments and funding agencies to integrate numeracy more explicitly into high-volume, entry-level mathematics courses; and (5) support models of campus-wide programs that include a center for faculty and student support that is led by a numeracy education professional.

Characterizing the Mathematics Anxiety Literature Using Confidence Intervals as a Literature Review Mechanism

ABSTRACT The authors report the contextualization of effect sizes within mathematics anxiety research, and more specifically within research using the Mathematics Anxiety Rating Scale (MARS) and the MARS for Adolescents (MARS-A). The effect sizes from 45 studies were characterized by graphing confidence intervals (CIs) across studies involving (a) adults not participating in studies focusing on remedial or entry-level mathematics students or teachers, (b) remedial mathematics and entry-level college mathematics students, (c) preservice and inservice teachers, and (d) 7–12th-grade students and rising college students. The results also illustrate how CIs can be useful in research syntheses, because CIs (a) encourage meta-analytic thinking, (b) provide information about the research precision of a literature, and (c) provide plausible estimates for parameter values even if initial research expectations are wildly wrong.

Diagnostic assessment for Mathematics in a distance learning context

The idea of a diagnostic process to identify students likely to benefit from additional support originated from two separate investigations relating to the performance of entry-level mathematics students at the University of South Africa (UNISA). One project explored the relationship between reading skill and mathematical performance. This resulted in a reading intervention programme for students of mathematics. The other project considered an alternative method of assessment. This article explains why and how diagnostic assessment was developed for students who enrolled for the UNISA Mathematics Access Module. The article gives some initial the results, and an analysis of examination performance related to the risk categories identified by the diagnostic assessment. South African Journal of Higher Education Vol. 22 (3) 2008: pp. 556-574

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

Making meaningful connections between mathematics and other scientific disciplines has become a priority in education. In recent years, numerous national reports have called for more cross-disciplinary material in entry-level mathematics courses. (Cohen 1995 is one such example.) In this article, we consider an application of quadratic equations to a standard problem in chemistry. We show how quadratic equations arise naturally in solving the problem and then go on to consider a standard approximation using a simpler quadratic. This focus brings to light several important mathematical ideas. They include the sensitivity of the solutions on the equation coefficients and the use of inequalities to obtain upper bounds on the error

STUDYING THE PLACEMENT OF STUDENTS IN THE ENTRY-LEVEL COLLEGE MATHEMATICS COURSES

ABSTRACT Placing undergraduate students in appropriate entry-level mathematics courses is a problem that all colleges and universities face. This article is a summary of findings from a study of students enrolled in college algebra. The predicted success of students is related to explanatory variables using a linear model. Advising cut-off scores are discussed in terms of student-success rates as well as the mission statement and philosophy of the university.