Math Courses Research Articles

A Comparison of Students’ Quantitative Reasoning Skills in STEM and Non-STEM Math Pathways

Quantitative Reasoning (QR) is essential for today’s students, yet most higher education institutions have not effectively addressed this issue. This study investigates students’ quantitative reasoning in STEM and Non-STEM math pathways using a non-proprietary, NSF grant-funded instrument, the Quantitative Literacy & Reasoning Assessment (QLRA). Participants were students enrolled in at least one college-level math pathway course at a large public institution in the southeastern US. The results showed a significant difference between STEM and Non-STEM students’ QLRA scores, with STEM students (n = 244, M = 27%, SD = 16.21%) scoring, on average, about 6% higher than Non-STEM students (n = 295, M = 21.1%, SD =11.38%). STEM students who were further along in their math sequence, i.e. Pre-calculus/Trigonometry and Calculus I, had a higher QLRA score than those taking the gateway math courses in that pathway. Non-STEM students who took additional math courses also had a higher QLRA score than those in the entry-level math course. However, the students overall had relatively low QR skills (n = 539, M = 23.78%, SD = 14.07%). These results highlight the need for an increased understanding of the math pathways initiative and its relationship with quantitative reasoning. Thoughtful and deliberate scrutiny of curriculum and pedagogy is important in all math pathways as it relates to the development of quantitative reasoning skills.

College developmental math students’ knowledge of the equal sign

Decades of research have documented young students’ misinterpretations of the equal sign and the impediments these present for children’s mathematical development. Much less is known about individual differences in adults’ knowledge of the equal sign. We assessed 182 college students from developmental math courses and present analyses from a subset of items on a previously validated assessment of mathematical equality. College students exhibited variability in their interpretations of the equal sign, and these individual differences were related both to their solutions for open equations with variables and to their interpretations of an algebraic expression. Students who provided a relational interpretation of the equal sign were most successful on target algebra problems and students who only provided an operational interpretation of the equal sign were least successful. These results show that misinterpretations of the equal sign can persist well beyond elementary school and can provide a critical indicator of broader mathematical reasoning among college students.

Integrating co-requisite math for STEM student success.

Gateway math courses can be a major hurdle for students to get over in order to continue on with their majors, especially STEM majors. Previously, students could have taken up to four semesters of remedial math before being able to place into the first gateway math course needed for their major. With Math Support, students no longer have to take those remedial courses; the remediation is built in to the course in addition to the regular level content. These co-requisite courses allow students to start into their major courses much sooner than in the past, therefore allowing them to stay on track in their major and finish successfully. Attendees will be given an overview of Math Support at Fairmont State. Developmental math courses have been replaced with co-requisite and accelerated learning models. All students can now progress through gateway courses within their first year, regardless of test scores. Gateway courses are offered with additional support to aid students in learning and understanding and fill in any gaps. Fairmont State was one the first colleges in WV to offer these services at full-scale. Initial data reports show students who took a Math Support course completed the course successfully at the same rate as students in non-support courses. More data will be reported.

And Yet They Persisted: Early Evaluation of the First2 Network

The first two years of an undergraduate student’s STEM program of study are particularly treacherous, with roughly half of STEM majors switching to other fields or dropping out entirely after their sophomore year. Moreover, attending a rural high school that was unable to offer higher-level math courses and being a first-generation college student further increase the likelihood of STEM attrition. This presentation will feature early evaluation results from the First2 Network’s first 18 months of operation. Funded by the National Science Foundation, the First2 Network is a collective impact effort to improve STEM persistence among rural, first-generation college students in West Virginia. With students themselves as co-creators of solutions to problems of persistence, core Network activities include iterative testing of improvements to practice, development of a statewide network to support student success, and capacity building to ensure sustainability. Study methods include surveys and interviews, observation of Network activities, document review, social network analysis, and tracking of student progress. Key findings suggest rapid Network expansion, establishment of core processes to support workgroups, provision of Network-wide training in improvement science, and successful facilitation of four summer immersive research experiences for targeted students. Early outcomes include statistically significant improvements in students’ STEM efficacy and STEM identity following summer immersive experiences, and improved survey scores indicating progress through iterative testing cycles. Early persistence data from participating students will be available by the time of the conference. The First2 Network is supported by National Science Foundation INCLUDES Award Nos. 1834595, 1834586, 1834601, 183457, and 1834569.

What Happens to Efficiency and Equity? The Cost Implications of Developmental Education Reform

Florida passed legislation in 2013 that exempted many students from developmental education, and required colleges to implement new instructional modalities for optional developmental education courses. This paper uses an economic model of remediation to examine how changes in college course taking before and after the reform altered costs to completing introductory college-level courses in math and English for students and institutions, and whether cost savings differ by racial/ethnic subgroup. We also take into account changes in short-term costs relative to course completion rates to examine whether the reform is cost effective overall. We find that the total cost per completer (including costs to both students and institutions) decreased after the reform by $894 in English and $1851 in math. This resulted in efficiency gains of 34% in English and 30% in math. The results from Florida provide promising evidence that statewide developmental education reforms may be an effective mechanism for reducing costs to students and institutions. Reform efforts may also help to reduce racial/ethnic gaps in the costs to gateway completion in both subject areas, which has important implications for equity.

Analysis of the Relationships between Mathematics Achievement, Reflective Thinking of Problem Solving and Metacognitive Awareness

In this study, it was examined that in what level reflective thinking towards problem solving skills and metacognitive awareness explained maths course achievements of the students and the relationships among these variables were studied. In this study, relational survey model was applied. The study included 412 seventh grade students from two different secondary schools within each of the three central districts located in Ankara. In this study, “Reflective Thinking Skill Scale to Problem Solving (RTSSPS)” and “The Metacognitive Awareness Inventory for Children (MAI-C)” and the scores of “Maths Course Achievement” were used. “Pearson Momentler Correlation Coefficient” and “Multiple Linear Regression Analysis” were used in the correlational and regression analysis. It was determined that there was a strong positive significant correlation between students’ maths achievement, reflective thinking towards problem solving and metacognitive awareness. It was also determined that there was a strong positive significant correlation between reflective thinking towards problem solving and metacognitive awareness.

Educação Matemática e Formação Inicial: uso de novas tecnologias em sala de aula

Este artigo é produto decorrente do projeto de ensino de graduação intitulado “O uso do Software SuperLogo no Desenvolvimento de Conceitos Geométricos” vinculado ao Programa de Consolidação das Licenciaturas (Prodocência). O projeto de ensino teve como principais objetivos: aumentar a qualidade das ações voltadas à formação de professores, bem como, explorar as formas de contribuições do programa SuperLogo para o ensino de geometria com prioridade para a formação inicial. O projeto contempla diretamente a formação e o aprendizado profissional dos futuros docentes. Baseado em reflexão sobre diversos autores que abordam a discussão sobre a formação continuada, assim como a utilização das novas tecnologias nesse processo, somado a análise de todo o material do Programa de Ensino aqui relatado, pudemos constatar resultados relevantes que serviram para dinamizar o curso de matemática do Campus do Pantanal (CPAN/UFMS), contribuindo para uma melhor formação acadêmica, científica e técnica dos futuros docentes.

İlköğretim Matematik Dersine İlişkin Tutum, Kaygı ve Öz Yeterlilik ile İlgili Yapılan Deneysel Araştırmalar

Bu araştırma, ilköğretim matematik dersine ilişkin tutum, kaygı ve öz yeterlilik ile ilgili yapılan deneysel araştırmaların incelenmesi amacıyla yapılmıştır. Yapılan araştırmalar sonucunda 2000-2018 yılları arasında konuya ilişkin toplamda 21 araştırmaya ulaşılmıştır. Nitel araştırma yöntemiyle gerçekleştirilen bu çalışmada verilerin analizi için içerik analizi kullanılmıştır. Araştırmaların bazı sorulara göre dağılımları incelendiğinde; en çok tutuma yönelik araştırmaların yapıldığı, araştırmaların tamamına yakınının tez olduğu, araştırmalarda birbirinden farklı strateji, yöntem ve teknikler kullanıldığı, birinci sınıf düzeyinde hiçbir araştırmanın yapılmadığı ve en çok araştırmanın dördüncü sınıf düzeyinde yapıldığı görülmektedir. Tam deneysel araştırmaların daha fazla yapıldığı, en fazla araştırmanın 2015 yılında yapıldığı ve bazı yıllarda ise hiçbir araştırmanın yapılmadığı sonucuna ulaşılmıştır.

ДО ПИТАННЯ ПРО ЗМІСТ МАТЕМАТИЧНОЇ КОМПЕТЕНТНОСТІ МАЙБУТНІХ СПЕЦІАЛІСТІВ РІЧКОВОГО ТА МОРСЬКОГО ТРАНСПОРТУ

The main goal of the modern competence-oriented teaching of mathematics at higher educational institutions of the first level of the accreditation is formation and development of mathematical competence of students. The contents of the article reveals the author`s attempt to define the term «Mathematical competence” of future specialists of river and sea transport. In the course of the research it was discovered that the notion “Mathematical competence” stands in line with a higher notion “Competence” In this connection, the author in her research rests on the definition “Competence” stated in the National Standard of secondary education. In the process of analysis of approaches as to how to treat the notion “Mathematical Competence” the author bases on the ideas of contemporary scientists and Methodists and believes that the mathematical competence of future specialists of river and sea transport is a complex, integrated feature of a personality which means not only knowing mathematical knowledge but also readiness of a personality to use acquired knowledge when solving professional tasks. As mathematical competence is an integrated feature of a personality, so it is necessary to regard it from the point of view of the systematic approach. Considering all the above the author sticks to a three-tiered structure of the mathematical competence and distinguishes such components as cognitive, activity-based and personal-based (motivational, reflexive, valuable). And the cognitive component of the mathematical competence includes knowledge in mathematics which a student must acquire in the process of the Maths course; activity-based component includes student’s skills to use the acquired knowledge in mathematics while solving practical, applied and professional tasks; personal-based component includes motivational, reflexive and valuable components. Wherein the valuable component is system formation factor of the educational and informative process as the students’ real educational results depend on what goals, values, ideals the students adhere to in their educational activity. The author also points out the functions which “the mathematical competence” must perform Key words: educational process, competence, mathematical competence, specialist of river and sea transport, structure and function of the mathematical competence.

The Gender Gap in Stem Attainment

I investigate the determinants of high school completion and college attendance, the likelihood of taking science, technology, engineering or math (STEM) courses in the first year of college and the probability of earning a degree in a STEM field. The focus is on women, who tend to be underrepresented in STEM fields. Tracking four cohorts of students throughout Florida, women perform nearly as well as men on math achievement tests through high school and are more likely to finish high school and attend college than males. Among college students, however, women are less likely than men to take courses in the physical sciences in their first year and are less likely to earn a degree in physics or engineering, even after adjusting for pre-college test scores. Gender matching of students and math/science teachers in middle and high school tends to increase the likelihood that female college freshman will take at least one STEM course. However, conditional on first-year coursework, neither gender matching at the secondary or college levels appears to have any effect on the likelihood of completing a major in a STEM field. For all students, having high school math and physics teachers with a degree in math or physics, respectively, (as opposed to education) is associated with a higher likelihood of taking STEM courses as college freshmen.

How do students prepare in the pre-class setting of a flipped undergraduate math course? A latent profile analysis of learning behavior and the impact of achievement goals

Pre-class preparedness is critical to students' in-class learning and overall success in the flipped classroom. This study used both trace data and self-report data to identify students' pre-class learning behavior profiles and investigate the relations of the identified learning profiles with the achievement trajectory over time and students' perceived achievement goal orientations in a flipped undergraduate math class. Three distinctive types of pre-class learning profiles emerged from the study, including the lecture-focused and low time-spent profile, lecture-quiz-balanced and average time-spent profile, and quiz-focused and high time-spent profile. The results show that students' performance trajectories were significantly different among the three learning profiles. In addition, achievement goals significantly impacted the membership of the learning profiles, indicating students' perceived goal orientations shape their pre-class learning behaviors. The theoretical and instructional implications are discussed, and specific design suggestions were provided to improve students' pre-class preparedness in the flipped math classroom.

The Attitudes of Jordanian School Students towards M-Learning in Math: An Empirical Study: اتجاهات طلبة المدارس الأردنيين نحو تعلم الرياضيات باستخدام الموبايل: دراسة تطبيقية

The present study aimed to explore the attitudes of Jordanian school students towards M-learning in math. A descriptive analytical approach was adopted and a five point Likert questionnaire was developed. A purposive sample was selected from Omar bin Al-Khatab School for Boys in Amman, Jordan. It consists from 52 9th grade male students. The questionnaire forms were distributed to all the students. All the forms were retrieved and considered valid for statistical analysis. SPSS was used. It was found that Jordanian school students have positive attitudes towards M-learning in math. It was found that most of the respondents use mobile for academic goals. It was found that M-learning in math raises students’ academic achievement in math course and motivates them to learn math. However, M-learning in math doesn’t participate in improving students’ communication skills. The researcher recommends setting policies by the Jordanian Ministry of Education for encouraging teachers and students to practice m-learning.

Heterogeneous Effects of Early Algebra across California Middle Schools.

How should schools assign students to more rigorous math courses so as best to help their academic outcomes? We identify several hundred California middle schools that used 7th-grade test scores to place students into 8th-grade algebra courses and use a regression discontinuity design to estimate average impacts and heterogeneity across schools. Enrolling in 8th-grade algebra boosts students' enrollment in advanced math in ninth grade by 30 percentage points and eleventh grade by 16 percentage points. Math scores in tenth grade rise by 0.05 standard deviations. Women, students of color, and English-language learners benefit disproportionately from placement into early algebra. Importantly, the benefits of 8th-grade algebra are substantially larger in schools that set their eligibility threshold higher in the baseline achievement distribution. This suggests a potential tradeoff between increased access and rates of subsequent math success.

Student Participation in Supplemental Instruction in STEM Courses at a Large Urban Community College in California

ABSTRACT A realist evaluation framework asks what works best for whom under what circumstances. This study utilized a realist evaluation framework to determine which students benefited under what circumstances from supplemental instruction, an academic support program using peer-assisted problem-solving techniques. The study setting was a large urban community college that was also a Hispanic-Serving Institution (HSI), with 80% Hispanic students and over 50% of all students qualifying for financial aid. Two sources of existing administrative data were analyzed using a quasi-experimental design. All science, technology, engineering, and math (STEM) courses in one semester with supplemental instruction (SI) (n = 18 courses in spring 2015) were matched to STEM courses that did not have SI (n = 35). Student-level comparisons based on the number of SI sessions attended were also made (N = 1,851). Three research questions were analyzed: (a) what was the pattern of SI participation?; (b) Did course pass rates increase with SI participation?; and (c) Were grade outcomes different based on SI participation? Results indicated that as expected, SI participation was higher among students in SI STEM courses (33.4%) compared to those in non-SI supported STEM courses (5.3%). In addition, increasing numbers of students passed their courses with increasing SI session attendance. Mean grade differences of just under half a grade were found, favoring students who attended one or more SI sessions. Across all students and in math courses, more students who attended SI earned higher grades (A’s, B’s, C’s) and fewer withdrew or received an F compared to students who did not attend SI.

Genetic associations with mathematics tracking and persistence in secondary school

Maximizing the flow of students through the science, technology, engineering, and math (STEM) pipeline is important to promoting human capital development and reducing economic inequality. A critical juncture in the STEM pipeline is the highly cumulative sequence of secondary school math courses. Students from disadvantaged schools are less likely to complete advanced math courses. Here, we conduct an analysis of how the math pipeline differs across schools using student polygenic scores, which are DNA-based indicators of propensity to succeed in education. We integrated genetic and official school transcript data from over 3000 European-ancestry students from U.S. high schools. We used polygenic scores as a molecular tracer to understand how the flow of students through the high school math pipeline differs in socioeconomically advantaged versus disadvantaged schools. Students with higher education polygenic scores were tracked to more advanced math already at the beginning of high school and persisted in math for more years. Analyses using genetics as a molecular tracer revealed that the dynamics of the math pipeline differed by school advantage. Compared to disadvantaged schools, advantaged schools buffered students with low polygenic scores from dropping out of math. Across all schools, even students with exceptional polygenic scores (top 2%) were unlikely to take the most advanced math classes, suggesting substantial room for improvement in the development of potential STEM talent. These results link new molecular genetic discoveries to a common target of educational-policy reforms.

Initial implementation of active learning strategies in large, lecture STEM courses: lessons learned from a multi-institutional, interdisciplinary STEM faculty development program

BackgroundA faculty development program was implemented over four years at a 4-year regional comprehensive university and two partnering community colleges. This project was focused on improving student learning in introductory Science, Technology, Engineering, and Math (STEM) courses at each institution, by helping faculty adopt inclusive, student-centered pedagogies. Survey data were combined with data from classroom videos, faculty interviews, and student questionnaires collected during the first two years of the project to give insight into how faculty initially implemented the theory and strategies they learned and how the students perceived instruction from participating faculty.ResultsThese data sources were combined to generate four overall themes to characterize our project and guide future projects. These are: (1) implementation of student-centered learning took a variety of forms; (2) quality implementation of student-centered teaching practices lagged behind understanding of the theory behind those practices; (3) the most robust perceived barriers to implementation of student-centered teaching stayed constant, while more moderate barriers were ranked differently from year 1 to year 2; and (4) faculty perceptions of student-centered learning practices were not always the same as students’ perceptions. These themes build from the extant faculty development literature in that they are drawn from the unique context of a multidisciplinary, multi-institutional project, and that they represent an “on the ground” perspective from case studies combined with “big picture” findings from surveys.ConclusionsThis paper describes the faculty development project, as well as our collection and interpretation of data from surveys and case studies, to ultimately develop the four themes. Recommendations deriving from these themes are also described. These include modeling a variety of pedagogies; adopting realistic expectations for faculty change; institutionalizing faculty development so it can take place over multiple years; being transparent with faculty about known barriers and aligning supports with those barriers; and helping faculty develop strategies for transparency with students about student-centered pedagogies.

Mastery-Based Testing to Promote Learning: Experiences with Discrete Mathematics

Math courses graded on homework, tests, and a final examination can result in students putting together enough partial credit to pass the class without gaining a reasonable mastery of the course content. Mastery-based testing can help to address this by allowing the instructor to align course grades with mastery of the learning objectives for the course. This article is a reflection on my experiences implementing mastery-based testing in Discrete Mathematics. I give a brief introduction to the ideas behind mastery-based testing and discuss the construction of two of my mastery tests. The change affected my teaching, helping me to see where students need help understanding the material. Instructor observation and feedback from student evaluations of instruction indicate that student learning was improved with the change.

Simple Specifications Grading

Specifications grading is a version of mastery grading distinguished by giving students clear specifications that their work must meet, and grading most things pass/fail based on those specifications. Mastery grading systems can get quite elaborate, with hierarchies of objectives and various systems for rewriting and retesting. In this article I present and discuss the results of two relatively simple implementations of specs grading, one in a differential equations course, and one in a discrete math course that includes an introduction to proof writing. I highlight several novel aspects of my systems: a buy-in activity, a “catch-up” quiz, and an oral quiz option.

ОСОБЕННОСТИ ПРИМЕНЕНИЯ ПАКЕТА MAPLE В ШКОЛЬНОМ КУРСЕ МАТЕМАТИКИ

This article discusses the features of using the Maple package in a school math course. The school mathematics course consists of basic mathematical concepts, ideas and principles. The scientific nature of the course content and the abstract nature of the topics studied make this course difficult to study in the classroom. The current situation with the coronavirus pandemic has completely eliminated full-time education and made distance education more relevant. The share of independent work of students has increased significantly. This negatively affects the ability to read and understand very complex material. In this regard, the choice of the Maple package as a method of computer technology and its technological possibilities for the organization of independent work of students in school mathematics courses are justified. The authors of the article developed a technology of teaching using the Maple package for school mathematics courses on the basis of the South Kazakhstan State Pedagogical University. This teaching method is aimed at organizing the independent work of students in the study of school mathematics. Examples of the use of the Maple package to solve some problems in a school math course are presented. Taking into account the specifics of the tasks of teaching mathematics at school, the possibilities and advantages of the technology of organizing students' independent work with the help of the Maple package are considered in detail.

A meta-analysis of the effectiveness of the method of creative drama in math courses in regard to student scores in achievement, attitude and retention

In this study, pretest-posttest control group design thesis in experimental models was investigated by meta-analysis for preschool , primary and secondary school mathematics classes based on creative drama method, between years 2000-2020 which are accepted by universities in Turkey. 3doctoral theses and 20 master's theses that are suitable for the problem of this research and have sufficient statistical data were included in the meta-analysis. In the analysis of data, meta-analysis of transaction effectiveness was used. In this study, the effect of creative drama method on students' academic achievement, retention(remembering) and affective (attitude) scores were examined. As a result of meta-analysis calculations, the effect size value of creative drama method on students' academic achievement scores was 0.926, the effect size on retention scores was 1.414 and the effect size value on attitude scores was 0.600. These values determined as a result of the analysis; shows that the effect size is wide for academic success and retention and medium for attitude. According to these findings, the academic success and retention of creative drama method in preschool and elementary mathematics lessons is wide; it can be said that it affects attitude at a moderate level significantly.