Collaborative Workshops and Student Academic Performance in Introductory College Mathematics Courses: A Study of a Treisman Model Math Excel Program

High failure rates in introductory college mathematics courses, particularly among underrepresented groups of students, have been of concern for many years. One approach to the problem experiencing some success has been Treisman's Emerging Scholars workshop model. The model involves supplemental workshops in which students solve problems in collaborative learning groups. This study reports on the effectiveness of Math Excel, an implementation of the Treisman model for introductory mathematics courses (college algebra, precalculus, differential calculus, and integral calculus) at Oregon State University over five academic terms. Regression analyses revealed a significant effect on achievement (.671 grade points on a 4‐point scale) favoring Math Excel students. Even after adjusting for prior mathematics achievement using linear regression with SAT‐M as predictor, Math Excel groups' grade averages were over half a grade point better than predicted (significant at the .001 level). This study provides supporting evidence that programs like Math Excel can help students in making a successful transition to college mathematics study.     

A mathematics support programme for first-year engineering students

This article describes a mathematics support programme at the University of Queensland, targeted at first-year engineering students identified as having a high risk of failing a first-year mathematics course in calculus and linear algebra. It describes how students were identified for the programme and the main features of the programme. The success of the programme was evaluated using student feedback as well as a comparison of the performance of students who participated in the support programme with those of a similar background who briefly attended or did not attend the programme. The pass rate in the supported group of regular attendees was 79% compared with 43% and 46% in the briefly supported and unsupported groups, respectively. Both student feedback and statistical data indicate that the programme was highly successful in improving the performance of those who regularly engaged with it.     

Are beginning calculus and engineering students adequately prepared for higher education? An assessment of students’ basic mathematical knowledge

Are students transitioning from the secondary level to university studies in mathematics and engineering adequately prepared for education at the tertiary level? In this study, we discuss the prior mathematical knowledge and skills demonstrated by Norwegian engineering (N?=?1537) and calculus (N?=?626) university students by using data from a mathematics assessment administered by the Norwegian Mathematical Council. The assessment examines students’ conceptual understanding, computation skills and problem solving skills on the basis of the mathematics curriculum of lower secondary education. We found that calculus students significantly outperformed engineering students, but both student groups struggled to solve the test, with the calculus and engineering groups scoring an average of 60% and 46%, respectively. Beginning students who fail to master basic skills, such as solving arithmetic and algebra problems, will most likely face difficulties in their further courses. Although few female students enrol in calculus and engineering programmes compared with male ones and are thus underrepresented, male and female students at the same ability level achieved comparable test scores. Furthermore, students reported high levels of intrinsic and extrinsic motivation, and a positive relationship was observed between intrinsic motivation and achievement.     

The interaction between dropout,graduation rates and quality ratings in universities

This paper investigates in a non-parametric framework whether academic programmes maximize their student graduation rates and programme quality ratings given the first-year student dropout rates. In addition, it explores what institutional and programme characteristics explain this interaction. The results show a large variation in how academic programmes are able to deal with the selective nature of first-year dropout. Nevertheless, we can accurately explain the variation among programmes by programme and institutional characteristics. It seems that universities can maximize the relation between first-year dropout, graduation rates and quality ratings in several ways: (1) by improving student programme satisfaction, (2) by better preparing certain groups of students for higher education, (3) by supporting male students, (4) by supporting ethnic minority students, (5) by attracting older staff, and (6) by strengthening the selective nature of the first year (ie, increasing the academic dismissal policy threshold).     

On flipping first-semester calculus: a case study

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are ‘flipping’ (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.     

A hybrid model of mathematics support for science students emphasizing basic skills and discipline relevance

The problem of students entering university lacking basic mathematical skills is a critical issue in the Australian higher-education sector and relevant globally. The Maths Skills programme at La Trobe University has been developed to address under preparation in the first-year science cohort in the absence of an institutional mathematics support centre. The programme was delivered through first-year science and statistics subjects with large enrolments and focused on basic mathematical skills relevant to each science discipline. The programme offered a new approach to the traditional mathematical support centre or class. It was designed through close collaboration between science subject coordinators and the project leader, a mathematician, and includes resources relevant to science and mathematics questions written in context. Evaluation of the programme showed it improved the confidence of the participating students who found it helpful and relevant. The programme was delivered through three learning modes to allow students to select activities most suitable for them, which was appreciated by students. Mathematics skills appeared to increase following completion of the programme and student participation in the programme correlated positively and highly with academic grades in their relevant science subjects. This programme offers an alternative model for mathematics support tailored to science disciplines.     

Preservice Teachers of High School Mathematics: Success,Failure, and Persistence in the Face of Mathematical Challenges

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five‐year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade point average (GPAs) upon entering the program, earned higher grades in their first college mathematics course, and failed fewer courses than students who left the program or university. Learning and performance motivational goals did not predict success in the program. Performance goals decreased over time. Nearly half the successful students repeated one or more mathematics courses. Ten students completed their degrees, obtained a teaching license, and are teaching despite the need for multiple repetitions of the same mathematics courses. These persistent students did not differ from their peers in motivational goals. Our results suggest that although students with higher GPAs and initial mathematics grades were more likely to complete the program, students who experienced challenges in mathematics courses were able to succeed. We discuss the implications of these results for recruiting, advising, and retention of students in mathematics education programs.     

Impact of first-year mathematics study groups on the retention and graduation of engineering students

Many interventions have been proposed to improve the retention and graduation rates of engineering students. One such intervention is to use study groups for first-year college students; such groups provide a structured environment in which the students can learn course material from each other outside of class and can provide the students with a sense of community. In this paper, we report on the impacts fostered by study groups in first-year mathematics courses on the odds of retaining and graduating engineering students. Students who participated in the study groups are compared to students of similar academic preparation who did not participate in such groups. It is found that student participation in study groups is significantly associated with the higher odds of being retained in engineering studies through the first 3 years of college. The results reported here are not as certain for the effect of study group participation on 5-year graduation odds for engineering students and some possible reasons for this are discussed.     

Redesigning the calculus sequence at a research university: issues,implementation, and objectives

The paper discusses the progress and challenges of a new reformed calculus sequence for science, engineering, and mathematics students developed by the Institute of Technology Centre for Educational Programs and School of Mathematics, University of Minnesota. The main objective of the Initiative is to enable undergraduates to better learn calculus and the critical thinking skills necessary to apply it in a variety of science and engineering problems. Changes in content and pedagogy are emphasized, including instructional teamwork and student-centred learning, involving students working cooperatively in small groups and exploring mathematical ideas using appropriate technologies. Achievement and retention of Initiative students are compared with a control group from the standard calculus sequence. Student attitudes about the usefulness of the Initiative's curriculum, pedagogy, and its influence on learning are discussed. Future implications including new uses of distributed learning are also addressed.     

A support learning programme for first-year mathematics*

ABSTRACT

This article is a follow-up to an earlier paper on the mathematics support learning tutorial programme (SLT), an intervention programme at The University of Queensland that targets students considered to be at risk of failing Calculus and Linear Algebra I, the first tertiary level mathematics subject at The University of Queensland. The first paper (Hillock, P., Jennings, M., Roberts, A., & Scharaschkin, V. (2013). Amathematics support programme for first-year engineering students. International Journal of Mathematical Education in Science and Technology, 44(7), 1030–1044) reported on the inaugural programme implemented in 2012. This article provides an update of the progress of the SLT since 2012. We provide statistics for the subsequent 12 semesters to Semester 2, 2018 and describe the evolution of the SLT since its implementation. Statistical analysis of the additional data and student feedback indicate that the SLT continues to have a positive impact on student learning, with weak students making significant gains from attending the programme.     

Enhancing the Success of African-American Students in the Sciences: Freshman Year Outcomes

The Meyerhoff Program is an intensive, multicomponent program focused on enhancing the success of talented African-American students in science and engineering at a predominantly white, medium-sized university. The program components, taken together, address the four primary factors emphasized in the research literature as limiting minority student performance and persistence in science: knowledge and skills, motivation and support, monitoring and advising, and academic and social integration. Outcome analyses indicated that the first three cohorts of Meyerhoff students (total N=69) achieved an overall GPA (mean=3.5) significantly greater than that of an African-American historical comparison sample (mean=2.8) of comparably talented science students at the university. This difference was even greater for first year science GPA (means of 3.4 and 2.4, respectively), and in specific science and mathematics courses. Observational and questionnaire data indicated that the Meyerhoff program study groups, peerbased community, financial scholarships, summer bridge program and staff appear to be especially important contributors to student success. Implications of the findings for enhancing the success of African-American and other underrepresented populations in science are discussed.     

Improving student learning in calculus through applications

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.     

Factors influencing first-year students' success in mathematics

Qualitative data from lecturers and students were used to identify factors which were perceived as making the most important contributions to students' academic success or failure in first-year mathematics courses. The study was conducted in three phases involving exploratory open-ended questionnaires, Likert-type questionnaires, and interviews. The results highlight both areas of similarities and areas of differences in lecturers' and students' perceptions about influences on student success and failure. While both students and lecturers acknowledged the importance of motivation, differences in perceptions suggest further research is needed in the areas of active learning, help-seeking, and student effort and workload.     

Factors affecting student success in a first-year mathematics course: a South African experience

In spite of sustained efforts tertiary institutions implement to try and improve student academic performance, the number of students succeeding in first-year mathematics courses remains disturbingly low. For most students, the gap between their mathematical capability and the competencies they are expected and need to develop to function effectively in these courses persists even after course instruction. In this study, an instrument for identifying and examining factors affecting student performance and success in a first-year Mathematics university course was developed and administered to 86 students. The overall Cronbach's Alpha coefficient for the questionnaire was found to be 0.916. Having identified variables from prior research known to affect student performance, factor analysis was used to identify variables exhibiting the greatest impact on student performance. The variables included prior academic knowledge, workload, student approaches to learning, assessment, student support teaching quality, methods and resources. From the analysis, students' perceptions of their workload emerged as the factor having the greatest impact on student's performance, followed by the matriculation examination score. The findings are discussed and strategies that can be used to improve teaching and contribute to student success in a first-year mathematics course in a South African context are presented.     

Retention of differential and integral calculus: a case study of a university student in physical chemistry

This paper reports a study on retention of differential and integral calculus concepts of a second-year student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly reconstruct the knowledge, given a few hints, this is just as good as retention. The study was conducted using a mixed method approach investigating students’ knowledge in three worlds of mathematics. The results showed that the student had a very low retention of concepts, even after hints. However, after completing the calculus course, the student had successfully used calculus in a physical chemistry study programme. Hence, using calculus in new contexts does not in itself strengthen the original calculus learnt; they appeared as disjoint bodies of knowledge.     

Active learning: a case study of student engagement in college Calculus

This paper presents a case study for strategic engagement of students in a Calculus course in order to produce increased learning in the classroom. Since it has been shown that active learning can promote greater comprehension for students in science, technology, engineering, and mathematics (STEM) courses, the researcher utilized many types of active learning techniques to enhance classroom instruction. The key components implemented are presented as a model of enhanced learning through developed classroom engagement. This course redesign model entitled, Strategic Engagement for Increased Learning (SEIL), has the potential to (1) contribute to the body of knowledge on ways to improve mathematics skills for college students, (2) identify successful teaching strategies and technologies that will promote the retention of STEM students, (3) increase the success rate of students taking Calculus, and (4) help produce more STEM graduates needed for the STEM workforce in the United States of America.     

Differentiation of teaching and learning mathematics: an action research study in tertiary education

Diversity and differentiation within our classrooms, at all levels of education, is nowadays a fact. It has been one of the biggest challenges for educators to respond to the needs of all students in such a mixed-ability classroom. Teachers’ inability to deal with students with different levels of readiness in a different way leads to school failure and all the negative outcomes that come with it. Differentiation of teaching and learning helps addressing this problem by respecting the different levels that exist in the classroom, and by responding to the needs of each learner. This article presents an action research study where a team of mathematics instructors and an expert in curriculum development developed and implemented a differentiated instruction learning environment in a first-year engineering calculus class at a university in Cyprus. This study provides evidence that differentiated instruction has a positive effect on student engagement and motivation and improves students’ understanding of difficult calculus concepts.     

How to make mathematics relevant to first-year engineering students: perceptions of students on student-produced resources

Many approaches to make mathematics relevant to first-year engineering students have been described. These include teaching practical engineering applications, or a close collaboration between engineering and mathematics teaching staff on unit design and teaching. In this paper, we report on a novel approach where we gave higher year engineering and multimedia students the task to ‘make maths relevant’ for first-year students. This approach is novel as we moved away from the traditional thinking that staff should produce these resources to students producing the same. These students have more recently undertaken first-year mathematical study themselves and can also provide a more mature student perspective to the task than first-year students. Two final-year engineering students and three final-year multimedia students worked on this project over the Australian summer term and produced two animated videos showing where concepts taught in first-year mathematics are applied by professional engineers. It is this student perspective on how to make mathematics relevant to first-year students that we investigate in this paper. We analyse interviews with higher year students as well as focus groups with first-year students who had been shown the videos in class, with a focus on answering the following three research questions: (1) How would students demonstrate the relevance of mathematics in engineering? (2) What are first-year students' views on the resources produced for them? (3) Who should produce resources to demonstrate the relevance of mathematics? There seemed to be some disagreement between first- and final-year students as to how the importance of mathematics should be demonstrated in a video. We therefore argue that it should ideally be a collaboration between higher year students and first-year students, with advice from lecturers, to produce such resources.     

Mathematical aspects of educating architecture designers: a college study

This paper considers a second-year Mathematical Aspects in Architectural Design course, which relies on a first-year mathematics course and offers mathematical learning as part of hands-on practice in architecture design studio. The 16-hour course consisted of seminar presentations of mathematics concepts, their application to covering the plane by regular shapes (tessellations), and an architecture design project. The course follow-up examined the features of mathematical learning in the studio environment using qualitative methods. It showed students’ curiosity and motivation to deepen in mathematical subjects and use them in their tessellation design projects. The majority of the students refreshed and practically applied their background mathematical knowledge, especially in calculus, on a need-to-know basis.     

The mathematics textbook at tertiary level as curriculum material – exploring the teacher's decision-making process

This paper reports on a study about how the mathematics textbook was perceived and used by the teacher in the context of a calculus part of a basic mathematics course for first-year engineering students. The focus was on the teacher's choices and the use of definitions, examples and exercises in a sequence of lectures introducing the derivative concept. Data were collected during observations of lectures and an interview, and informal talks with the teacher. The introduction and the treatment of the derivative as proposed by the teacher during the lectures were analysed in relation to the results of the content text analysis of the textbook. The teacher's decisions were explored through the lens of intended learning goals for engineering students taking the mathematics course. The results showed that the sequence of concepts and the formal introduction of the derivative as proposed by the textbook were closely followed during the lectures. The examples and tasks offered to the students focused strongly on procedural knowledge. Although the textbook proposes both examples and exercises that promote conceptual knowledge, these opportunities were not fully utilized during the observed lectures. Possible reasons for the teacher's choices and decisions are discussed.