First-year Mathematics Research Articles

Effectiveness of OER use in first-year higher education students' mathematical course performance: A case study

This chapter aims to understand the impact of Open Educational Resources (OER) on first-year mathematics students at the Instituto Profesional Providencia (IPP) in Santiago, Chile, where more than half (52%) of first-year students typically drop out of their studies. In order to address this, the institution established an innovation fund and a project to profile, assess and monitor student performance through an early warning system. IPP stakeholders envisioned that a strategy to promote OER uptake could complement these efforts. By looking at an OER intervention amongst firstyear students, this study seeks to identify ways in which OER can provide new tools, opportunities, and contexts to improve student performance and lower dropout rates by answering the following research questions: What is the effect of OER use on firstyear students’ mathematics course performance? In face-to-face instruction, what is the effect of OER use on first-year students’ class attendance? What are teachers’ and students’ perceptions of the OER adoption process? To answer questions one and two, this study used a quantitative method to estimate the effect of OER use on students’ mathematical course performance and class attendance. Five groups of first-year students were compared based on the analysis of two scenarios. In Scenario 1, a control group and two treatment groups were in a traditional face-to-face classroom setting. The control group relied on a proprietary textbook; the first treatment group was taught with the help of a Khan Academy OER collection; and the second treatment group was taught by means of a custom-designed Open Textbook. Scenario 2 compared two classes in blended-mode Algebra and Calculus courses. The control group relied on a proprietary resource, and the treatment group used a Khan Academy collection of OER in addition to the proprietary resource. In order to estimate the effectiveness of OER use on students’ mathematical performance, the impact analysis focused on three result variables: (1) students’ marks before the final exam, (2) students’ final exam marks, and (3) students’ final course marks after the exam. To answer research question three, a mixed-methods approach was applied in the form of a series of semi-structured interviews, a focus group discussion and a student survey. The students who used the Khan Academy OER collections or the Open Textbook were asked to participate in this study in order to better comprehend learners’ and teachers’ perceptions of OER. Students in Scenario 1 who used Khan Academy resources obtained statistically significantly better exam grades than those who used the proprietary resource or the Open Textbook, suggesting that not all kinds of OER have the same effect on student performance. In Scenario 2, there was no improvement in mathematical course performance amongst students using OER. In terms of student attendance, face-to-face mode students who used Khan Academy OER had significantly lower attendance levels than those who relied on the proprietary textbook, which may be due to the fact that when students have access to the infrastructure required to access OER remotely they tend to work more from home. With regard to student and teacher perceptions of the OER adoption process, the qualitative and quantitative data confirmed the assumption that OER can be relevant and useful to Chilean students. The chapter concludes with the insight that “openness” does not necessarily produce an impact in and of itself, but is instead part of a greater set of tools and practices in which many variables exert an influence. Neither the intrinsic nature of information and communication technologies nor openness are tools or instruments that can be said to result in a specific outcome. The dataset arising from this study can be accessed at: https://www.datafirst.uct.ac.za/dataportal/index.php/catalog/577

Assessing and Modeling Student Academic Practices and Performance in First-Year Mathematics Courses in Higher Education

Objectives: This research brief explores literature addressing developmental education to identify successful interventions in first-year math courses in higher education. Our goal is to describe the relationship between students’ academic practices and their final course grade in their first-year math courses.
 Method: Data on 3,249 students have been gathered and analyzed using descriptive statistics and predicative analytics. We describe the Math program, which includes a supplemental support component, and the environment under which it was created. We then examine the behavior between students’ participation in supplemental support and their academic performance.
 Results: We used classification and regression tree algorithms to obtain a model that gave us data-driven guidelines to aid with future student interventions and success in their first-year math courses.
 Conclusions: Students’ fulfillment of the supplemental support requirements by specified deadlines is a key predictor of students’ midterm and final course grades. 
 Implications for Theory and/or Practice: This work provides a roadmap for student interventions and increasing student success with first-year mathematics courses.
 Keywords: First-year mathematics courses, supplemental support, higher education

The impact of peer assessment on mathematics students’ understanding of marking criteria and their ability to self-regulate learning

At the University of Nottingham peer-assessment was piloted with the objective of assisting students to gain greater understanding of marking criteria so that students may improve their comprehension of, and solutions to, future mathematical tasks. The study resulted in improvement in all four factors of observation, emulation, self-control and self-regulation thus providing evidence of a positive impact on student learning.The pilot involved a large first-year mathematics class who completed a formative piece of coursework prior to a problem class. At the problem class students were trained in the use of marking criteria before anonymously marking peer work. The pilot was evaluated using questionnaires (97 responses) at the beginning and end of the problem class. The questionnaires elicited students’ understanding of criteria before and after the task and students’ self-efficacy in relation to assessment self-control and self-regulation.The analysis of students’ descriptions of the criteria of assessment show that their understanding of the requirements for the task were expanded. After the class, explanation of the method and notation (consistent and correct) were much more present in students’ descriptions. Furthermore, 67 per cent of students stated they had specific ideas on how to improve their solutions to problems in the future. Students’ self-perceived abilities to self-assess and improve were positively impacted. The pilot gives strong evidence for the use of peer-assessment to develop students’ competencies as assessors, both in terms of their understanding of marking criteria and more broadly their ability to self-assess and regulate their learning.

A support learning programme for first-year mathematics

ABSTRACTThis 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.

Early Career Teacher Struggles: An Administrator’s Influence on Retention

Rebecca Ashe, a first-year mathematics teacher at North Hills High School, considered herself well-prepared after her university preparation. She is energetic and dedicated to her students, providing real-world examples in her classes from past experiences as an engineer. After 3 months in the classroom, however, Rebecca had become disheartened and exhausted. Moreover, Rebecca felt her school principal, Andy Anderson, had provided only superficial support. This case study explores obstacles that early career teachers face and asks readers to consider strategies that school administrators can employ to support these teachers. This case is suited for use in administrative preparation courses, specifically those focusing on human resources, evaluation, leadership, and supervision.

남한과 북한의 고등학교 1학년 수학 교과서 비교

Recently, there has been a growing interest in the exchanges and cooperations in the field of mathematics education between South Korea and North Korea. In this study, we compared and analyzed South and North Korean high school first-year mathematics textbooks based on the 2015 Mathematics Curriculum of South Korea and the 2013 Mathematics Gyosuyogang(Curriculum) of North Korea. The comparative analysis of the textbooks in this study was done in terms of the distribution of content areas and units, and the components and contents of units. As a result of comparing the distribution of content areas, the textbooks of South and North Korea differ in the proportion of each area, but they include all five content areas such as numbers and operations, letters and expressions, geometry, functions, probability and statistics. In the aspect of compositions of the unit, the textbooks of South and North Korea commonly contain the components playing similar roles. However, in most unit components, South Korean textbook contains more tasks and materials than North Korean textbooks, with using a wider range of materials and presenting in more depth.

Fostering Germane Load Through Self-Explanation Prompting In Calculus Instruction

The purpose of this research was to investigate the effect of self-explanation prompting to students’ germane load while studying mathematics in the multivariable calculus course. This research employed a quasi-experimental method with matching-only posttest-only control group design. The subject of the research consists of 72 first-year mathematics education undergraduate students. The results indicated that there was no significant difference in students’ germane load between students who implemented worked-example with self-explanation prompting and students who implemented worked-example without self-explanation prompting. However, it was revealed that the students' germane load was categorized high in both classes. It indicates that the worked-example method could foster students' germane load. Nonetheless, these results cannot be evidence that self-explanation prompting is capable to foster students' germane load. However, there is an association between germane load and learning objectives. When students achieve the learning objectives, then its learning method is able to foster the germane load. To assess the learning objectives, the posttest was arranged. The results stated that students who implemented the worked-example method with self-explanation prompting had better test scores than students who implemented the worked-example method without self-explanation prompting. This result was sufficient to provide evidence that the use of worked-example with self-explanation prompting could foster students’ germane load students in the multivariable calculus course.

Quantifying participation in, and the effectiveness of, remediating assessment in a university mathematics module

In Maths for Business, a large first-year mathematics module, the continuous assessment component comprises 10 weekly quizzes which combine to contribute 40% of the final module mark. If students did not receive the full five marks on their weekly quiz, they were provided with the opportunity to resubmit their corrected weekly quiz with an explanation of their error(s) for one additional mark. We refer to this process as ‘remediation’. Of the students who had the opportunity to remediate, ∼70% did. Through examining learning management system data, we show that the remediation process encouraged students to access module resources. Furthermore, by using a Bayesian hierarchical model to account for students’ level of participation, achievement and prior knowledge, we show that participation in the remediation process positively impacted the final examination marks of moderate to high-achieving students (based on initial continuous assessment marks). However, participation in the remediation process provided limited benefit to low-achieving students. We conjecture this is because these students had not achieved a level of understanding whereby participation in the remediation process could progress their knowledge.

Students’ activities for understanding function shifting by using GeoGebra

The needs of worker for STEM-related jobs caused STEM education becomes an important focus. Designing activities by combining Science, Technology, Engineering and Mathematics itself (STEM) is possible to do in mathematics learning. This paper aimed to describe students’ understanding on function shifting rules in calculus course through activities using GeoGebra as a technology application. A contextual problem was given to students and required them to solve it by using GeoGebra and using their prior knowledge in mathematics and physics. Teaching experiment was conducted to first-year mathematics education students. The data were obtained from the students’ worksheet and depth interview. The results showed that the students were interested with the learning approach and they could understand the rules of function shifting.

Students’ understanding of geometry terminology through the lens of Van Hiele theory

After a long six-year lapse, the Curriculum and Assessment Policy Statement introduced in 2012 included geometry as part of the South African Grade 12 Mathematics Paper 2. The first cohort of matriculation students wrote Paper 2 in 2014. This article reports on the understanding of geometry terminology with which a group of 154 first-year mathematics education students entered a rural South African university in 2015; 126 volunteered to be part of the study. Responses to a 60-item multiple-choice questionnaire (30 verbally presented and 30 visually presented items) in geometry terminology provided the data for the study. A concept’s verbal description should be associated with its correct visual image. Van Hiele theory provided the lens for the study. An overall percentage mean score of 64% obtained in the test indicated that the majority of the students had a fairly good knowledge of basic geometry terminology. The students obtained a percentage mean score of 68% on visually presented items against that of 59% on verbally presented items implying a lower level thinking as per Van Hiele theory. The findings of this study imply a combination approach using visual and verbal representations to enhance conceptual understanding in geometry. This has to be complemented and supplemented through scaffolding to fill student teachers’ content gap.

The experiences of first-year students in mathematics in using an e-learning platform at a university of technology

Abstract Universities of technology in South Africa have been trying to provide effective and flexible learning experiences to cater for the influx of students enrolling in the institutions who come from diverse educational backgrounds. One of the challenges arising from their diverse educational backgrounds is their poor background in the use of technologies for teaching and learning. The teaching of mathematics, particularly, is made more difficult because of the large number of students who have many misconceptions as a result of problems from the basic education that they were part of, for a period of 12 years. Consequently, a number of them do not make it to the mainstream education system due to poor performance in first-year mathematics. The purpose of the study on which this article reports was to determine the impact that an e-learning platform could have on mathematics first-year students when used as a supplement to the traditional methods of teaching. The study utilised quantitative and qualitative methods, with the qualitative data being used to interpret and make sense of the quantitative data. Participants were 35 first-year students in the Department of Civil Engineering at a university of technology. Data were generated from questionnaires and focus group interviews. It was found that the actual use of the system is dependent not only on student behavioural intention to use the system, but external factors also contribute negatively to the actual system use. Some external factors that were identified include poor Internet connectivity, insufficient computers and an inflexible timetable. The study recommends that universities of technology should take greater care in designing their academic calendars, so that it alleviates instead of tighten the constraints under which students work.

Sdrawkcab scitamehtam: The case for understanding mathematics backwards

Despite the widespread acknowledgement of the need for graduates with quantitative problem-solving skills, many students enter university having relied heavily on pattern recognition techniques for high school mathematics. While these can often lead students to obtaining correct solutions for problems similar to those which they have practised, they do not lead to a deeper understanding of the material and, critically, may not develop more widely-applicable skills. Even when correct solutions are obtained, students can sometimes not understand or explain why their solution is indeed correct. Here, I present an argument in favour of avoiding predictability in question structures and, in particular, asking questions ``backwards'' to how they might traditionally be asked. Some mathematical topics readily lend themselves to such approaches --- the Fundamental Theorem of Calculus tells us that an integral problem is inherently linked to an antiderivative problem --- whereas other require much more care and subtlety to avoid routine or predictable assessments. I will discuss some preliminary results from a first year probability subject at the University of Technology Sydney (UTS) which suggest that student understanding of material can be increased when they feel that prioritising pattern recognition over problem solving is unlikely to be rewarded with high marks. References Khan academy. expected value. URL: https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/e/expected_value . Mark Asiala, Anne Brown, David J. Devries, Ed Dubinsky, David Mathews, and Karen Thomas. A framework for research and curriculum development in undergraduate mathematics education. Maa Notes, pages 37–54, 1997. I. Chubb. Science, technology, engineering and mathematics in the national interest: a strategic approach. Australian Government, Canberra, 7 2013. URL: http://www.chiefscientist.gov.au/2013/07/science-technology-engineering-and-mathematics-in-the-national-interest-a-strategic-approach/ . Ted Dunning. Accurate methods for the statistics of surprise and coincidence. Computational Linguistics, 19(1):61–74, 1993. Justin Kruger and David Dunning. Unskilled and unaware of it: How difficulties in recognizing one's own incompetence lead to inflated self-assessments. Journal of Personality and Social Psychology, 77(6):1121–1134, 1999. doi:10.1037/0022-3514.77.6.1121 . Fengshan Liu. 14 - teaching inverse problems in undergraduate level mathematics, modelling and applied mathematics courses. In Qi-Xiao Ye, Werner Blum, Ken Houston, and Qi-Yuan Jiang, editors, Mathematical Modelling in Education and Culture, pages 165–172. Woodhead Publishing, 2003. doi:10.1533/9780857099556.4.165 . David S. Moore, George P. McCabe, and Bruce A. Craig. Introduction to the Practice of Statistics. W. H. Freeman and Company, New York, 6th edition, 2009. Terezinha Nunes, Peter Bryant, Rossana Barros, and Kathy Sylva. The relative importance of two different mathematical abilities to mathematical achievement. British Journal of Educational Psychology, 82(1):136–156, 2012. doi:10.1111/j.2044-8279.2011.02033.x . L. J. Rylands and C. Coady. Performance of students with weak mathematics in first-year mathematics and science. International Journal of Mathematical Education in Science and Technology, 40(6):741–753, 2009. doi:10.1080/00207390902914130 . R. R. Sokal and F. J. Rohlf. Biometry: The Principles and Practice of Statistics in Biological Research. W. H. Freeman and Company, New York, 2nd edition, 1981. Arathi Sriprakash, Helen Proctor, and Betty Hu. Visible pedagogic work: parenting, private tutoring and educational advantage in australia. Discourse: Studies in the Cultural Politics of Education, 37(3):426–441, 2016. doi:10.1080/01596306.2015.1061976 . Jon R. Star. On the relationship between knowing and doing in procedural learning. In B. Fishman and S. O'Connor-Divelbiss, editors, Proceedings of fourth international conference of the Learning Sciences, pages 80–86. Erlbaum, 2000. S. Woodcock and S. Bush. Slipping between the cracks? maximising the effectiveness of prerequisite paths in uts mathematics degrees. In Mark Nelson, Tara Hamilton, Michael Jennings, and Judith Bunder, editors, Proceedings of the 11th Biennial Engineering Mathematics and Applications Conference, EMAC-2013, volume 55 of ANZIAM J., pages C297–C314, 8 2014. URL: http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/7943 . Stephen Woodcock. Development of enquiry-oriented learning in the mathematical sciences. In Mark Nelson, Dann Mallet, Brandon Pincombe, and Judith Bunder, editors, Proceedings of the 12th Biennial Engineering Mathematics and Applications Conference, EMAC-2015, volume 57 of ANZIAM J., pages C1–C13, 5 2016. URL: http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10439 . F. P. Yee. Open-ended problems for higher-order thinking in mathematics. Teaching and Learning, 20(2):49–57, 2000. URL: https://repository.nie.edu.sg/handle/10497/365 .

Revelations from an online diagnostic arithmetic and algebra quiz for incoming students

A review of relevant literature revealed that research indicates an alarming number of secondary school students who enter tertiary institutions display a serious lack of mathematical basics required for the study of university mathematics. This so-called change from the secondary school to tertiary study of mathematics has become an important field of mathematical learning research. In this context, at the University of KwaZulu-Natal, online diagnostics for pre-calculus knowledge and skills were made available to first-year mathematics students. We report here on some findings from an analysis of the provision of diagnostic questions for basic arithmetic and algebra. The results show that the diagnostic questions which were in the form of an online quiz assisted students to cope with their mathematics module in the sense that it positively impacted on the final results of students who attempted the quiz.
 Significance:
 
 Students who completed an online quiz on basic arithmetic and algebra to identify their strengths and weaknesses indicated that the quiz prepared them for the material they had to study for their mathematics module.

You’ve got mail: The impact of online message-boards on performance in first year undergraduate mathematics and statistical methods units

As a supplement to face-to-face lectures and classes, message board software was introduced in a first year mathematics and statistical methods unit in a UK Russell Group University. Fifty percent of students signed up to this software, so when combined with a further first-year mathematics and statistical methods unit, without message board software, this enabled the opportunity to use a difference in difference methodology to find the causal impact of message board software on student examination performance. The results suggest that students who actively engage with message boards perform significantly better than students who sign up for the message boards, but neither ask, nor answer, questions. However, the results for the impact compared to non-participants is mixed, and may be related to behavioural change in students.

First-year secondary mathematics teachers’ metacognitive knowledge of communication activities

ABSTRACTResearch has documented that mathematics teachers rarely use communicative activities; activities that allow for the sharing of ideas and clarification of understandings (NCTM, 2000). Teacher metacognitive awareness provides a possible framework for understanding the difficulties secondary mathematics teachers face when attempting to incorporate communicative activities. Without metacognitive knowledge and awareness about communicative activities, teachers lack the understanding of the purpose of such activities, procedures used to implement such activities successfully, and/or the conditions under which such activities are useful. This case study analyzed the metacognitive knowledge and awareness of two first-year high school mathematics educators by asking what metacognitive knowledge and awareness of communicative activities did the participants have or were developing and what experiences helped the participants to develop this knowledge. Findings indicate that the participants believed used communicative activities in their classrooms. However, the communicative activities used by the participants rarely engaged students in communicating about their understandings of mathematics; instead, the participants engaged their students in communicative activities in order to construct classroom norms or to shift the responsibility for learning to the students. Thus, while the participants clearly demonstrated declarative knowledge of communicative activities, their procedural and condition knowledge, that is how, when, and why to use such activities, was not well formed. These finding suggest that more emphasis is needed on developing pre-service teachers procedural and conditional metacognitive knowledge of communicative activities. In addition, more qualitive research on mathematics teachers’ understanding of communicative activities is needed.

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

ABSTRACTMany 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.

First-Year Mathematics and Its Application to Science: Evidence of Transfer of Learning to Physics and Engineering

Transfer of mathematical learning to science is seen as critical to the development of education and industrial societies, yet it is rarely interrogated in applied research. We present here research looking for evidence of transfer from university mathematics learning in semester one to second semester sciences/engineering courses (n = 1125). A transfer index measure was derived from extant university assessments, calculated on content-matched questions requiring mathematical concepts and skills in students’ completed mathematics and science/engineering exams. We found that transfer could be measured in this way, and present path models of how transfer is associated with educational attainment and other factors. However, transfer was observed only in physics (n = 258) and engineering (n = 426); biology and molecular bioscience assessments did not provide opportunities for students to demonstrate their mathematical learning. In physics and engineering courses, mathematical attainment had a strong, direct, positive effect, with transfer of learning providing an additional direct and mediating effect upon students’ performance in these subjects. In physics and engineering, transfer was also associated with higher levels of educational attainment in general. This new, applied approach to examining transfer trialed here may provide opportunities for analysing, evaluating, and improving cross-disciplinary transfer of learning within universities.

Factors Affecting the International Students Success in a First-Year Mathematics Courses at ZUST

Factors Affecting the International Students Success in a First-Year Mathematics Courses at ZUST

Rethinking course structure: increased participation and persistence in introductory post-secondary mathematics courses

High failure and withdrawal rates in introductory post-secondary mathematics courses are a problem locally, nationally, and internationally. This leads to first-year mathematics courses creating a closed door, or a barrier, to further study of mathematics, of STEM disciplines, and in University as a whole. In this article, the authors describe the implementation of a modified course structure in a first-year undergraduate mathematics course. The new structure makes use of a combination of mastery learning strategies together with the beneficial effects of small class sizes to address the issues of historically high failure and withdrawal rates and low grade-point averages. Results show that careful planning of the structure of a course can have a positive effect on student success, and thus on attitude towards mathematics.

\u201cThis is what you need to be learning\u201d: an analysis of messages received by first-year mathematics students during their transition to university

This paper explores the messages that first-year mathematics students receive in the context of their academic studies during their transition from school to university mathematics. Through observations of lectures and discussions with first-year mathematics undergraduates in an English university, we identified and analysed the messages that two of their lecturers transmitted to them during this transitional phase. The results suggest that strongly framed messages are more easily perceived by students and affect them during their transition. Additionally, messages that have been received in the school context continue to have control over students’ thinking and on many occasions can impede adjustment to the new setting.