A Study of Calculus Instructors’ Perceptions of Approximation as a Unifying Thread of the First-Year Calculus

Sofronas, Kimberly S.; DeFranco, Thomas C.; Swaminathan, Hariharan; Gorgievski, Nicholas; Vinsonhaler, C.; Wiseman, Brianna; Escolas, Samuel

doi:10.1007/s40753-015-0019-5

Cited by 6 publications

(4 citation statements)

References 39 publications

(62 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar observations were reported by Snyder fifty years ago in his seminal book on college learning (Snyder, 1971). Even honest efforts to enrich curricula often failed due to the impacts of tacit knowledge held by students.…”

Section: Theoretical Backgroundsupporting

confidence: 78%

“…Some evidence to confirm this hypothesis was found by Heid (1988), while also assuming that the introduction of computing devices would be helpful tools for the refocusing of mathematics curricula with an emphasis on conceptual learning. Furthermore, foundational ideas in differential calculus have proven difficult to learn by using traditional instructional methods (Sofronas et al, 2015). Typical misconceptions include confusing a function with a formula and not accepting other representations: "In addition, though students primarily regard a function as 'something you plug numbers into,' they still manage to consider it static, making it difficult to understand concepts such as limits" (Pyzdrowski et al, 2013, p. 513).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

Can Students' Attitudes and Behaviors be Changed by Educational Interventions?

Gynnild¹,

Tyssedal²

2020

DUT

View full text Add to dashboard Cite

This study examined engineering students’ attitudes and behaviors in a first-year Calculus course. Not surprisingly, High School mathematics and physics grades correlated closely with self-reported Calculus grades, and a student survey conducted four years apart demonstrated almost identical attitudes and behaviors despite the introduction of a range of measures aimed to enhance learning. The better the grades, the fairer students deemed it to be, and the less of in-depth learning, the poorer the grades. The higher the ambitions, and the more active and hardworking, the better the grades. Academic success factors included an ability to keep pace with progression, and a commitment to advance learning. The minimal impact of interventions appears as surprising; however, this study brings perspectives to make sense of such data, also capable of producing greater future successes.

show abstract

Section: Theoretical Backgroundsupporting

confidence: 78%

Section: Theoretical Backgroundmentioning

confidence: 99%

Can Students' Attitudes and Behaviors be Changed by Educational Interventions?

Gynnild¹,

Tyssedal²

2020

DUT

View full text Add to dashboard Cite

show abstract

“…Simpson (2011, 2012) have posited that there is a fundamental lack of students' ability to explain their mathematical ideas in an academic manner, which is suggestive of a requirement for more universities to place emphasis on these issues as early as possible in their BSc Mathematics programmes. This assertion is supported by Sofronas et al (2015), who note that calculus is used as a unifying thread in the first year of undergraduate teaching, and the contextualisation of calculus as a pure mathematical concept is directly beneficial to students in this regard. This ties back into the aforementioned requirement for students' to possess a keen understanding of the applications of pure mathematics and the theories behind calculus and analysis, as noted by Jaworski, Mali and Petropoulou (2017), who state the importance of explaining the reasoning mathematical principles to students.…”

Section: Literature Review: Issues In Transition -Further To Highermentioning

confidence: 87%

Essential Concepts for the First Year of Study for BSc Mathematics

Capes

Rowlett

2018

MSOR

View full text Add to dashboard Cite

To inform discussion about content for the first year of undergraduate mathematics, a study was completed which reviewed: the A-level Mathematics specification; published literature on the transition from A-level to university mathematics; the second and third year curricula of modules at three English universities with different foci. This aimed to investigate what students might reasonably be expected to have covered when they arrive at university, what happens in practice at the transition to university, and the role of the first year as preparation for later study. Content suggestions focus on calculus, linear algebra and analysis as core topics. There is also evidence of the need to focus on students' understanding of where formulae and solutions originated as well as their ability to produce pieces of academic and mathematical writing. Findings also include suggestion that what happens in the first year, while similar between institutions, does depend on the overall focus of the degree programme.

show abstract

“…Understanding limits and continuity prepares students for more advanced study of differential and integral calculus, which are basic ideas in college-and university-level mathematics. According to Sofronas et al (2015), many first-year university students cannot link concepts to skills, nor can they master calculus concepts or the fundamental skills of calculus. The abstract nature of calculus can result in a negative attitude toward mathematics and science at secondary and university levels.…”

Section: Research Problemmentioning

confidence: 99%

Students’ misconceptions and difficulties with learning limits and the continuity of functions at selected Rwandan secondary schools

Munyaruhengeri,

Umugiraneza,

Ndagijimana

et al. 2024

View full text Add to dashboard Cite

This study investigates students’ difficulties and misconceptions with learning limits and explores the factors contributing to these misconceptions. The study used a mixed method approach, and the participants comprised 252 students and 21 teachers. Data collection methods included the Limits and Continuity of Functions Achievement Test, classroom observations, and focus group interviews. The study's findings revealed significant differences in the mean scores of the Limits and Continuity of Functions Achievement Test among different representations. It also identified that students' misconceptions stemmed from their limited exposure to active learning approaches and their tendency to rely on rote memorization. The study pointed out that teaching strategies, along with students' haste in providing responses, contributed to these misconceptions and learning difficulties. The fast-paced nature of teaching aimed at covering the syllabus requirements also played a role in creating knowledge gaps and reinforcing misconceptions. Through continuous professional development, this study recommends improving mathematics teachers’ content, pedagogical knowledge of teaching and learning limits, and continuity of functions.

show abstract

A Study of Calculus Instructors’ Perceptions of Approximation as a Unifying Thread of the First-Year Calculus

Cited by 6 publications

References 39 publications

Can Students' Attitudes and Behaviors be Changed by Educational Interventions?

Can Students' Attitudes and Behaviors be Changed by Educational Interventions?

Essential Concepts for the First Year of Study for BSc Mathematics

Students’ misconceptions and difficulties with learning limits and the continuity of functions at selected Rwandan secondary schools

Contact Info

Product

Resources

About