A Study of Students’ Readiness to Learn Calculus

Carlson, Marilyn P.; Madison, Bernard L.; West, Richard

doi:10.1007/s40753-015-0013-y

Cited by 50 publications

(32 citation statements)

References 19 publications

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“…Generally speaking, in many countries high school graduateseven those choosing advanced mathematics coursesseem to not meet an intermediate benchmark of mathematics achievement, that is they are struggling to demonstrate knowledge of concepts and procedures in algebra, calculus and geometry to solve routine problems (Mullis et al 2009;Mullis et al 2016). In more detail, new STEM undergraduates seem to employ surface learning and understanding, to be inflexible in switching between the embodied, symbolic and formal worlds, to focus on an exclusive process view and to apply only intuitive thinking (e.g., Godfrey and Thomas 2008 for abstract algebra; Thomas and Stewart 2011 for linear algebra; Carlson et al 2015 for calculus and analysis). For instance, students were reported to have a limited concept of equality that is not based on a formal understanding of equivalence relation and its properties (Godfrey and Thomas 2008) and to view functions as a picture of an event and recipe to get an answer instead of two quantities changing together and a mapping of input values of the function's domain to output values in the function's range (summarized by Carlson et al 2015).…”

Section: The Person-side: Mathematical Abilities and Interests Of Firmentioning

confidence: 99%

“…In more detail, new STEM undergraduates seem to employ surface learning and understanding, to be inflexible in switching between the embodied, symbolic and formal worlds, to focus on an exclusive process view and to apply only intuitive thinking (e.g., Godfrey and Thomas 2008 for abstract algebra; Thomas and Stewart 2011 for linear algebra; Carlson et al 2015 for calculus and analysis). For instance, students were reported to have a limited concept of equality that is not based on a formal understanding of equivalence relation and its properties (Godfrey and Thomas 2008) and to view functions as a picture of an event and recipe to get an answer instead of two quantities changing together and a mapping of input values of the function's domain to output values in the function's range (summarized by Carlson et al 2015). Students were also found to have an unstable conceptualization of slope preventing covariational reasoning (Nagle et al 2013;Thompson 1994).…”

Section: The Person-side: Mathematical Abilities and Interests Of Firmentioning

confidence: 99%

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Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

Deeken

Neumann

Heinze

2019

Int. J. Res. Undergrad. Math. Ed.

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In many countries STEM degree programs face high dropout rates, which are often attributed to insufficient mathematical preparation of incoming undergraduates. However, it is largely unclear which mathematical prerequisites universities expect from their new STEM undergraduates. There are hardly official documents and it is even an open question whether there is a consensus among university instructors. The main goal of this study is therefore to describe the expected mathematical prerequisites for new STEM undergraduates. We conducted a Delphi study with German university instructors for first semester mathematics courses in STEM programs. The participants identified 179 prerequisites addressing: (1) mathematical content, (2) mathematical processes, (3) views about the nature of mathematics, and (4) personal characteristics. For 140 of these prerequisites there was a consensus regarding their necessity among the university instructors. The expected mathematical prerequisites are mainly on a basic level and do not require formalistic or abstract mathematical knowledge or abilities.

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Section: The Person-side: Mathematical Abilities and Interests Of Firmentioning

confidence: 99%

Section: The Person-side: Mathematical Abilities and Interests Of Firmentioning

confidence: 99%

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

Deeken

Neumann

Heinze

2019

Int. J. Res. Undergrad. Math. Ed.

View full text Add to dashboard Cite

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“…J. Dougherty, Bryant, Bryant, Darrough, & Pfannenstiel, 2015;Sangwin & Jones, 2017;Simon, Kara, et al, 2016;Vilkomir & O'Donoghue, 2009). Likewise, with investigations about inverse functions, most focus more on errors made by students in solving problems (Carlson et al, 2015;Kontorovich, 2017;Paoletti et al, 2018;Zazkis & Kontorovich, 2016;Zazkis & Zazkis, 2011). In this section, the researchers conclude reversible reasoning during the process of solving inverse function problems.…”

Section: Discussionmentioning

confidence: 97%

“…It is in accordance to the findings of the previous study ( Paoletti et al, 2018;Wasserman, 2017), which suggested that researchers need to survey to assess teachers' mathematical knowledge in interpreting inverse functions. So the factors that cause students to experience confusion in the rank -1 (Kontorovich, 2017;Zazkis & Kontorovich, 2016;Zazkis & Zazkis, 2011) and students interpret functions and inverses analytically and graphically (Carlson et al, 2015) can be described in detail.…”

Section: Implication Of Reversible Reasoning For Education Learning Pmentioning

confidence: 99%

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Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Ikram¹,

Purwanto²,

Parta³

et al. 2020

Journal for the Education of Gifted Young Scientists

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Researchers have argued that reversible reasoning is involved in all topics in mathematics. The study employed a qualitative research approach, consisted of three sessions (pre-assessment, thinking-aloud, and interview), and involved eight participants enrolled in Algebra class. The aim was to explore the potential role of reversible reasoning on students' inverse functions. The result of study indicated that there three categories of reversible reasoning that refer to the consistency of students in completing inverse function tasks, which are relational-harmonic, relationalvisual, and relational-identity. Mental activities performed by the students in constructing and reasoning inverse functions were also explained. In addition, potential aspects of the students' reversible reasoning created during the process of constructing meaning were highlighted. These findings provide perspectives on reversible reasoning, students' understanding of inverse functions, and areas of future research

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First mathematics course in college and graduating in engineering: Dispelling the myth that beginning in higher‐level mathematics courses is always a good thing

Wilkins

Bowen

Mullins

2021

J of Engineering Edu

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Background Graduation rates in engineering programs continue to be a concern in higher education. Prior research has documented an association between students' experiences in first‐year mathematics courses and graduation rates, but the influences of the mathematics courses completed and the grades earned are not fully understood. Purpose The purpose of this study was to investigate the relationship among the first undergraduate mathematics course a student completes, the grade they earn in this course, and the likelihood of graduating with a degree in engineering within six years. Method The study involved 1504 students from five consecutive cohorts of first‐year students enrolled in an engineering degree program at a medium‐sized Midwestern public university. Logistic regression was used to model the interrelationship between course and grade in predicting the relative likelihood of graduation for students enrolled in 16 different mathematics courses. Results Overall, students who take Calculus I or a more advanced mathematics course as their first mathematic course and who are more successful in their first mathematics course are more likely to graduate with a degree in engineering. However, considering grade and course together, some groups of students who are more successful in lower‐level mathematics courses are as likely to graduate as students who are less successful in upper‐level mathematics courses. Conclusions Evidence from this study helps to dispel the myth that beginning with higher‐level mathematics courses is the optimal course‐taking strategy when pursuing an engineering degree. Findings have implications for student advising, curriculum and instruction, high school course‐taking, and broadening participation in engineering.

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A Study of Students’ Readiness to Learn Calculus

Cited by 50 publications

References 19 publications

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

First mathematics course in college and graduating in engineering: Dispelling the myth that beginning in higher‐level mathematics courses is always a good thing

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