Calculus Students’ and Instructors’ Conceptualizations of Slope: A Comparison Across Academic Levels

Nagle, Courtney; Moore‐Russo, Deborah; Viglietti, Janine M.; Martin, Kristi

doi:10.1007/s10763-013-9411-2

Cited by 48 publications

(44 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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%

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

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.

show abstract

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

show abstract

“…Considering the history of mathematics, even the transition from geometric ratio to algebraic transition is apparent, literature indicates that students are often taught slope as a fraction, with the change in y over the change in x not as a ratio (Walter& Gerson, 2007). Moreover, students develop algorithmic knowledge about the slope (Nagle & Moore-Russo, 2013). It was seen in literature that teaching process, not giving opportunity to relate various representations of slope, stimulate this unfavorableness (Stump, 1999(Stump, , 2001.…”

Section: The Concept Of Slopementioning

confidence: 99%

“…Dr., Anadolu University, Faculty of Education, Department of Elementary Education, Eskişehir-Turkey. email: tuygur@anadolu.edu.tr ISSN: 1300-5340 http://www.efdergi.hacettepe.edu.tr/ derivative (Nagle, Moore-Russo, Viglietti & Martin, 2013). Slope is expected to conceptualize as a constant rate of change in middle school, as average rate of change in high school.…”

Section: Introductionmentioning

confidence: 99%

Students' Mathematization Process of the Concept of Slope within the Realistic Mathematics Education

Kabael¹,

Deniz²

2016

HUJE

View full text Add to dashboard Cite

ABSTRACT:The aim of this study is to analyze eight grade students' mathematizing processes of the concept of slope in light of the teaching process designed based on Realistic Mathematics Education. Participants of this design based research study were chosen via purposeful sampling in accordance with results of an open-ended test intended for prerequisite information before design teaching-learning environment. Survey data was acquired from open-ended test, researcher log, individual and group study papers and clinical interviews. Contexts, which provide opportunities to reflect preliminary conceptions of slope to teaching process are revealed. Conceptualization process of slope as ratio started with the need to be base of informal linear constant. Then it develops with the need of measurement of slope. Students reinvent that the slope is also an algebraic ratio by reflecting geometric ratio representation to coordinate plane. Designed teaching in this study was revealed that mathematization is important in transition among representations. Development of right triangle model occurred in three phases: (i) a context-dependent interpretive tool, (ii) a physical tool used to calculate the slope, (iii) a cognitive tool that that is no longer needed to be represented physically. Keywords: Slope, Mathematization, Realistic Mathematics Education ÖZ: Bu çalışmada Gerçekçi Matematik Eğitimine dayalı olarak desenlenen öğretim sürecinde sekizinci sınıf öğrencilerinin eğim kavramını matematikleştirme süreçlerinin incelenmesi amaçlanmıştır. Desen tabanlı bu araştırmanın katılımcıları, ön koşul bilgilere yönelik olarak hazırlanan açık uçlu testin sonuçlarına göre amaçlı örneklem yolu ile seçilmiştir. Araştırmanın verileri, açık uçlu test, araştırmacı günlüğü, bireysel ve grup çalışma kâğıtları ile katılımcılarla öğretim boyunca birebir gerçekleştirilen üçer klinik görüşmeden elde edilmiştir. Eğimin başlangıç kavramsallaştırmalarının öğretim sürecine yansıtılmasına fırsat veren bağlamlar ortaya konmuştur. Eğimin bir oran olarak kavramsallaştırılması süreci informal olarak edinilen doğrusal sabitlik kavramsallaştırmasına dayanak yaratma gereksinimi ile başlamıştır. Ardından eğimi ölçme gereksinimi ile gelişim göstermiştir. Eğimin geometrik oran temsilinin koordinat düzleminde yansıtılması yoluyla aynı zamanda cebirsel bir oran oluşunun öğrenciler tarafından keşfedilmesi sağlanmıştır. Ortaya konan öğretim temsiller arası anlamlı geçişlerde matematikleştirmenin önemini ortaya koymuştur. Ayrıca öğrenciler tarafından geliştirilen dik üçgen modelinin gelişimi üç aşamada olmuştur: (i) duruma bağlı olarak yorumlamaya yarayan bir araç, (ii) eğimin hesaplanmasında kullanılan henüz fiziksel olarak ortaya konulma gereği duyulan bir araç (iii) fiziksel olarak ortaya konulma gereği duyulmayan bilişsel bir araç.

show abstract

“…With regard to the analytical mode students have difficulties understanding the need for equality of lateral limits when using the concept of the derivative as the limit of the difference quotient (Zandieth, 2000). Regarding the graphical mode, in the study of Nagle, Moore-Russo, Viglietti & Martin (2013) is considered that the most frequently used conceptualizations for students align with past research findings on the emphasis of the secondary mathematics curriculum, supporting the possibility of cultural influences (academic and geographic) on individuals' conceptualizations of slope.…”

Section: Understanding the Derivative Conceptmentioning

confidence: 99%

Developing Pre-Service Teachers’ Noticing of Students’ Understanding of the Derivative Concept

Sánchez-Matamoros

Fernández

2014

Int J of Sci and Math Educ

View full text Add to dashboard Cite

Abstract. This research study examines the development of the ability of pre-service teachers to notice signs of students' understanding of the derivative concept. It analyses pre-service teachers' interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers' progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

show abstract

Calculus Students’ and Instructors’ Conceptualizations of Slope: A Comparison Across Academic Levels

Cited by 48 publications

References 27 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?

Students' Mathematization Process of the Concept of Slope within the Realistic Mathematics Education

Developing Pre-Service Teachers’ Noticing of Students’ Understanding of the Derivative Concept

Contact Info

Product

Resources

About