Promoting students’ graphical understanding of the calculus

Berry, John; Nyman, Melvin A.

doi:10.1016/j.jmathb.2003.09.006

Cited by 101 publications

(90 citation statements)

References 8 publications

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“…Poor ability to interpret and construct graphs among both students and adults is well documented in the mathematics education literature and related fields (e.g., Berry & Nyman, 2003;Carlson, Jacobs, Coe, Larsen, & Hsu, 2002;Gattis, 2002Gattis, , 2004Gattis & Holyoak, 1996;Paulos, 1988;Tufte 1983Tufte , 1990. Such studies suggest that poor performance may not reflect poor understanding of the concept of accumulation but rather difficulty in extracting the information needed to answer the questions from graphical displays.…”

Section: Experiments 1: Cognitive Burden and Data Displaymentioning

confidence: 99%

Why don’t well-educated adults understand accumulation? A challenge to researchers, educators, and citizens

Cronin

González

Sterman³

2009

Organizational Behavior and Human Decision Processes

276

457

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a b s t r a c tAccumulation is a fundamental process in dynamic systems: inventory accumulates production less shipments; the national debt accumulates the federal deficit. Effective decision making in such systems requires an understanding of the relationship between stocks and the flows that alter them. However, highly educated people are often unable to infer the behavior of simple stock-flow systems. In a series of experiments we demonstrate that poor understanding of accumulation, termed stock-flow failure, is a fundamental reasoning error. Persistent poor performance is not attributable to an inability to interpret graphs, lack of contextual knowledge, motivation, or cognitive capacity. Rather, stock-flow failure is a robust phenomenon that appears to be rooted in failure to appreciate the most basic principles of accumulation, leading to the use of inappropriate heuristics. We show that many people, including highly educated individuals with strong technical training, use what we term the ''correlation heuristic", erroneously assuming that the behavior of a stock matches the pattern of its flows. We discuss the origins of stock-flow failure and implications for management and education.Ó 2008 Elsevier Inc. All rights reserved.Understanding and managing stocks and flows-that is, resources that accumulate or deplete and the flows that alter them-is a fundamental process in society, business, and personal life. At the macroeconomic level, for example, exploration increases known petroleum reserves, while oil production reduces the stock of oil remaining for the future. In turn, petroleum combustion increases the stock of carbon dioxide in the atmosphere and contributes to global warming. At the organizational level, firms' capabilities and competitive advantages arise from the accumulation of resources and knowledge. Firms must manage their cash flows to maintain adequate stocks of working capital, and production must be adjusted as sales vary to maintain sufficient inventory. Individuals, too, face similar stock management challenges: we manage our bank accounts (stock of funds) to maintain a reasonable balance as our incomes (inflows) and expenses (outflows) vary, and we struggle to maintain a healthy weight by managing the inflow and outflow of calories through diet and exercise. Accumulation is a pervasive process in everyday life, and arises at every temporal, spatial and organizational scale.All stock-flow systems share the same underlying structure. The resource level (stock) accumulates the inflows to it less the outflows from it. 1 Although the relationship between stocks and flows is a fundamental concept of calculus, knowledge of calculus is not necessary to understand the behavior of stocks and flows. Any stock can be thought of as the amount of water in a tub. The water level accumulates the flow of water into the tub (the inflow)0749-5978/$ -see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.obhdp.2008.03.003 * Corresponding author. E-mail addresses: mcronin@gmu.edu (M.A. ...

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Section: Experiments 1: Cognitive Burden and Data Displaymentioning

confidence: 99%

Why don’t well-educated adults understand accumulation? A challenge to researchers, educators, and citizens

Cronin

González

Sterman³

2009

Organizational Behavior and Human Decision Processes

276

457

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“…Alan yazında yer alan farklı çalışmalarda (Açıkyıldız, 2013;Amit & Vinner, 1990;Amoah & Laridon, 2004;Aspinwall & Miller, 1997;Baker, Cooley & Triguros, 2000;Berry & Nyman, 2003;Bezuidenhout, 1998;Duru, 2006;Ferrini-Mundy & Graham, 1991, 1994Hacıömeroğlu, 2007;İşleyen ve Akgün;Kertil, 2014;Orton, 1983;Park, 2011;Thompson, 1994;Ubuz, 2001;Yiğitcan-Nayir, 2013) da söz konusu sonuçlara benzer sonuçların elde edildiği görülmektedir. Bu çalışmalardan biri olan Yiğitcan-Nayir (2013), öğretmen adaylarının türev kavramı ile ilgili çeşitli zorluklar yaşadıklarını, anlık hızı, ortalama değişim oranından ayırt edemediklerini, fonksiyonun özellikleri ile birinci ve ikinci türevi arasındaki ilişkiyi anlamakta zorlandıklarını, birinci ve ikinci türev arasındaki ilişkiyi de anlamlandırmakta problemler yaşadıklarını ifade etmektedir.…”

Section: Türev Kavramı Ile İlgili Elde Edilen Sonuçlar Ve Tartışmaunclassified

A Theoretical Examination of the Mathematical Connection Skill: The Case of the Concept of Derivative

Mumcu¹

2018

Turkish Journal of Computer and Mathematics Education (TURCOMAT)

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Öz: Bu çalışmanın amacı öğretmen adaylarının matematiksel ilişkilendirme becerilerinin türev kavramı bağlamında ele alınarak yorumlanmasıdır. Bu kapsamda öncelikle matematiksel ilişkilendirme becerisi kuramsal olarak analiz edilerek bu becerinin değerlendirilmesinde kullanılabilecek bir kuramsal yapı oluşturulmaya çalışılmıştır. Daha sonra ise bir devlet üniversitesinin eğitim fakültesi son sınıf öğrencilerinden seçilen ve 51 kişiden oluşan matematik öğretmen adaylarına araştırmacı tarafından geliştirilmiş olan İlişkilendirme Beceri Testi (İBT) uygulanmıştır. İlişkilendirme Beceri Testi'nin temel bileşenleri farklı gösterimler arası ilişkilendirme, kavramlar arası ilişkilendirme, gerçek yaşamla ilişkilendirme ve farklı disiplinlerle ilişkilendirme olarak ifade edilebilir. Çalışma sonucunda öğretmen adaylarının genel olarak türev kavramına yönelik ders kitaplarında yer alan ezberi bir takım bilgilere sahip oldukları fakat bu bilgileri birbiri ile ilişkili olarak anlamlandırmakta ve kullanmakta güçlük çektikleri gözlenmiştir. Matematiğin daha anlamlı ve ilişkisel olarak öğrenilmesi anlamında, matematik eğitimcilerinin sınıflarında, kavramsal anlamaya odaklanmaları ve kavramların anlamlı öğrenilmesini ve gerçek yaşamla ilişkilendirilebilmesini sağlayacak etkinlik ve uygulamalara yer vermeleri önerilmiştir.

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“…Sin embargo, es exiguo el estudio de conexiones en el Cálculo. ISSN 1980-4415 DOI: http://dx.doi.org/10.1590/1980 No obstante, algunos estudios en el campo de la educación matemática reconocen la existencia de la conexión entre la derivada y la integral sin ser su objetivo principal (BERRY; NYMAN, 2003;HACIOMEROGLU;ASPINWALL;PRESMEG, 2010;SCHROEDER, 2011;SOFRONAS et al, 2011;DREYFUS, 2013DREYFUS, , 2014. De las metodologías propuestas para lograrlo, destacan las que proponen el manejo de distintas representaciones (MARRONGELLE, 2004;HOFFKAMP, 2011;MAMOLO;ZAZKIS, 2012;DAWKINS;MENDOZA, 2014;HONG;THOMAS, 2015) y las que promueven la modelación de situaciones en contexto (YOON;THOMAS, 2010;KLYMCHUK et al, 2010;PARK J. et al, 2013;WEBER;TALLMAN;MIDDLETON, 2015).…”

Section: Estado Del Arteunclassified

Conexiones Intramatemáticas y Extramatemáticas que se producen al Resolver Problemas de Cálculo en Contexto: un Estudio de Casos en el Nivel Superior

Flores

García‐García

2017

Bolema

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 ResumenEn el presente artículo se reporta una investigación cuyo objetivo fue identificar las conexiones que un grupo de estudiantes universitarios establecen al resolver problemas en contexto. Estos problemas pueden resolverse utilizando la relación entre la derivada y la integral establecida en el Teorema Fundamental del Cálculo. Para identificar las conexiones adoptamos el marco teórico que al respecto plantea Businskas (2008). Como método de investigación utilizamos el estudio de casos y aplicamos un cuestionario integrado por cinco problemas, de cuyas soluciones obtuvimos los datos. Los datos indican que los estudiantes establecen conexiones extramatemáticas e intramatemáticas al resolver problemas en contexto, pero principalmente utilizan las de tipo procedimental y las representaciones diferentes, además notamos una fuerte conexión con sus conocimientos previos aprendidos en los niveles de educación precedentes al nivel superior.Palabras clave: Conexiones matemáticas. Estudios de Caso. Teorema Fundamental del Cálculo. Nivel Universitario. AbstractThis paper reported a research which aims to identify connections that a university student group established to solve problems in a context. These problems can be solved using the relationship between the derivative and integral established in the Fundamental Theorem of Calculus. To identify such connections, we adopted the theoretical framework proposed by Businskas (2008). As a research method, we used the case study and applied a questionnaire which included five problems, the solutions of which we obtained the data. The data indicate that students establish extra-mathematics and intra-mathematics connections when they solve problems in a context, but mainly used the procedural type and the different representations. We also noticed a strong connection with their prior knowledge learned in previous levels of education rather than at the university level.

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Promoting students’ graphical understanding of the calculus

Cited by 101 publications

References 8 publications

Why don’t well-educated adults understand accumulation? A challenge to researchers, educators, and citizens

Why don’t well-educated adults understand accumulation? A challenge to researchers, educators, and citizens

A Theoretical Examination of the Mathematical Connection Skill: The Case of the Concept of Derivative

Conexiones Intramatemáticas y Extramatemáticas que se producen al Resolver Problemas de Cálculo en Contexto: un Estudio de Casos en el Nivel Superior

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