APOS theory

I Arnon, J Cottrill, E Dubinsky, A Oktaç… - A framework for …, 2014 - Springer
The interest in producing this book arose out of a concern for the education of graduate
students and young researchers in mathematics education. A few years ago, as a result of …

Areas, anti-derivatives, and adding up pieces: Definite integrals in pure mathematics and applied science contexts

SR Jones - The Journal of Mathematical Behavior, 2015 - Elsevier
Research in mathematics and science education reveals a disconnect for students as they
attempt to apply their mathematical knowledge to science and engineering. With this …

Geometrical representations in the learning of two-variable functions

M Trigueros, R Martínez-Planell - Educational studies in mathematics, 2010 - Springer
This study is part of a project concerned with the analysis of how students work with two-
variable functions. This is of fundamental importance given the role of multivariable functions …

Approaches to integration based on quantitative reasoning: Adding up pieces and accumulation from rate

SR Jones, R Ely - International Journal of Research in Undergraduate …, 2023 - Springer
Calculus education research on integration is coalescing around the theme that teaching
integration based on quantitative reasoning is crucial for robust understanding of and usage …

[PDF][PDF] La noción de esquema en la investigación en matemática educativa a nivel superior

M Trigueros - Educación matemática, 2005 - redalyc.org
El trabajo de Piaget es la fuente epistemológica de algunas de las teorías que se utilizan en
el campo de la investigación en matemática educativa. En este trabajo, se presentan las …

The Teaching and Learning of Definite Integrals: A Special Issue Guest Editorial

R Ely, SR Jones - International Journal of Research in Undergraduate …, 2023 - Springer
International Journal of Research in Undergraduate Mathematics Education (2023) 9: 1–7
population. Rather, the ability to interpret integrals in context and to model quantitative …

Definite integral registers using infinitesimals

R Ely - The Journal of Mathematical Behavior, 2017 - Elsevier
I propose a theoretical model of representation registers for definite integral notation. The
two registers, adding up pieces (AUP) and multiplicatively-based summation (MBS), are …

Influencia de las pruebas de acceso a la universidad en la enseñanza de la integral definida en el bachillerato

ÁC de la Fuente, MR Wilhelmi - Enseñanza de las ciencias: revista de …, 2010 - raco.cat
La integral definida es considerada un tópico matemático central en el bachillerato. Un
indicador empírico de este hecho son las pruebas de acceso a la universidad que …

Scalar and vector line integrals: A conceptual analysis and an initial investigation of student understanding

SR Jones - The Journal of Mathematical Behavior, 2020 - Elsevier
This paper adds to the growing body of research happening in multivariable calculus by
examining scalar and vector line integrals. This paper contributes in two ways. First, this …

Students' understandings of multivariate integrals and how they may be generalized from single integral conceptions

SR Jones, A Dorko - The Journal of Mathematical Behavior, 2015 - Elsevier
Prior research has documented several conceptions students have regarding the definite
integral, but these largely describe how students understand single-variable integral …