Exploring how teachers support students’ mathematical learning in computer-directed learning environments
| DOI | https://doi.org/10.1108/ILS-07-2019-0075 |
| Date | 16 December 2019 |
| Published date | 16 December 2019 |
| Pages | 52-78 |
| Author | Aaron Kessler,Melissa Boston,Mary Kay Stein |
| Subject Matter | Library & information science,Librarianship/library management,Library & information services |
Exploring how teachers support
students’mathematical learning
in computer-directed
learning environments
Aaron Kessler
Open Learning, Massachusetts Institute of Technology,
Cambridge, Massachusetts, USA
Melissa Boston
Department of Instruction and Leadership in Education, Duquesne University,
Pittsburgh, Pennsylvania, USA, and
Mary Kay Stein
Learning Research and Development Center, University of Pittsburgh,
Pittsburgh, Pennsylvania, USA
Abstract
Purpose –This study explores the teacher’s role for implementing a cognitive tutor (CT) intended to
increasestudents’knowledge of proportional reasoning and potentialimpacts on students’learning.
Design/methodology/approach –Using a mixed methods approach to design-based research, the
authors examine results from three different phases of the CT implementation using frameworks from
mathematicseducation research.
Findings –Based on observations of 10 educators, the authors identify 4 different types of interactions
among the CT, students and educators. Using observations and student assessment results (n= 134), the
authors begin to buildan argument that different types of interactions have thepotential to impact students’
opportunitiesto learn in computer-directed learning environments.
Originality/value –The authors conclude that research on the efficacy of computer-directed learning
environmentsshould consider differences in implementation of CT materialsand that the types of CT, student
and educatorinteractions described herein provide a frameworkto support such exploration.
Keywords Design-based research, Interaction patterns, Cognitive tutor,
Computer-directed learning environments, Mathematics learning, Teachers’role
Paper type Research paper
1. Introduction
Technology offers exciting innovations for teaching and learning mathematics, from
graphing calculators, classroom presentation technology, web-based resources and
computer-directed learning.While the presence of these resources in classrooms holds great
potential for enhancing students’learning, research consistentlyindicates that instructional
innovations are only as effective as their implementation. Across a range of innovations,
including standards-based curricula (Grouws et al.,2013), cognitively demanding
mathematical tasks (Henningsen and Stein, 1997; Stein et al., 2007), cooperative learning
(Horn, 2005) and technology (Kessler et al.,2015;Sherman, 2011), significant impacts on
ILS
121,1/2
52
Received19 July 2019
Revised13 September 2019
28October 2019
Accepted17 November 2019
Informationand Learning
Sciences
Vol.121 No. 1/2, 2020
pp. 52-78
© Emerald Publishing Limited
2398-5348
DOI 10.1108/ILS-07-2019-0075
The current issue and full text archive of this journal is available on Emerald Insight at:
https://www.emerald.com/insight/2398-5348.htm
students’learning are associated with how the innovation is used to engage students in
learning mathematics.Despite this fact, much of the development associated with computer-
directed learning environments has not fully accounted for how the innovations are
implemented in complex formal education settings. Because of the complexity of these
settings (e.g. number of available computers, teacher training and internet access),
developers of computer-directed learning environments often have the goal of creating
context agnostic environments. In otherwords, to allow for massive implementation across
large numbers of complex sites, the designof the cognitive tutor (CT) system is purposefully
aimed at the widest audience, with implementation standardized to promote fidelity to the
system. More to the point, these environments have typically minimized the role of an
instructor in their design.
In this study, we examine the design, development and implementation of computer-
directed instruction. We seek to define and describe an array of possible active roles for
teachers in computer-directed learning environments, and we propose that these different
roles impact implementation,thus having the potential to impact students’opportunities for
learning. More broadly, we argue for the importance of analyzing computer-directed
learning environments through an instructional frame that considers three essential
components of teaching and learning and the interactions between these components: the
curriculum (computer-directed instructional materials and tasks posed to students), the
teacher and the students. We present research from mathematics education that can inform
the design and use of computer-directed instruction in the classroom, including new ways
for conceptualizingthe role of the teacher in this environment.
We ground our work by examining the specific case of an intelligent tutoring system
(ITS) or CT environment. CTs are a specific type of ITS that uses technologies associated
with curriculum sequencing, intelligent solutions analysis and/or problem solving support
to assist students’learning (Brusilovsky and Peylo, 2003). In this environment, the CT
presents students with instructional tasks in a developmental sequence (curriculum
sequencing), diagnosesstudents’solutions and types of errors (intelligent solutionsanalysis)
and offers problem-solving support often tailored to specific types of errors or strategies.
Hence, the CT is designed to deliver instructionand perform several functions of a “teacher”
by selecting and presenting instructional tasks, offering feedback and support as students
complete those tasks, and assessing students’progress toward a mathematical goal. Given
these designs, CT systems are often envisioned as being used in a one-to-one environment
between an individual student and the technology, with previous work showing that this
model has implications for the way in which students enact instructional tasks (Kessler
et al.,2015).
Despite the original one-to-one design of CT systems, recent research has noted the
importance of considering therole of teachers’instructional actions as a way to increase CT
implementation and effectiveness (Ritter et al., 2016a;Baker, 2016). In this study, we
examine the use of a CT system inclassrooms and other educational settings with multiple
students and a human teacher. We explore various ways in which teachers may take an
active role in influencingthe CT environment and supporting students’learning.
The specific CT program examined in this study introduces robotics and proportional
reasoning to students in Grades 4-8, as programming the robots involves proportional
relationships (e.g. lineardistance and turn angle are linear functions of wheel size and motor
rotations). Proportional reasoning is a key mathematical idea in middle school [National
Council of Teachers of Mathematics (NCTM), 2006;Lobato and Ellis, 2010; common core
initiative (National Governors Association Center for Best Practices and Council of Chief
State School Officers, 2010)]; hence, this CT program aims to enhance students’knowledge
Exploring how
teachers
support
students’
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