Proceedings of the Fourth Annual Teachers College Educational ...

Connected to Word Problems:
Improving Mathematical Problem Solving While Exergaming
Benjamin Friedman,
Teachers College, Columbia University, New York, NY,
Email: bpf2103@tc.columbia.edu
Abstract: How can we best prepare students for instruction and practice in solving
mathematical word problems? What instructional methods best promote understanding of
problem situations and sense making in students? These are important questions given
the prominent place making sense of problems and working to solve them has in the
Common Core State Standards for Mathematical Practice (2010).
This quasi-experimental study seeks to answer these questions by comparing an
instructionally embodied teaching method (Black, Segal, Vitale, & Fadjo, 2011) with a
conceptual model based method (Xin, Wiles, & Lin, 2008; Xin & Zhang, 2009) as well as
a mix between the two methods. Twelve second-grade students from a high-needs urban
public school participated through an after-school program. All students participated in
fitness game activities through the Xbox Kinect. Word problem situations were based off
those students experienced in the fitness game for instructionally embodied conditions
but not for the conceptual model condition.
Relevant Literature
Word problems are the most common problem type encountered by students at all levels of education
(Jonassen, 2003). Many students in the early grades have difficulty solving mathematical word problems,
especially English Language Learners (ELLs) and those with learning disabilities (Jitendra, 2008). In the
context of this study word problems are defined as problems taken from situations in the real-world that
require the use of mathematical concepts in order to obtain a solution (Verschaffel, Greer, & De Corte,
2000). These types of problems provide an important connection between situations expressed through
language and the abstract mathematical language that is expressed in numbers and symbols. Solving
mathematical word problems involves both reading comprehension and mathematical skills such as
conceptual understanding of operations and computational ability (Kintsch & Greeno, 1985).
One reason for a lack of student success in solving mathematical word problems is the suspension of
sense making that occurs when students focus on obtaining an answer without first attempting to make
sense of the problem. Consequently, students may ignore clues that explain what information needs to be
used and what procedures are necessary to find the correct solution (Verschaffel, Greer, & De Corte
2000). Sense making ability may improve through instruction that engages students in using problem
solving skills and provides opportunities for them to reason about the information contained in the
problem as well as the information that is missing.
Types of Instruction
This study attempted to engage students in sense making by comparing instructional methods, namely,
an instructionally embodied approach (Black, Segal, Vitale, & Fadjo, 2011), a conceptual model based
approach (Xin, Wiles, & Lin, 2008; Xin & Zhang, 2009), and a mix between the two methods. Twelve
second-grade students from a high-needs urban public school participated in the study through an afterschool
program in one of the three groups. All groups took part in exergame activities (described below)
through the Xbox Kinect gaming system.
For students in the instructionally embodied and mixed groups, these exergame activities became the
basis for experimenter written problems used during instruction (see Table 1). This was meant to ground
their internal representations of problem situations in physical and perceptual experiences (Barsalou,
2010). Students were then taught to visualize their exergame activities in order to mentally manipulate
problem elements, resulting in improved ability to solve problems independently. Conceptual model
based instruction consisted of teaching specific word problem story grammars that led students to identify
mathematical structural relations for specific problem types. This knowledge then allowed them to
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