Module 2-Literature Review
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5153
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Mathematics
Date
Apr 3, 2024
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1
Literature Review: The Problem with Students’ Understanding of Mathematical Word
Problems
Breanna Lilly
American College of Education
RES 5153: Research Methods
Dr. Harold Fisher
March 6, 2023
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Introduction
A problem that has been happening in classrooms for many years is students’ lack of
understanding while completing word problems. The purpose of this action research is to
investigate the reasons why students are struggling with word problems and the best strategy to
support students in solving word problems. My action research will be guided by the following
questions.
1.
Will breaking apart the word problem improve student comprehension of it?
2.
Why would problem type knowledge impact students’ ability to complete word
problems?
3.
How will knowing mathematical vocabulary improve students' ability to solve a word
problem?
I have completed a literature review using peer review articles I have found through the ACE
library databases.
Literature Review
During this literature review I have analyzed and evaluated seven peer reviewed pieces of
literature related to word problems and strategies to teach word problems. The literature was
connected though many common themes like: the importance of word problems, math attitudes,
math foundations, interpret the meaning, keywords, schema, and graphics. The information
found during this literature review will help guide the rest of this action research.
The Importance of Word Problems
The articles in this literature review all discussed different strategies or reasons on why
students have a hard time understanding word problems. One thing that all of the articles agreed
on was the importance of students solving word problems. Word problems are important because
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word problems show students the connection of math and our everyday lives (Khoshaim, 2020).
Word problems give students concrete examples of how they will use math concepts and their
knowledge throughout their lives. Word problems are also shown to improve a student’s math
understanding (Dofková & Surá, 2021) because they are using more cognitive skills and
reasonings while solving the problems (Powell et al., 2022).
Math Attitudes
Throughout the articles the idea of how a student’s attitude affects their ability to
complete word problems was continually brought up. Khoshaim stated that the first step in
success in math is a positive attitude (Khoshaim, 2020). This information is important to
unlocking students' understanding of word problems because it may not be the math that is
causing them trouble, it could be the attitude they have about math. Students often have a poor
attitude about math or math anxiety because of how it is presented to them (Csíkos et al., 2022).
From an early age mathematics is presented to students as being serious and difficult. This
causes students to have 3 types of reactions (direct, evasive, and resignation) when they
encounter math problems, specifically word problems. The most common reactions are evasive,
students try the problem but give up, or resignation, students give up right away after reading the
problem. One way to get a student to have a direct (taking on the challenge and persevering)
reaction to a word problem could be to add humor to the word problems. Studies show that
students were more willing and successful when solving a word problem when humor was
involved (Csíkos et al., 2022).
Math Foundations
Many articles brought up factors that could hinder students’ understanding of word
problems is their mathematics foundations. These foundations include number reasoning,
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mathematical operations, and problems types of schemas (Khoshaim, 2020). Students' lack of
math foundations is a barrier in understanding and solving word problems because if they are
unable to solve the algorithm they are unable to get the correct answer (Capone et al., 2021).
Interpret the Meaning
Another factor hindering students’ understanding that was brought up throughout the
articles was their ability to interpret the meaning of it. Often students will only focus on the
numbers in the problem or try to infer from the text the steps to solve instead of representing the
situation described (Capone et al., 2021). When students are able to interpret the meaning of the
problem and what is being asked of them they have a higher success rate at completing the
problem correctly. The articles described different strategies that can be used to help students
understand the meaning of the problem, these strategies include: asking guiding questions (Ma et
al., 2021), having students paraphrase the problem by using attack strategies (Powell & Fuchs,
2018), and drawing pictures or using graphics (Dofková & Surá, 2021).
Keywords
One idea that was included in all the articles was students needed to understand the
language of the word problem to understand what is being asked. Another way to put this is
students need to understand the keywords that often come up in math problems. Many teachers
currently have students focusing on the keyword in math to mean a specific operation, this is
called the keyword strategy (Powell et al., 2022). While this is a common strategy to teach
according to research it is actually harmful to students’ math reasoning because keywords in
math problems are not always alluding to the same operation. An example of this is
Joe has 5
apples, he has 3 more apples than Tom, how many apples does Tom have?
The word more is
taught as a cue for addition but the example problem involves subtraction (Ma et al., 2021).
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While the current keyword strategy is not appropriate to teach, keywords are still important for
students to learn. The strategy that should be taught involving keywords is that keywords cue
students to the action or schema of the problem not just an operation ( Powell et at., 2022).
Schemas
An instruction type that was discussed throughout the articles in this review was schema
based instruction. Schema based instruction is when students learn to categorize word problems
based on the structure type. There are 2 categories of schemas additive and multiplicative. The
additive schema involves combine, compare, and change problems. The multiplicative schema
includes equal-group, proportional, and comparison problems (Powell & Fuchs, 2018). By
teaching students problem types this will lead to students having strategies on how to solve the 6
different types of problems they will encounter.
Graphics
Another strategy that was included in many of the articles was having students use
graphics to help them solve a word problem. Graphics could involve a student drawing a picture,
filling out a graphic organizer, or filling in a problem’s structure pattern. In a study about
students’ success in solving word problems, students who were the most successful in solving
the problems correctly used a graphic to solve (Dofková & Surá, 2021). Graphics help students
with organizing information and seeing the relationships between patterns.
Conclusion
While completing this literature review I found many connections and common themes in
relation to students’ understanding of word problems. This review has been insightful with
giving background information to affirm some of my hypotheses while showing that I need to
6
change others. The information found during this literature review will guide the rest of this
action research project.
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References
Capone, R., Filiberti, F., & Lemmo, A. (2021). Analyzing Difficulties in Arithmetic Word
Problem Solving: An Epistemological Case Study in Primary School.
Education
Sciences
,
11
.
Csíkos, C., Biró, F., & Szitányi, J. (2022). Incorporating Humor into Mathematical Word
Problems: Is There a Negative Effect on Students’ Performance?
International Journal of
Instruction
,
15
(3), 1079–1098.
Dofková, R., & Surá, M. (2021). Nonstandard Math Word Problems and Analysis of the Partial
Stages of Its Solution. Problems of Education in the 21st Century, 79(5), 716–727.
Khoshaim, H. B. (2020). Mathematics Teaching Using Word-Problems: Is it a Phobia!
International Journal of Instruction
,
13
(1), 855–868.
https://doi.org/10.29333/iji.2020.13155a
Ma, X., Bofferding, L., & Xin, Y. P. (2021). Addition and subtraction word problem tasks in
reform-based textbooks.
School Science & Mathematics
,
121
(5), 263–274.
https://doi.org/10.1111/ssm.12468
Powell, S. R., & Fuchs, L. S. (2018). Effective Word-Problem Instruction: Using Schemas to
Facilitate Mathematical Reasoning.
Teaching Exceptional Children
,
51
(1), 31–42.
https://doi.org/10.1177/0040059918777250
Powell, S. R., Namkung, J. M., & Lin, X. (2022). An Investigation of Using Keywords to Solve
Word Problems.
Elementary School Journal
,
122
(3), 452–473.
https://doi.org/10.1086/717888