Kendra_Seitz_Action_Research_Proposal_Week_5

Running head: SUPPORTING ESL STUDENTS 1

Supporting English as a Second Language Students with Mathematical Story Problems

Kendra L. Seitz

Concordia University

A Research Report Presented to

The Graduate Program in Partial Fulfillment of the Requirements

For the Degree of Masters in Education

Concordia University - Portland

November 2015

SUPPORTING ESL STUDENTS 2

Supporting English as a Second Language Students with Mathematical Story Problems

Students who are learning English as a second language encounter many difficulties in

the classroom. It may seem that mathematics should not present as many difficulties for language

learners as other subjects, because numbers and concepts in mathematics are largely universal.

However, the language of mathematics is unique and complex. ESL students often struggle in

mathematics due to limited English proficiency. One area that is especially difficult for ESL

students is mathematical word problems. The Common Core State standards, adopted by 46

states and the District of Columbia, include word problem standards at every grade level

(National Governors, 2010). The purpose of this review is to examine the existing research in

order to discuss strategies for improving ESL students’ success with mathematical story

problems.

Review of the Literature

Language Difficulties with Story Problems

English language learners encounter difficulties with story problems for a number of

reasons. Story problems are often complex, use content specific language, and involve problem

solving skills as well as comprehension to solve (Barwell, 2003; Bernard & Calleja, 2005;

Cardelle-Elawar, 1990; Gerofsky, 1996; Mayer, 1987; Whang, 1996). Word problems typically

follow a three-part structure: a “set-up,” a collection of information, and a question (Gerofsky,

1996). In order to be successful with these types of problems, students must be familiar with

story problem structure as well as understand the context of the “story” and the information

given (Ambrose & Molina, 2014; Barwell, 2003; Bernard & Calleja, 2005; Whang, 1996).

Furthermore, readers of story problems must analyze text in a unique way, utilizing a different

set of comprehension skills than used when reading stories or essays (Kintsch & Greeno, 1985).


Barwell’s (2003) case study found that familiarity with word problems as well as real-world

experiences were necessary in solving story problems. Similarly, Bernard and Calleja (2005)

found that “real-life constraints prevented straightforward application of mathematical

procedures” (p. 177). Additionally, Ambrose and Molina (2014) found that while unfamiliar

vocabulary tended not to be an issue for students, difficulties arose from a lack of context to

connect to personal experience. In a case study of English-Korean bilingual students evaluating

the source of difficulty in solving mathematical word problems, Whang (1996) found that

students had trouble with nonsense problems, as well as problems written in a passive voice,

written with events described in reverse order, or involving irrelevant information. In another

study analyzing Hispanic students’ mathematical performance, students were asked to analyze

difficulties according to four categories based on Mayer’s (1987) model of problem solving.

Difficulties were categorized into problems with translation, integration, planning, or execution

(Cardelle-Elawar, 1990). English language learners struggle with mathematical story problems

for a variety of reasons including difficulty translating problems, unfamiliarity with the structure

of word problems, and the inability to connect with the context of the problem, which would

enable them to plan steps for solving (Barwell, 2003; Cardelle-Elawar, 1990; Gerofsky, 1996;

Mayer, 1987; Whang, 1996).

Small Group Instruction

Academic outcomes may be improved for English as a Second Language students

receiving small group or individualized instruction (Brenner, 1998; Cardelle-Elawar, 1990;

Kamps et. al., 2007). In a study describing evidence-based, second-tier interventions in schools

serving ESL students, Kamps et. al. (2007) discovered that students receiving direct, small-group

instruction in reading outperformed students in other intervention programs. In a previous study,


Brenner (1998) concluded that large-group instruction did not successfully facilitate

mathematical conversation with ESL students, while small groups were more successful.

Cardelle-Elawar’s (1990) study resulted in improved mathematical performance for students who

received specific feedback based on errors they made with story problems. The feedback was

individualized or tailored to the needs of groups of students, and given one-on-one or in small

groups. Students in this study demonstrated increased comprehension of key words and

sentences in story problems (Cardelle-Elawar, 1990). When instruction is given in small groups

or one-on-one, students have a greater opportunity improve skills in both language and problem-

solving (Brenner, 1998; Cardelle-Elawar, 1990; Kamps et. al., 2007).

Peer Discussion

Academic success increases when students have the opportunity to discuss concepts with

peers (Barwell, 2003; Brenner, 1998; Fuchs, Fuchs & Karns, 2001; Kemps et. al., 2007).

Mathematical discussion with peers supports language development as well as discovery of

mathematical solutions (Barwell, 2003; Brenner, 1998). ESL students are supported when they

are given opportunities to solve contextualized math problems, communicate their solutions, and

represent their thinking (Musanti, Celedon-Pattichis, & Marshall, 2009). In a case study of two

teachers implementing an algebra program, Brenner (1998) concluded that the teacher who

created a classroom climate for mathematical discussion was more successful. Large group

instruction was not successful in facilitating back-and-forth communication with ESL learners,

suggesting that the opportunity for mathematical discussion in small groups may be a

prerequisite for participation in large group settings (Brenner, 1998). Barwell’s (2003) case study

of an ESL and native speaking pair of students writing and solving a story problem together,

though it analyzed only two students rather than a whole class, found that the meaning-rich


nature of peer discussion assisted the ESL participant in both developing academic vocabulary

and mathematical knowledge. Similarly, a study of kindergarten students concluded that the use

of a specific program involving peer mediation, in which partners discussed and coached each

other, improved outcomes for all students, most significantly those with initial academic need

(Fuchs, Fuchs & Karns, 2001). Peer interaction provides language learners a setting in which

they can develop language skills as well as deepen their understanding of mathematics (Barwell,

2003; Brenner, 1998; Fuchs, Fuchs & Karns, 2001; Kemps et. al., 2007).

Visual Representations

Students tend to be more successful with mathematical story problems that are

represented in a drawn format, with pictures of items mentioned in the story accompanied by

brief captions (Beckman, 2004; Moyer, J., Sowder, Threadgill-Sower & Moyer, M., 1984).

Beckmann (2004) analyzed the success of students from Singapore in mathematics. The analysis

concluded that students’ strong mathematical performance may be a result of the use of simple

pictorial representations and diagrams used in textbooks and instructional materials.

Singaporeans use “strip diagrams” as representations for many different types of word problems

in grades 4-6 texts. Echevarria, Vogt, and Short (2010) support the use of graphic organizers in

assisting ESL students with English comprehension as well.

Analysis

Studies suggest that students must be able to utilize a problem-solving approach to

successfully solve story problems (Barwell, 2003; Whang, 1996). In Barwell’s (2003) study,

peers mediated the problem-solving process, while in Whang’s (1996) research, teachers assisted

the process. Both studies indicate that ESL students will need support in identifying and applying

problem-solving strategies. The research also indicates that ESL students encounter difficulties


with story problems due to a lack of comprehension of the context of the problems (Ambrose &

Molina, 2014; Barwell, 2003; Bernard & Calleja, 2005; Whang, 1996). For teachers, this finding

suggests the need for scaffolding in order to assist ESL students’ in contextualizing mathematical

problems.

It is unclear whether or not small-group interventions offer the most benefit for ESL

students struggling with mathematical word problems. The research presenting the strongest

evidence in favor of this strategy analyzed reading, rather than math instruction (Brenner, 1998).

Although Cardelle-Elawar’s (1990) favored differentiated over whole-group discussion, the

success of the study was attributed to the specific feedback teachers gave students, rather than

the small-group or individualized setting in which the feedback was given.

A stronger argument arises in support of peer discussion as an effective strategy for

supporting ESL students with story problems. The research spans multiple grade-levels in order

to evaluate mathematical discussion with peers, suggesting that peer discussion may be an

effective strategy for improving academic success for students of all ages (Barwell, 2003;

Brenner, 1998; Fuchs, Fuchs & Karns, 2001). The literature described multiple approaches to

peer collaboration, from partnerships to cooperative work groups, and all of the research

indicated academic benefit for students engaging in mathematical discussion with peers

(Barwell, 2003; Brenner, 1998; Fuchs, Fuchs & Karns, 2001). Only one of the studies reviewed,

however, compared students engaging in mathematical discussion with partners to a control

group (Fuchs, Fuchs & Karns, 2001). Additionally, only one of the studies focused on word

problems specifically (Barwell, 2003).

Further research may be needed to determine if and how students must be trained to have

mathematical discussions. Brenner’s (1998) research suggested that a positive classroom climate


for discussion must be established in order for ESL students to participate in meaningful

mathematical conversation. It did not, however, discuss specifics as to how this climate can be

achieved. In contrast, the kindergartners in the peer-mediation study were specifically trained in

mediation strategies (Fuchs, Fuchs & Karns, 2001).

While the literature reviewed supports the practice of students engaging in mathematical

conversation with peers, it does not explicitly address the use of peer discussion in order to

improve success for ESL students with story problems over time. Peer discussion was successful

in terms of promoting academic language and problem solving, as well as improving overall

math outcomes. Such interactions may have the added benefit promoting socioemotional skills in

native speaking peers who have ESL classmates (Gottfried, 2011).

Finally, the literature also supports the use of graphic organizers and other visual

representations to increase student success with mathematical word problems (Beckman, 2004;

Echevarria, Vogt, & Short, 2010; Moyer, J., Sowder, Threadgill-Sower & Moyer, M., 1984).

Visual representations may be especially beneficial for ESL students, and are considered an

effective strategy for scaffolding content for language learners (Echevarria, Vogt, & Short,

2010). One visual model that may be useful in multiple contexts is the strip diagram used in

textbooks in Singapore (Beckman, 2004). The research did not indicate any other specific visual

representations.

Conclusions

The ability to understand and solve word problems is essential for success in mathematics

courses throughout K-12 education. Story problems are an area that cause difficulty for many

students whose first language is not English. These problems require real-world experiences


within American culture to comprehend, as well as familiarity with story problem structure, and

an understanding of academic vocabulary, all of which ESL students may lack.

Small group instruction as well as allowing students to collaborate with peers may be

effective strategies for improving ESL students’ success with story problems in mathematics.

According to the reviewed literature, peer discussion can be a contributing factor to language

development as well as problem solving skills in ESL students. In order for peer discussion to be

successful, teachers must provide a safe environment for discussions to take place, and it is likely

that students need to be trained in mathematical discussion protocol. Additionally, visual

representations of data and the use of graphic organizers may be beneficial in scaffolding story

problems for ESL students. Further research needs to be conducted to evaluate these strategies

specific to language learners’ ability to solve mathematical word problems.

Demographic Data for the Proposed Project

The research will take place in the homes of three ESL fifth-grade students in two

households, in a private tutoring environment. The students include two boys, (twins), and a girl,

all of whom speak German as their first language. All three students attend a public elementary

school in a Midwestern metropolitan area. The school is a Title 1 building and was formerly an

ESL magnet school, contributing to the large population of ESL students in the school. General

education classrooms consist of 25-75% ELLs and there are over 20 first languages spoken in the

building. The study will involve the students as well as their tutor, who formerly taught these

students in third and fourth grade. The students in the study come from upper-middle class

families and receive weekly tutoring from their former teacher.

The study will target three ESL students struggling in the area of applied mathematics.

The participants were selected according to three criteria: (1) According to benchmark data, the


selected students struggle with application of mathematics but have strong computational skills,

(2) students fall within the intermediate level of English language proficiency, and (3) students

have been receiving mathematical instruction in English for at least two years. Furthermore,

students were available after school for a study group and parents agreed to have them

participate in the research.

Students chosen for this study scored below 75% on classroom and district math

benchmark assessments throughout fourth grade. They have stronger computational skills but

have difficulty processing word problems and explaining computations in writing. All three

students scored at level four (expanding) English proficiency on the WIDA ACCESS for ELLs

exam in fourth grade. In the language dFomain of writing, the students fell within the developing

level of English proficiency (level three).

Proposed Action

Several strategies have been identified for implementation in order to explore outcomes.

The research will combine the strategies of peer discussion, small group instruction, and

vocabulary instruction, and evaluate these strategies as possible solutions for supporting ESL

students with mathematical story problems. Much of the existing literature indicated that

providing students with opportunities to discuss mathematical concepts has a positive impact on

learning. Mathematical discussion with peers supports language development as well as

discovery of mathematical solutions (Barwell, 2003; Brenner, 1998). Two of the fifth-grade

students participating in this study are twins from Germany, and the third fifth-grader is also

from Germany, lives nearby the twins, and their families know one another. As a result, the

participants and their families have agreed to take part in a study group. The teacher will guide

them in solving complex, open-ended mathematical problems together. They may be able to


discuss concepts in their native language. The researcher hypothesizes that having the

opportunity to explore solutions together in an environment that is low-stakes will encourage

discussion and risk-taking. Additionally, research supports the use of small-group instruction as a

best practice (Brenner, 1998; Cardelle-Elawar, 1990; Kamps et. al., 2007). The small study-

group setting will allow the instructor to guide students in deepening their understanding.

Explicit vocabulary instruction will take place in conjunction with the aforementioned

strategies. The language of mathematics is unique and complex. Part of the difficulty that ESL

students have with word problems stems from the language used in such problems (Cardelle-

Elawar, 1990). Marzano (2004) recommends following a six-step process when explicitly

teaching vocabulary. The first step is to provide students with the dictionary definition of a word,

along with a non-linguistic representation. Next, students restate the description in their own

words. (Students may do so in their home language.) Then, students construct a picture or

diagram that relates to the vocabulary word. In the last steps, students periodically are engaged in

reviewing the terms through activities, discussion, and games. These strategies would work well

in a tutoring setting. Instruction will focus on words that are indicators of certain mathematical

operations, such as sum, difference, product, quotient, groups, each, etc.

Data Collection and Analysis Methods

Triangulation

Table 1

Triangulation Matrix

Issues to consider in attempting to answer

the research question

Data Source

#1

Data

Source #2

Data Source

#3

How does the study group change student

performance in regards to attempting

mathematical word problems?

Benchmark

assessments

Student

survey

Field notes

Student

work



performance in regards to comprehension of


Student survey Student

work

Field notes


performance in regards to accurately solving


Benchmark

assessments

Student

work

Field notes

The study will combine qualitative and quantitative data collection methods in a mixed-

method approach. Several factors will be considered in order to more fully answer the research

question. Multiple data sources will be analyzed in consideration of each factor including (1)

benchmark assessments, (2) a student pre- and post- survey, (3) field notes from the study group,

and (4) artifacts gathered from student work.

Benchmark Assessment

At the beginning of fifth grade, the participants took a district benchmark assessment

“screener” based on fourth grade math concepts. Data from this assessment will be analyzed to

determine how many word problems were attempted, what, if any, strategies were used, and if

they were solved accurately. At the end of the study, results from the latest benchmark

assessment, (they are administered quarterly), will be analyzed in the same way, and compared

to the pre-test results. The researcher will look for trends in the data.

Student Survey

A student survey (Appendix A) will be administered at the beginning and end of the

study. The survey will collect information regarding students’ attitudes toward and

comprehension of story problems. The survey will allow the researcher to analyze students’

feelings about mathematical word problems and how their feelings change over the course of the

study. Questions are asked regarding comprehension and problem solving strategies, which the

literature shows as two main areas of difficulty for ESL students, in order to determine if the

strategies implemented throughout the research project have an impact on these areas.


Field Notes and Artifacts

Detailed field notes will be taken throughout the study. As students work together to

solve word problems in the small group, artifacts of student work will be collected as well. The

researcher will code the data and look for patterns and trends. For example, students may begin

to attempt problems in different ways. One student may gravitate toward one strategy such as

representing a problem with pictures, while another student may tend to use a different strategy.

The researcher will look for changes over time as students attempt to solve problems and discuss

problems using the language of mathematics.

Ideas for Sharing Findings

The conclusions drawn from this study may be transferable to others teaching students of

similar backgrounds in similar settings. The researcher will share the results of the study first

with the participants’ classroom teachers. These discussions would allow the classroom teachers

to extend successful practices into their classrooms and continue to support the participants in

effective ways. The researcher will also present findings to colleagues in a district professional

development session. A break-out session model for professional development utilized within the

school district allows teachers to select which sessions to attend based on interest and

applicability. Furthermore, the researcher intends to present the results of the research to other

professionals at a best practices conference held by a local intermediate school district.


References

Ambrose, R., and Molina, M. (2014). Spanish/English bilingual students’ comprehension of

arithmetic story problem texts. International Journal of Science and Mathematics

Education 12(6). 1469-1496. http://dx.doi.org/10.1007/s10763-013-9472-2

Barwell, R. (2003). Patterns of attention in the interaction of a primary school mathematics

student with English as an additional language. Educational Studies in Mathematics

53(1), 35-59. http://dx.doi.org/10.2304/ciec.2012.13.1.74

Beckmann, S. (2004). Solving algebra and other story problems with simple diagrams: A method

demonstrated in grade 4-6 texts used in Singapore. Mathematics Educator 14(1). 42-46.

http://tme.journals.libs.uga.edu/index.php/tme/index

Brenner, M. E. (1998). Development of mathematical communication in problem solving groups

by language minority students. Bilingual Research Journal 22(2), 103–28.

http://dx.doi.org/10.1080/15235882.1998.10162720

Cardelle-Elawar, M. (1990). Effects of feedback tailored to bilingual students’ mathematics

needs on verbal problem solving. The Elementary School Journal 91(2), 165-175.

http://dx.doi.org/10.1086/461644

Echevarria, J., Vogt, M., and Short, D. (2010). Making content comprehensible for English

language learners: The SIOP model. Boston: Allyn & Bacon.

Fuchs, L.S., Fuchs, D., and Karns, K. (2001). Enhancing kindergartners’ mathematical

development: Effects of peer-assisted learning strategies. The Elementary School

Journal, 101(5), 495-510. http://dx.doi.org/10.1086/499684

Gerofsky, S. (1996). A linguistic and narrative view of word problems in mathematics education.

For the Learning of Mathematics 16(2), 36-45. Retrieved from http://flm-journal.org/


Gottfried, M. (2011). The positive peer effects of classroom diversity: Exploring the relationship

between English language learner classmates and socioemotional skills in early

elementary schools. The Elementary School Journal, 115(1), 22-48.

http://dx.doi.org/10.1086/676948

Kamps, D., Abbot, M., Greenwood, C., Arreag-Mayer, C., Willis, H., Longstaff, J., … Walton,

C. (2007). Use of evidence-based, small-group reading instruction for English language

learners in elementary grades: Secondary-tier intervention. Learning Disability Quarterly

30(3), 153-168. http://dx.doi.org/10.2307/30035561

Kintsch, W., and Greeno, J. G. (1985). Understanding and solving word arithmetic problems.

Psychological Review 92(1). 109-129. http://dx.doi.org/10.1037/0033-295x.92.1.109

Marzano, R. J. (2004). Building background knowledge for academic achievement: Research on

what works in schools. Alexandria, VA: ASCD.

Mayer, R. (1987). Educational psychology. Boston: Little, Brown.

Moyer, J. C., Sowder, L. Threadgill-Sower, J., and Moyer, M. B. (1984). Story problem

formats: Drawn versus verbal versus telegraphic. Journal for Research in Mathematics

Education 15(5). 342-351. http://dx.doi.org/10.2307/748424

Musanti, S., Celedon-Pattichis, S., Marshall, M. (2009). Reflections on language and

mathematics problem solving: A case study of a bilingual first-grade teacher. Bilingual

Research Journal 32(1). 25-41. http://dx.doi.org/10.1080/15235880902965763

National Governors Association Center for Best Practices & Council of Chief State School

Officers. (2010). Common Core State Standards. Washington, DC: Authors.


Whang, W-H. (1996). The influence of English-Korean bilingualism in solving mathematics

word problems. Educational Studies in Mathematics 30(3), 289-312.

http://dx.doi.org/10.1007/bf00304569


Appendix A

Student Survey

Question 1- Always 2-Most of

the Time

3-

Sometimes

4-Never

Word problems are difficult for

me. 1 2 3 4

I know what to do first when I

read a story problem. 1 2 3 4

I understand the words in a story

problem. 1 2 3 4

I can picture the story in my head

when I read a story problem. 1 2 3 4

I make a plan to solve story

problems. 1 2 3 4

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Kendra_Seitz_Action_Research_Proposal_Week_5