The problem which this study seeks to address is that fifth grade children particularly those who are underprivileged and encountering challenging issues are struggling in mathematics. This is evidenced by their significantly lower and below-standard grades in mathematics and their difficulty to solve world problems.
The study's purpose is to determine if research-based vocabulary instruction using the Montgomery Public Schools' Resources for Vocabulary Instruction will result to an improvement in the fifth graders' capacity to solve math problems.
Description of Community
The Montgomery Public Schools (MPS) has a total enrolment of around 3,681 students, making it the third largest school system in Alabama. It encompasses a total number of 59 schools - "32 traditional elementary, 10 traditional middle/junior high schools, 4 high schools, 9 magnet schools, 2 alternative schools, and 2 special education centers" (Alabama Department of Education, 2010). Following a "students-first philosophy," the MPS offers a diverse academic programs as well as services to respond to the needs of its surrounding communities. The school district strives to be an inclusive school in adherence to the "No Child Left Behind Act" and has received more than $1.2 million from grants to support this goal. With its headquarters set up in Montgomery, Alabama, the MPS employs around 4,500 people including 1,600 full-time teachers, 900 substitute teachers, 150 part-time teachers, and 350 part-time support staffs. The school district serves Montgomery and the surrounding areas in Montgomery County (Alabama Department of Education, 2010).
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MPS has a particular thrust on children with special needs. There are alternative transportations routes to support underprivileged children. The schools throughout the MPS feature services for special students and gifted students. The MPS houses two centers for special education and offers various early childhood education programs. The mission of MPS is to "offer stimulating environments led by qualified and dedicated teachers". The Montgomery Public Schools focuses on the vision of "preparing students for life" (Alabama Department of Education, 2010). The MPS is rated as one of the best in the country in terms of accomplishing federal goals under the NCBA. As of 2009, over 91% of the schools within the MPS district achieved state and federal accountability requirements. Moreover, three high schools belonging to the MPS were rated among the nation's best schools by Newsweek Magazine. Four high schools were rated as the top schools by U.S. News and World Report (Alabama Department of Education, 2010).
This action research project will take place in one fifth grade classroom in XYZ Elementary School. This school is a part of the MPS system and is located in Montgomery, Alabama. The student population in this school is approximately ______ students. The ethnic distribution of the school is approximately ___% Caucasian, ___% Hispanic, ___% African American, ___% Asian, and ___% other.
Description of Work Setting
This action research will take place in two fifth grade classrooms at the XYZ Elementary School. Both classes total 50 students in all (25 students per class). The problem-solving skills of this particular class are roughly the same as evidenced by their grades in math which range from good to below-standard. Aside from their relatively low grades in math, both classes are composed predominantly of underprivileged children, many of whom are ELL students.
XYZ Elementary School's current mathematics curriculum follows the Alabama Mathematics Content Standards which expects that at the end of the fifth grade, students will have improved on competencies in the four fundamental arithmetic operations (addition, subtraction, division, multiplication) and applying these operations to decimals, fractions, as well as positive and negative numbers. Moreover, they are expected to be skilled in using common measurements in determining area, length and volume of basic geometrical figures. They are also expected to apply measurement concepts to angles using tools such as the compass and protractor in solving problems. Problem-solving skills will also be supplemented with the use to tables, graphs, charts, and grids for recording and analyzing data (Alabama Department of Education, 2010).
This action research is designed to be a pre-test/post-test quasi-experimental study. The people involved in this action research are two fifth grade teachers and the 50 students in their math classes. One class will be assigned as the control group (class receiving no direct math vocabulary instruction) and the other class will be designated as the experimental group (class receiving direct math vocabulary instruction. Since both classes have relatively similar achievement level in math and roughly the same student characteristics, the control and experimental group are well matched for this quasi-experimental research.
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The writer has been a math teacher for 16 years and is presently a substitute teacher of fifth grade students at XYZ Elementary School. She has held this position for 5 years now. The writer's responsibility as a substitute teacher in Math is not only to instruct them on mathematical concepts and operations. As a substitute teacher, the writer tries to motivate students and determine what their true needs are in order to be able to assist them more effectively with learning. The writer will facilitate the implementation of the proposed mathematics vocabulary instruction to the target fifth grade classes. She will conduct the study with the help of two (2) qualified math teachers handling fifth grade math classes.
Chapter Two: Study of the Problem
The problem being studied is that the fifth grade students at the XYZ Elementary School are struggling with math, particularly in solving word problems. As a result, many fifth grade students at the XYZ Elementary School score below the 40th percentile, or do not meet the state's score standards for math in the Alabama Reading and Mathematics Test (ARMT). The Mathematics portion of the achievement test measures a student's competency in the following content areas and their corresponding points: Number operations (28 points), Algebra (8 points), Geometry (7 points), Measurement (10 points), Data Analysis and Probability (10 points) totaling to a possible 63 points. Students who score below the 40th percentile are considered to have failed to meet the state's standards for learning (Alabama Department of Education, 2005).
One form of documentation that could be used to evaluate proficiency in math problem-solving is to review the students' scores on tests or quizzes. It is not uncommon to see that students score low on problem-solving compared to quizzes that include numerical computations alone. Teachers are also able to look at facial expressions or reactions toward word problems well enough to conclude that this is something students struggle over.
Another form of documentation that could be used to measure lack of problem-solving skills are standardizes state accountability measures such as the Alabama Reading and Mathematics Test (ARMT). The ARMT is one of the indicators of students' progress in learning as well as a gauge whether or not the school meets the minimum requires of the No Child Left Behind policy. The Mathematics part of this test measures competency along various content areas such as Number operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. Students who fall behind the 40th percentile are considered to have failed to meet the state's standards for learning (Alabama Department of Education, 2005).
The review of literature indicated that mathematics vocabulary is a significant factor in a student's mathematics aptitude particularly in problem-solving (Larson, 2007; Barton & Heidema, 2000). More than a subject studded with numbers, mathematics is considered itself as a language (Adams, 2003). Researchers have estimated that by the time learners are through with the fourth grade, they will have to learn more than 500 mathematical symbols and terms (Riccomini & Witzel, 2009). What differentiates mathematics from other forms of language however is that it employs "very technical and context-specific terms," meaning that learners have to establish a separate vocabulary in order to understand and communicate the language of mathematics (Riccomini & Witzel, 2009, p. 216).
Newman (2006) considered mathematics as "the science which uses easy words for hard ideas" (p. 41). Despite its relatively simpler vocabulary than other sciences like biology, chemistry, or physics, mathematics is considered an abstruse subject and a scary one even from the perspective of the regular student. Newman (2006) insists however that once students are able to penetrate the barrier, they will find that mathematics is "a fairyland which is strange, but makes sense, if not common sense" (p. 41).
In my personal experience as a math teacher, I have observed firsthand how students struggle with word problems. Lack of proficiency in mathematics vocabulary has been found by many research projects to be a cause for learner's underperformance as problem solvers (Sullivan, 1982; Blessman & Myszczak, 2001). Sullivan (1982) noted that students who are low achievers answer math word problems impulsively, meaning that students race to solve the problem without necessarily understanding what it is being asked for. According to the WGBH Educational Foundation (2009), a relatively neglected aspect in teaching mathematics is that vocabulary is a problematic area for children. Some children have confusions or misconceptions regarding the use of operational terms which are not used or encountered in everyday conversations. A possible cause of inability to solve word problems may be that students understand a concept clearly but cannot recall what specific term it is related to.
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Therefore, mathematics is really a language issue after all. Blessman and Myszczak (2001) found that among the most confusing issues in mathematics is its vocabulary. According to the authors, "[m]uch of the research on problems students encounter in mathematics courses points to the many language-based misconceptions that students develop" (Blessman & Myszczak, 2001, p. 13). Failing to understand mathematical terms that they encounter in word problems leads to a loss of ability to solve them.
There are three levels of mathematics vocabulary: the general, the technical, and the symbolic (Monroe & Panchyshyn, 1995). Technical vocabulary are words falling under the mathematical terminology. These are mathematical concepts not found or encountered in everyday usage. As a result, they are "foreign" to students. Some of examples of technical vocabulary are integer, greatest common factor, Venn diagram, quadrilateral, etc.). This is the type of mathematical vocabulary generally taught in the classroom. General vocabulary includes words in which students are exposed to in their reading as well as their experiences every day. General vocabulary can be found in most textbooks. Symbolic vocabulary is viewed by others as the real vocabulary of mathematics. This vocabulary consists of alphabet symbols and numerals. Examples are "five to the second power," or "six squared" etc. Abbreviations are also considered symbolic vocabulary, which creates more confusion for students. Examples are lb. for pound, or ft. for feet.
Sullivan (1982) opined that the general and symbolic vocabulary in mathematics are largely ignored in instruction. According to her, teachers may assume that there is no need to teach general vocabulary as the students can draw meanings out of their concrete experiences. Nonetheless, Sullivan (1982) consider that the failure to solve word problems may be caused by an incorrect understanding of so-called "little words."
Research has established how important mathematical vocabulary is in developing effective problem-solving skills among students (Barton & Heidema, 2000; Monroe & Panchyshyn, 1995). Since mathematics itself demands an understanding of language, learners' capacity to understand the words embedded in the problems influences their problem-solving ability immensely. Because students understand the language behind the word problems, they are able to apply the correct mathematical concepts in solving them. As such, it has been recommended that teachers allocate time to providing direct vocabulary instruction on essential mathematical concepts (Barton & Heidema, 2000).
The language demands of mathematics are extensive (Harmon, Hedrick & Wood, 2005). A child's capacity to comprehend the language that is found in math word problems affects his or her proficiency in solving them. Children face the challenge of not only understanding teacher explanations and instructions in math but to understand the meanings of particular words and sentences in order to effectively solve a problem presented in word form.
Research has shown that knowledge of mathematics vocabulary affects student achievement in mathematics-particularly in the area of problem solving. According to Barron and Heidema (2000), being able to comprehend the mathematics language forms part of "sense making" in the subject (p. 132). Larson (2007) further argues that in order to understand mathematics, one should not rely solely on numbers but there has to be a conscious understanding behind the formulas and the processed involved in the calculations. Because mathematics uses symbols and numbers, students often get confused when asked to apply them because they do not completely understand. It is only when they are able "put a name with a face" will they start making sense out of the terminology and effectively use it to solve daily assignments.
Riccomini and Witzel (2009) indicated that problem-solving proficiency lies on acquiring the basic mathematic skills as well as being able to comprehend and use the language. Before this skills acquisition can translate into application of concepts in problem solving, students must first have knowledge of mathematical vocabulary. Mathematical language is considered important by National Research Council, which noted that there are five steps toward mathematical proficiency: 1) understanding mathematics; 2) computing fluently; 3) applying concepts to solve problems; 4) reasoning logically; and 5) engaging in mathematics. As such, learning mathematics does not simply involve having to apply its procedures and concepts. Rather it is "the all-around ability to communicate mathematically" (Riccomini & Witzel, 2009, p. 218).
In my 16 years as a math teacher, I have observed how students like problem solving in mathematics the least. Often, they are able to calculate problems when presented in number form but are taken aback or feel powerless when faced with word problems. The difficulty is especially apparent with English learners and those with special needs since the language barrier continues to be an obstacle for them. I learned by carefully reviewing research and past studies that this is a common problem for students of all ages. It is therefore important that vocabulary instruction be emphasized as a vital part of mathematics teaching. As teacher and researcher, my goal is to enhance mathematics vocabulary among students in order to transform them into more proficient problem solvers.
There are recommendations when launching a vocabulary instruction program. Foul and Alder (as cited in Riccomini & Witzel, 2009) recommended four basic guidelines which will not only improve comprehension but also motivate and capture the interests of students:
1. Employ a variety of methods and strategies;
2. Actively involve students in vocabulary instruction;
3. Provide instruction that enables students to see how target vocabulary words relate to other words;
4. Provide frequent opportunities to practice reading words in many contexts to help students gain a deeper and automatic comprehension of target words. (p. 211)
There are many reasons why fifth graders are presently struggling with solving word problems in mathematics. They are particularly finding it difficult to solve problems involving multiple steps and which include a combination of technical vocabulary and higher-order numerical operations. One cause behind lack of proficiency in problem solving is "an emphasis on repetition and rules, inadequate language skills and the lack of prior knowledge of mathematical concepts" (Schoenberger & Liming, 2001, p. 4). Newman (2006) also emphasized that math has a language of its own and when students are unable to grasp the language, they will undoubtedly struggle over answering it. Riccomini and Mitzel (2009) suggested that the issue in mathematics problem-solving is that the students are aware of the words themselves but are unable to connect it to their understanding of it. Based on their experience, Riccomini and Mitzel noted that students are able to solve problems when presented numerically. However, when the mathematical concepts are presented in the form of word problems, students feel panic or feel that they are incapable of solving them. Hence, in this action research, I am looking for three gains. First, I want students to master the required language to help them solve problems. Second, I want them to be able to improve their problem-solving skills as a result of developing vocabulary. Third, I want them to be confident about themselves as problem solvers.
Chapter III: Outcomes and Analysis
Goals and Expectations
The goal is to significantly improve problem-solving skills among fifth grade students who receive mathematics vocabulary instruction based on the Resources for Vocabulary Instruction Curriculum (RVI) as compared to fifth grade students who continued to receive mathematics lessons without vocabulary instruction.
There are four specific outcomes that fifth grade students will achieve by receiving the RVI curriculum:
RVI students' scores on chapter vocabulary inventories will be 20% higher than the scores of the students in the control group.
RVI students' general vocabulary test scores will be 20% higher than the scores of the students in the control group.
RVI students' scores on chapter problem-solving tests will be 20% higher than the scores of students in the control group.
RVI students' attitudes on their problem-solving capabilities will be more positive after the research than those of students in the control group.
Measurement of Outcomes
There are four ways the writer will employ in order to accurately measure the outcomes of this action research on improving problem-solving skills through vocabulary instruction.
First, fifth grade students from the experimental and control group will be given pre- and post- chapter vocabulary lists when a new chapter in the math curriculum begins. These vocabulary lists will consist of 10 important terms which will be used in that specific chapter. The challenge is to have the students match the definitions found on one side of the page to the words on the opposite side. Students' papers will be rated in the number of correct matches out of 10 possible correct answers. The same vocabulary list will be used during the pre-test and post-test.
Second, a general vocabulary exercise will be given to students at the start and at the end of this action research. Unlike the chapter vocabulary lists, the general vocabulary exercise will have students write their own definition of common mathematical terms that appear in the curriculum. Students will be familiar to some of the terms while some of the terms will be discussed in subsequent chapters. The purpose of this exercise is to determine whether there is improvement in vocabulary among the students.
Third, in order to determine whether the vocabulary instruction implemented resulted to an improvement in problem-solving skills, students' scores on chapter tests will be recorded. Chapter tests will specifically include items that require problem solving. The objective of the chapter test is to pinpoint growth in the students' capacity as problem solvers which will be reflected in their scores.
Fourth, an attitudes survey will be performed among students in order to evaluate any mark of improvement as far as students' perceptions of their capacity as problem solvers after the implementation.
Analysis of Results
Data analysis for this study will use quantitative methods. First, scores on the pre- and post- chapter vocabulary lists will be computed and compared using percentages and graphs. Second, scores on general vocabulary exercises will be computed and compared to determine whether students from the experimental group outperform their counterparts from the control group in defining common and new mathematical terms. Third, scores obtained by the two groups on chapter exercises will be computed and compared to determine whether or not the scores of the students in the experimental group are higher than those of the control group, implying a higher skill or improvement in problem solving abilities. Fourth, the perceptions of the students regarding their capacity in vocabulary and problem-solving will be gathered and described in order to compare whether there is a positive change in attitude in the experimental group as a result of the implemented intervention.
Chapter IV: Solution Strategy
Statement of Problem
As indicated, the problem being addressed in this study is that the fifth grade students at the XYZ Elementary School are struggling with math, particularly in solving word problems as evidence by their poor performance in classroom tests as well as their below-standard scores in the AMRT.
Students who are English learners and those with special needs have unique needs when it comes to language. Hence, any approach toward addressing problem-solving skills in mathematics through vocabulary instruction need to be able to respond to their needs. Teaching vocabulary using mere definitions will not work. There has to be word-learning strategies incorporated in vocabulary instruction for it to result to a better comprehension.
Riccomini and Witzel (2009) delineated 6 instructional activities which could assist in developing vocabulary understanding among students. These are: 1. The use of technology and other resources; 2. The use of journaling; 3. Teaching the origins of words and their parts; 4. Pre-teaching vocabulary before going into the lesson; 5. Providing opportunities for practice to increase fluency; 6. The use of graphic organizers.
There is a growing concern that the language of mathematics has only become more abstruse over the years without changing fundamental ideas. In order to make vocabulary more attuned to students' everyday experiences, Schoenberger and Liming (2001) suggested using "student-built glossaries" (p. 12). The idea behind developing glossaries is that writing enhances comprehension of vocabulary terms. As a vocabulary building strategy, writing is said to be an authentic demonstration of student's comprehension of the material which is presented by the teacher.
Another idea is to launch direct journaling activities to facilitate vocabulary building. Salinas (2004) noted how important journal writing is in building an academic vocabulary in mathematics. According to her, journal writing assists in clarifying student's thinking and developing a greater understanding of mathematical concepts. When students are able to write down the processes involved in the math problems they work on, this will help them evaluate their work and provide them a view of the steps toward the correct solutions. Moreover, journaling will also reveal what areas students find problematic in so these entries will help teachers assess and gauge level of understanding. Journaling according to Salinas (2004) further gives motivation to students by letting them express their feelings as learners.
Another strategy in improving problem-solving skills through vocabulary instruction is practice. Struggling students, English learners, and those with learning disabilities are often hampered by limited capacity to memorize concepts. In order to learn and remember mathematical vocabulary, practice is a vital factor. Based on a report by the National Mathematics Advisory Panel (as cited in Riccomini & Witzel, 2009), practice will help students in overcoming their weakness in automatic recall. It is advised that practice activities be offered to students immediately after material is presented so students can accurately master concepts and definitions. Providing opportunities for practice will enhance fluency and helps students retain the definition in their vocabulary. Opportunities could come in different activities such group exercises, independent practice, peer tutoring or in game show activities.
Another strategy recommended in helping students improve their mathematics vocabulary is through organization of concepts (Riccomini & Witzel, 2009). Low achievers struggle because they learn is a disorganized manner. Their notes are messy and sometimes difficult to read. This becomes an obstacle towards learning because students will struggle with referring back to previously discussed concepts and terms. This is where graphic organizers become helpful. Graphic organizers are a technique in letting students organize the information they take in better. Organizing concepts through concept maps will facilitate students' understanding of how concepts are related with each other. They are also motivational materials that provide an alternative to the traditional note-taking that students usually do.
To meet its objective of improving the problem solving skills of fifth grade students, a single approach will be implemented in this study. Specifically, 25 students (experimental group) from a fifth grade class will receive mathematics vocabulary instruction using the Resources for Vocabulary Instruction curriculum, which integrates several techniques and resources in order to facilitate students' deeper understanding of mathematical concepts and definitions. I hope that through this strategy, not only will the students' capacity to solve problems improve, but it will lead to a more positive perspective on problem solving and mathematics in general. On the other hand, the control group will receive mathematics instruction using the basal program.
The interventions included in the proposed solution strategy include:
Creation of a glossary of mathematical terms which is expanded with additional chapters
Using concept maps or other graphic organizers to review and clarify relationships of terms
Providing problem solving activities daily for practice
Developing pre- and post- vocabulary inventories
The implementation of the selected curriculum will commence for a period of 8 weeks. Students belonging to the experimental group will receive 8 weeks of vocabulary instruction using the proposed curriculum. Each group will receive daily instruction on mathematics computations and concepts for one-half hour. Another half-hour was spent on individual skills. Another half-hour was spent on the experimental or control treatment. The control group will receive drills on the mathematical operations or concepts presented per chapter using the basal module while the experimental group will receive mathematics vocabulary instruction using a) glossary building; b) concept maps; c) direct journaling; and d) pre- and post- vocabulary inventories.
Weeks 1-2 will focus on number sense particularly on fractions and decimals, rounding, and ordering of numbers. Weeks 3-4 will focus on applying the four mathematical operations using seven-digit numbers, two-digit multipliers, and two-digit divisors. Weeks 5-6 will focus on mixed fractions and divisibility. Weeks 7-8 will focus on polygons, shapes, and computing perimeter, area, and volume.
The two teachers who will participate in this study have at least 6 years experience teaching mathematics and are qualified to do the proposed curriculum.