Improving Math Problems Solving Skills Education Essay
The problem which this study seeks to address is that 50% of fifth grade math students at XYZ School are failing mathematics word-problems tests.
The study's purpose is to determine whether or not a specific solution strategy will lead to an improvement in the fifth graders' proficiency to solve math problems.
Description of the Community
As of the census of 2000, there were 223,510 persons, 86,068 households, and 56,804 families in the county. The population density was 283 persons per square mile (109/kmÂ²). There were where is the source citation?Where is the reference?95,437 housing units, at an average density of 121 per squareÂ mile (47/kmÂ²). The racial makeup of the county was 48.85% White, 48.58% Black or African American, 0.99% Asian, 0.25% Native American, 0.03% Pacific Islander, 0.35% from other races, and 0.94% from two or more races. Hispanics and Latinos, of any race, made up 1.19% of the population.
The total population was estimated to have grown by 61 persons from 2000 to 2006.
By 2005, 52.5% of the population was black, 44.0% was non-Hispanic white, 1.4% was Hispanic, 1.2% was Asian, 0.2% was Native American, and 0.9% of the population reported two or more races. This excludes those who reported "some other race" and "white", because the Census Bureau reclassified all who reported "some other race" as white (American FactFinder, 2010).
There were 86,068 households, 32.20% of which included children under the age of 18, 43.80% were married couples living together, 18.60% had a female householder with no husband present, and 34.00% were non-families. Single-persons households were 29.50% of the total; 9.40% had someone living alone who was 65 years of age or older. The average household size was 2.46. The average family size was 3.06.
Persons younger than 18 were 25.80% of the population; those 18-24, 11.70%; 25-44, 29.80%; 45-64, 20.90%; and 65 and older, 11.80%. The median age was 34 years. For every 100 females there were 90.80 males. For every 100 females aged 18 and over, there were 86.70 males.
The median income for a household in the county was $35,962, and the median income for a family was $44,669. Males had a median income of $32,018; females, $24,921. The per capita income for the county was $19,358. About 13.50% of families and 17.30% of the population.
The community belongs to the Montgomery Public Schools (MPS) system which is the third largest school system in Alabama. This is NOT in outline form
1. The MPS has undergone significant growth over the years.
The school district has over 3,681 students enrolled (Alabama Department of Education, 2010).
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).
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 (Alabama Department of Education, 2010).
The school district's goals focus on academic excellence for its students.
The mission of MPS is to "offer stimulating environments led by qualified and dedicated teachers" (Alabama Department of Education, 2010).
The MPS focuses on the vision of "preparing students for life" (Alabama Department of Education, 2010).
The MPS is dedicated to its accountability goals under the No Child Left Behind policy.
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.
Description of Work Setting
The research project will take place at Johnson Elementary School located within Montgomery, Alabama, serving Pre-K through sixth grade students. The administration structure of the school has one principal, assistant principal, and two counselors. The staff is comprised of 40 certified teachers, 2 physical education teachers, and 15 support staff (Alabama Department of Education, 2010).
The student population in this school is approximately 900 students consisting of 55% girls and 45% boys.
The ethnic distribution of the school is approximately 34 % Caucasian, 10 % Hispanic, 25 % African American, 10 % Asian, and 9 % other.
The school's current mathematics curriculum follows the Alabama Mathematics Content Standards.
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.
Students 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 (Alabama Department of Education, 2010).
Involved in this project will be two fifth grade classrooms and their teachers.
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.
Both classes have relatively similar achievement level in math and roughly the same student characteristics.
The writer has been a math teacher for 16 years and is presently a substitute teacher of fifth grade students at the present elementary school.
The writer's responsibility as a substitute teacher in Math is not only to instruct students on mathematical concepts and operations.
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.
Chapter II: Study of the Problem
The problem being studied is that many fifth grade students at the target elementary school are struggling with math, particularly in solving word problems.
Many students fail quizzes in math.
Many students fail chapter tests particularly in world problems.
Many students function below grade level on tests.
Many students earn low report card grades in math.
Many (32%) fifth graders fail to pass fifty percent 50% of their chapter exercises in mathematics.
Many (23%) fifth graders score below average in terms of general mathematics vocabulary.
Majority (53%) fifth graders fail their chapter problem solving tests in mathematics.
Majority (56%) of fifth graders evaluate their problem-solving skills negatively and have anxiety about solving word problems.
The review of literature indicated that mathematics vocabulary is a significant factor in a student's mathematics aptitude particularly in problem-solving.
Vocabulary proficiency is an important aspect in math learning.
Math learners have to establish a separate vocabulary in order to understand and communicate the language of mathematics.
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).
Failing to understand mathematical terms that they encounter in word problems leads to a loss of ability to solve them (Larson, 2007).
Math students need to process a word and its various meanings similar to what is practiced in reading (Pierce & Fontaine, 2009; Foster, 2007).
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).
Proficiency in the English language is a contributor to low problem-solving skills.
In an experimental study involving non-proficient English speakers in the eighth grade, the pre-test and post-test results of the students varied significantly according to their level of proficiency in the English Language (Brown, 2007).
According to Bernardo (2005), ELLs are disadvantaged when it comes to solving math problems because they have to apply mathematical operations through problems written in a foreign language.
Lack of confidence in problem solving leads to a decreased capacity of success in mathematics learning.
Mathematics is considered an abstruse subject and a scary one even from the perspective of the regular student (Rossnan, 2006).
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).
Research has established that implementing mathematical vocabulary instruction leads to improved problem-solving skills among students.
Since mathematics itself demands an understanding of language, learners' capacity to understand the words embedded in the problems influences their problem-solving ability immensely (Marzano, 2005).
Vocabulary instruction needs to incorporate one or more strategies in order to become effective.
According to Boon, Foren and Lowrie (2007), vocabulary instruction using the concept model was a more effective teaching strategy than instruction using the definition model for students with learning disabilities.
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 are a number of causes which cause the deficiency among fifth graders to become efficient problem solvers.
Students' difficulty with solving word problems is because of the lack of mastery of the technical operations involved.
Students' difficulty with solving word problems in math lies in the difficulty understanding the words or the language behind the problem.
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).
Students' difficulty in solving math problems may be due to lack of proficiency in the English language.
Non-proficient English speakers who have been under formal education from their countries of origin generally do not find mathematical operations difficult but struggle when they face word problems presented in language that remains unmastered (Bernardo, 2005).
Learning math is a complicated for most ELLs because the words presented in the classroom have no equivalent in their native tongue and confusion may arise because of the lack of similar or comparable terms (Carirer, 2005).
Students may have an understanding of the words in the problem but are unable to connect the words to their own understanding.
Students find it hard to comprehend and be conscious of mathematical concepts because they could not relate it to real-life experiences (Coggins, Kravin, Coates, & Carroll, 2007).
Students are unable to effectively solve word problems because of the lack of confidence and sometimes fear overcomes them when they are unable to understand what they need to solve (Rossnan, 2006).
Providing opportunities for peer group work in math problem solving gives students, particularly ELLs the support and encouragement they need to face their fears in problem solving (Thompson et al., 2008).
Alabama Department of Education. (2005). Alabama Reading and Mathematics Test: item specifications for Mathematics. Retrieved from: ftp://ftp.alsde.edu/documents/91/ARMT%20Mathematics%20Item%20Specifications%20for%20Grade%205.pdf.
American FactFinder. (2010). United States Census Bureau. Retrieved from: http://en.wikipedis.org/wiki/Montgomery_County_Alabama#cite_note-GR2-1.
Bernardo, A. I., (2005). Language and modeling word problems in mathematics among bilinguals. The Journal of Psychology, 139(5), 413-425.
Carrier, K. A. (2005). Key issues for teaching English language learners in academic classrooms. Middle School Journal, 37(2), 4
Coggins, D., Kravin, D., & Carroll, M. D. (2007). English language learners in the mathematics classroom. Thousand Oaks, CA: Corwin Press.
Boon, R. T., Fore, C. III, & Lowrie, K. (2007). Vocabulary Instruction for Middle School Students with Learning Disabilities: A Comparison of Two Instructional Models. Learning Disabilities: A Contemporary Journal 5(2), 49-73.
Brown, G. D. (2007). Mathematics vocabulary instruction for current non-proficient students with and without IEPs: A study of three methods of instruction. Retrieved from Proquest: http://gradworks.umi.com/
Foster, S. (2007). The day math and reading got hitched. Teaching Children Mathematics, 196-201.
Kersaint, G., Thompson, D. R., & Petkova (eds.) (2008). Teaching mathematics to English language learners. New York: Routledge.
Larson, C. (2007). The importance of vocabulary instruction in everyday mathematics. Action Research Project Report submitted to University of Nebraska, Lincoln, Nebraska.
Marzano, R. J. (2005). Building background knowledge for academic achievement. Alexandria, VA: ASCD.
Newman, J. R. (2006). "The vocabulary of mathematics." In J. R. Newman (ed). The world of mathematics Vol. 3 (pp. 1996-2009). New York: Simon & Schuster.
Pierce, M. & Fontaine, M. Designing vocabulary instruction in mathematics. The Reading Teacher, 53 (3), 239-243.
Riccomini. P. J. & Witzel, B. S. (2009). Response to intervention in Math. Thousand Oaks, CA: Corwin Press.
Rossnan, S. (2006). Overcoming math anxiety. Mathitudes, 1 (1), 1-4.
Thompson, D. R., Kersaint, G., Richards, J. C., Hunsader, P. D., Rubenstein, R. N. (2008) Mathematical literacy: Helping students make meaning in the middle grades. Portsmouth, NH: Heinemann.
Chapter III: Outcomes and Analysis
Fifth graders, when taught special mathematics vocabulary instruction, will show year-to-year progress in math tests, assignments, report cards, and standardized mathematics tests.
Expected Outcomes (i.e., Measurable Objectives)
Several specific outcomes will be achieved by fifth graders who will benefit from mathematics vocabulary instruction.
Fifth graders' scores on chapter vocabulary inventories will be 20% higher because of introduced vocabulary instruction.
Fifth graders' general vocabulary test scores will be 20% higher because of introduced vocabulary instruction.
Fifth graders' scores on chapter problem-solving tests will be 20% higher because of introduced vocabulary instruction.
Fifth graders' attitudes on their problem-solving capabilities will be more positive after the introduction of vocabulary instruction.
Measurement of Outcomes
The following methods will be employed to measure the effectiveness of the mathematics vocabulary instruction.
Fifth graders from the experimental and control group will be given pre- and post- chapter vocabulary list when a new chapter in the math curriculum begins and their grades will be recorded by the teacher.
Fifth graders will be given a general vocabulary exercise at the start and at the end of this action research.
Fifth graders' scores on chapter tests will be recorded.
An attitudes survey (pre- and post- implementation) 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
Scores on the pre- and post- chapter vocabulary lists will be computed and compared using percentages and graphs.
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.
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.
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.
Four separate z-tests (one for each of the objectives) will be used to compare pre- and post-implementation percentage data to see whether there is an increase at the .05 level of significance.
Chapter IV: Solution Strategy
The problem being studied is that many fifth grade students at the target elementary school are struggling with math, particularly in solving word problems.
Students struggling with mathematics particularly in problem solving will benefit from mathematics vocabulary instruction.
Students will be able to understand the language of the math problem and know exactly what the problem requires them to do (Pierce & Fontaine, 2008; Harmon, Hendrick & Wood, 2005).
Students will be able to connect the terms in the problem to their own concrete understanding and definition of the word (Nelson, 2006; Hyde, 2007).
ELL students will be able to comprehend mathematical terms crucial to problem solving despite not having mastered the English language through the use of simple and creative teaching strategies such as concept maps and other graphic organizers (Foster, 2007).
Strategies for teaching ELL learners in mathematics include the TESOL Sheltered Instruction which makes the math curriculum adaptive to suit the level of English proficiency of students (Slavit & Slavit, 2007; TESOL, 2006).
Particular strategies are recommended in mathematics vocabulary instruction.
There has to be word-learning strategies incorporated in vocabulary instruction for it to result to a better comprehension (Thompson et al., 2008).
The use of picture books, puzzles, and other creative tools are helpful in making mathematics vocabulary learning not only effective, but interactive and fun as well (Coggins et al., 2008; Harmon, Hendrick & Wood, 2005).
There has to be corresponding instruction to enable students to learn in a more organized manner.
One 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.
b. Graphic organizers become helpful. Graphic organizers are a technique in letting students organize the information they take in better (Kersaint, Rubilee, & Petkova, 2008). 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.
Students' success rates in mathematics are higher when they have positive attitudes about the subject and in their own competence to solve problems.
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 (Larson, 2007).
Developing positive attitudes about mathematics through peer, teacher or parental support will reduce children's fears about math (Rossnan, 2006; Murray, 2005).
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 (Brown, 2007; Thompson et al., 2008).
Another idea is to launch direct journaling activities to facilitate vocabulary building. Salinas (2005) 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.
Description of Selected Solutions/Calendar Plan
The selected solution strategy is direct mathematics vocabulary instruction. Several strategies to improving the capacity of fifth graders to become problem solvers will be implemented.
Fifth graders who are struggling with mathematics will receive vocabulary instruction on mathematical terms and concepts using creative strategies which will enable them not only to become more proficient in concepts but to allow them to learn and solve in a more organized manner.
Fifth graders will be allowed to evaluate their own competencies and attitudes toward math through direct journaling activities (Salinas, 2005).
The following steps will be taken.
One group will be designated as the control group receiving standard mathematics instruction while another group will be assigned as the experimental group receiving vocabulary instruction.
The following vocabulary teaching strategies will be used by the teachers.
A glossary of mathematical terms will be built by the students with the help of the teacher (Brown, 2007).
Vocabulary instruction will use concept maps or other graphic organizers to review and clarify relationships of terms (Thompson et al., 2008).
Teachers will provide problem solving activities daily for practice (Pierce & Fontaine, 2008).
Teachers will develop pre- and post- vocabulary inventories for evaluation purposes.
This schedule will be followed:
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 from the teachers for one-half hour. Another half-hour will be spent on individual skills. Another half-hour will be spent on the experimental (vocabulary instruction) 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.
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