Improving the Success Rate of Third Grade Students in Solving Math Word Problems - Assignment Example

Improving the Success Rate of Third Grade in Solving Math Word Problems Background Information The school in question is one of approximately 317 schools that make up the fifth largest school district in the nation with a student population over 290,000. The city where the school is located has gained recognition for being one of the largest cities in the United States with a population over 560,000. However, this state is recognized as being ranked poorly, coming in at 49th place in the country for educational achievement overall. The school district is divided into six regions. These regions include the Northeast, Northwest, East, Southeast, Southwest, and the Superintendent’s Schools. The mission of the district is to increase student achievement and to provide professional development for teachers. The school is located in the Northeast region. The Northeast region consists of fifty elementary and secondary schools that provide education to approximately 50,000 students. The school’s location is in a very low-income area. The area consists of a variety of different types of housing developments that include apartments, trailers, homes, and government housing. The school is a neighborhood school; thus, all students live within walking distance and school bus transportation is not required. The area has recently experienced the demolition of many trailer parks and construction of new housing and apartment buildings. Purpose and Discrepancy Statement The students are not meeting grade level expectations for mathematics word problem solving and the school is in need of implementing and enforcing new math word problem strategies to increase the achievement of students in this highly tested area. Survey 3rd Grade Students and Math Word Problems: Creating Future Success The following set of statements is concerned with math word problems and 3rd grade students. Please read through each statement carefully and choose one answer: agree, disagree or uncertain. The opinions of elementary teachers on this topic will be considered carefully in the expansion of specific math problem tutoring. 1) It is important that word problems relate to real-life situations so that students understand their relevance. AGREE/DISAGREE/UNCERTAIN 2) Students with strong academic skills in other subjects are more likely to solve word problems in math easily. AGREE/DISAGREE/UNCERTAIN 3) One-on-one tutoring is more successful in dealing with math word problems than lectures. AGREE/DISAGREE/UNCERTAIN 4) There is a difference in the academic success of individual students when it comes to word problems and different types of math problems. AGREE/DISAGREE/UNCERTAIN 5) Visual aids can help students to solve math word problems more easily. AGREE/DISAGREE/UNCERTAIN 6) Teaching students to find keywords in math word problems strengthens their ability to solve such problems correctly. AGREE/DISAGREE/UNCERTAIN 7) Rephrasing the problem can help students to solve it more easily and quickly. AGREE/DISAGREE/UNCERTAIN 8) Students with limited reading and writing skills should not only receive extra help with math word problems, but with strengthening their language skills. AGREE/DISAGREE/UNCERTAIN Literature Review The National Council of teachers of mathematics (NCTM) published Curriculum and Evaluation Standards for School Mathematics in the late 1980s. This publication led to the evolution of the focus of more problem-solving and higher order thinking skills curriculum and the demise of the arithmetic and isolated facts-based approach used at that time. The new approach of the mathematics curriculum is to get the students to read, write, and discuss mathematics. According to Marzano’s Building Academic Background Knowledge, many researchers have discovered that the lack of academic vocabulary may trigger one’s performance in mathematics. The cause of a student to be deprived of the proper amount of vocabulary may be due to the fact that these students come from low-income families. Hart and Risley, researchers mentioned in the book, have concluded that the children who come from welfare families “were exposed to a fraction of the language” (Marzano, 2004) compared to those children who come from wealthier families. “One salient characteristic of English Language Learners students is that their academic English is below grade level – sometimes several grades below.” (Brown, 2005). This research investigated the math achievement differences between ELL students and fully English proficient students (FEP). It is expected that ELL students not only must learn the language, but they also must learn mathematics language. “ELL students have to learn math in their less fully developed language” (Brown, 2005) and they are required to take tests and express their thinking and ideas in a language they have not mastered yet. According to Cummins theory of language acquisition, ELL students become proficient in conversational English over one to two year period. However, it may take from five to seven years to acquire academic language that is appropriate for their grade level. What are some reasons and factors that make mathematics a very difficult subject among ELL students? The language of mathematics is difficult for the non-proficient FEP student; therefore, for an ELL student this would be the third language that they must learn through the use of their second new language. If the students are still learning English, then it may be very difficult to understand math concepts that are presented in math word problems. The students may be able to complete the computational part, but the breaking down and translating English into mathematic equations may be difficult. In Understanding and Supporting Children’s mathematical Vocabulary, Rubenstein and Thompson point out the difficulties in learning mathematical vocabulary. There are many mathematical terms, phrases, and symbols that have multiple meanings. These multiple meanings may be confusing for students acquiring or learning a new language, as well as for students still developing the English language. Jones (1982) discusses “an important step in solving word problems in arithmetic is the translation from the verbal formulation to the underlying mathematical relationship.” Jones research stresses that full understanding of the word problem requires more than simply reading the problem and understanding the words in isolation. It involves comprehension of the whole text or word problem statement. If the students are not reading at or above their reading level, then it will be difficult for them to be able to read and understand math word problems. In order for students to solve math word problems, they have to connect the math process to the situation being presented in the story. Due to the fact that students have difficulty making this connection, they are unsuccessful with solving math word problems. Having the ability to understand the problem may not be difficult as deciding what to do with it. Math vocabulary is not commonly used in daily settings. The lack of language experiences for students hinders their ability to be successful with word math problems. They do not know enough to translate math language into simple equations or have enough experiences to express orally how to arrive at the answer. The answer is no longer the only important thing in math, but also “the process by which a student arrives at the answer to a problem becomes as important as the answer itself.” (Buschman, 1995.) Engaging in a conversation about math concepts helps develop an understanding of the “third language.” Bernardo and Calleja (2005) show that bilingual students understand word problems better in their more proficient language. However, the language used in math word problems might not always be an important factor. The researchers point out that “certain problems or difficulties that bilingual students have with solving word problems is not considered or applied to real-world knowledge.” It is important to keep in mind that before a concept can be truly understood, children must experience math concretely. Burns (1979) discusses that “children need hands-on experiences to make connections between the concepts that they have learned with manipulative and the symbols on the page.” Transforming a problem full of words into a real-life situation or translating using pictures will help learners develop understanding of the situation and be able to solve the problem. Students are too focused on arriving at the answer. When asked to provide evidence on how they arrived to the answer, the students stumble upon words to explain their thinking process. Often, the students are not provided with enough opportunities to discuss their thinking process that led to the answer. Language and Modeling Word Problems in Mathematics among Bilinguals By Allan B. Bernardo This study served to answer the question, “Does using a bilingual’s first or second language have an effect on problem-solving in semantically rich domains like school mathematics?” (2002, p. 1) The author of this study checked to see if Filipino-English bilingual students responded differently when presented problems in their first language versus their second language. The author used two different groups of students: some spoke Filipino as their first language, and the others spoke English as their first language. The problems that were presented varied from easy to difficult. “The author used a recall paradigm to assess how students understood the word problems and coded the solution accuracy to assess problem solving. The results indicated a first language advantage; that is, the students were better able to understand and solve problems in their first language, whether the first language was Filipino or English” (2002, p. 1). It is also important to note that the advantage was even more substantial with the easier problems. Bilingual Students’ Articulation and Gesticulation of Mathematical Knowledge During Problem Solving By Higinio Dominguez This article asked two questions: “How do second grade bilingual students communicate their mathematical reasoning” and “What is the role of the mathematical tasks in eliciting this mathematical reasoning?” Seven second grade bilingual Spanish-English students were analyzed solving addition and subtraction problems. The research in this article shows that the students “simultaneously used words and gestures to communicate their mathematical reasoning to others and to regulate their own cognitive activity. In general, the students demonstrated that their developing bilingual proficiency did not constitute an impediment for guiding mathematical tasks to resolution; rather, students imparted mathematical meaning to each task by mutually supporting their verbal and nonverbal behaviors” (2005, p. 269). Overcoming Obstacles to Understanding and Solving Word Problems in Mathematics By Allan B. Bernardo Understanding the structure of word problems is often the hardest part for students to grasp. However, if a student fails to understand the structure of a problem he or she is trying to solve, it is unlikely that the problem will be solved correctly. This article discusses a study that was conducted on Filipino-English bilingual students in the Philippines. “The results showed better understanding and solution performance when problems were written in the students’ first language, when the problems were re-worded to state more explicitly the relationship among the known and unknown quantities, for students in higher levels of schooling, and for students with higher levels of academic achievement” (1999, p. 149). The Effects of Stating Problems in Bilingual Students’ First and Second Languages on Solving Mathematical Word Problems By Allan B. Bernardo and Marissa O. Calleja This article tells about how many researchers have stated for years that linguistic factors play a role in bilingual students’ abilities to solve word problems. Others argue that the tendency to omit real-world constraints is the real culprit. The article talks about a study in which word problems in either Filipino or English were provided to students and the solution to each of the problems required that the students applied real-world knowledge. “The authors analyzed the students’ solutions to determine whether the language of the word problems affected the tendency to apply real-life constraints in the solution. Results showed that the bilingual students rarely considered real-life constraints in their solutions, were more successful in understanding and solving word problems that were stated in their first language, and were more likely to experience failure in finding a solution to problems stated in their second language” (2005, p. 117). Methods Goal The target students will solve math word problems on grade level. Objective By the end of six weeks of intervention, at least 9 to 12 students will be able to model and solve basic math word problems with no errors. Activity 1 Students will be individually assessed on their ability to model and solve basic math word problems. Activity 2 Students will be assigned word problems that meet with their own individual levels. Matrix Weeks Teacher Tasks Materials Teaching Strategies Learning Activities Prior to Implementation Assess students as shown above Assessment tests that contain math word problems N/A N/A Week 1: Paraphrase Instruct, demonstrate, and model Paper and pencil Demonstration Step 1: Paraphrase Skill 1: Underline important information Skill 2: Put problem in own words Students make up and solve their own word problems; students listen to a variety of statements and pick one that best represents the problem Week 2: Visualize Instruct, demonstrate, and model Paper and pencil Demonstration Step 2: Visualize (a diagram or a picture) Skill 1: Make a drawing or diagram Students presented with short problems that do not ask questions and are asked to tell what they know from the information given Week 3: Hypothesize Instruct, demonstrate, and model Paper and pencil Demonstration Step 3: Hypothesize (number of steps, operation, equation) Skill 1: Describe how many steps are needed Students are provided with 2-step color-coded word problems and are asked to identify the different parts Week 4: Hypothesize Instruct, demonstrate, and model Paper and pencil Demonstration Step 3: Hypothesize (number of steps, operation, equation) Skill 2: Decide which operation(s) is needed Students are provided with examples of word problems and are asked to circle all the problems that would be answered using the same operation Week 5: Hypothesize Instruct, demonstrate, and model Paper and pencil Demonstration Step 3: Hypothesize (number of steps, operation, equation) Skill 3: Write the equation Students are presented with exercises in which the focus is writing a math expression rather than solving an equation and with exercises that explicitly state the meanings of words in mathematics Week 6: Estimate Instruct, demonstrate, and model Paper and pencil Demonstration Step 4: Estimate (predict the answer) Skill 1: Estimate the solution Students are read a word problem and asked to estimate the answer. Answers are plotted on a number line and when different answers would be acceptable is discussed, along with how estimating is a way to check to see if answers are reasonable (Gallagher Landi, 2001) Reference List Bernardo, A.B.I. and M.O. Calleja. (2005). ‘The effects of stating problems in bilingual students’ first and second languages on solving mathematical word problems’, The Journal of Genetic Psychology, 166(1): 177-128. Bernardo, A.B.I. (2002). ‘Language and mathematical problem solving among bilinguals’, The Journal of Psychology 130(63): 283 – 297 Bernardo, A.B.I. (2005). ‘Language and modeling word problems in mathematics among bilinguals’, The Journal of Psychology, 139(5): 413-425. Bernardo, A.B.I. (1999). ‘Overcoming obstacles to understanding and solving word problems in mathematics’, Educational Psychology, 19(2): 149-162. Bresser, R. (2003). ‘Helping Engligh-language learners develop computational fluency’, Teaching Children Mathematics, 294 – 299. Brown, C. (2005). ‘Equity of literacy-based math performance assessments for English Language learners’, Bilingual Research Journal, 29(2). Burns, M. (1979). ‘The math connection is yours to make’, Learning, 7(5). Buschman, L. (1995). ‘Communicating in the language of mathematics’, Teaching Children Mathematics, 1(6). DeGeorge, B. and A.M. Santaro. (2004). ‘Manipulatives: A hands-on approach to math’, The H.W.Wilson Company, 28. Dominguez, H. (2005). ‘Bilingual students’ articulation and gesticulation of mathematical knowledge during problem solving’, Bilingual Research Journal, 29(2): 269 – 296. Gallagher Landi, M.A. (2001). ‘Helping students with learning disabilities make sense of word problems.’ Guillaume, A.M. and L. Kirtman. (2005). ‘Learning lessons about lessons: Memories of mathematics instructions’, Teaching Children Mathematics, 302 – 309. Jensen, C.; T. Whitehouse; and R. Coulehan. (2000). ‘Engaging children in the work of mathematics’, Teaching Children Mathematics, 490 – 495. Jones, P. (1982). ‘Learning mathematics in a second language: A problem with more and Less’, Educational Studies in Mathematics, 13(3). Retrieved January 31, 2008 from JSTOR archive. Marzano, Robert. (2004). ‘Building background knowledge for academic achievement’, Alexandria, VA: Association for Supervision and Curriculum Development. Rubenstein, R. & Thompson, D. (2002). ‘Understanding and supporting children’s mathematical vocabulary development’, Teaching Children Mathematics, 9(2). Whitin, P. and D.J. Whitin. (2006). ‘Making connections through math –related book pairs’, Teaching Children Mathematics, 196 – 202. Read More