Abstract

The purpose of this quantitative action research study was to determine the impact of students' written explanations demonstrating their conceptual understanding of math problem-solving on students' math performance and their perceptions of their understanding of mathematics. The primary research question for this study was: What is the impact of involving students in written explanations of their problem-solving on fifth grade students math achievement? The students who were involved in this study included fifth grade students enrolled in a public elementary school in a small, rural Midwestern community. The Star Math Assessment was given the second week of school. No intervention took place for the first five weeks of school. Starting with the sixth week of school and for the next five weeks the intervention, using writing to conceptualize the understanding of problem-solving in math, was in place. At the end of the study period, November 3rd, students were given the Star Math Assessment. Quantitative data were collected prior to and following the intervention period using the Star Math assessment. Perception surveys were administrated to examine students perceptions about their understanding of math problem-solving.

Impact of Involving Students in Written Explanations of their Problem-Solving on Fifth Grade Students' Math Achievement

Statement of the ProblemEvery day student enters the classroom, sit down, listen, participate, and complete mathematics problems. It is unclear how many of the students realize what they are actually doing and how many of the students understand and could explain the process and what each step really means. Procedural knowledge is Like a toolbox, it includes facts, skills, procedures, algorithms or methods (Barr, Doyle et. el., 2003). Teachers often question whether students have the conceptual understanding of mathematics or if they just understand that if I do step one, then step two, step three, and step four I get the answer I was looking for and the teacher will be happy. Conceptual understanding knows more than isolated facts and methods. Conceptual knowledge is Learning that involves understanding and interpreting concepts and the relations between concepts (Arslan, 2010). The successful student understands mathematical ideas, and has the ability to transfer their knowledge into new situations and apply it to new contexts.

Purpose StatementThe purpose of this action research study was to determine the impact of students written explanations of their math processes on math problem-solving proficiency. The primary question that guided this study was: What is the impact of involving students in written explanations of their problem-solving on fifth grade students math achievement? The research study also investigated: What is the impact of involving students in written explanations of their problem-solving on fifth grade Students perceptions about their understanding of mathematics and what is the impact of involving students in written explanations of their problem-solving on low-achieving students performance in the fifth grade math classroom?

The independent variable was the incorporation of students daily writing about their conceptual problem-solving in the fifth grade math classroom. The dependent variable was the students achievement in mathematics.

Research question:What is the impact of involving students in written explanations of their problem-solving on fifth grade students math achievement?

Sub:What is the impact of involving students in written explanations of their problem-solving on fifth grade students perceptions about their understanding of mathematics?

What is the impact of involving students in written explanations of their problem-solving on low-achieving students in the fifth grade math classroom?

Action Research Study Data/Intervention PlanThe research project started with the collection of data containing students current performance on the Star Math Assessment. The Star Math Assessment was given the second week of school. No intervention took place for the first five weeks of school. Starting with the sixth week of school and for the next five weeks the intervention, using writing to conceptualize the understanding of problem-solving in math, was in place. The data collected and monitored during the first five weeks of no intervention was in their math journals. The next five weeks the intervention was in place and the data collected and monitored was in their math journals. At the end of the study period, November 3rd, students were given the Star Math Assessment.

IntroductionYour students walk into class, take their seat, and look to the front of the room waiting for the teacher to start talking about what we will be doing in class today. The teacher teaches their lesson, the students start working on their math problems, and before you know it the bell has rung and off to the next class the students go. The teacher feels really good about the lesson. The teacher feels confident that the students got it. They understood why the property of operations is important. Most of the students were engaged. Three or four students took a little longer to grasp the concept and two or three others had a blank look on their faces.

How often does this happen in classrooms today? Do the students really understand the conceptual problem-solving of mathematics? What is the impact of involving students in written explanations of their problem-solving? Mathematics is not just a process or set of rules to be followed in calculations or other problem-solving operations nor is it just rote memorization. The researcher of this paper has struggled over this problem-solving issue. The researcher sees the students that really understand the conceptualization of problem-solving. These students are excited and want the challenge of more problem-solving. Then the students that dont quite understand need a little prompting before they feel comfortable with their knowledge of problem-solving. Lastly, the research sees the students that just look at the teacher and wants nothing more than to just get the answer to the problem so that they can finish their assignment. Students cannot become successful problem solvers overnight. Helping students become successful problem solvers should be a long-term instructional goal, so effort should be made to reach this goal at every grade level, in every mathematical topic, and in every lesson.

The research has also seen the students struggle in being able to write their ideas down on paper. Some students struggle with writing what they are thinking. They are lacking in the conceptual problem-solving area. It is hard for students to put down in words the steps they took to solve the problem and what those steps really mean and how this problem solving can help them solve other types of mathematical problems.

Literature Review

In the fifth grade, the curriculum expects the learners to be able to recognize prime numbers ranging up to 100 and be able to recognize shapes such as squares and rectangles (Time4Learning, 2016). At this level, students should also be taught how to find factors of numbers and the divisibility rules and judge if the numbers are either composite or prime. The learners also express whole numbers as products of prime factors and also evaluate either the least common factor or the greatest common factor of numbers to the tune of 100. Moreover, according to Time4Learning (2016), the learners multiply by powers of 10 and should be able to demonstrate patterns. For divisions, the fifth-grade learners should be able to both identify and apply the laws of the division for the numbers between 2 and 10 and apply the various models to identify perfect squares for the numbers up to 144 (Jayne & Lynch, 2007).

Knowledge at this stage can be better imparted through self-explanation which refers to the art of explaining the meaning of a text while either reading or writing (McNamara, 2004, p. 2). This has been found to be effective by some scholars for the fifth grade where students are introduced to the mastery of the concepts and mechanics of division and multiplication including their distributive, associative, and commutative properties. According to Chi et. al. (1993) and Chi & Bassok (1989), this can be better done through self-explanation which is one of the most effective ways to make the knowledge memorable to the young learners (p. 441; p. 280). Similarly, Kastens & Liben (2007) postulate that students who explain the reasons behind their working ultimately perform better than students who do not explain their procedures (p. 63).

Moreover, the measurement of competence in Mathematics goes beyond students performance in automated skills in the fifth grade as in the other grades. According to National Research Council (1993), assessments in math should encompass the study of how well the learners are able to connect the imparted concepts, how easily they can recognize the principles behind the concepts they have learned, and their sense on when to apply either strategies or processes (p. 72). Additionally, it should assess whether each learner can bring the skills and the concepts together to bring a smooth and proficient performance (National Research Council, 1993, pp. 72-73). Beals and Garelick (2015) explain the significance of the need for students to explain their mathematical solution by explaining the distinction between doing and knowing. Additionally, the use of self-explanation technique after working out a math problem helps students to memorize and better present their work and this improves with time (Jayne & Lynch, 2007; Dunlosky et al., 2013, p. 12; Woodward, Monroe & Baxter, 2001, p. 18; Aleven & Koedinger, 2002, p. 173). When for instance a student in Canadian middle school was asked to write down her explanations of the Mathematics problems, her response was, Why cant I just do the problem, enter the answer and be done with it? (Beals & Garelick, 2015). However, the meaning of the term understanding in the context of Mathematics has been a long debate. Recently, the argument has been among the students doing and knowing the concepts. For instance, it has been founded that many students are able to calculate math questions and arrive at the correct answer without getting the concepts behind their procedures (Beals & Garelick, 2015). As Beals & Garelick (2015) postulate, this can be caused by the students memorizing the procedure thus arrive at the answer but do not understand how to perform the steps by rote.

A major question in this discussion is thus, how best should teachers assess their learners understanding the mathematical concepts?

One way is to ask the student to justify, in a way that is appropriate to the students mathematical maturity, why a particular mathematical statement is true, or where a mathematical rule comes from (...

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