The Impact of Fraction Manipulatives on 5th Grade Students' Confidence and Math Skills

Rationale

Having a deep understanding of fractions beginning in grade five is crucial for future success in mathematics, specifically algebra (National Mathematics Advisory Panel, 2008). Recent studies show that 42% of sixth grade students fail to understand fraction concepts (Namkung & Fuchs, 2016). Being that nearly half of sixth graders nationally have difficulty understanding fractions something has to be done to improve this deficit. The current study will discuss the impact and effectiveness of utilizing fraction manipulatives in a fifth grade classroom. The rationale for this research stemmed from the deficits seen among the fifth grade students in my classroom. I have observed learning gaps among the students in my class and hypothesize that implementing the use of manipulatives may be impactful to their learning, specifically with fractions. While the implementation of manipulatives in math is nothing groundbreaking, it is a strategy that needs to be done effectively in order to be successful. The research aims to answer the question: What is the impact of concrete manipulatives while learning fractions in a fifth grade classroom?

Context

This research was completed at A.D Henderson University School in one 5th grade classroom. A.D Henderson University School is a public elementary and middle school. This lab school’s mission is to design and implement a curriculum that challenges students. This is my first-year teaching and my second school year being a part of the staff at A.D Henderson University School. As an educator my goal is to provide all students with the necessary instruction required for them to exceed beyond where they believe they can. By conducting this research in my own classroom, I will be able to learn more about myself as a math teacher as well as best practices when using manipulatives and how it impacts my students. Data to support this research will be collected from the 23 students in the class who perform at various achievement levels and analyzed to determine the impact and effectiveness of manipulatives when learning fractions. The lessons used to teach fractions are included in the Savvas EnVision Florida B.E.S.T grade 5 curriculum which is the district wide mathematics curriculum.

Supportive Literature

Fractions are a challenging concept for many elementary students to grasp and research has shown that hands-on experiences using manipulatives can be an effective way to support students' understanding of fractions. When utilizing manipulatives in the classroom it is important to implement the usage in a way that is going to be effective and beneficial to students. Concrete math manipulatives should be reviewed for appropriateness and chosen to meet the specific goals and objectives of the mathematical program (Boggan et al., 2010). The complexity of the manipulative as well as the difficulty of use should only increase as student understanding increases. According to Seefeldt & Wasik (2006) as students understand more complex mathematical concepts the complexity of the materials, or manipulatives, provided increases as well. It is not enough to just implement manipulatives, but it is important to think about who is using the manipulatives, while also considering how and when they will be used.

One of the most apparent benefits of concrete manipulative is that it allows the learner freedom in how they choose to learn content. Manipulatives are one solution for educators who wish to cater to a variety of learning styles within a single lesson. Larbi and Mavis (2016) suggest that concrete manipulatives enable students with different learning styles to benefit equally. Content is explained for auditory learners, demonstrated for visual learners, and manipulated or modeled by the individual student for kinesthetic learners.  By incorporating manipulatives into mathematics instruction in a thoughtful way, educators can support students' understanding of abstract math concepts.

Research Methods

This action research took place over six weeks and includes data from three fraction units, addition and subtraction of fractions, multiplication of fractions, and division of fractions. Over the course of the study, students were provided with direct instruction, graded classwork assignments, non-graded quick check assignments, and culminating assessments.

To determine the impact of concrete fraction manipulatives on individual students, all 23 students were provided with access to their own set of manipulatives. As the unit progressed, I observed that students were not using the fraction bars as much as they did at the start of the unit, but all 23 students were still allowed to use them on all assignments and as needed to complete their work during class. For the units on multiplication and division of fractions data was collected from the six students who displayed the need for intervention. These six students became the main focus group of the study being that they displayed the need for intervention in all four areas of fraction concepts taught.

Throughout the study I maintained a research journal which included notes regarding classroom observations, lesson implementation, student interviews, and moments of reflection. To collect qualitative data on how students felt while using concrete manipulatives, data was collected using surveys. The first two surveys were given to all 23 students in the class, but the following surveys were given based on intervention groups. Overall, six surveys were provided for the previously identified focus group to complete regarding their experience with concrete fraction manipulatives. The surveys were used to determine confidence level with the subject and how much the student enjoyed working with the manipulatives.

To collect quantitative data, students were given various assessments throughout the study. Data was collected from quick check formative assessments, graded classworks, and culminating assessments on each topic. These assessments were assessed based on accuracy, not the method used for solving the problem. The assessments were given digitally through the Savvas Learning digital platform and Edulastic. Students who were absent were given the assessments when they returned to school.

Google Form responses were exported to Google Sheets and were manually coded, resulting in 10 codes. The total sample size from the Google Forms is 23 students. These codes were analyzed to identify trends among the responses and were taken into consideration when placing students in intervention groups.

Assessment data from the Savvas Learning digital platform was entered into Google Sheets for each student, resulting in a total sample size of 23 students. Class averages for each assessment were totaled, resulting in both individual and group percentages. The identified focus group was analyzed and group averages were collected from the scores of six students. This group was analyzed separately as there are students in the class who perform above grade level, sixth and seventh grade, and have previously learned fraction skills. The scores from these students would skew data as individualized instruction was provided differently based on student performance level. Assessment data from Edulastic did not need to be transferred as it provided me with a comprehensive overview of all student data and class averages.

Results

Improved Confidence in Math Thinking

Analysis of student questionnaires found that students reported an improvement in their self-confidence with math thinking. When first exposed to the addition and subtraction of fractions one student reflected “i am horrible at this, and i need help with fractions”, but by the end of the fraction units during a one on one conference the student reflected “i feel much better at doing fractions because i was able to touch and see them. I feel i can do better solveig [solving] it on paper thank you for helping me”. When working with Play-Doh to solve fraction problems involving multiplication and division one student reflected “it helps me see the overlapping number better and helps me count the denominator better”. Following this interaction I continued to observe the student and noted that they appeared excited to work in a small group and were eager to take part in class discussions about math. During assessments I noticed that students in the focus group were more confident in their work and after submitting their assessments they celebrated their success.

Metacognition of the Benefits of Manipulatives

The results indicated that students became aware of the benefits that manipulatives had on their learning over the course of six weeks. Sixteen students noted that they had the desire to use fraction manipulatives after their first experience with them, including one student who stated “yes they were great and help me a lot because I can see it touch it play around with it”. After students had interacted with a variety of manipulatives across three different fraction units, nineteen students responded that the manipulatives prepared them for more challenging questions. A student who had initially responded “it [the manipulative] was fine” changed their response to “yes because I can see it and it feels like I am way more engaged”. The overall change in student responses shows a 13% increase in students who felt that the manipulatives were beneficial to their learning. Six students responded that the fraction manipulatives were not helpful to their learning because they preferred to use their own strategies or it was confusing. Students who responded that the fraction bars were not beneficial supported their reasoning by stating they had other strategies that worked for them or that they had experience with fractions in previous grades. It should also be noted that all students who responded no are in an advanced intervention group that focuses on sixth grade mathematics skills. One student in particular noted that “in life situations, we will have to use mental math most of the time” even though mental math was not required of them throughout this unit.

Increased Performance

Analysis of pre and post test data across the three fraction units found that students had an increase in performance throughout each unit. This change was evident in analysis of the results from the focus group. The average score increased 27% when assessed on addition and subtraction of fractions, 44% when assessed on multiplication of fractions, and 1% when assessed on division of fractions. After discussing the results of these assessments with the focus group one student reflected that “divison of fractions was easy because it was basically the same as multiplying”. During a one-on-one conference another student reflected “i was prepared for division after doing multiplication so I don't think my score changed much”.

Figure I - Analysis of Pre and Post Assessment Focus Group Scores

Implications

The study’s findings suggest that using concrete manipulatives, specifically with fractions, can have a positive impact on students' confidence in their thinking and math performance when assessed on knowledge of concepts. As a result of these findings, math teachers should consider incorporating manipulatives into their lessons to help students develop their mathematical skills. The research demonstrated that not all students required manipulatives and therefore educators should use fraction manipulatives to support their struggling students. If educators are unable to use best practices while implementing manipulatives class-wide, they may want to consider using manipulatives as a way to provide additional support for students who are struggling. Throughout this research students also showed an understanding of how manipulatives were beneficial to their learning. Because of this finding, educators may want to encourage metacognition strategies in their classroom to further encourage students to develop an understanding of how their thinking of mathematical concepts works.

References