THE USE OF HANDS-ON LEARNING TECHNIQUES TO PROMOTE STUDENT ACHIEVEMENT IN SECONDARY MATHEMATICS CLASSROOMS
Except where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my advisor. This thesis does not include proprietary or classified information.
Samantha A. Bullard
Certificate of Approval
_____________________________ ______________________________
Donald R. Livingston, Ed.D. Sharon M. Livingston, Ph.D.
Thesis Co-Chair Thesis Co-Chair
Education Department Education Department
THE USE OF HANDS-ON LEARNING TECHNIQUES TO PROMOTE STUDENT ACHIEVEMENT IN SECONDARY MATHEMATICS CLASSROOMS
A thesis submitted
by
Samantha A. Bullard
to
LaGrange College
in partial fulfillment of
the requirement for the
degree of
MASTER OF EDUCATION
In
Curriculum and Instruction
LaGrange, Georgia
May 10, 2011
Mathematical Hands-on Learning Techniques vi
Abstract
This study aimed to determine whether the use of hands-on learning increased achievement in secondary math classrooms. This study was completed using an action research design in a suburban Georgia high school. A treatment and control group comprised of Math 2 students was studied to determine differences in student attitudes and test scores. Several different hands-on learning techniques were researched and implemented in the treatment group. Pre and post test scores were analyzed quantitatively while the lesson plan, student and teacher surveys, focus group and reflective journal were coded for themes. The post-test scores from the treatment and control groups failed to show significant gains in the treatment group over the control group. However, student attitudes were more positive and several students expressed more motivation in the treatment group.
Table of Contents
Abstract …………………………………………………………..……………………….iii
Table of Contents …………………………………………………………………………iv
List of Tables ………….. …………………………………………………………………v
Chapter 1: Introduction ……………………………………………………………………1
Statement of the Problem ………………………………………………………….1
Significance of the Problem ……………………………………………………….1
Theoretical and Conceptual Framework …………………………………………..3
Focus Questions ……………………………………………………………...……5
Overview of Methodology ………………………………………………………...5
Human as Researcher ……………………………………………………………...6
Chapter 2: Review of the Literature ………………………………………………………7
Types of Hands-on Learning……………………………………………………...7
Computer Manipulatives………………………………………………………….8
Virtual Manipulatives……………………………………………………………..9
Direct Instruction………………………………………………………………...11
Student Attitudes…………………………………………………………………13
Negative Impact of Manipulatives……………………………………………….14
Summary...………………………………………………………………...……..15
Chapter 3: Methodology …………………………………………………………………16
Research Design …………………………………………………………………16
Setting ……………………………………………………………………………16
Sample and Participants……. ……………………………………………………17
Procedures and Data Collection Methods …………………………….………….18
Validity, Reliability, Dependability and Bias …………...……………………….20
Analysis of Data ………………………………………………………………….22
Chapter 4: Results ……………………………………………………………………..…26
Chapter 5: Analysis and Discussion of Results ……………………………………….…37
Analysis ………………………………………………………………………..…37
Discussion …………………………………………………………………….….41
Implications ………………………………………………………………………43
Impact on Student Learning ……………………………………………………...44
Recommendations for Future Research ………………………………………….45
References ………………………………………………………………………………..46
Appendices ……………………………………………………………………………….48
List of Tables
Tables
Table 3.1 Data Shell………………………………………………….18
Table 4.1 Treatment and Control Group Prior to Treatment…………27
Table 4.2 Pre-Test/Post-Test Data Control Group…………….……..28
Table 4.3 Pre-Test/Post-Test Data Treatment Group………………...29
Table 4.4 Post-Test Scores-Treatment and Control Group…………..30
Mathematical Hands-on Learning Techniques 55
CHAPTER ONE: INTRODUCTION
Statement of the Problem
Discipline issues are becoming more prevalent in secondary mathematics classrooms. Students can be rude, defiant and disobedient. The number of students displaying chronic behavior issues is growing. Students in the classroom who do not exhibit these behavior problems are displaying frustration in the lack of time they are being served in the classroom while teachers are occupied with disciplinary action.
The Georgia Performance Standards outline a performance task driven curriculum for high school math students that is very difficult to implement while dealing with discipline problems within the classroom. In conjunction with discipline problems, the amount of time that students are off-task is also rising. Students are spending less time engaged in instructional activities and are found to be unmotivated to attempt new assignments. Deshler states, “It soon became clear that many classrooms were out of control: large numbers of students were tardy for class, student behavior during class was inappropriate, and the amount of time spent teaching the targeted interventions was limited” as cited in Sprick, (2006). These discipline issues are often the result of students being off task and not engaged in the current activity or instruction. This thesis will investigate the effects incorporating more interactive teaching techniques has on the behavior, achievement, and attitude of students in secondary mathematics classrooms.
Significance of the Problem
With the implementation of the state of Georgia’s staunch standards in secondary mathematics classes, it is critical for disciplinary distractions to be limited. Teachers are required to teach in-depth concepts to students that require attention and participation. With the implementation of these new standards comes rigorous standardized testing. Struggling students are becoming frustrated, resulting in off task behaviors and negative attitudes. These off task behaviors result in lower test scores and poorer performance in subsequent classes. With the implementation of spiraling curriculum, success in following classes is critical to the understanding of concepts in previous classes.
Many students are also becoming frustrated with constant classroom interruptions. Teachers are exhausting efforts to correct behavior problems rather than devoting needed time to answering questions and providing intervention methods aimed to help struggling students. Deshler also states, “When instruction did take place, it didn’t reach all of the students and was often compromised because of the poor work environment; teachers were frequently interrupting their lesson to regain control of their class.” (as cited in Sprick, 2006, p.xv)
Students who are disengaged, off task and often engage in inappropriate behaviors, distract other students who were previously on-task and require disciplinary action. This results in lower grades for many students. In particular, the grading rubric for math support classes is largely based on the participation of students during class. Their behavior and ability to remain engaged is used to determine their grade for these classes. Students with chronic behavior issues are compromising not only their grade but the grades of those that they are distracting.
Students are frustrated and are losing interest in the study of mathematics. With dropping scores on the End of Course Tests in Georgia, along with the rising drop out rates in our school, many students are failing to meet the math requirements for a high school diploma and are becoming more likely to drop out of high school (Georgia Department of Education, 2010).
Theoretical and Conceptual Frameworks
When examining the underlying theories related to this thesis, one will find that it is heavily influenced by constructivist thought. In 2001, Tomlinson asserts that constructivist classrooms require teachers to be learning facilitators, rather than lecturers (as cited by LaGrange College of Education, 2008). This thesis will investigate the association of hands-on discovery tasks to enhance student learning and decrease student behavior problems. When implementing hands-on activities, teachers play a facilitator role, aiding students in their discovery of new knowledge. This thesis aligns with the first tenet of the LaGrange College of Education’s Conceptual Framework, enthusiastic engagement in learning, since it promotes a constructivist approach to teaching students using hands-on discovery.
This thesis demonstrates a deep knowledge of curriculum as outlined by the first tenet of the Conceptual Framework, as well as the first and second domains of the Georgia Framework for teaching and the second Core Proposition for Experienced Teachers (LaGrange College of Education, 2008). Teachers must use a wide variety of methods and resources in order to implement the activities, techniques and behavior plans. Teachers will also follow all national and state standards in the construction and implementation of these lesson plans. Teachers must demonstrate knowledge of learners as they implement these strategies. Educators must understand how to provide diverse learning instruction to support different learning styles of students and promote active engagement in these lessons.
On a national level, the second proposition of the National Board for Professional Teaching Standards states, “Teachers know the subjects they teach and how to teach those subjects to students” (as cited by the Lagrange College Education Department, 2008, p.12). To implement hands-on activities educators, must have a deep understanding of their content in order to adapt it to different activities and modes of instruction. The idea of hands on instruction also aligns with the second tenet in the Conceptual Framework. The first competency cluster of this tenet outlines the planning skills needed adequately facilitate a constructivist learning environment. The hands-on activities outlined in this thesis require educators to plan appropriate lessons and prepare accordingly. This planning and preparation also reinforces the third domain in the Georgia Framework and the second and third Core Propositions for Experienced Teachers. Teachers will support the personal development of all students by learning their individual needs and learning styles.
A great deal of reflection and subsequent action is required when implementing behavior plans and hands-on activities. The third tenet in the Conceptual Framework describes how teachers must reflect on the effects of actions on students and others and should seek to grow professionally based on these reflections to improve their own practice. On a state level, the fifth and sixth domains of the Georgia Framework for Teaching require educators to implement instructional experiences based on their knowledge of students, and contribute to teaching as a profession. Nationally, the fourth domain of the National Board for Professional Teaching Standards states, “Teachers think systematically about their practice and learn from experience” (as cited by the LaGrange College Education Department, 2008, p.12). Educators must constantly be learning from experiences and adapting to better serve students. Focusing on behavior plans and hands-on activities, teachers must constantly be reflecting in order to continually be implementing plans and activities that work for a specific group of students. Educators must also remember that plans that work with a specific group of students must sometimes be altered to serve the needs of a different group of students.
Focus Questions
The main research question of this study was analyzed by investigating three direct focus areas. The first focus question centers on the pedagogy of the problem. The second aims to answer questions directed at student outcomes and the third focus question aims to reflect holistically on the implementation of the study.
1.) What is the process of implementing hands-on learning techniques?
2.) How do math grades differ in classrooms utilizing hands-on learning techniques versus traditional, direct instruction?
3.) What are the attitudes of teachers and students about hands-on learning techniques?
Overview of Methodology
This study was modeled using a classroom action research design with both quantitative and qualitative components. The study was conducted using two Math II classes in a suburban area high school. Two samples of students were chosen based on pre-test scores, one sample from a treatment class that will employ hands-on learning techniques and another sample from a control class that will continue to utilize direct instruction. An instructional coach also critiqued the unit lesson plan of the treatment group, and several teachers took surveys regarding their opinions on the implementation of hand-on learning techniques. In addition to the qualitative data gathered with the lesson plan rubric, interviews and a reflective journal kept by the researcher, quantitative data was gathered in the form of pre and post test scores of both the treatment and control group. Issues of validity, reliability and bias were considered and addressed to ensure that the study was valid, reliable, and free of bias. All data gathered in this study was organized and analyzed by focus question as well as holistically.
Human as Researcher
With less than three full years of experience, I am fairly new to the classroom. However, I have studied both mathematics and education extensively. I teach at a Title One low income high school with more than 2,400 students. I have also interacted with students outside of the classroom by coaching Junior Varsity Volleyball. I have previously taught sections of Algebra 2, Mathematics I, Mathematics II, as well Mathematics II Support classes. I believe that by utilizing more hands-on activities, disciplinary issues in classrooms will decrease, thus strengthening students’ scores and understanding in mathematics. I believe that these plans will increase student engagement and will encourage them to behave in order to maximize time in the classroom.
CHAPTER TWO: REVIEW OF THE LITERATURE
Hands-on learning techniques are slowly becoming more and more prevalent in secondary mathematics classrooms. Teachers are finding the students need to become more engaged in the material to stay focused and gain an interest in the field. The goal of mathematics teachers is to help all students understand math in a dynamic and coherent way. While most people view mathematics as a collection of unrelated ideas, it is the responsibility of the teacher to show these as interconnected concepts. It is very important for students to create and understand their own visual representations of mathematical concepts. These goals are achieved through the use of five critical best practice strategies. Small group discussion, the use of manipulatives, physical representations, visual representations, and symbolic representations are used to promote student achievement (Zemelman, Daniels, & Hyde, 2005).
Types of Hands-on Learning
There are several different types of hands-on techniques that are being utilized in math classrooms today. The most prevalent, especially in geometry classrooms, is the use of physical manipulatives. James Heddens (1997) defines manipulatives as concrete models that involve mathematics concepts, appealing to several senses that can be touched, and moved around by the students. He also goes on to state that the manipulative can be any material or object from the real world that children can move around to show a mathematics concept (Heddens, 1997). These physical objects can range from 3-dimensional shapes such as spheres and cylinders to tiles used to demonstrate fractional pieces in terms of a whole unit.
Cooperative learning is also a technique that can be utilized in many of today’s classrooms. Cooperative learning involves students working in groups to collaborate to solve a problem. Groups are given a task in which the input of all members is essential to completing the task (Schul, 2011).
Manipulatives and cooperative learning are also often intertwined in lesson plans together. With the use of graphing calculator software students can now use programs geared toward the discovery of new concepts in math. Students can cooperatively use these programs to answer specific questions in the hopes that they will discover overarching mathematical concepts. While the technology has changed drastically in the past decade, Ernest (1994) found that after a review of the manipulatives, calculators were identified as one of the most useful items. In 1994, Ernest observed teachers using TI-81 graphing calculators with fewer capabilities of the TI-84 and TI-89 graphing calculators we have teachers have today.