Precise Mathematical Language: Exploring the Relationship Between Student Vocabulary Understanding and Student Achievement

In this action research study of my classroom of fifth grade mathematics, I investigate the relationship between student understanding of precise mathematics vocabulary and student achievement in mathematics. Specifically, I focused on students’ understanding of written mathematics problems and on their ability to use precise mathematical language in their written solutions of critical thinking problems. I discovered that students are resistant to change; they prefer to do what comes naturally to them. Since they have not been previously taught to use precise mathematical language in their communication about math, they have great difficulty in adapting to this new requirement. However, with teaching modeling and ample opportunities to use the language of mathematics, students’ understanding and use of specific mathematical vocabulary is increased.

Student Problem Solving

The purpose of this study is to determine if students solve math problems using addition, subtraction, multiplication, and division consistently and whether students transfer these skills to other mathematical situations and solutions. In this action research study, a classroom of 6th grade mathematics students was used to investigate how students solve word problems and how they determine which mathematical approach to use to solve a problem. It was discovered that many of the students read and re-read a question before they try to find an answer. Most students will check their answer to determine if it is correct and makes sense. Most students agree that mastering basic math facts is very important for problem solving and prefer mathematics that does not focus on problem solving. As a result of this research, it will be emphasized to the building principal and staff the need for a unified and focused curriculum with a scope and sequence for delivery that is consistently followed. The importance of managing basic math skills and making sure each student is challenged to be a mathematical thinker will be stressed.

Increasing Student Confidence and Knowledge through Student Presentations

In this action research study of a 9th grade Algebra classroom, I investigated the influence of having students present homework solutions and what effect it had on student learning and student confidence. Students were asked to present solutions to homework problems each day and were rated on how well they did. The students were also surveyed about their confidence and feelings about mathematics. Students were also observed for information about who they asked questions of when presented with a math problem they did not understand. In this classroom, two teachers were involved in instruction and this study examines what affect this had on student learning and who was asked for help. As a result of presentations, students’ confidence increased and students reacted positively to both the presentations and their own mathematical learning. The students felt the presentations were a benefit to the class and watching their peers solve mathematical equations helped them to better understand the mathematics.

Writing Relevant Word Problems: Seeking to Increase Student Mathematical Achievement

In this action research study of eighth grade mathematics, I investigated my students’ use of writing and solving word problems. I collected data to determine if writing and solving word problems would have a positive effect on students’ abilities to understand and solve word problems. These word problems are grade-level appropriate and are very similar to the problems on the eighth grade online assessment of state standards. Pre- and post-test data, weekly word problems that focus on specific mathematics topics, beginning and end surveys about word problem perceptions, and a teacher journal reveal that student engagement in this weekly practice of writing and solving word problems did influence the students’ overall abilities for, achievement in and attitudes toward solving word problems. Except for some students’ perceptions, the influence was largely positive. This suggests that word problems can be a constructive feature in eighth mathematics instruction.

The Effects Improving Student Discourse Has on Learning Mathematics

In this action research study of my 8th grade mathematics classroom, I investigated how improving student discourse affects learning mathematics. I conducted this study because I wanted to give students more opportunities to develop and share their ideas with their peers as well as with me. My idea was to create a learning environment that encouraged students to voice their opinions. In order to do so, I needed to reassure and model with my students that they were in a classroom where it was safe to take risks, and they should feel comfortable sharing their ideas. By facilitating activities for students to complete in groups, asking students to prepare work to share with the class, and offering more opportunities for students to work with each other on discovering and exploring math skills being presented, I set the tone for abundant student discourse to take place in the mathematics classroom. I discovered that students became more comfortable with math skills the more opportunities they had to discuss the ideas in various settings. I also found that as the study went on, students discovered the importance of being able to share their mathematical ideas and valued the ability to verbalize their thoughts with others. As a result of this study, I plan to continue offering many opportunities for students to work in groups as well as to share their ideas with the class.

Improving Student Engagement and Verbal Behavior Through Cooperative Learning

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and understanding when compared to individual practice. At the end of the action research, students were questioning each other, and the instructor was answering questions only when the entire group had a question. The third area of data collection focused on what effect heterogeneous cooperative groups had on students’ listening skills when compared to individual practice. In the research I implemented individual quizzes and individual presentations. Both of these had a positive effect on listing in the groups. As a result of this research, I plan to continue implementing the round robin style of in- class practice with heterogeneous grouping and randomly selected individual presentations. For individual accountability I will continue the practice of individual quizzes one to two times a week.

Improving Student Engagement and Verbal Behavior Through Cooperative Learning

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and understanding when compared to individual practice. At the end of the action research, students were questioning each other, and the instructor was answering questions only when the entire group had a question. The third area of data collection focused on what effect heterogeneous cooperative groups had on students’ listening skills when compared to individual practice. In the research I implemented individual quizzes and individual presentations. Both of these had a positive effect on listing in the groups. As a result of this research, I plan to continue implementing the round robin style of in- class practice with heterogeneous grouping and randomly selected individual presentations. For individual accountability I will continue the practice of individual quizzes one to two times a week.

How Student Self-Assessment Influences Mastery Of Objectives

In this action research study of my classroom of 7th grade students, enrolled in Pre- Algebra (an 8th grade course), I investigated: rate of homework completion when not taken as part of the academic grade, cognizant self-assessment and its affect on mastery of objectives, and use of self-assessment to guide instruction and re-teaching of classroom objectives. I learned that without sufficient accountability homework completion rates drop with time. Similarly, students can be overconfident in their abilities but unmoved when their summative reports do not match their initial perceived formative benchmarks. Finally, due in part to our society’s reactive nature; students find it more practical to play catch-up rather than staying caught up. As a result of this research, I plan to create, with the help of the students, an accountability statute to help students stay caught up with their understanding of the objectives, as well as allow additional time and energy spent by both student and teacher to react in a timely manner to complete student knowledge within a day or two rather than a week or two later.

Student Understanding and Achievement When Focusing on Peer-led Reviews

Math in the Middle Institute Partnership, Action Research Project Report, In partial fulfillment of the MAT Degree. Department of Mathematics. University of Nebraska-Lincoln. July 2009.

Student Transition to College

In this action research study of recent graduates from my district, I investigated their level of readiness for college-level mathematics courses. I discovered that the students have a wide variety of experiences in college. There are many factors that determine success in college mathematics courses. These factors include size of college, private or public, university or community college. Other factors include students’ choice of major, maturity level, and work ethic. As a result of this research, I plan to raise the individual expectations in my classroom. It is our duty as high school educators to prepare the students for a wide variety of experiences in college. We cannot control where the students attend college or what they study. High schools need to prepare the students for all possibilities and ensure that they have a solid knowledge of the baseline mathematics skills.

Student Writing Performance: Identifying the Effects when Combining Planning and Revising Instructional Strategies

The purpose of the current study is to identify the impact of teaching students to revise their stories on writing production (Total Words Written; TWW), writing accuracy (Percent Correct Writing Sequences; %CWS), number of critical story elements included in stories, and quality of writing. Three third-grade and one fourth-grade student who were experiencing difficulties in the area of writing were involved in the study. The students were first taught to plan their stories using the evidence-based program, Self-Regulated Strategy Development (SRSD), which has frequently been implemented to teach students to plan their stories. Students were then taught to revise their stories using SRSD procedures modified for instruction in revision strategies. Student progress was evaluated through a multiple-probe design across tasks and a multiple-probe design across participants, which allowed for experimental control over time and across story probes. In addition to the previously mentioned variables, student’s acceptability of the intervention and their attitudes toward writing were also assessed. Results indicated that instruction in revising increased student writing accuracy beyond the effects of instruction in planning. Additionally, although instruction in planning was shown to increase writing production, number of critical story elements, and quality of writing, instruction in revising produced additional improvement in these variables as well. Finally, results indicated that students liked the intervention and their attitudes toward writing generally increased. Implications for practice and future research directions will be discussed. Advisor: Merilee McCurdy

Awareness of Daylighting on Student Learning in an Educational Facility

This study examines how awareness of the interior architecture of a building, specifically daylighing, affects students academic performance. Extensive research has proven that the use of daylighting in a classroom can significantly enhance students’ academic success. The problem statement and purpose of this study is to determine if student awareness of daylighting in their learning environment affects academic performance compared to students with no knowledge of daylighting. Research and surveys in existing and newly constructed high schools were conducted to verify the results of this study. These design ideas and concepts could influence the architecture and design industry to advocate construction and building requirements that incorporate more sustainable design teaching techniques.

Student and Faculty Perceptions of Technology’s Usefulness in Community College General Education Courses

Educational institutions of all levels invest large amounts of time and resources into instructional technology, with the goal of enhancing the educational effectiveness of the learning environment. The decisions made by instructors and institutions regarding the implementation of technology are guided by perceptions of usefulness held by those who are in control. The primary objective of this mixed methods study was to examine the student and faculty perceptions of technology being used in general education courses at a community college. This study builds upon and challenges the assertions of writers such as Prensky (2001a, 2001b) and Tapscott (1998) who claim that a vast difference in technology perception exists between generational groups, resulting in a diminished usefulness of technology in instruction. In this study, data were gathered through student surveys and interviews, and through faculty surveys and interviews. Analysis of the data used Kendall’s Tau test for correlation between various student and faculty variables in various groupings, and also typological analysis of the transcribed interview data. The analysis of the quantitative data revealed no relationship between age and perception of technology’s usefulness. A positive relationship was found to exist between the perception of the frequency of technology use and the perception of technology’s effectiveness, suggesting that both faculty members and students believed that the more technology is used, the more useful it is in instruction. The analysis of the qualitative data revealed that both faculty and students perceive technology to be useful, and that the most significant barriers to technology’s usefulness include faulty hardware and software systems,lack of user support, and lack of training for faculty. The results of the study suggest that the differences in perception of technology between generations that are proposed by Prensky may not exist when comparing adults from the younger generation with adults from the older generation. Further, the study suggests that institutions continue to invest in instructional technology, with a focus on high levels of support and training for faculty, and more universal availability of specific technologies, including web access, in class video, and presentation software. Adviser: Ronald Joekel

Student Leader LMX Relationships as Moderated by Constructive-Developmental Theory

This study examined how the quality of Leader-Member Exchange (LMX) relationships was moderated by the Constructive-Developmental stage or Order of Consciousness of both leader and follower. Using student organization presidents and officers on a small, private, liberal arts college campus in the Midwest, the researcher used a sample of 37 students to study the impact developmental stage had on the leadership relationship. Using the Leader Member Exchange-Multi-Dimensional Measure (LMX-MDM), four dimensions of LMX were examined. The four dimensions were Affect, Contribution, Loyalty and Professional Respect. There was no significant relationship between Order of Consciousness and quality of LMX relationship. While there was no significant difference in LMX relationship based on gender of participants, there was a significant difference between how male presidents and officers perceived their relationship in the Loyalty dimension. Directions for further research and implications for practice were discussed.