Strategies and Precise Vocabulary Knowledge: Exploring the Relationships Among Mathematics Vocabulary, Problem Solving, and Confidence

In this action research study I focused on my eighth grade pre-algebra students’ abilities to attack problems with enthusiasm and self confidence whether they completely understand the concepts or not. I wanted to teach them specific strategies and introduce and use precise vocabulary as a part of the problem solving process in hopes that I would see students’ confidence improve as they worked with mathematics. I used non-routine problems and concept-related open-ended problems to teach and model problem solving strategies. I introduced and practiced communication with specific and precise vocabulary with the goal of increasing student confidence and lowering student anxiety when they were faced with mathematics problem solving. I discovered that although students were working more willingly on problem solving and more inclined to attempt word problems using the strategies introduced in class, they were still reluctant to use specific vocabulary as they communicated to solve problems. As a result of this research, my style of teaching problem solving will evolve so that I focus more specifically on strategies and use precise vocabulary. I will spend more time introducing strategies and necessary vocabulary at the beginning of the year and continue to focus on strategies and process in order to lower my students’ anxiety and thus increase their self confidence when it comes to doing mathematics, especially problem solving.

Improving Mathematics Problem Solving Through Written Explanations

In this action research study of two classrooms of 7th grade mathematics, I investigated how requiring written explanations of problem solving would affect students ability to problem solve, their ability to write good explanations, and how it would affect their attitudes toward mathematics and problem solving. I studied a regular 7th grade mathematics class and a lower ability 7th grade class to see if there would be any difference in what was gained by each group or any group. I discovered that there were no large gains made in the short time period of my action research. Some gains were made in ability to problem solve by my lower ability students over the 7 weeks that they did a weekly problem solving assignment. Some individual students felt that the writing had helped them in their problem solving because they needed to think and write each step. As a result of this research I plan to continue implementing writing in my classroom over the entire school year requiring a little more from students each time we problem solve and write.

Building Math Esteem in Fifth Grade Students

In this action research study of my classroom of 5th grade mathematics, I investigate the levels of math esteem in each student and as a classroom. The definition of esteem on which I am basing my research is the judgment or estimation of the self-assurance of a student in math. I discovered that several of the students entered my classroom with a middle to low level of esteem in math, and about a third of the class already exhibited a positive, high esteem in math. After implementation of the research, and interpreting the data, I believe almost all the students achieved higher math esteem by the end of the school year. The surveys and interviews I performed with the parents and students lead me to believe the four components of my research had an affect on this outcome. As a result of this research, I plan to continue to facilitate a high level of math esteem in each one of my students.

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.

An Investigation into Careless Errors Made by 7th Grade Mathematics Students

In this action research study, I investigated the careless errors made by my seventh-grade mathematics students on their homework and tests. Beyond analyzing the types of careless errors and the frequency at which they were made, I also analyzed my students’ attitudes toward reviewing their work before they turn it in and self-reflection about the quality of work that they were producing. I found that many students did not know how to review their test before turning it in; no one had ever taught them how to do so. However, when students were given tools to help them with this task, they were able to make strides towards reducing the number of careless errors that they made and began to turn in high quality work that demonstrated their understanding of the content that had been taught. As a result of this research, I plan to teach my students how to go back over their homework and tests before turning them in. I also intend to continue to use the tools that I have produced to encourage students to self-reflect on the work that they have done. Assessment is such an important piece of educating my students and the careless errors made on these assessments needed to be addressed.

Math Anxiety: What can teachers do to help their students over come the feeling?

In this action research study of my classroom of 7th and 8th grade mathematics, I investigated how math anxiety relates to the student work and behavior in the classroom, and how this can affect the student’s overall relationship to mathematics. I discovered that the harder the work, the more math anxiety was displayed. The harder I pushed students to think more deeply, the fewer responses to my questions I received. I noticed difference in the students’ body language and overall behavior. As a result of this research, I plan to help my students try to overcome the feeling of math anxiety and try to teach them different methods to use when they are feeling anxious. The methods that I plan to use hopefully will help the students when they are feeling anxiety and help the students to understand the math being taught and how to apply the math they learn to everyday life.

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.

Here is the Plan: So What is the Question?

In this action research study of my classroom of 5th grade mathematics students, I investigated their understanding of the mathematical operations by having them write problems to match given equations. I discovered that writing a story to match an equation does provide insight into a student’s understanding of mathematical concepts, however, reading comprehension is a factor in the understanding. Readers who struggle with comprehension do struggle with understanding and writing math story problems. The discussion that follows the writing of a math story problem and the solving of the written problems helps to strengthen the students’ mathematical abilities as well as their communication skills and confidence levels. Through my study, students learned that it was alright to make mistakes because the learning from those mistakes is what is important. As a result of this research, I plan to continue to have students write stories to match given equations as a source of information about student understanding. I will continue to give opportunities to revisit those written problems as a tool to increase students’ comprehension and communication skills, as well as their confidence.

Cooperative Learning Groups in the Eighth Grade Math Classroom

In this action research study of my classroom of 8th grade mathematics students, I investigated whether cooperative learning would lead to a better understanding of the mathematical concepts and thus more success for the students. I used my three eighth grade classes with two using cooperative groups and the third not. I discovered that the students who wanted to work in cooperative groups were more successful than they had been. I also discovered that the grouping itself has a great effect on how the group works together. The wrong grouping of students can lead to disaster and many headaches for the teacher. Overall the two classes that used cooperative groups did better grade wise than the one class that was taught using the traditional way of not using cooperative groups. As a result of this research, I plan to continue using cooperative groups but will be more aware of the students who are grouped together.

Using Non-Traditional Activities to Enhance Mathematical Connections

In this action research study of my classroom of seventh grade mathematics, I investigated the use of non-traditional activities to enhance mathematical connections. The types of nontraditional activities used were hands-on activities, written explanations, and oral communication that required students to apply a new mathematical concept to either prior knowledge or a realworld application. I discovered that the use of non-traditional activities helped me reach a variety of learners in my classroom. These activities also increased my students’ abilities to apply their mathematical knowledge to different applications. Having students explain their reasoning during non-traditional activities improved their communications skills, both orally and in writing. As a result of this research, I plan to incorporate more non-traditional activities into my curriculum. In doing so, I hope to continue to increase my students’ abilities to solve problems. I also plan to incorporate the use of written explanations of my students’ mathematical reasoning in order to continue to improve their communication of mathematics.

Mathematical Communication, Conceptual Understanding, and Students' Attitudes Toward Mathematics

This action research study of my 8th grade classroom investigated the use of mathematical communication, through oral homework presentations and written journals entries, and its impact on conceptual understanding of mathematics. This change in expectation and its impact on students’ attitudes towards mathematics was also investigated. Challenging my students to communicate mathematics both orally and in writing deepened the students’ understanding of the mathematics. Levels of understanding deepened when a variety of instructional methods were presented and discussed where students could comprehend the ideas that best suited their learning styles. Increased understanding occurred through probing questions causing students to reflect on their learning and reevaluate their reasoning. This transpired when students were expected to write more than one draft to math journals. By making students aware of their understanding through communicating orally and in writing, students realized that true understanding did not come from mere homework completion, but from evaluating and assessing their own and other’s ideas and reasoning. I discovered that when students were challenged to communicate their reasoning both orally and in writing, students enjoyed math more and thought math was more fun. As a result of this research, I will continue to require students to communicate their thinking and reasoning both orally and in writing.

Using Descriptive Feedback In a Sixth Grade Mathematics Classroom

In this action research of my 6th grade math class, I investigated whether or not my students would improve their ability to reflect on their learning process when they received descriptive feedback from a peer. I discovered the process of giving and receiving feedback was challenging for the students to initially learn, but eventually using the feedback was highly beneficial. Descriptive feedback allowed the students to learn and understand their mistakes immediately, which in turn improved their learning. In my action research, I also began to discover more ways to implement descriptive feedback in my instruction so it could be more effectively for the students and efficiently so there would be less time taken out from instruction. As a result of this research, I plan to continue having students provide and receive descriptive feedback and to find more evidence of how descriptive feedback could influence student achievement.

Departmentalization in the 5th Grade Classroom: Re-thinking the Elementary School Model

In this action research study of my 5th grade classroom, I investigated the benefits of a modified block schedule and departmentalization. The research consisted of dividing the 5th grade curriculum into three blocks. Each block consisted of two primary subject areas: Mathematics was paired with Social Studies, Reading was paired with Health, and Writing was paired with Science. These groupings were designed to accommodate district time-allotment requirements and the strengths of each teacher within the 5th grade team. Thus, one teacher taught all of the Mathematics and Social Studies, another all of the Reading and Health, and another all of the Writing and Science. Students had classes with each teacher, each school day. I discovered that this departmentalization had many benefits to both students and teachers. As a result of this research, we plan to continue with our new schedule and further develop it to more fully exploit the educational and professional advantages we found to be a part of the project.

An Uphill Battle: Incorporating cooperative learning using a largely individualized curriculum

In this action research study of my classroom of 8th grade mathematics, I investigated if cooperative learning could be an effective teaching method with the Saxon curriculum. Saxon curriculum is largely individualized in that most lessons could be completed without much group interaction. I discovered that cooperative learning was very successful with the curriculum as long as it was structured. Ninety-five percent of the students in the study preferred to work in groups, and I observed mathematical communication grow with most of the students. As a result of this research, I plan to continue to incorporate cooperative learning into my mathematics classroom. I will use cooperative learning with all of my mathematics classes, even the ones that do not use the Saxon curriculum. I believe in the power of working together.

Using Cooperative Learning In A Sixth Grade Math Classroom

In this action research study of my classroom of sixth grade mathematics, I investigated the impact of cooperative learning on the engagement, participation, and attitudes of my students. I also investigated the impact of cooperative learning upon my own teaching. I discovered that my students not only preferred to learn in cooperative groups, but that their levels of engagement and participation, their attitudes toward math, and their quality of work all improved greatly. My teaching also changed, and I found that I began to enjoy teaching more. As a result of this research, I plan to continue and expand the amount of cooperative group work that happens in my classroom.