The Importance of Vocabulary Instruction in Everyday Mathematics

In this action research study of my 6th grade math students I try to answer the question of how mathematical vocabulary plays an integral role in the understanding and learning of middle level mathematics. It is my belief that mathematics is a language, and to be fluent in that language one must be able to use and understand vocabulary. With the use of vocabulary quizzes and mathematically-centered vocabulary activities, student scores and understanding of math concepts can be increased. I discovered that many of the students had never been exposed to consistent mathematical terminology in their elementary education, which led many to an unfavorable impression of math. As a result of my research, I plan to incorporate vocabulary as a regular part of my mathematical teaching. As the students understood the language of math, their confidence, attitudes, and scores all began to improve.

Oral Communication and Presentations in Mathematics

In this action research study of my classroom of eighth grade mathematics, I investigated the attitudes of students toward mathematics along with their achievement levels with the use of oral presentations in my Algebra class. During the second semester the class was divided into groups of two for each presentation, changing partners each time. Every other week each group was given a math problem that required more work than a normal homework type problem. On the last day of that week the students gave a short presentation on their problem. I discovered that while there was no significant evidence that student achievement increased, the students did enjoy the different aspect of presentations in a math class. I plan to implement presentations in my classroom more often with the intent to increase student enjoyment.

“Let’s Review.” A Look at the Effects of Re-teaching Basic Mathematic Skills

In this action research study of my classroom of 8th grade mathematics, I investigated the effect of reviewing basic fraction and decimal skills on student achievement and student readiness for freshman Algebra. I also investigated the effect on the quality of student work, with regards to legibility by having students grade each other’s work anonymously. I discovered that students need basic skill review with fractions and decimals, and by the end of the research their scores improved. However, their handwriting had not. At the end of the research, a majority of the students felt the review was important, and they were ready to take math next year in high school. As a result of this research, I plan to implement weekly fraction and decimal review assignments in all middle school grades: 6th, 7th, and 8th. In addition, fraction and decimals must be incorporated into daily assignments, where appropriate, in order to encourage students to retain these skills.

The Role of Manipulatives in the Eighth Grade Mathematics Classroom

In this action research study of my classroom of eighth grade mathematics, I investigated the use of manipulatives and its impact on student attitude and understanding. I discovered that overall, students enjoy using manipulatives, not necessarily for the benefit of learning, but because it actively engages them in each lesson. I also found that students did perform better on exams when students were asked to solve problems using manipulatives in place of formal written representations of situations. In the course of this investigation, I also uncovered that student attitude toward mathematics improved when greater manipulative use was infused into the lessons. Students felt more confident that they understood the material, which translated into a better attitude regarding math class. As a result of this research, I plan to find ways to implement manipulatives in my teaching on a more regular basis. I intend to create lessons with manipulatives that will engage both hands and minds for the learners.

Writing In Math Class? Written Communication in the Mathematics Classroom

In this action research study of my seventh grade mathematics classroom, I investigated what written communication within the mathematics classroom would look like. I increased vocabulary instruction of specific mathematical terms for my students to use in their writing. I also looked at what I would have to do differently in my teaching in order for my students to be successful in their writing. Although my students said that using writing to explain mathematics helped them to better understand the math, my research revealed that student writing did not necessarily translate to improved scores. After direct instruction and practice on math vocabulary, my students did use the vocabulary words more often in their writing; however, my students used the words more like they would in spelling sentences rather than to show what it meant and how it can be applied within their written explanation in math. In my teaching, I discovered I tried many different strategies to help my students be successful. I was very deliberate in my language and usage of vocabulary words and also in my explanations of various math concepts. As a result of this research, I plan to continue having my students use writing to communicate within the mathematics classroom. I will keep using some of the strategies I found successful. I also will be very deliberate in using vocabulary words and stress the use of vocabulary words with my students in the future.

Connections Between Communication and Math Abilities

In this action research study of my Class I School’s 5th and 8th grade mathematics, I investigated students’ connections between communication of math skills and their math abilities. I discovered that students can increase their math abilities with the opportunities to discuss their thinking as well as evaluate thinking and strategies of other students. Electronic communication can be a valuable source for students to communicate further to other students.

Writing in the Mathematics Classroom: Does It Have an Effect on Students’ Mathematical Reasoning?

In this action research study of my classroom of 5th grade mathematics, I investigate how to improve students’ written explanations to and reasoning of math problems. For this, I look at journal writing, dialogue, and collaborative grouping and its effects on students’ conceptual understanding of the mathematics. In particular, I look at its effects on students’ written explanations to various math problems throughout the semester. Throughout the study students worked on math problems in cooperative groups and then shared their solutions with classmates. Along with this I focus on the dialogue that occurred during these interactions and whether and how it moved students to a deeper level of conceptual understanding. Students also wrote responses about their learning in a weekly math journal. The purpose of this journal is two-fold. One is to have students write out their ideas. Second, is for me to provide the students with feedback on their responses. My research reveals that the integration of collaborative grouping, journaling, and active dialogue between students and teacher helps students develop a deeper understanding of mathematics concepts as well as an increase in their confidence as problem solvers. The use of journaling, dialogue, and collaborative grouping reveals themselves as promising learning tasks that can be integrated in a mathematics curriculum that seeks to cultivate students’ thinking and reasoning.

Vocabulary Instruction as a Tool for Helping Students of Diverse Backgrounds and Ability Levels to Understand Mathematical Concepts

This action research project describes a research project designed and implemented specifically with an emphasis on the instruction of mathematical vocabulary. The targeted population was my second period classroom of sixth grade students. This group of seventeen students represented diverse socioeconomic backgrounds and abilities. The school is located in a community of a population of approximately 5,000 people in the Midwest. My research investigation focused on the use of specific methods of vocabulary instruction and students’ use of precise mathematical vocabulary in writing and speaking. I wanted to see what effects these strategies would have on student performance. My research suggested that students who struggle with retention of mathematical knowledge have inadequate language skills. My research also revealed that students who have a sound knowledge of vocabulary and are engaged in the specific use of content language performed more successfully. Final analysis indicated that students believed the use of specific mathematical language helped them to be more successful and they made moderate progress in their performance on assessments.

A Study of Written Communication: Showing Your Steps

In this action research study of my teaching of sixth grade mathematics, I investigated the importance of showing work on daily assignments. I wanted to find out what happens when I ask students to show their work, specifically, whether it would improve students’ grades or not and whether I could help the students to understand the importance of showing their work. I discovered that students need to be shown the proper way to show their work, how to look at a problem and then how to show all of their steps to get to the answer. They need to be encouraged and be held accountable for showing their work when asked. Once they were able to show work, they could start to see the value in showing their work and they tended to show their work more often. Students became more confident in themselves as mathematics students and, in some cases, their grades improved. As a result of this research, I plan to teach and explain to my future classes about how showing their work can benefit them in a variety of ways. They will be able to use the knowledge that they gain in my classroom in their future math classes in middle and high school.

Attitudes, Confidence, and Achievement of High-Ability Fifth Grade Math Students

In this action research study of my fifth grade high-ability mathematics class, I investigated student attitudes of mathematics and their confidence in mathematics. Student achievement was compared to two different confidence scales to identify a relationship between confidence and achievement. Six boys and eleven girls gave their consent to the study. I discovered there seems to be a connection between confidence and achievement and that boys are generally more confident than girls. Most students liked math and were comfortable sharing answers and methods of solving problems with other students. As a result of this study I plan to use my survey and interview questions at the beginning of the school year with my new class in order to assess their attitudes and confidence in math. I can use this information to identify potential struggles and better plan for student instruction.

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.

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.

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.

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.