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.

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.

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.

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.

The Importance of Teaching Students How to Read to Comprehend Mathematical Language

In this action research study of my classroom of 8th and 9th grade Algebra I students, I investigated if there are any benefits for the students in my class to learn how to read, translate, use, and understand the mathematical language found daily in their math lessons. I discovered that daily use and practice of the mathematical language in both written and verbal form, by not only me but by my students as well, improved their understanding of the textbook instructions, increased their vocabulary and also increased their understanding of their math lessons. I also found that my students remembered the mathematical material better with constant use of mathematical language and terms. As a result of this research, I plan to continue stressing the use of mathematical language and vocabulary in my classroom and will try to develop new ways to help students to read, understand, and remember mathematical language they find daily in their textbooks.

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.

Mathematical Communication through Written and Oral Expression

In this action research study of my classroom of sixth grade mathematics, I investigated the use of communication of mathematics through both written and oral expression. Giving my students the opportunity to communicate mathematics both in writing and orally helped to deepen the students’ understanding of mathematics. The students’ levels of comprehension were increased when they were presented with a variety of instructional methods. Through discussion and reflection the students were able to find methods that worked best for them and their learning ability. Students’ understanding increased from probing questions that made the students reflect and re-evaluate their solutions. This learning took place when students were made aware of different solutions or ways of doing things from the class discussions that were held. I discovered that when students are challenged to express their thinking both in writing and orally, the students found that they could communicate their thinking in a new way. Some of my students were only comfortable expressing their thoughts in one of the two ways but by the time the project was completed, they all expressed that they enjoyed both ways, and maybe changed the original way they preferred doing mathematics. As a result of this research, I will continue to require students to communicate their thinking and reasoning both in writing and orally.

Rubric Assessment of Mathematical Processes in Homework

In this action research study of my classroom of 11th grade geometry, I investigated the use of rubrics to help me assess my students during homework presentations. I wanted to know more about the processes students went through as they did their homework problems, so homework presentations were implemented with the rubrics being the main form of assessment. I discovered that students are willing to speak about mathematics and can gain more understanding of mathematical processes as a result of homework presentations. The scores of the class improved after they talked about the homework assignments with each other. As a result of this research, I plan to keep on using homework presentations in my classroom to talk about homework, but discontinue the use of rubrics in assessment of students in mathematics. I also found students going to the board to solve problems in small groups are another helpful way to use presentations prior to assessment to help me understand where the students are with a new concept prior to assigning homework or giving an assessment.

Written Solutions of Mathematical Word Problems

In this action research study of my classroom of ten ninth grade algebra students, I investigated how my students expressed written solutions of mathematical word problems. I discovered that my students writing and performance improved as they experienced different strategies to attack problem solving. These experiences helped improve the confidence of my students in their problem solving skills and in their mathematical writing. I also discovered that my teaching style changed, as my students took on more responsibility for their learning. As a result of this research, I plan to implement problem solving activities in all my classrooms next year. I also plan to have my students develop their written communication skills by presenting their solutions to their problem solving activities in writing.

Understanding the Mathematical Language

In this action research study of my calculus classroom consisting of only 12th grade students, I investigated activities that would affect a student’s understanding of mathematical language. The goal in examining these activities in a systematic way was to see if a student’s deeper understanding of math terms and symbols resulted in a better understanding of the mathematical concepts being taught. I discovered that some students will rise to the challenge of understanding mathematics more deeply, and some will not. In the process of expecting more from students, the frustration level of both the students and the teacher increased. As a result of this research, I plan to see what other activities will enhance the understanding of mathematical language.

Exploring the Influence of Vocabulary Instruction on Students’ Understanding of Mathematical Concepts

In this action research study of my classroom of 8th grade mathematics, I investigated the influence of vocabulary instruction on students’ understanding of the mathematics concepts. I discovered that knowing the meaning of the vocabulary did play a major role in the students’ understanding of the daily lessons and the ability to take tests. Understanding the vocabulary and the concepts allowed the students to be successful on their daily assignments, chapter tests, and standardized achievement tests. I also discovered that using different vocabulary teaching strategies enhanced equity in my classroom among diverse learners. The knowledge of the math vocabulary increased my students’ confidence levels, which in turn increased their daily and test scores. As a result of this research, I plan to find ways to incorporate the vocabulary teaching strategies I have used into current math curriculum. I will start this process at the beginning of the next school year, and will continue looking for new strategies that will promote math vocabulary retention.

Reasonable or Not? A Study of the Use of Teacher Questioning to Promote Reasonable Mathematical Answers from Sixth Grade Students

In this action research study of my sixth grade mathematics class, I investigated the influence a change in my questioning tactics would have on students’ ability to determine answer reasonability to mathematics problems. During the course of my research, students were asked to explain their problem solving and solutions. Students, amongst themselves, discussed solutions given by their peers and the reasonability of those solutions. They also completed daily questionnaires that inquired about my questioning practices, and 10 students were randomly chosen to be interviewed regarding their problem solving strategies. I discovered that by placing more emphasis on the process rather than the product, students became used to questioning problem solving strategies and explaining their reasoning. I plan to maintain this practice in the future while incorporating more visual and textual explanations to support verbal explanations.

Daily Problem-Solving Warm-Ups: Harboring Mathematical Thinking In The Middle School Classroom

In this action research study of my classroom of 8th grade mathematics, I investigated the use of daily warm-ups written in problem-solving format. Data was collected to determine if use of such warm-ups would have an effect on students’ abilities to problem solve, their overall attitudes regarding problem solving and whether such an activity could also enhance their readiness each day to learn new mathematics concepts. It was also my hope that this practice would have some positive impact on maximizing the amount of time I have with my students for math instruction. I discovered that daily exposure to problem-solving practices did impact the students’ overall abilities and achievement (though sometimes not positively) and similarly the students’ attitudes showed slight changes as well. It certainly seemed to improve their readiness for the day’s lesson as class started in a more timely manner and students were more actively involved in learning mathematics (or perhaps working on mathematics) than other classes not involved in the research. As a result of this study, I plan to continue using daily warm-ups and problem-solving (perhaps on a less formal or regimented level) and continue gathering data to further determine if this methodology can be useful in improving students’ overall mathematical skills, abilities and achievement.