Homework: Is There More To It Than Answers?

In this action research study of my two high school geometry classrooms, I investigated the use of homework. By changing the focus on homework away from the answers to the process involved in getting the answers, I found that students felt more confident, utilized their class time better, and placed more effort on complex problems. Their questions also became more specific and more effective for finding gaps in their understanding. As a result of this research, I plan to change my strategy in the practice of homework. I will give students the answers on multi-step problems to allow them the opportunity to utilize problem solving and critical thinking skills to gain practice in autonomous learning.

Written Communication in a Sixth-Grade Mathematics Classroom

In this action research study of my sixth grade mathematics classroom, I investigated what happened to students’ mathematical achievement when they had increased practice on written explanations to problems. I wanted to see if writing out solutions to problems helped them overall in daily mathematics. By using specific mathematic vocabulary more frequently and deliberately during my instruction, I wanted to investigate whether students would correctly use specific math vocabulary in their written explanations. I also increased my expectations of the students’ written explanations throughout the research project. I wanted to determine whether students would try to meet or even exceed my expectations. I discovered that students used vocabulary more frequently in their written explanations by providing definitions of vocabulary versus using the vocabulary in context. I found little to no evidence suggesting that my students’ mathematical achievement changed through more practice on written communication; however, I did find as my expectations for the quality of students’ written explanations increased, most of my students improved their written explanations of problems and my teaching became more deliberate and specific. As a result of this research, I plan to continue having students communicate their mathematical ideas through written communication while continuing to focus on specific mathematical vocabulary and its purpose in written communication.

Oral and Written Communication in Classroom Mathematics

In this action research study of my classroom of sixth grade mathematics, I investigated the impact of an increase in student oral and written communication on student level of understanding and student self-confidence. I also investigated the changes in my teaching as I increased opportunities for student oral and written communication of mathematics. While I discovered that student level of understanding was not necessarily increased if written communications were increased, I did find that there seemed to be a rise in student level of self-confidence and understanding throughout the course of the research project due to an increase in oral communication. Additionally, my intentions as a teacher were to become less dominating as communication was increased, but the opposite occurred. As a result of this research, I plan to continue to allow oral discourse to take place in my classroom much like it has in the past.

Cooperative Learning in Relation to Problem Solving in the Mathematics Classroom

In this action research study of my classroom of 5th grade mathematics, I investigated cooperative learning and how it is related to problem solving as well as written and oral communication. I discovered that cooperative learning has a positive impact on students’ abilities in problem solving and their overall impression of mathematics and group work. I also found that my students’ communication skills improved in oral explanations of their work. As a result of this research I plan to continue my implementation of cooperative learning in my classroom as a general method of teaching. I also plan to continue to use cooperative learning in working with my students to increase their achievement in problem solving and communication of mathematics.

Bad Medicine: Homework or Headache? Responsibility and Accountability for Middle Level Mathematics Students

In this action research study of my 5th grade mathematics class, I investigated the issue of homework and its relationship with students and parents. I made some interesting observations and discovered that the majority of students and parents felt that the math homework that was given was fairly easy, yet issues of incomplete assignments and failing homework quizzes were notorious for some individuals. Comments were also made to make homework even easier and have shortened assignments despite the already indicated ease of the work. As a result of this research, I plan to look more closely at the history and development of homework, as well as the psychological implications and “hereditary” issues involving homework, which I believe are passed from one generation of learners to the next. My intent is to continue to study this phenomenon in future school years, trying to develop methods of instilling successful, intrinsic motivational skills to aid students in their homework endeavors. Finally, I will take a close inventory of my own beliefs and understandings toward homework: What is the purpose of having students do work away from the classroom, and how can homework serve as a proactive service for all who are involved?

Writing in a Mathematics Classroom: A Form of Communication and Reflection

In this action research study, I investigated the use of journaling in my seventh grade mathematics classroom. I discovered that journaling can be a very rewarding and beneficial experience for me and for my students. Through journaling, my students became more adept at using correct mathematical terminology in writing and in speaking. The students also believed that they learned the content more deeply and retained it better. Additionally, implementing mathematical journals caused me to emphasize the use of correct terminology and thorough explanations of mathematical thinking in classroom discussions. As a result of this research, I plan to refine my journaling process and continue to use mathematical journals with my future classes.

Meaningful Independent Practice in Mathematics

In this action research of my seventh grade mathematics classroom, I investigated how students’ explanations of math homework would improve their learning in math. I discovered these explanations can be very beneficial in helping students to improve their understanding of current skills although it did not affect all students. As a result of this study, I plan to incorporate these student explanations in my instruction next year but not as a daily expectation.

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.

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.

Generating Interest in Mathematics Using Discussion in the Middle School Classroom

In this action research study of my classroom of 8th grade algebra, I investigated students’ discussion of mathematics and how it relates to interest in the subject. Discussion is a powerful tool in the classroom. By relying too heavily on drill and practice, a teacher may lose any individual student insight into the learning process. However, in order for the discussion to be effective, students must be provided with structure and purpose. It is unrealistic to expect middle school age students to provide their own structure and purpose; a packet was constructed that would allow the students to both show their thoughts and work as a small group toward a common goal. The students showed more interest in the subject in question as they related to the algebra topics being studied. The students appreciated the packets as a way to facilitate discussion rather than as a vehicle for practicing concepts. Students still had a need for practice problems as part of their homework. As a result of this research, it is clear that discussion packets are very useful as a part of daily instruction. While there are modifications that must be made to the original packets to more clearly express the expectations in question, discussion packets will continue to be an effective tool in the classroom.

Reading as a Learning Strategy for Mathematics

In this action research study of 55 sophomore and junior students in my Algebra II/Trigonometry classrooms, I investigated a reading strategy of learning mathematics. Students were given background information about reading and explored the benefits of reading for themselves. Next, students were taught to read their textbook, analyzing one section of the textbook at a time. Throughout the research project, students were given reading guides to fill out during class with whole class discussion following the reading time. I discovered that students are able to read a mathematics textbook with understanding and students who are gone for activities can learn independently. Teacher observations, student surveys, and student interviews provide quantitative evidence of increased student understanding and achievement. As a result of this research, I plan to continue utilizing the reading guides and incorporating reading as a method of learning mathematics within my classrooms.

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.

The Use of Think-Aloud Strategies to Solve Word Problems

In this action research study of my sixth grade mathematics class, I investigated how students’ use of think-aloud strategies impacts their success in solving word problems. My research reveals that the use of think-aloud strategies can play an important role in the students’ abilities to understand and solve word problems. Direct instruction and modeling of think-aloud strategies increased my students’ confidence levels and the likelihood that they would use the strategies on their own. Providing students with a template to use as they solve a word problem helps students to better focus in on the think-aloud strategies I had been modeling for them.