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.

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.

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.

Using Math Vocabulary Building to Increase Problem Solving Abilities in a 5th Grade Classroom

In this action research study of my 5th grade mathematics class, I investigated how students’ understanding of math vocabulary impacts their understanding of the curriculum. I discovered math vocabulary plays an important role in a student’s ability to understand daily lessons, complete homework, discuss ideas in groups, take tests and be successful on achievement tests. A student’s ability to understand the words around him (or her) in math class seem very related to his or her ability to solve word problems. Word problems are what our national assessments are all about. I also discovered that direct instruction and support of math vocabulary increased test scores and confidence in students as test takers. As a result of this research, I plan to continue to find ways to emphasize the vocabulary used in our current math curriculum. This process will start at the beginning of the year. I will continue to look for strategies that promote math vocabulary retention in my students. And finally, I will share my findings with my colleagues, so my research can be used as part of our School Improvement Goals.

Enhancing Problem Solving Through Math Clubs

This action research paper was about a mandatory math club of seventh graders that met once per week over a 12-week period. The students gathered in the classroom during their regularly scheduled math class. The focus of the math club was to solve challenging math problems, usually cooperatively, and sometimes competitively. The math club activities varied from week to week to offer an element of surprise. Frequently, the students presented their solutions to peers, along with an explanation of the way they solved the problem. Instruments were used to collect information about problem-solving accuracy, student attitudes, and student and teacher behaviors. I discovered a slight improvement in problem solving. Also, on Math Club days, the teaching was less teacher-centered and more student-centered. As a result of this research, I plan to offer my middle school students more problem-solving opportunities and I plan to allow my students to work cooperatively on a regular basis.

Does Decoding Increase Word Problem Solving Skills?

In this action research study of my classroom of 7th grade mathematics, I investigated whether the use of decoding would increase the students’ ability to problem solve. I discovered that knowing how to decode a word problem is only one facet of being a successful problem solver. I also discovered that confidence, effective instruction, and practice have an impact on improving problem solving skills. Because of this research, I plan to alter my problem solving guide that will enable it to be used by any classroom teacher. I also plan to keep adding to my math problem solving clue words and share with others. My hope is that I will be able to explain my project to math teachers in my district to make them aware of the importance of knowing the steps to solve a word problem.

Improving Students’ Story Problem Solving Abilities

In this action research study of my classroom of 8th grade mathematics students, I investigated if learning different problem solving strategies helped students successfully solve problems. I also investigated if students’ knowledge of the topics involved in story problems had an impact on students’ success rates. I discovered that students were more successful after learning different problem solving strategies and when given problems with which they have experience. I also discovered that students put forth a greater effort when they approach the story problem like a game, instead of just being another math problem that they have to solve. An unexpected result was that the students’ degree of effort had a major impact on their success rate. As a result of this research, I plan to continue to focus on problem solving strategies in my classes. I also plan to improve my methods on getting students’ full effort in class.

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.

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.

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.