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.

What is higher education?

"The problems that exist in the world today cannot be solved by the level of thinking we were at when we created them." - Albert Einstein What is higher education? It is a key tool to our gaining the level of thinking Einstein describes - the level of thinking needed to solve the problems that exist in the world today. I am not saying higher education is the only thing that prepares people to think - far from it. But higher education, if it does what it is meant to do, prepares us with a solid base of skills to think critically and analytically to deal successfully with an ever-changing world. It instills in us the desire and ability to be lifelong learners, able to grow and participate as members of both local and global communities. Learning skills, critical analysis skills, skills that allow us to deal with and be successful in the ever-changing world around us are the skills higher education must provide.

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.

Why Are We Writing? This is Math Class!

In this action research study of my classroom of 8th grade mathematics, I investigated writing in the content area. I have realized how important it is for students to be able to communicate mathematical thoughts to help gain a deeper understanding of the content. As a result of this research, I plan to enforce the use of writing thoughts and ideas regarding math problems. Writers develop skills and generate new thoughts and ideas every time they sit down to write. Writing evolves and grows with ongoing practice, and that means thinking skills mature along with it. Writing is a classroom activity which offers the possibility for students to develop a deeper understanding of the mathematics they are learning. Writing encourages students to reflect on and explore their reasoning and to extend their thinking and understanding. Students are often content with manipulating symbols and doing routine math problems, without ever reaching a deep and personal understanding of the material. My goal through this project was to help students understand why they were doing certain operations to solve math problems. Writing is an essential tool for thinking and is fundamental in every class, in every subject, and on every level of thinking; skills in writing must be practiced and refined, and students must have frequent opportunities to write across the curriculum. Communication in mathematics is not a simple and unambiguous activity.

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.