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.

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.