Building Depth of Understanding of the Concept of Number Sense and Algebra in Students Grades 7 and 8

Mathematics instruction offers both challenges and rewards to students. Teachers tend to focus on transmission of knowledge. Student creativity and problem-solving skills are not typically activated with common teaching practices. When students are engaged in mathematics they are recognizing patterns, making connections on their own, coming up with creative solutions, and discussing mathematical ideas with peers and adults. The purpose of this study was to identify, employ, and evaluate strategies that engage students in these practices and assist them in developing a deep understanding of mathematics concepts such as number sense and algebra. The review of the literature began with the history of mathematics instruction. The research reviewed alternative methods in mathematics education that engage students in mathematical practices. The research concerning cognitive development indicated that these strategies are successful in teaching mathematics to adolescents. This was a participatory teacher action research study. The participants were groups of fifteen 7th and 8th grade students from lower- and middle-class families. Student pre- and post-test scores on a standard chapter test on number sense and algebra were compared following teaching practices involving teacher-student and student-student interaction. Students asked each other questions about the material and verbally justified their methods. Data along with student and teacher observations were analyzed to evaluate the effectiveness of those strategies on the participants’ understanding of mathematics. Results indicated that there was an increase in student understanding of number sense and algebra based on pre- and post-test score comparisons and student and teacher narrative