Great Ideas of Primary Mathematics

Overview

"Our classrooms are filled with students…who think of mathematics as rules and procedures to memorize without understanding the numerical relationships that provide the foundation for these rules." ¹ In other words, they are lacking number sense. Number Sense is included in the Delaware standards, as well as the Common Core State Standards beginning in Kindergarten; however, I continue to have Precalculus students tell me they cannot do basic arithmetic without a calculator. The goal of this unit is to boost my students' conceptual number sense and build their confidence in mental calculations. According to John Threlfall, mental math is worth teaching because most calculations in adult life are done mentally. He believes that mental math develops problem-solving skills, as well as increases success in later written calculations using algorithms. ² In Rheta Rubenstein's opinion, mental math liberates students from calculator dependence, builds confidence, makes them more flexible thinkers, and makes them more able to use multiple approaches to problem solving. ³

I have compiled the key components from Roger Howe's seminar entitled "Great Ideas of Primary Mathematics" along with the recurring weaknesses that I see in my classroom to create this curriculum unit. The great ideas we worked with are place value, measurement and the number line, and operations. This unit will encompass all of these ideas in the form of calculator-free, daily warm-up/bell-ringer activities for one semester, focusing on one topic per week, and spiraling some concepts back throughout the semester. Throughout the unit, I will expect students to describe and defend their thought processes to their classmates, so everyone is exposed to multiple strategies and learns from each other. Although I am writing this unit for upper-level math students, many of the ideas are basic enough to be used in upper elementary or middle school.

I teach in a vocational school district consisting of four high schools that draw from middle schools in all five districts in New Castle County, Delaware so that my students have varying mathematical experiences. We separate the highest- and lowest-performing students based on 8 ^th grade state test results and a placement test, then group the rest of the incoming freshman heterogeneously. We use the Core Plus integrated math curriculum. With the exceptions just noted, students take four semesters (including two semesters in their freshman year) of Core Plus before having the option to take Intermediate Algebra and then Precalculus – both traditional math courses. Students in Precalculus are all college bound, and typically the strongest students in the school. I plan to test this unit with Precalculus students, and if it is successful, I will pass the problem sets along to the rest of my department to begin in ninth grade.