Jessica Jones believes the dislike some students have towards math could change “if math could be taught through conceptual understanding, NOT through proper use of when and how to apply formulas.” Jones, who teaches middle school math at Gompers Preparatory Academy, had the opportunity to learn more about teaching for conceptual understanding of mathematics at this summer’s “Quantitative Reasoning and Early Algebra in the Common Core State Standards” summer institute.
Developed specifically for fifth through eighth grade teachers, Math for America San Diego’s annual institute in July focused on quantitative reasoning, fractions and early algebra within the Common Core State Standards-Mathematics (CCSS-M). The week-long program addressed the critical need for better mathematics instruction and understanding of key math concepts in pre-high school grades.
“The middle grades are where students lose interest and confidence in mathematics, by failing to understand proportional reasoning and other mathematically important building blocks essential for future success in mathematics,” said Barbara Edwards, executive director for Math for America San Diego (MfA SD). “We felt it was important to offer a summer institute devoted entirely to helping teachers in these grades improve their approach to teaching mathematics.”
Dr. Guershon Harel, a mathematics professor at UC San Diego and MfA SD’s director of professional development, led the institute. Prof. Harel is an internationally renowned mathematics educator who has devoted his career to understanding how students learn mathematics, and the implications of those understandings for curricula, teacher preparation and professional development.
“Mathematics learned in the middle grades is of a different nature than that learned in the primary grades,” Harel said. “The nature of arithmetic operations changes as children transition from addition, subtraction, or repeated-addition or repeated-subtraction, to multiplication with division with decimals and fractions. Because children in the middle grades have to deal with a greater variety and more complex problem situations involving different types of units and interpretations, having a framework that can help students know why a problem is solved in a particular manner, not only how, is critical to future success in mathematics.”
A group of 16 teachers from three charter schools and the San Diego Unified School District attended the institute, immersing themselves in applying the Standards for Mathematical Practice (SMP) for the Common Core State Standards (CCSS-M) to their grade levels.
“By attending the MfA SD summer institute, I gained a deeper understanding of the ways of thinking in relation to repeated reasoning, using structures, reasoning quantitatively, and contextualizing and decontextualizing,” said one institute teacher. “I have a better idea of how to implement these habits of mind to support students to compute.”
“Struggling with the concepts myself, and seeing how one idea built upon the previous idea without resorting to the standard algorithms is so convincing that I want my students to learn this way also,” she said. “If there is a true understanding of whatever concept we are working on, then there is no need to just memorize formulas and blindly apply them. There must be meaning behind what we do!”
“This institute has given me the opportunity to become a better advocate for math and for what my students need to learn. I feel Professor Harel has found a method to [break] down even the most complicated mathematics and give it reasoning,” said another institute teacher. “As a middle school teacher, I am so used to pushing through content to ‘get it done,’ when what I have learned this week is less is more. My students need the ‘why’ behind the math. I need to show them how to find it.”
Earlier in the summer, Prof. Harel directed the seventh annual summer institute for MfA SD’s 14 fellows and master teaching fellows. Participants at the 12-day institute learned more deeply about systems of linear equations and built a stronger foundation for their own mathematical knowledge.
“From a small number of theorems, we expanded and reasoned through a series of challenging problems,” said Trang Vu, MfA SD master teaching fellow and mathematics teacher at La Jolla High School. “I will revise the unit on solving systems of equations in algebra courses to help students understand their reasoning.”
To celebrate completion of the institute, Prof. Harel and MfA SD fellows went bowling, where they mathematically figured out how to make the 7-10 split and how not to throw a gutter ball.
Math for America San Diego is housed at the Center for Research on Educational Equity, Assessment and Teaching Excellence (CREATE) at UC San Diego. For more information on MfA SD’s teacher professional development programs contact Barbara Edwards at sandiego@mathforamerica.org.
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