摘要 : Research in mathematics and science education reveals a disconnect for students as theyattempt to apply their mathematical knowledge to science and engineering. With this conclusion in mind, this paper investigates a particular ca... 展开 Research in mathematics and science education reveals a disconnect for students as theyattempt to apply their mathematical knowledge to science and engineering. With this conclusion in mind, this paper investigates a particular calculus topic that is used frequentlyin science and engineering: the definite integral. The results of this study demonstrate thatcertain conceptualizations of the definite integral, including the area under a curve and thevalues of an anti-derivative, are limited in their ability to help students make sense of contextualized integrals. In contrast, the Riemann sum-based "adding up pieces" conceptionof the definite integral (renamed in this paper as the "multiplicatively-based summation"conception) is helpful and useful in making sense of a variety of applied integral expressionsand equations. Implications for curriculum and instruction are discussed. 收起