Additionally, one-third of life science students reported high cost (anxiety and effort) of using mathematics in biology courses. For example, Andrews and Aikens (2018) found that, although the average score for students’ interest in using mathematics to understand biology was 4.5 on a scale from 1 to 7, 1 SD around the mean encompassed values from 2.8 to 6.2. Although recent work did not demonstrate particularly poor motivational attitudes among life science majors toward the use of mathematics in biology courses, it did reveal a tremendous amount of variation in these attitudes ( Andrews and Aikens, 2018). However, life science students are often perceived to be math averse and, therefore, may be less than enthusiastic about taking a calculus course. Therefore, many life science students are required to take a calculus course to satisfy their major or pre-med requirements. For example, calculus is used in population growth models to account for complex demography ( Ellner and Rees, 2006), in Susceptible-Infectious-Removed (SIR) models to understand disease spread (e.g., Buceta and Johnson, 2017), and in tumor growth and metastasis models (e.g., Bilous et al., 2019). Because biological systems are dynamic, calculus plays a key role in the modeling of biological systems. These skills include the ability to create and interpret graphs, the ability to statistically analyze data, and the ability to mathematically model systems ( NRC, 2003 AAMC-HHMI, 2009 AAAS, 2011). Thus, communicating the utility value of mathematics to biology through integrated mathematics–biology courses can contribute to improved attitudes toward mathematics that can impact students’ motivation and performance.ĭue to an increasing demand for quantitative skills among life scientists, undergraduates in biology today need to demonstrate competency in a variety of quantitative skills ( National Research Council, 2003 Steen, 2005 Association of American Medical Colleges–Howard Hughes Medical Institute, 2009 American Association for the Advancement of Science, 2011). Students whose attitudes toward mathematics improved primarily attributed these changes to a better understanding of the utility of mathematics to biology, feelings of competence in mathematics, or rapport with the instructor. Using pre and post surveys, we found that students’ interest in mathematics increased by the end of the semester, and they demonstrated a more sophisticated understanding of how mathematics is used in biology. This study examines how two different biocalculus courses, which integrated calculus and biological concepts and successfully halved the rates of students earning a D, F, or withdrawing (DFW), affected life science students’ utility value, interest, and overall attitudes toward mathematics. Therefore, according to expectancy-value theory, life science students may experience lower motivation, which can impact their performance in a calculus course. However, many life science students do not understand the utility value of mathematics to biology. Calculus is important for understanding dynamical systems in biology and, therefore, is often a required course for life science students. This means that the initial statement is false.The next generation of life science professionals will require far more quantitative skills than prior generations. Summarizing this, we see that all three trigonometric functions are positive in two quadrants. And the tangent function is positive in the first and third quadrants. The cosine function is positive in the first and fourth quadrants. We can therefore conclude that the sine function is positive in the first and second quadrants. Finally, in the fourth quadrant, the cosine of any angle is positive, whereas the sine and tangent of any angle is negative. In the third quadrant, the tangent of any angle is positive, whereas the sine and cosine of any angle between 180 and 270 degrees is negative. However, the cosine and tangent of any angle in this quadrant is negative. The sine of any angle in the second quadrant between 90 and 180 degrees is also positive. The letter A in the first quadrant stands for all, as all three of sin □, cos □, and tan □ are positive when the angle □ lies between zero and 90 degrees. One way of recalling whether the trigonometric functions are positive or negative in each quadrant is using the CAST acronym. This means that the first quadrant contains angles between zero and 90 degrees, the second quadrant between 90 and 180 degrees, and so on. We measure positive angles in a counterclockwise direction from the positive □-axis. We begin by recalling that the four quadrants in the □□-plane are as shown. True or False: Each of the trigonometric functions is positive in only one quadrant.
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