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Undergraduate Students' Ways of Thinking About Function Notation

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Previous research has examined difficulties that students have with understanding and productively working with function notation. Function notation is very prevalent throughout mathematics education, helping students to better understand and more easily work with functions. The goal of my research

Previous research has examined difficulties that students have with understanding and productively working with function notation. Function notation is very prevalent throughout mathematics education, helping students to better understand and more easily work with functions. The goal of my research was to investigate students' current ways of thinking about function notation to better assist teachers in helping their students develop deeper and more productive understandings. In this study, I conducted two separate interviews with two undergraduate students to explore their meanings for function notation. I developed and adapted tasks aimed at investigating different aspects and uses of function notation. In each interview, I asked the participants to attempt each of the tasks, explaining their thoughts as they worked. While they were working, I occasionally asked clarifying questions to better understand their thought processes. For the second interviews, I added tasks based on difficulties I found in the first interviews. I video recorded each interview for later analysis. Based on the data found in the interviews, I will discuss the seven prevalent ways of thinking that I found, how they hindered or facilitated working with function notation productively, and suggestions for instruction to better help students understand the concept.

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2018-05

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Ways of Thinking for Developing an Understanding of Covariational Reasoning in Undergraduate Calculus Students

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Previous research discusses students' difficulties in grasping an operational understanding of covariational reasoning. In this study, I interviewed four undergraduate students in calculus and pre-calculus classes to determine their ways of thinking when working on an animated covariation problem. With

Previous research discusses students' difficulties in grasping an operational understanding of covariational reasoning. In this study, I interviewed four undergraduate students in calculus and pre-calculus classes to determine their ways of thinking when working on an animated covariation problem. With previous studies in mind and with the use of technology, I devised an interview method, which I structured using multiple phases of pre-planned support. With these interviews, I gathered information about two main aspects about students' thinking: how students think when attempting to reason covariationally and which of the identified ways of thinking are most propitious for the development of an understanding of covariational reasoning. I will discuss how, based on interview data, one of the five identified ways of thinking about covariational reasoning is highly propitious, while the other four are somewhat less propitious.

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Date Created
2014-05

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Analysis of Learning Retention throughout Aging

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In this paper, it is determined that learning retention decreases with age and there is a linear rate of decrease. In this study, four male Long-Evans Rats were used. The rats were each trained in 4 different tasks throughout their

In this paper, it is determined that learning retention decreases with age and there is a linear rate of decrease. In this study, four male Long-Evans Rats were used. The rats were each trained in 4 different tasks throughout their lifetime, using a food reward as motivation to work. Rats were said to have learned a task at the age when they received the highest accuracy during a task. A regression of learning retention was created for the set of studied rats: Learning Retention = 112.9 \u2014 0.085919 x (Age at End of Task), indicating that learning retention decreases at a linear rate, although rats have different rates of decrease of learning retention. The presence of behavioral training was determined not to have a positive impact on this rate. In behavioral studies, there were statistically significant differences between timid/outgoing and large ball ability between W12 and Z12. Rat W12 had overall better learning retention and also was more compliant, did not resist being picked up and traveled more frequently at high speeds (in the large ball) than Z12. Further potential studies include implanting an electrode into the frontal cortex in order to compare neuro feedback with learning retention, and using human subjects to find the rate of decrease in learning retention. The implication of this study, if also true for human subjects, is that older persons may need enhanced training or additional refresher training in order to retain information that is learned at a later age.

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2014-05