This present study investigated engineering students' conceptions and misconceptions related to derivative, particularly interpreting the graph of a function and constructing its derivative graph. Participants were 147 first year engineering students from four universities enrolled in first year undergraduate calculus courses with or without the incorporation of computers for the purposes of seeing the power of visualization, investigating worked examples given in steps and solving various questions related to the worked examples, assisting conceptual understanding, and/or providing feedback besides lectures in the classroom. Students were tested before and after being exposed to instruction on differentiation and integration by a diagnostic test measuring their understanding of major aspects of calculus. Follow-up interviews were conducted with 18 students. Analyses of the results revealed that A-level student's performance was improving more than non-A-level students, particularly in computer groups. The analyses of the students' written and oral responses in all groups indicated that prototypes, poor understanding of the notion of limit, confusion between the process and the product, and difficulties in using graphical information to give meaning to symbolic representation account for the errors and the misconceptions identified.

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To take its due place in the world of education, Turkey has been through serious reform initiatives in the curriculums of various school subjects since 2003. The new Turkish elementary school curriculum was prepared considering the research studies conducted in Turkey and in other countries, as well as the educational systems of developed countries and previous experiences with mathematics education in Turkey. This study attempts to provide a perspective on the nature of the instructional tasks in the new elementary school mathematics curriculum. In particular, our focus is to explore the level of cognitive demands (LCD) in the algebra tasks provided in the national elementary mathematics curriculum guidebook. This curriculum document is a major resource for administrators, stakeholders, textbook publishers and ultimately for teachers. For every learning objective, it provides sample tasks to be used in mathematics instructions. In this study, our purpose is to explore the LCD of each of these tasks by utilizing a framework developed by Smith and Stein (Math Teach Middle School 3:344-350, 1998). The framework classifies mathematical tasks according to the level of demands: lower-level and higher-level demands. While the lower-level demands are related to memorization and procedures without connections, the higher-level demands are related to procedures with connections and doing mathematics. The findings revealed that 60% of algebra tasks for each grade level required higher LCD and a great majority of the remaining tasks were at the level of procedures without connections. The findings of the study particularly inform curriculum developers about issues regarding the quality of the tasks given in the curriculum guide and provide possible suggestions to improve the implementation of the curriculum change process.

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