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In multivariable calculus, the concept of multivariable function is one of the most difficult for undergraduate students to study. The main objective of this study is to establish a model of teaching and learning to support students' mathematical thinking in the learning of two-variable functions through a blended learning environment. The impact of this environment on students' learning of two-variable functions and in overcoming students' obstacles are put forward. Findings revealed that blended learning supports students' mathematical thinking and helps in overcoming additional obstacles in mathematical learning. Poor mathematical knowledge of single-variable functions and poor algebraic manipulations are still the main reasons behind student obstacles in learning two-variable functions.

Derivation is one of the fundamental concepts in the learning of university mathematics. It is a prerequisite for other concepts in undergraduate level and its traces are visible in the majority of mathematical courses at university level. Students have difficulties in the learning of this concept which mostly come back to lack of conceptual understanding. The purpose of this study is to investigate the reasons of difficulties, which faced students in conceptual understanding of derivation. The design of this study is qualitative analysis of open-ended questions, and its subjects consisted of 63 undergraduate students. The findings showed students have serious difficulties in understanding conceptually of derivation. The students' responds indicated that main reasons of difficulties in conceptual understanding of derivation come back to focusing on symbolic aspect more than embodied aspect, lack of making logical connection between these aspects, and weakness of dealing with generalized question. Findings of this study provide information to undergraduate instructors and students to overcome learning difficulties of derivation.

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