The purpose of this study was to examine a group of eleventh grade high school students, who has successfully completed 2008-2009 academic year, conceptual and procedural understanding of the logarithmic function. “Conceptual knowledge of mathematics includes logical relationships constructed internally and existing in the mind as a part of a network of ideas” (Van De Walle, 2007, p.30). Conceptual knowledge includes a deep understanding related to the meaning of mathematics (Miller &Hudson, 2007). It is a ability to show understanding of mathematical concepts by being able to interpret and apply them correctly to a variety of situations as well as the ability to translate these concepts between verbal statements and their equivalent mathematical expressions.  

It is a connected network in which linking relationships is as prominent (Harding & Potgieter, 2005; Groth & Bergner, 2006). It is a kind of knowledge which is connected to the other pieces of knowledge. Moreover, the connections between the pieces of knowledge are as important as the pieces themselves (Mahir, 2009).  For instance, “a student may understand that addition means joining two groups to get a bigger group and may also understand that subtraction means starting with a bigger group, taking some away to get a smaller group. The student’s conceptual knowledge is increased when he recognizes that a relationship exists between addition and subtraction. A practical application of this conceptual knowledge might involve the student understanding that if he borrows 4 dollars from his 10-dollar emergency cash fund to buy lunch, he is going to have to add 4 dollars to get back to his original 10 dollar fund (i.e., 10 − 4 = 6 and 6 + 4 = 10)” (Miller & Hudson, 2007, p.49).

As we understand from the previous paragraph, conceptual learning requires serious mental activity, and to avoid this, students prefer to memorize procedural rules and algorithms (Mahir, 2009). This is because of conceptual knowledge typically requires conscious thinking, on the other hand, procedural knowledge often calls for automated and unconscious thinking (Kadijevich & Haapasalo, 2001).  

Procedural knowledge is the second type of knowledge that students solve computation problems as well as word problems or real-world tasks such as making change or calculating the area of a room (Miller & Hudson, 2007). Procedural knowledgeis the ability to physically solve a problem through the manipulation of mathematical skills, such as procedures, rules, formula, algorithms and symbols used in mathematics (Harding & Potgieter, 2005; Mahir, 2009). Consisting of formal language of mathematics, and of rules, algorithms and procedures, prosedurel knowledge uses to solve mathematical tasks memorized. The flexibility needed to deal with different kinds of problems can only be gained by conceptual understanding (Mahir, 2009). Procedural knowledge that is not supported by conceptual understanding can produce only limited success. Moreover, Chapell and Killpatrick (2003) in their expetimental study showed that the students exposed to the concept-based learning environment scored significantly higher than the students in procedure-based environment on assessment that measures conceptual understanding as well as procedural skills. 

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