The purpose of the study was to determine students’ knowledge construction process in random thinking style including concrete random (CR) and abstract random (AR) where spatial ability was at the mental rotation level in resolving non-routine issues related  to the block geometry. This was an exploratory study with a qualitative approach, in which the researcher himself was the main instrument. Data ware collected through the provision of math construction tes (MCT) and unstructured interviews. The subjects of the study consisted of two students, one concrete random (CR) and one abstract random (AR). The subjects were chosen by testing the thinking style and spatial ability tests. The results of the study showed that (1) CR in problem identification indicator was able to understand the problem well and gave clear verbal response and had a process of assimilation for a long time in understanding the information, relations, and brought the situation of the problem in the form of images; whereas, the indicator of the problem solving process could be completed well but it had accommodation when determining the completion and fnding the value of unknown variable. This accommodation process lasted longer and let to the completion and the right answers as well as using procedural and meta-cognition knowledge to solve the problem; (2) AR in problem identification indicator was able to understand the problem well and gave clear verbal response and had a process of assimilation in understanding the information, relations, and brought the situation of the problem into a more complex form; whereas, the indicator of the problem solving process could be complete well in number 1 question and different assimilation process occurs in number 2 question. The accommodation process occurred on the phases of information simplification into the form of equations and finding the variable value by means of substitution between exsisting equations. This accommodation process lasted longer and led to the completion and the right answers as well as used factual and conceptual knowledge to solve the problem