Constructivism Theory

Constructivism theory encourages learners to make new concepts based upon their current/past knowledge. In this sense, the learner selects and transforms information, assembles hypotheses, and formulates decisions relying on a cognitive structure. Cognitive configuration provides meaning and organization to experiences and allows the individual to "go beyond the information given" (Culatta, 2015). Students in this case ascertain, and assess what they know. They are active creators of their own knowledge. The effectiveness of this theory is proven by many researches, and one of these studies is that of Tyagi (2013). In his study “Influence of Constructivism in Teaching on Academic Achievement of Primary Students”, the constructivist-based teaching

It guides students to make wide-ranging use of their own mathematical knowledge and skills. In addition, students will develop splendid experiences in the pleasures of discovery and receive the approval of their colleagues. Even the low achieving students can respond to the problem in some significant (Takahashi, 2005).

An open-ended approach breaks students’ understanding that every problem has one correct solution. Hence, students are encouraged to work on the same problem using and discovering different methods. However, students must use to learn various strategies and thus deepen the students ' mathematical knowledge and develop their creative mathematical thinking (Klavir & Hershkovitz, 2015).

The formulation of the solutions enables teachers to establish the level of the students’ active knowledge and enables them to discuss and raise the level of the conversation they gain. The discussion on the terms employed and the higher concepts that could have been employed can provide students with the necessary support to progress toward higher levels of knowledge and understanding (Klavir, 2014).

Many researches quantified the positive effect of using open-ended approach in the teaching-learning

The aforecited study was backed up by the study conducted by Munroe (2012), which confirmed the effectiveness of using open-ended approach in increasing students understanding of concepts and consequently, their performance in the subject. This was done by establishing a friendly environment where students were free to share ideas and opinions without being teased by their group mates. In like manner, students encourage their peers and at the same time, being encouraged to do their best. More advanced students were asked to assist the struggling