Exploring mathematical investigations among selected students

An excellent activity that can develop students\u27 investigative skills, mathematical thinking processes and good mental habits is to engage them in mathematical investigations. Mathematical investigation is a sustained exploration of an open-ended mathematical situation where students investigate, look for patterns, explore possibilities and establish relationships. Two groups of freshmen students were given pre-activity and post-activity interviews regarding their views in doing mathematics. The activity consisted of a mathematical investigation task, the task being complex, gave students opportunities to make their own decisions of which particular situation to explore. Both groups made choices that are consistent with established truths and from their existing knowledge, they were able to construct new ones through reasoning and argumentation, and through deliberate application of problem-solving strategies. Students in both groups went through the creative and inventive phases and writing their report on the activity through collaborative learning. They were able to negotiate the task requirements with their peers and the teacher. Through relating their ideas to others, they were able to internalize and transform learning into something that has personal relevance and meaning. Moreover, they also developed their social skills and dispositions such as respect for others, reliance on others for assistance and sensitivity to, group discussions. After doing the mathematical investigations, the participants had a change of views regarding doing mathematics. Instead of viewing mathematics as a body of facts and formulas, they view mathematics as a growing and dynamic body of knowledge. Observations from their activity and the analysis of their output in the given task indicated that they used scientific method and inquiry. Steps and processes in doing mathematical investigations were evident as students investigated the situation, formulated problems and conjectures, verified relationships, were able to explain and justify conjectures, and reorganized or synthesized these conjectures with previous results already established