|Dr. Soledad A. Ulep|
Director, UP NISMED
In teaching mathematics through problem solving, the teacher uses a problem as context for developing concepts, principles, procedures or algorithms, higher order thinking skills, and desirable dispositions. A problem is an unfamiliar situation requiring a solution for which the problem solver has no readily available procedure or algorithm to use in obtaining the answer. A problem may have different solutions and at times even different correct answers.
In teaching mathematics through problem solving, the problem appears at the start of the lesson and learners have to think of their own ways of solving it to get the answer/s. In the process of doing so, they use different thinking skills and dispositions to make sense of the problem, connect what they have learned in the past to the task at hand, provide reasons for mathematical relationships they discover, and communicate their thinking using various representations. Thus in the process also, it is possible for the teacher to assess learners' mathematical thinking.
Similarly, teaching science through inquiry starts with a question or initial problem. Through well-designed hands-on activities, concrete setups, working models, or audiovisual representations or simulations, accompanied by questions that hone the learners' science process/thinking/inquiry skills, the learners generate their own knowledge/ideas until they construct concepts aligned with those of scientists. Through discussions among themselves and with the teacher, learners form conclusions or generalizations, though these may not always be in agreement.
The initial question or problem may be teacher-initiated but of genuine concern to the learners. As learners grow in confidence and skill, they are to be encouraged to design ways of finding answers to their own questions through setups and experiments that will test their hypotheses. The experiments will enable them to make observations, gather data, process and analyze these, and at the end draw conclusions. The development of the students' presentation and communication skills as they write and report their findings are part and parcel of this teaching-learning approach.
Teaching mathematics and science to students through problem solving/inquiry is very important. If students are exposed to these approaches as early as grade 1 (or 3 in the case of science), they will gain confidence in thinking independently and in exploring various solutions/ answers to the problems/questions individually or with others, rather than just rely on the teacher. And so they acquire the skills and dispositions to learn on their own. With the use of the mother tongue in teaching, learning, and assessment in grade 1 (or 3), these approaches can bring about more mathematical and scientific reasoning and communication in the classroom.
The materials that NISMED developed and the training that it conducted modeled learner-centered approaches. Learner-centeredness depends on the extent and quality of thinking that learners engage in to genuinely contribute to the development and application of mathematical and scientific ideas in the classroom. So if there are adequate opportunities for learners to make inferences, predict, make and test hypothesis or conjectures, analyze relationships, generalize, evaluate, connect, synthesize, and the like, then the teaching approach is learner-centered. It is what NISMED refers to as a teaching approach that truly values the learners.