The current research implemented the Predict Observe and Explain (POE) instructional approach in mathematics and examined its efficacy in enhancing students' understanding of functions in terms of their ability to connect algebraic and graphical representations in optimization problems. Two grade 11 classes (40 students in total) and two grade 10 classes (42 students in total) participated in this study, for a combined total of 82 students. Following a quasi-experimental design, students in the experimental group solved six open mathematical tasks in a small group setting. They were explicitly asked to predict the outcome before attempting to solve the tasks, make observations using concrete materials and finally attempt a solution. They were then expected to reflect on their observation and initial predictions to interpret their findings. The control group students were given the same tasks without an explicit heuristic. They directly attempted to solve the same problems without prediction and observation. The data were collected using students' written responses to each task. Students' responses to the tasks were assessed based on the following criteria: understanding, constructing, using a mathematical model, communicating and interpreting results. An independent samples t-test showed that the POE strategy improved students' learning in cognitive domains. The POE strategy helped students better understand the problem, select and apply appropriate mathematical methods and interpret their findings. Students in the control group spent more time discussing and integrating clues into possible solutions to the given tasks. The results were interpreted within the framework of inquiry-based education, informed by semiotic representation theory.