Abstract:

The official documents of the European Commission focused on mathematics education emphasize that inquiry-based learning is an important innovative strategy of mathematics teaching. The implementation of inquiry-based learning is in the focus of mathematics and science educators in Slovakia. Appropriate application of inquiry-based learning in mathematics teaching should stimulate the development of students' inquiry skills. The skills to analyze and determine relationships between variables are among the basic inquiry skills. Development of these inquiry skills requires that students initially work with simple models that would lead them to explore and use numerical and graphical representations of dependencies between variables. Active engagement of students in appropriately prepared inquiry activities should encourage students' understanding of connections between numerical, graphical and symbolic representations of functional dependencies.

Our research is currently focused on implementation of inquiry approaches to mathematics teaching and exploring the impact of inquiry-based learning on developing students' inquiry skills. Within the framework of the national project, we prepared inquiry activities for various mathematical topics and teachers have tried the inquiry activities in mathematics teaching. A test to diagnose the level of development of selected inquiry skills and understanding the concept of function was given to students from six grammar schools in Slovakia at the beginning of the project. The sample consisted of 216 students. The test was given to the same students after one year, during which the teachers should use several inquiry activities for teaching functions and other topics. The paper analyses and interprets the results of solving three tasks focused on creating tables and graphs and characterizing the relationship between variables.

Two inquiry activities are presented in the second part of the paper. Inquiry activity focused on temperature transfer was designed for teaching linear function. GeoGebra is used to create a stimulating interactive learning environment in which feedback on student performance control is also implemented. An important part of the activity is a model for identifying matching temperature pairs in the Celsius and Fahrenheit scales by which students can create a table and analyse the relationship between the obtained data. The second inquiry activity focused on investigating the relationship between side lengths of rectangles with the same area was designed based on the identified lacks in students' inquiry skills. By sketching several rectangles with the given area and creating a table with their side lengths, students can explore the dependence between the side lengths of the rectangles in a dynamic graphical model created in GeoGebra. The dynamic model allows students not only to explore the functional dependency between variables, but also to find rectangles having the minimum circumference for the given area.

Keywords:

Inquiry-based learning, Inquiry skills, Mathematics teaching, Inquiry activities, Functional dependencies, GeoGebra.