Horizontal and Vertical Mathematization Processes of Junior High School Students in Solving Open-Ended Problems

Abstract

Mathematization is converting information from problems into mathematical models. The mathematization process is divided into horizontal and vertical mathematization. This descriptive qualitative research aimed to describe junior high school students' horizontal and vertical mathematization process in solving open-ended problems. The subjects are three students with good, medium, and poor mathematical problem-solving abilities. The instruments used were interview guidelines, mathematical problem-solving ability tests, and open-ended problem tests with topics area and perimeter of rectangles and circles. This research shows the horizontal and vertical mathematization process in solving open-ended problems. The horizontal mathematization process was; identifying the information and topics area and perimeter from the problem; representing the problem into some rectangle and circle figures and expressing the problem in the subject’s own words; writing the mathematics language; finding the regularity of the relations to find the possible solutions; and making mathematical models. The vertical mathematization process was; using mathematical representations with symbols and formulas related to the area and perimeter of rectangles and circles; using formal algorithms; customizing and combining some models to get the correct answers; making logical arguments to support the solution and other possible solutions that suit the problem; and generalizing the solution using the concepts of area and perimeter of rectangles and circles to solve similar problems. Every student may have different strategies and solutions when solving open-ended problems.