Difficulties of construction and formulating geometric proofs by Lebanese middle school students learning math in English. (c2013)

Abstract

Developing geometric proofs is an important aspect of the Lebanese mathematics curriculum. Accordingly, exploration of the difficulties that the Lebanese middle school students who learn mathematics using their non-native language (English) is a crucial issue for research. The present study aims at exploring the difficulties, particularly language difficulties that the Lebanese middle school students (grades 6 to 9) who learn mathematics using their non-native language (English) face when constructing and formulating geometric proofs. The study took place at a private school located in Beirut during one academic year. Difficulties were investigated through interviews, tests, and clinical interviews. The interview was with the middle school math coordinator. Two Tests 1 and 2 were specifically prepared based on the Lebanese national curriculum objectives at each of the grade levels 6 to 9 and held at the end of the academic year separated by a duration of one week. Tests 1 and 2 consisted of isomathic problems that varied in terms of proof and language complexity levels. During each of the Tests 1 and 2 at each grade level, randomly selected students were clinically interviewed to provide the researcher with better insightful interpretation of the difficulties faced. Results of the study showed that students’ difficulties when constructing and formulating geometric proofs were related to difficulties in Understanding the Notion of Proof (UNP), Setting Proof Plans (SPP), Conducting Deductive Reasoning (CDR), Understanding-Applying Mathematical Concepts (UAMC), Comprehending Mathematical Texts (CMT), and Writing Mathematical Texts (WMT). Yet, these difficulties varied in their level from grade level to another and according to the proof and language complexity levels of the proof tasks.