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Flaws in Proof Constructions of Postgraduate Mathematics Education Student Teachers

“…It can be, therefore, noted that Hanna and Barbeau's suggestion on how to evaluate proof understanding is similar to the encapsulation level of proof conceptualisation proposed by Yang and Lin (2008). Conradie and Frith (2000) stated that students often fail to grasp the meaning of terms when trying to comprehend a proof thereby hindering their ability to understand other aspects of the proof.…”

“…To get a sense of students' grasp of key terms to a theorem, Conradie and Frith (2000) suggest that a researcher can ask students to define the key terms or sentences. This technique of determining understanding features at the surface level of Yang and Lin's (2008) model.…”

The Influence of Proof Understanding Strategies and Negative Self-concept on Undergraduate Afghan Students’ Achievement in Modern Algebra

“…Teaching experience as well as literature (Conradie & Frith 2000;Porteous 1986;Rowland 2001) shows that students and their educators struggle to comprehend as they read proofs of theorems. As a supporting evidence, it has been observed that students are struggling to comprehend the statement of some theorems in modern algebra, let alone to understand its proof.…”

“…(p.292) Therefore, according to this model, the indicator of understanding a proof is, knowing the meaning terms and statements in a proof, being able to justify how new assertions followed from the previous ones, being able to identify the proof framework being used, being able to provide a summary of the proof, apply the proof method in other situations to prove a new theorem, break the statement of the proof in main parts or subproofs, and apply the general method of proof on a specific example. In order to extend indicators of knowing about one's holistic understanding of the proof, Weber (2015) also incorporated some other researchers' findings such as stating that students did not understand the theorem statement before reading its proof (Conradie & Frith, 2000;Selden, 2012), and mathematics students often do not justify how new assertion in a proof was derived logically from the previous statement(s) in the proof (Alcock, 2009). After conducting an extensive analysis of the theoretical and empirical studies on proof comprehension strategies in order to identify six strategies that successful students use to comprehend proofs and mathematicians' desire that students used these strategies, Weber (2015) proposed the following six effective proof reading strategies for understanding mathematical proof: Strategy#1: understanding the theorem statement before reading its proof.…”

Every Sparrow that Falls to the Ground

“…Ernst Conradie seeks a view of divine transcendence that respects the otherness of God but does not detract from ecological commitment (Conradie 2000). Material Inscription.…”