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All Journal International Journal of Educational Innovation and Research Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang
Benjamin Tatira
Walter Sisulu University
Education Languange, Linguistic, Communication & Media Mathematics Other

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Students’ Cognition of The Induction Step in Proving Inequality Propositions Benjamin Tatira
Jurnal Pendidikan Matematika IKIP Veteran Semarang Vol 7 No 2 (2023): Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang
Publisher : Urogram Studi Pendidikan Matematika, Universitas IVET

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31331/medivesveteran.v7i2.2571

Abstract

The induction step in proof by induction requires some clever tricks in order to get the expected formula for , especially in statements with inequalities. The purpose of this study was to determine undergraduate students’ cognition regarding the induction step in proving inequality propositions in order to create opportunities to teach the principle of mathematical induction better. A class of 67 students participated in the study on learning proof by induction using the problem-based approach. The Action-Process-Object-Schema theory was used to structure the study and the cyclic activities-class-discussion-exercises instructional approach was used to teach proof by induction. Data for the study was comprised of individual students’ written responses to a task of two questions and the transcriptions of the semi-structured interviews. The findings revealed that students at most showed indication of partial understanding of proof by induction. Executing the induction step sits at the heart of proof by induction and necessitates logical reasoning at the object-level conception. Inadvertently, the implication was the most challenging aspect in proof by induction. The majority of students made inroads in setting up the proof properly but could not succeed in proving that . Some students had challenges of where to begin a proof, so much that they chose to start with direct substitution. In line with that, most students also concluded without deriving the expected formula required to draw a conclusion. Keywords: induction step; proof by induction; APOS-ACE teaching cycles; inequalities.
The Impact of exposing rural grade 10 mathematics learners to Artificial Intelligence 1Ndimeni KaNdimeni Olibhisi Majingo; Tirivanhu Muchuweni; Benjamin Tatira
International Journal of Educational Innovation and Research Vol. 5 No. 2 (2026)
Publisher : Universitas Majalengka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31949/ijeir.v5i2.15457

Abstract

Artificial Intelligence (AI) is transforming classroom learning by providing instant feedback, multiple solution strategies, and opportunities for independent exploration. AI tools such as Photomath can enhance mathematics understanding and engagement, yet many rural schools face significant barriers, including inadequate infrastructure, poor internet connectivity, and limited digital skills. This study explored the impact of introducing Photomath as an AI-based tool to Grade 10 mathematics learners in a rural South African school. Drawing on the Technological Pedagogical Content Knowledge (TPACK) framework, this qualitative study collected data through learner interviews and classroom observations during a six-week intervention. A total of 47 Grade 10 learners participated in the study. Findings revealed increased learner confidence, improved conceptual understanding, and greater willingness to participate in class discussions, as reported by learners and teachers. Learners valued the ability to revisit explanations, explore multiple solution paths, and learn at their own pace. Teachers observed that AI encouraged more focused engagement and active questioning. However, limited access to devices and unreliable connectivity restricted consistent use. The study concludes that, with improved access, teacher training, and infrastructure, AI has strong potential to support inclusive and equitable mathematics education in under-resourced rural contexts, with practical implications for classroom instruction and teacher support in rural schools.
Co-Authors 1Ndimeni KaNdimeni Olibhisi Majingo Tirivanhu Muchuweni