<![CDATA[The simple iteration material in the numerical methods course is material related to functions and derivatives. Apart from this, simple iteration material requires one or two initial guesses that do not require bracketing the roots. This method will produce a root approximation as a solution, which will show convergent or divergent results. The convergence criteria are influenced by the derived results and the initial guesses provided. Because of this, this research aims to analyze the results of student answers to prove the convergence criteria of a given simple iterative problem. The method used in this research is a case study, analyzing the results of the answers of five randomly selected students studying numerical methods courses. Based on the results of the analysis of the convergence criteria based on initial guesses, it was concluded that only 5 students could prove the convergence criteria correctly. In general, students made mistakes in deriving algebraic functions, carried out division operations, and incorrectly determined the convergence criteria because they only proved the possibility of the function. given so that students only focus on convergence criteria without carrying out iterative analysis.]]>
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