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Generalization is one of the core aspects of algebraic thinking, and research literature points to the importance of objectification when generalizing mathematical discourses. To increase the field's understanding of the objectification process in various algebra discourses, our study analyses Grade 6 teachers' use of words, symbols, routines and narratives when they introduce various algebraic concepts. Our results show that there exist instances of objectification in the teachers' discourses, but these are all implicit, which can make them difficult for students to notice. Thus, teachers need to be made more aware of the importance of making the objectification process explicit. Furthermore, our results show that instances of objectification are tightly connected to the use of formal algebraic symbols. This highlights the importance of the transition from concrete/iconic to formal/arbitrary representations. [ABSTRACT FROM AUTHOR]

Function is a multifaceted and essential concept in mathematics that includes various complex ideas such as mapping, relations between variables, algebra, input-output, and rule. Pre-service mathematics teachers' (PMTs) should have a rich understanding of these ideas for their future teaching practices. However, research showed that PMTs had a limited and superficial understanding of function as students do. Thus, a learning module was designed for improving PMTs' conceptualizations of function ideas as they relate to their personal concept definitions and examples of functions. A design-based research study was conducted with 17 senior PMTs. The study results suggest an improvement in the way PMTs define functions and identify a variety of function ideas in definitions and examples. Even if the mapping idea became dominant among all ideas in PMTs' personal concept definitions and examples, they could identify the implicit function ideas and develop an understanding of connections between ideas. We also provide suggestions for the second cycle of the intervention. [ABSTRACT FROM AUTHOR]

This study investigated the methods that pre-service teachers employed while finding volume using integration and the reasons why they utilized these methods (problems); the accuracy of their solutions was also analyzed in this study. Case study design, a qualitative research method, was used for this study. 45 sophomore pre-service teachers studying for the Middle School Mathematics Education degree programme at an Education Faculty in Anatolia. It is used to mean 45-second class preservice teachers studying for the Middle School Mathematics Education degree programme at an Education Faculty in Anatolia. It is used to mean 45-second class preservice teachers studying for the Middle School Mathematics Education degree programme at an Education Faculty in Anatolia. Pre-service teachers were provided with a training programme that made use of GeoGebra software for four weeks as part of their mathematical analysis course. Pre-service teachers were provided with a written form containing five open-ended questions and given time to answer them. Data from the study was analyzed using the content analysis method. Results from these analyses showed that half of the pre-service teachers chose problems that requires the shell method to calculate volume and that the main determining factor was the ease of mathematical calculation provided by the shell method. Also, it was found out that the mistakes made by pre-service teachers originated from issues such as the inability to fully comprehend the subject at hand, errors in formulization and/or graphing, and problems taking the integral. [ABSTRACT FROM AUTHOR]

This study aims to investigate the non-algebraic solution strategies that prospective mathematics teachers use to solve word problems and their thought process while they were solving the problems. A total of 76 prospective mathematics teachers were asked to solve two word problems without using algebraic solutions and, then, clinical interviews were conducted with a sub-sample of 20 participants. The solutions used by the participants were analysed according to the type and frequency of the strategy. The results show that prospective mathematics teachers did not use various non-algebraic solutions for word problems and that they used the guess and check strategy most often. According to the findings obtained from the interviews, it was found that the participants tended to rely on solutions that used algebraic equations related to the problem while producing solution strategies. Furthermore, the participants were found to have a limited understanding of how to interpret the algebraic equations within their context, the difference between algebraic and non-algebraic solutions, and problem-solving strategies, which prevented the participants from producing alternative solution strategies. [ABSTRACT FROM AUTHOR]