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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 work deals with the results of a research with basic school mathematics teachers about their conceptions for Algebra and its teaching. The theoretical framework that we adopted was the Anthropological Theory of Teaching. The objective was to verify which characteristics of the dominant epistemological model on teaching algebra are revealed in the conceptions of the teachers investigated. To collect date it was adopted as the methodological procedure Course of Study and Research. The results show, as the spontaneous epistemology teacher, the predominant view of algebra in the sense of operation with letters and numbers and generalizing patterns, which characterizes it as generalized arithmetic. [ABSTRACT FROM AUTHOR]

The article examines some views of algebraic reasoning, discusses a controversy on patterns, and describes the use of three types of patterns in the development of teachers' algebraic reasoning. It references the book "Principles and Standards for School Mathematics," which focuses on four major themes of algebraic reasoning for grades Pre-K-12. It suggests teachers to develop their own algebraic reasoning and understanding of the role of patterns.

The article focuses on the importance of storytelling in teaching algebra 1 and helping students integrate their mathematical experience with their understanding of the human condition. Mathematics teachers can start their lessons by citing the cave paintings early hunter-gatherers as an early example of myth making and scientific reasoning and how they use their powers of observation to build a general model of animal behavior. Teachers can evaluate the effectiveness of enrichment topics and the extent to which students have mastered critical thinking by letting students write essays describing how humans make sense of the world. Students gain confidence and the flow of ideas moves easily into solving equations that have a single unknown by having a sense of numeracy.