Search

WOS: 000461077700004, The purpose of this study was to investigate prospective middle school mathematics teachers' perspectives about mathematical modeling tasks. Specifically, prospective teachers' views about how modeling tasks are differ from textbook problems was examined. Furthermore, what prospective teachers think about how modeling tasks would reflect classroom learning environment and whether or not they could be used in mathematics teaching were examined. A basic qualitative approach was utilized in the study. Data were gathered through open-ended questionnaires at the end of the semester from 40 prospective middle school mathematics teachers who enrolled an elective modeling course. Data were analyzed using content analysis. The findings of the study showed that prospective teachers initially did not consider modeling tasks as mathematics problems. As compared to textbook problems, prospective teachers indicated that mathematical modeling problems have many differences in terms problem structure and problem solving process. Prospective teachers stated that role of a teacher and students should be changed and formative assessment and evaluation methods should be utilized in a modeling-problem based environment. While majority of prospective teachers considered that modeling-based instruction was hard to implement because of time and classroom management, if it is accomplished it may well support many mathematical thinking skills. It is proposed that mathematical modeling problems should be integrated into formal mathematics lessons or elective courses.

Elementary pre-service teachers in an upper-division algebra mathematics content course explored graphing through the use of Calculator-Based Rangers™ (CBRs). This study explores how they used the Distance Match feature of the technology to engage in algebraic thinking. Operating CBR technology, pre-service teachers’ perceptions regarding how position/time graphs represent algebraic concepts was explored with an emphasis on physical movement. Using an inductive approach for qualitative data, the pre-service teachers’ reflections regarding the use of CBRs were analyzed. Specifically, patterns and structures were discovered through coding of the pre-service teachers’ raw descriptions of their movements. Using the data sources (a reflection and assignment), the results showed increased understanding and beneficial affordances with the use of CBRs. However, the pre-service teachers failed to connect the graphs thoroughly to numeric representations and described slope only superficially. For example, movement was not contextualized using numbers but rather using verbal descriptions. Implications are provided for the integration of CBRs as tools for enhancing pre-service teachers’ knowledge for teaching mathematics with technologies

WOS: 000297741300005, This article reports an analysis of 44 prospective middle school mathematics teachers' pre-existing knowledge of rigid geometric transformations, specifically the geometric translations. The main data source for this study was the participants' responses to the tasks that were presented during semi-structured clinical interviews. The findings of the study revealed that prospective teachers had difficulties recognizing, describing, executing, and representing geometric translations. The results indicated that teacher candidates held various views about the geometric translations: (1) translation as rotational motion, (2) translation as translational motion, and (3) translation as mapping. The results further revealed various interpretations of the vector that defines translations: (1) vector as a force, (2) vector as a line of symmetry, (3) vector as a direction indicator, and (4) vector as a displacement. Although many of the teacher candidates interviewed knew that a vector has a magnitude and a direction, this knowledge did not generally lead them to conclude that vectors define translations.

WOS: 000374494500013, …

WOS: 000354282000007, The aim of this study was to observe the development process of the concept of a parabola in Taxicab geometry. The study was carried out in two stages. First, some activities related to Euclidean geometry and Taxicab geometry were designed based on concept development and real-life applications, and they were administered to a ninth-grade student. According to the findings, once the student learnt the definition of a parabola in Euclidean geometry, she was able to define a Taxicab parabola using the distance function in Taxicab geometry. Also, she came up with an algebraic definition of a Taxicab parabola based on this geometric definition of the concept of a parabola. Moving from algebraic definition to geometric representation, she configured the concept of a parabola in Taxicab geometry. By means of this application activity, the student had the opportunity to observe and practise the concept of a parabola in a real-life situation based on Euclidean geometry and Taxicab geometry.