The aim of this study is to examine middle school mathematics teachers’ concept definitions of five geometric objects (prism, pyramid, cone, cylinder, and sphere). The study was carried out with the participation of 99 mathematics teachers who have been working in middle schools located in three different provinces and districts. The data were gathered through a form consisting of six open-ended questions, which were prepared to reveal the participants’ Concept Definition (CD) of Geometric Objects (GOs). Via content analysis technique, codes from the data and categories from the codes were obtained. Results showed that some of the participants could not make the CDs of GOs correctly, that they generally drew the square or rectangular forms and only included the vertical states of the GOs objects. It was found that participants generally could not establish a relation between “cylinder and prism” and “cone and pyramid”. Evidence was also found that some of the participants saw themselves as inadequate in defining the GOs. On the other hand, it can be said from their explanations and drawings that the teachers’ professional experiences do not have much effect on defining those concepts.
This study aimed to investigate how pre-service middle school mathematics teachers attend, interpret and respond to the students' thinking about statistical concepts in a case-based teacher training environment. 25 pre-service middle school mathematics teachers participated in the study and they were asked to make evaluations on the cases given. Based on these evaluations, classroom discussions were held on student thinking, the reasons for students’ difficulties and how to overcome these difficulties. The discussions and evaluation reports were analyzed within the framework of professional noticing of children’s mathematical thinking. The results obtained showed that although the pre-service teachers were mostly able to attend to student thinking correctly, these identifications remained superficial. The pre-service teachers were mostly able to interpret student thinking in such a way as to indicate the state of understanding or misunderstanding. When the pre-service teachers’ responding skills were examined, it was revealed that they mostly suggested approaches based on partial conceptual understanding to overcome the difficulties of students. In addition, the results obtained from the study revealed that the pre-service teachers’ noticing skills differed from one case to another.
Adopting corequisite mathematics models to accelerate students’ completion of their introductory college-level mathematics course in their first year of college is prevalent across higher education institutions. This systematic review demonstrates the known research, evidence, and diversity of implemented corequisite mathematics models for prevailing themes across peer-reviewed articles.
Mastery-based testing (MBT) is a form of categorical grading where students are repeatedly assessed until they achieve a level of mastery. This paper describes the implementation of MBT in a university quantitative literacy class using a web-based homework system. Qualitative evidence in the form of student comments showed that quantitative literacy students preferred MBT because it reduced their stress levels and was perceived as substantially different from traditional assessment. Students’ differentiation of assessments based solely on nomenclature was an unexpected and significant finding.
This study concerns preservice teachers’ knowledge of student thinking at the secondary level. In particular, it examines in what ways a three-week unit integrating content and student thinking was beneficial in developing preservice teachers’ knowledge of student thinking associated with big ideas in algebra—such as variation, Cartesian Connection, and graph as a locus of points. In the early stage of discussion of student work, preservice teachers tended to focus mostly on students’ errors/mistakes, correct ways the problems should have been solved, or the types of problems that students had. However, with the progress made in discussion, they were able to attribute students’ difficulties to a lack of understanding of qualities such as definitions, properties, and concepts, and further to a lack of the understanding of big ideas underneath the qualities, with the help from instructors. The majority were also able to design contextualized tasks that could stimulate students’ interests; yet they struggled to explain how they would use the tasks to promote students’ development of big ideas by connecting multiple representations.
