I explore some facts about the area, position, etc. of the Steiner ellipse using GeoGebra and numerical analysis. Students can use these for mathematical inquiry.

Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

Students' experience errors in solving proportional problems and prospective teachers' experience were the same thing. Research that explained the wrong strategy for understanding proportional problems still needed to be completed. Objectives to describe the wrong strategies chosen by prospective teachers in solving proportional questions and the…

We know that making mistakes in mathematics is an inherent attribute of doing mathematics deeply. Yet, making mistakes is at the root of mathematical fear and anxiety for elementary preservice teachers (PSTs). Valuing mistakes in mathematics is an essential part of shifting from deficient views to asset views of mistakes and having better…

One of the reasons why students fail in mathematics courses is that the problems used in the lessons are abstract. In this context, it is important to embody the problems used in the lessons. Fermi problems are open-ended problems, a type of problem that reflects real-life situations that are solved by making a series of predictions. In the…

Pedagogical content knowledge (PCK) begins to develop during teacher education and the teaching practicum reinforces its development. This study is an interpretive inquiry into pre-service mathematics teachers' practicum classrooms. The study explored four pre-service mathematics teachers' PCK through observations and interviews. The pre-service…

Teachers' ability to accurately judge difficulties of mathematical tasks is an essential aspect of their diagnostic competencies. Although research has suggested that pedagogical content knowledge (PCK) is positively correlated with the accuracy of diagnostic judgments, experimental studies have not been conducted to investigate how PCK affects…

Many countries do not include the normal distribution concept in their middle school mathematics curriculum, but on the grounds that middle school mathematics teachers need to know more than just mathematics, researchers argue that preservice teachers (PTs) ought to have knowledge and skills in this area. This study was aimed to investigate PTs'…

This study's purpose was to analyse the relationship between geometric thinking skills with self-regulated learning and with students' basic geometry skills. Furthermore, analyze student errors in solving geometry problems based on their self-regulated learning to determine the optimal geometry learning environment for geometry thinking skills.…

This research analyzed the effect of digital storytelling (DST) on the development of pedagological content knowledge (PCK) of prospective secondary school mathematics teachers on mistakes made by students in algebra. The research applied sub-domains of PCK, the knowledge of content and students (KCS) and the knowledge of content and teaching…

In this study we investigated pre-service teachers' (PSTs) proportional reasoning and how they interpret their calculations in proportional tasks. We administered a written questionnaire to 199 PSTs and used an inductive content analysis approach for data analysis. We found that one item, in which PSTs were asked to interpret the meaning of the…

A study of pre-service primary school teachers' content knowledge regarding real numbers related to infinity, i.e., division by zero and denseness of the real number line, was conducted at a Swedish university. Data were collected twice during the respondents' teacher education using questionnaires and interviews on both occasions. The data were…

This research aimed to determine the difficulties that the students experience in inequality solutions that contain inequality in general and rational (proportional) expressions, and to solve these difficulties with an activity. Totally 108 students, who were enrolled in the Department of Mathematics and Science Education, consisted respectively…

Fermi problems are useful for introducing modelling in primary school classrooms, although teachers' difficulties in problem solving may hinder their successful implementation. These difficulties are associated with the modelling process, but also with the estimation and measurement skills required by Fermi problems. In this work, a specific…

Students' contributions that are not yet mathematically complete, precise, or correct are crucial for learning through classroom discussions. We aim to support teacher candidates (TCs) to see students' ideas as evidence of sensemaking and to respond in ways that keep student thinking central to the discussion. Although approximations of practice…