The authors describe the benefit of launching mathematics lessons in ways that engage young learners. Short, meaningful introductions can motivate and focus students. Some features of interesting launches are drawn from Ben Dixon's Foundation classroom.

Generative artificial intelligence (AI)-powered conversation agents such as ChatGPT are increasingly being used in teacher education. Although ChatGPT can provide ample resources for lesson planning, little attention has been paid to how teacher candidates construct prompts and evaluate AI-generated outputs in real time to develop lesson plans.…

The introduction of large language models (LLMs) may change future pedagogical practices. Current research mainly focuses on the use of LLMs to tutor students, while the exploration of LLMs' potential to assist teachers is limited. Taking high school mathematics as an example, we propose a method that utilizes LLMs to enhance the quality of…

This study explores and analyzes the specific performance of large language models (LLMs) in instructional design, aiming to unveil their potential strengths and possible weaknesses. Recently, the influence of LLMs has gradually increased in multiple fields, yet exploratory research on their application in education remains relatively scarce. In…

To be successful in algebra, students need access to high-quality instruction that includes opportunities to develop their algebraic understanding. Yet research on algebra teaching suggests that instruction remains procedurally focused, indicating that teachers may need additional support to provide students such opportunities. One possible lever…

Background: Teachers must have the skills to find, select, design and use technology-based mathematical activities that focus on high-level cognitive demands--supporting student reasoning. However, they experience various difficulties in creating, planning and making decisions about how and when to utilize technological affordances. Objectives:…

This study introduces a framework for analyzing opportunities for mathematical reasoning (MR) in school mathematics, using MR-relevant claims and their derivation as the unit of analysis. We contend that this approach can effectively capture a broad range of opportunities for MR across various teaching situations. The framework, rooted in…

Sustainable education is becoming a burning concept in debates and discussions the world over. There are concerns that current systems of education are not providing for the needs of all people in a sustainable way. Many countries are taking steps to ensure a type of education that will not only sustain their citizens but will meet the challenges…

Discrete time models, one linear and one non-linear, are investigated, both with a herbivore species that consumes a basal food source species. Results are presented for coexistence of the species and to illustrate chaotic behaviour as parameters are varied in the non-linear model. The results indicate the benefit of fertilization in terms of the…

It is seen that there are few studies on the role of the knowledgeable other when the literature on Lesson Study [LS] is examined. However, for LS to be better understood and applied in different cultures, the role of the knowledgeable other in LS process should be clarified. This study aimed to determine the role of the researcher as the…

This study employed a qualitative research design to investigate the utilization of soft pedagogical documents among twelve mathematics teachers in five purposively sampled public secondary schools. Data was collected through interviews and analyzed thematically. The study, rooted in social constructivism theory, discovered a mixed pattern in the…

This research examined how pre-service mathematics teachers (PMTs) plan to support argumentation in their lessons about the hierarchical relationships among the quadrilaterals and what they notice during planning. The participants of this case study were eight pre-service middle-school mathematics teachers. Data consisted of the PMTs'…

This study explored four middle-school mathematics teachers' provision of non-examples and instructional explanations in teaching rational numbers to seventh-grade students. The data sources were 8 lesson hours of observations conducted in four different classrooms. Yin's [(2018). "Case study research and applications: Design and…

This study aims to clarify the role of generating questions in mathematical modeling and construct principles for teaching and learning mathematical modeling with an emphasis on generating questions. To achieve this purpose, the role of generating questions was determined by solving a sprinkler problem and considering the investigation process.…

Why do some mathematics lessons captivate high school students and others not? This study explores this question by comparing how the content unfolds in the lessons that students rated highest with respect to their aesthetic affordances (e.g., using terms like "intriguing," "surprising") with those the same students rated…