This study explored 54 preservice elementary teachers' identification and modification of mathematical tasks in raising cognitive demand and examined the features of their modified tasks. The study collected data using a three-phase activity: (a) identifying the level of cognitive demand of the given task, (b) modifying the low cognitive demand…

Productive struggle is an effective mathematics teaching practice that provides students opportunities to grapple with challenging mathematical concepts, connect prior knowledge, discover new ideas, and develop their critical thinking skills. Research has documented the benefits of secondary mathematics students engaging in productive struggle.…

The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public institution in Barranquilla,…

The aim of the study was to examine how students generate problems about the concept of series, and how they evaluate and solve these problems. The difficulties experienced by the students while posing problems and their perceptions of the posing-evaluating-solving approach were also explored. In the first stage, 46 second-year university students…

Background and Context: Integrating computer science (CS) and math in classrooms is an increasingly recognized way for schools to address national CS mandates. There is a need to understand how professional development (PD) can support teachers to integrate. Objective: We examined math teachers' interest, and confidence, in math, CS, and student…

To ensure the learning of mathematics, teachers must be able to analyse their students' mathematical practices when solving tasks, interpret the difficulties that students encounter, and decide how to manage students' difficulties. This competence in didactic analysis and intervention allows teachers to adapt their teaching to meet individual…

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…

Background: Collaborative learning is a widely used approach where students gather in small groups to solve problems and develop skills. However, grouping students is not always effective, and it may be necessary to provide task-specific collaborative experiences to optimize their interactions for subsequent learning tasks. Aims: To test this…

Covariational reasoning and the creation and interpretation of graphs of covariational situations are important skills in math and science. Unfortunately, research shows that students often struggle to make meaningful connections between graphs and the covariational situations they represent. Educational activities designed to help students…

Spanish educational curriculum adopts a mathematical process-based approach, which encompasses problem solving, reasoning and proof, communication, connections and representation. A fundamental role in the integration of these processes in mathematics teaching is played by teachers' professional practice of designing tasks. According to this, our…

This study examines secondary mathematics teachers' anticipations of student responses related to a series of cognitively demanding mathematics tasks from multiple mathematical domains presented in the context of voluntary and asynchronous online professional development modules. We analyze 283 anticipations made by 127 teachers to 17 mathematics…

This study examined the quality and types of mathematical tasks used for classroom instruction in an upper secondary school -- gymnasium. All the mathematical tasks presented in nine different school classrooms during the first semester of the school year 2018/2019 were analysed against a 5D analytical framework. The dimensions of the individual…

The objective of textbook study is to create high-quality textbooks. Analysis was done using a praxeological-didactical analysis (PDA) method. PDA offers space to analyze curriculum materials, such as math textbooks, which are the outcome of human action in the anthropology of a specific nation's society. There are 10 types of tasks given in the…

Students' issues dealing with reflection tasks, especially with inclined mirror lines, are widely known. Previous research conducted with primary school students mainly focussed on task difficulty and students' outcomes, especially their errors of reflection. Little is known about which not obviously sustainable understanding of reflection leads…

While contemporary mathematics education literature argues that curricular resources, such as textbooks, play a significant role guiding mathematics teachers in what and how they teach, it also shows that these resources often do not do what they say they will do, nor adhere to the standards they claim to further. When it comes to the most…