Using engineering design to teach science requires teachers to engage in noticing, interpreting, and responding to students’ needs in real-time. While research has begun to focus on how elementary teachers do so, less is known about how teachers instructionally support and optimize students’ ideas through engineering design feedback. In this study we investigate what instructional moves two elementary teachers’ employ to leverage students’ ideas and reasoning and create opportunities for students to exchange design feedback. Data were gathered using classroom observations of teachers’ implementations of a design task focused on sound and energy transformation. Observations were coded for teachers’ use of high-leverage practices, and event maps were created to chronicle teachers’ implementation of the task from start to finish. Event maps were analyzed and compared for discrete instructional activities and modes of classroom organization that supported opportunities for feedback. Findings suggested that while teachers used similar instructional moves, how and when they created opportunities for student design feedback differed, resulting in diverse ways of assessing and supporting students’ understandings. Implications suggest design feedback as both a purposeful and naturally present phenomenon throughout the design process, reflective of the nature of engineering design.

Preservice mathematics teachers' beliefs about actions related to the use of the technological tools in teaching mathematics may affect how they are going to use them in their classroom activities. However, there is a limited evidence of what beliefs they hold on their intended actions of using technological tools in teaching mathematics. This study presents two preservice high school mathematics teachers' actional beliefs related to their intended actions in teaching geometric transformations (GTs) using Geometer's Sketchpad (GSP). The study comprised of a series of five task-based qualitative interviews with each of two senior undergraduate preservice teachers at a medium-sized public university in the Rocky Mountain Region of the United States. This study used a radical constructivist grounded theory (RCGT) with five assumptions—symbiosis, voice, cognition, adaptation, and praxis as a theoretical framework to guide the study process. The thematic findings of the study included four in vivo categories of their beliefs associated with actions of teaching GTs with GSP – assessment of student learning, engaging students in a group activity in exploring GTs with GSP, engaging students in individual activity in exploring GTs with GSP, and exploring GTs with GSP as 'suck it up and do it.' Pedagogical implications of these categories have been discussed.

This mixed-methods, investigative case study explores the experience of a virtual learning environment (VLE) change and its effect on the use of digital learning tools specifically, and teaching practice more generally, for chemistry lecturers at TU Dublin (Ireland) prior to pandemic of the coronavirus disease COVID-19. Initially, a questionnaire examined the different teaching identities the participating lecturers might have and how they relate to the literature. These identities were examined under the following themes: sense of achievement, motivational factors for innovation, innovation positioning, as well as social and organizational factors influencing the decision making. A visual approach of representing the questionnaire data, termed ‘Lecturer Landscapes’, was developed which uncovered new trends based on the biographical descriptors of the research population. Subsequent interviews led to a more detailed investigation of the themes noted in the questionnaire and the Lecturer Landscapes to more holistically capture the professional identity of each respondent. The lens of experience during a VLE change was used to frame each respondent’s professional identity in context. Overall, a VLE change does not have to effect teaching practice and can be experienced as a positive change in teaching and learning. It was also noted that innovation can only occur when specific, and individual, needs and problems are addressed and when personal development is promoted by intrinsic, rather than extrinsic, motivational factors.

Mathematical connection ability is very important to be mastered by prospective mathematics teacher students as competency to teach in secondary schools. However, the facts show that there are still many students who have weak mathematical connection abilities. This qualitative descriptive study aimed to explore how the process, and product of the mathematical connection made by prospective mathematics teacher students when solving the integral calculus problems based on their prior knowledge. The research subjects were 58 students who were prospective high school mathematics teachers at the University of Jember, Indonesia. Data were collected using documentation, questionnaire, test, and interview methods. After the test results of all subjects were analyzed, six students were interviewed. To find the match between the results of the written test and the results of the interview, a triangulation method was carried out. Data analysis used descriptive qualitative analysis with steps of data categorization, data presentation, interpretation, and making conclusions. The results show that the research subjects have connected and used mathematical ideas in the form of procedures, facts, concepts/principles, and representations in solving integral calculus problems. Students with high prior knowledge abilities can make better mathematical connections than students with moderate and low prior abilities. From these results, it is recommended that lecturers need to improve students' prior knowledge and train the students more intensely to solve integral calculus problems so all students can develop their mathematical connection abilities into very strong categories.

3D printer technology and 3D design are used in many fields and are gaining various uses day by day. It is seen that the quality of education and training has increased with the effective use of 3D technology in the education and training environment. This study aims to investigate the attitudes of Pre-Service Teachers about the use of 3D printer activities made with Tinkercad in science education. 43 science pre-service teachers participated in the study, which lasted 8 weeks. A mixed research method was used in this study. The problem-solving scale and the attitude scale towards the use of 3D printers in science education were applied to the pre-service teachers. To collect the research data, the attitude scale was applied as a pre-test and post-test. For Paired samples, a t-test was applied and analyses were performed. In qualitative studies, semi-structured student interview questions were applied. According to the findings of the study, there was a significant increase in students' positive attitudes towards the use of 3D printers in science education. Tinkercad and 3D printer trainings have been given and applications have been made within the scope of these trainings. There have been 6 activities related to 3D printers. Thanks to 3D printers, students have the opportunity to present creative ideas and things they imagine to life by making designs in their minds. It seems that abstract concepts related to the sciences are embodied with a 3D printer and turned into tangible objects. Examining a physical object makes it easier for students to identify mistakes they have made in designs. It is seen that they do creative and solution-oriented work against the problems they encounter. Thus, it is predicted that learning will be more permanent and effective.

In the domain of engineering education, the crucial role of mathematics, especially Calculus, cannot be overstated, as it lays the foundational groundwork for numerous sciences, technology, engineering and mathematics (STEM) courses. The integration of mathematics into STEM disciplines is achieved through the practical application of mathematical concepts in real-world scenarios or in conjunction with other STEM subjects, thereby enhancing the coherence of engineering studies and acting as a significant motivational catalyst for students. This paper presents an analytical narrative of a practical mathematics assignment, woven into the Calculus curriculum and other STEM courses from 2013 to 2018. It delves into the potential impacts of these practical assignments on student performance and attitudes by evaluating data sourced from final exam scores and anonymous course surveys, both before and after the intervention period. Through the analysis of an extensive dataset comprising 1526 final exam scores, this study endeavors to make a substantive contribution to Future Technology Studies (FTS), focusing on the strategic harmonization of mathematics and STEM courses to enrich the educational experience and foster a more cohesive and applied learning framework in these disciplines.

Comparison of mathematics textbooks between Indonesia and Singapore is one way to assess the educational process. This article provides insight into how mathematical concepts are taught and applied in problem-solving in each country. The study provides knowledge about how mathematical concepts are constructed by teachers and students and implemented in problem-solving between countries. This study aims to compare task designs in high school mathematics textbooks between Indonesia and Singapore based on the type of task, technique, technology, and theory used, with a focus on cubes and cuboids. The comparative analysis of the two books uses praxeological theory, the main construction of Didactic Anthropology Theory, with reference to epistemological model (REM) model analysis. The research results show that there are differences in the approaches, methods, and habits used in task design in the two countries. The techniques, technology and theories found in the two task designs show that Indonesian mathematics textbooks use more verification and drawing up conclusions which are influenced by perceptual techniques. Meanwhile, the task of designing Singapore's mathematics textbooks involves more direct investigations into forming students' knowledge through physical and operational techniques. The techniques, technology, and theories used in both designs influence the number of learning obstacles. Epistemological constraints occur in Indonesian textbooks and only a few in Singapore textbooks. These findings provide insight into how to build mathematical knowledge for students through good assignment design based on a country's educational character.

Research consistently highlights the importance of promoting creativity in curricula worldwide and within school settings. However, teachers often fail to recognize mathematical creativity (mainly described and evaluated through fluency, flexibility, originality, and elaboration) and are usually ill-prepared to enhance it in their students. Few studies have incorporated educational programs focused on mathematical creativity, showing positive results in enriching participants' knowledge and perception of creativity. Nevertheless, participants' teaching practices were not observed, leading to uncertainty about whether these participants could integrate opportunities for students’ development of mathematical creativity in their lessons. In this qualitative study, we attempt to bridge this gap by observing teachers' practices before and after an intervention focused on mathematical creativity. Seven in-service primary school Greek teachers participated in the study. Their teaching practices were examined through classroom observation, using an observation protocol, before and after their voluntary participation in an educational program aimed at enriching their knowledge of mathematical creativity and their ability to cultivate it in the classroom. Observational data were coded and analyzed using thematic analysis. Results showed that prior to the intervention, participants sparsely employed creativity-fostering approaches in their teaching. However, after the intervention, they significantly increased the time spent on creativity-provoking tasks, utilizing various creativity-promoting approaches and primarily focusing on developing fluency, flexibility, and generating new knowledge. Nevertheless, they did not significantly develop their skills in originality and elaboration, indicating the need for further support in cultivating these aspects of creativity. Future implications for professional teacher training and mathematics textbook writing are discussed.

For decades, a global trend in mathematics curriculum development has placed greater emphasis on learning goals that seek to capture different kinds of processes that students should master. For Danish primary and secondary mathematics education, these ambitions are expressed in terms of a set of mathematical competencies, in line with the so-called KOM framework. However, it has proved challenging to implement the competencies in mathematics classrooms and actual teaching practice. Matematrix is a series of Danish mathematics textbooks for grades K-9 designed to support mathematics teachers in facing this challenge. Following a short introduction to the KOM framework, I – as one of the designers and authors of the textbooks – present a key element in this endeavour: A three-dimensional model of content and objectives combining mathematical competencies, mathematical core concepts and grade levels. I then describe the use of this model in the specific case of Matematrix at three different levels of textbook design: The structure of the general content of the books, the focal points for each chapter, and the development of different kinds of tasks for the students to work with.