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.

This article presents an international study that documented the conceptions of atomic models held by 1062 in-service high school science teachers from 58 countries. First, a previous study on pre-service science teachers’ conceptions of atomic models was successfully replicated as a pilot study with an international sample of in-service science teachers. Teachers’ conceptions were investigated by analysing their drawings of atomic models. Based on these results, a multiple-choice questionnaire was developed for the main study. This questionnaire collected data on teachers’ conceptions of atomic models, teachers’ knowledge about their students’ conceptions of atomic models, and teachers’ use of atomic models in the classroom. The results show that the teachers’ conceptions of atomic models are almost evenly distributed over six different atomic models. These models are the Bohr model, the Rutherford model, the probability model, the orbital model, the probability orbit model, and the wave model. The vast majority of teachers assume that their students’ conceptions are centred on two historical atomic models, namely the Bohr model and the Rutherford model. Furthermore, the majority of teachers prefer to use historical atomic models over modern atomic models in the classroom. However, the findings also highlight that the use of modern atomic models in the classroom is positively correlated with growing teaching experience, and that teachers’ conceptions of atomic models and their knowledge of students’ conceptions of atomic models significantly influence teachers’ classroom practice.

This study attempts to investigate the errors and misconception that form three students reveal using symbolic equation and word-problem representations. The participants were thirty form three students, from a high school in Zimbabwe. Three mathematics teachers from the same school also took part. Data was collected from the students through a questionnaire, a test, follow up interviews and semi-structured interviews. Semi structured interviews were also conducted with the three mathematics teachers. In data analysis, the students’ written responses and data from questionnaire were qualitatively analysed to determine the nature of the students’ errors when solving quadratic equations. The results revealed that the students had difficulties in solving symbolic quadratic equations by the factorisation method as well as the use of the quadratic formula such that many misconceptions were exposed. The following types of errors were revealed: conceptual, procedural and technical. It was found out that it is an advantage for teachers to teach students with the knowledge of these errors in an effort to eliminate them.

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.

In this paper, the categories and influence of teachers’ classroom characteristics relative to effective mathematics teaching in secondary schools in Plateau state, Nigeria were examined. The aim was to see how students are assisted to learn mathematics from teachers engaging fully their professional practices fully. Exploratory and descriptive survey research methods were used to examine the trajectories. Sample for the study consisted of 60 trained mathematics teachers from secondary schools in Plateau state that participated in a week-long capacity building workshop on teaching new concepts from secondary school mathematics curriculum in Nigeria organized recently by the state chapter of the Mathematics Association of Nigeria. Purposive sampling technique was used to select the sample based on the fact that the study targeted only mathematics teachers that participated in the capacity building workshop. A 52-item TCCQ on teacher effectiveness, interest, rapport with students, etc. was used for data collection. The findings from the study revealed that mathematics teachers’ ability to teach effectively is significantly associated with many factors including the use of different strategies (χ2=52.75), revision (χ2=47.13), good lesson plans (χ2=53.93) and being friendly with students (χ2=35.66). There was no significant variation regarding how the characteristics influence teacher effectiveness based on qualification (F2, 58=0.689). Among other things, therefore, it was recommended that teachers should be committed to teaching mathematics effectively in the classroom by taking cognizance of the variables especially designing of good lesson plans and previous knowledge irrespective of their qualifications.

As international concerns about the prevalence of out-of-field teaching have grown, so have discussions about how to support out-of-field teachers. In Ireland, the Professional Diploma in Mathematics for Teaching, a two-year professional development program, was created for out-of-field mathematics teachers. A pre-test, post-test, and final survey examined the program’s impact on participating teachers’ mathematical knowledge, confidence in teaching curricular content, and classroom practice. Findings offer evidence of development in participating teachers’ mathematical knowledge and self-efficacy after completing the program. They also raise important concerns about persistent weaknesses in participating teachers’ mathematical knowledge, particularly related to key areas of the curriculum.

In Nigeria, most teachers among other things lack the necessary teaching skills, and mastery of subject matter for effective teaching of mathematics at the secondary school level. These deficiencies have often resulted in high and repeated failure rates in national and standard mathematics examinations. The present study investigated the ability of mathematics teachers to construct practical and realistic word problems in bearing and distance toward mitigating the deficiencies. The research methods adopted were exploratory and descriptive surveys due to the need to explore and analyze the abilities using quantitative techniques. Sample consisted of 292 (35.48%) mathematics teachers who took part in the in-service training workshop organized by the Mathematical Association of Nigeria (MAN) in Plateau state, Nigeria. Purposive sampling technique was used to select the sample that involved the workshop participants only. The instrument ‘construction of practical and realistic word problems in bearing and distance test (CPRWPBDT)’ was used for data collection while the analysis was carried out using simple percentages, mean scores and one-way ANOVA. The findings of the study among other things revealed that the mathematics teacher participants constructed practical and realistic word problems in bearing and distance within 91.67% completion rate, 70.45% of the problems constructed were within the context, at least 75% rate of correctness with little difficulties/errors was observed in sketching (65.90%), and reality (40.90%). The variations observed within the participants in the construction of the problems were statistically not significant. Thus it was recommended among other things that mathematics teachers should undergo regular in-service workshop training to help in developing essential skills themselves for constructing practical/realistic word problems in bearing and distance; and should avoid unnecessary errors for meaningful teaching and learning of bearing and distance.

This study investigated how implementing inquiry-based learning (IBL) can be an effective tool for an instructor to conduct rich formative assessment. Many researchers have documented that IBL promotes active learning from students’ learning perspective. However, little research examines how IBL affects instructors’ teaching practice from teaching perspective. Based on the data collected from a Calculus II class, the author discussed how the structure of IBL class produced rigorous on-going formative assessment during classroom teaching from the three aspects: helping the instructor “see” student thinking; helping the instructor “see” the level of student understanding; helping the instructor catch teachable moments. The rigorous on-going formative assessment, in turn, helped change student classroom behaviors in terms of asking more questions, showing deep thinking, and gaining confidence.

Mathematics teaching efficacy is an important construct as confidence in one’s ability to teach influences teaching practices. This paper explores pre-service primary teachers’ mathematics teaching efficacy on entry to initial teacher education and the extent that pre-tertiary mathematics experiences and resultant beliefs affected their mathematics teaching efficacy. A mixed-methods approach combined the Mathematics Teaching Efficacy Beliefs Instrument (N=420) and qualitative interviews (N=30). The findings suggest medium personal mathematics teaching efficacy among participants with limited conceptions of what mathematics teaching involves. While uncertain regarding their immediate teaching ability, participants reported confidence regarding their potential. Mathematics teaching outcome expectancy was high; however, an undercurrent of conviction exists that external factors, most notably learners’ natural mathematical ability, are critical to student learning.

The study on mathematical performance was significant enough to be studied further to measure students' self-efficacy. Although studies on student self-efficacy in math performance from a gender perspective were abundant, studies on this relationship from the perspectives of ethnic culture and gender were scarce. Therefore, the objective of this study was to examine the self-efficacy of Bugis Junior High School students in solving math problems based on gender. The researchers used an algebra problem in the context of the Bugis ethnic culture. For this data set, two of 25 students at a public junior high school in Bone, South Sulawesi, Indonesia, were interviewed based on ethnicity and gender. Qualitatively, the triangulation technique was employed for data analysis. The study results revealed that male students outperformed girls in terms of self-efficacy, namely magnitude, strength, and generality, in math performance. Furthermore, female students had lower self-efficacy in terms of confidence, supportive experience in completing math tasks, and confidence in their ability to complete math tasks in similar or different contexts, compared to male students, who had higher self-efficacy. This result provided new knowledge by exploring the characteristics of students' self-efficacy by integrating ethnicity and gender.

The current study investigated whether: (1) using an interactive presentation (IP) platform could affect the amount of usage of the practices of making orchestrating mathematical discourse- sequencing and connecting students' responses. (2) using an interactive presentation (IP) platform could affect the amount of narratives constructed by students. Fifty seventh-grade students participated in the study; those students were divided into control and experimental groups. Qualitative and quantitative analyses were performed based on voice recordings and field notes. The results revealed that the teacher using (IP) asked nearly three times more questions that connected students’ responses (i.e., questions that involved valuing students' ideas, exploring students' answers, incorporating students’ background knowledge, and encouraging student-to-student communication). We also saw that the students participated in the learning processes. The students in the experimental group presented three times as many narratives as those in the control group. We present several excerpts from the transcripts of the classroom discussions to illustrate our findings. Discussion of the implications and limitations of these results and make recommendations based on those results.

Numerical literacy refers to the knowledge and ability to use various numbers and basic mathematical symbols to solve problems, while math self-concept means the assessment of students’ skills, abilities, enjoyment, and interest in the subject. However, children with special needs and normal students in inclusive Elementary Schools are yet to sufficiently acquire learning that accommodates literacy and maths self-concept. This causes a need for the implementation of a children-friendly learning process. Therefore, this study aimed to identify the factors influencing the numeracy level and math self-concept, and also explore the obstacles in implementing children-friendly learning in order to facilitate students’ abilities. A qualitative method was applied because of in-depth data exploration regarding children with special needs, while the utilized instruments include tests, questionnaires, and interviews. Both the data collected and the analysis are qualitative, which are obtained through excavation, identification, and description. Consequently, this paper was able to (a) describe the factors influencing the numeracy level and math self-concept in inclusive elementary schools; (b) explore the barriers to implementing children-friendly learning; and (c) identify the relationship between students’ numeracy and math self-concept.

This paper reports on part of an ongoing large-scale research on the need to improve science teaching and learning through investigating the Pedagogical Content Knowledge (PCK) of biology teachers for the topic Biodiversity. Six factors have been seen to affect teacher PCK, i.e., content knowledge, knowledge of students, science teaching orientations, knowledge of assessment, knowledge of instructional strategies and knowledge of the curriculum. This research aimed to examine the teacher’s level of content knowledge (CK). A qualitative research paradigm was adopted, and a case study research design used. The case (unit of analysis) was Biology teacher CK, and the subjects were the four teacher participants purposively selected. Lesson observations, teacher interviews and learner questionnaires were used to collect data on teacher CK. A content knowledge analytical framework consisting of five constructs was designed and used to analyse the teacher CK and data triangulated with data collected from interviews and questionnaires. This research revealed that ‘A’ level Biology teachers’ CK vary from teacher to teacher depending on several factors which include teacher identity, planning, workshopping, and motivation among others. Of the four Biology teacher participants, two had adequate CK and the other two exhibited inadequate CK. Inadequate CK was attributed to lack of planning, non-exposure to workshops and lack of teacher motivation. Consequently, this research recommends supervision of teachers from school level to national level, a series of teacher workshops on the demands of the competence-based curriculum and constructive teacher identity as well as introduce factors that enhance teacher motivation. Further research on the content knowledge of Biology teachers in other learning areas is recommended.

The purpose of this study was to evaluate synchronous and asynchronous mathematics teaching modalities at Isabela State University. The qualitative research method was used to collect information, opinions, and experiences of Isabela State University mathematics faculty in employing synchronous and asynchronous modes in teaching mathematical courses in terms of strengths, weaknesses, possibilities, and problems. The study's subjects were 15 Mathematics Instructors chosen at random from Isabela State University's nine campuses. A structured interview was created and distributed to participants using Google Form. The limitations on face-to-face encounters prompted the use of such data-gathering technique. The researcher followed up with another video call interview to validate the participants' responses. The data was transcribed and processed using thematic analysis. The findings demonstrated that the synchronous and asynchronous learning modalities both have strengths and disadvantages that influence the quality of the teaching-learning process throughout the epidemic. Given this, distant learning is thought to be more effective when both modalities are used rather to just one of the aforementioned. This is because the strengths of one of the two modalities can solve the flaws highlighted in the other. As a result, mathematics instructors may receive more in-depth training in both asynchronous and synchronous teaching approaches, as well as strategies for becoming more successful teachers during the present school closures.

The ability of students to build problem-solving models using procedural knowledge can be viewed from several aspects, including Mastery of Mathematical Problem Solving (MPS), understanding concepts and application of concepts, the relationship between learning outcomes of mathematics and interest in learning, and examine the contribution of the ability to understand concept problems, the application of concepts to the ability of MPS, as well as student difficulties and some of the advantages of students in solving problems. This experimental study aims to explain the effect of the MPS model using procedural knowledge on solving mathematical problems for Junior High School Students (JHSS). The findings showed that 1) The MPS method using procedural knowledge significantly improved learning outcomes, but the mastery of MPS for JHSS was still unsatisfactory. 2) MPS teaching could still not improve meaningful learning outcomes. However, when JHSS applied the concepts, calculations, and problem-solving aspects, MPS teaching improved meaningful learning outcomes. 3) Students' interest in learning mathematics in the two sample classes was classified as positive. Shortly, MPS teaching accustoms students to think systematically and creatively and not just give up on the problems they face.

This study tested hypotheses of a hypothetical model determining the influence of teacher clarity and real-world applications while teaching group theory concepts on students’ achievement in modern algebra. The data collected from 139 undergraduate students were analyzed by regression analysis using Stata14’s structural equation model building and estimation. The path regression analysis of the model using SEM model building and estimation confirmed the research hypotheses. First, the utilization of real-world application problems while teaching group theory concepts has a significant influence on students’ achievement in modern algebra. Second, the clear presentation of group theory concepts by the teacher has a significant influence on students’ achievement in modern algebra. Finally, both teachers’ clear presentation of group theory concepts and utilization of its real-world applications have a significant influence on students’ achievement in modern algebra.

Out-of-field teaching in science is a phenomenon in many secondary schools across the world. While the reasons for out-of-field teaching are complex, its incidence is heightened in low socio-economic communities and in regional and remote school locations. Research on out-of-field science teaching in secondary schools has tended to focus on teacher competence, particularly in relation to pedagogical content knowledge. However, while teachers’ beliefs and teaching practices within their specialist subject are shown to be related, it is unclear how teachers’ beliefs and practices alter when teaching across subject boundaries. Using a boundary-crossing lens, where teachers engage in passing back and forth between different contexts, this study explored the relationship between teachers’ beliefs about their in-field and out-of-field discipline (science) and the connections to their teaching practice. Interview data, including a video-stimulated interview of a lesson in a teacher’s specialist field and then a subsequent out-of-field lesson, were analysed using the framework of a belief that investigated the relationships between in-field and out-of-field beliefs and practices. Findings indicate that those who teach science out-of-field revert to traditional ways of teaching, despite being more open and adventurous in their in-field discipline areas. However, there were significant instances of boundary crossing with their pedagogy to support their teaching – both in-field and out-of-field. These findings support the development of structured mechanisms and strategies to assist teachers to cross boundaries to establish new and unique interdisciplinary practices.

In terms of learning and academic level, this study compares the development of mathematical creative thinking skills between students who use the Blended Learning Model with GeoGebra support (BLM-G) and students who use the Blended Learning Model without GeoGebra aid (BLM-non-G). A nonequivalent control-group design and a quasi-experimental research methodology are being used. The participants in this study were eighth-grade SMPN students in Ternate City, Indonesia. The research sample was 125 people from two schools with different grade levels. The instrument used is a mathematical creative thinking ability test. Research result; Learning using BLM-G influences students' mathematical creative thinking abilities at high and medium school levels, with very high categories. When compared to kids who learn using BLM-non-G learning, students who use BLM-G learning exhibit greater growth in their capacity for both mathematical and creative thought. This is based on high school level pupils. Kids who study using BLM-G learning and students who learn using BLM-non-G learning exhibit equal increases in their capacity for mathematical and creative thought at the middle school level.

The study investigated the attitudes of Biology teachers towards the Biology Competence-Based Curriculum (BCBC) and their instructional practices at the lower secondary school level in Nyamagabe district, Rwanda. A descriptive survey design was adopted. Also, a purposive sampling technique was used to select 26 (16 male and 10 female) teachers of Biology. Data were collected using a questionnaire addressed to Biology teachers in selected schools and analyzed and presented in terms of frequencies, percentages, mean, and standard deviation. A one-way ANOVA was employed in the hypothesis testing. The findings indicated that these teachers had positive attitudes towards the implementation of BCBC. As for female ones, they had more positive attitudes towards BCBC implementation than the male ones. Considering those from boarding schools, they had a more positive attitude than the ones from day schools. Additionally, teachers with less teaching experience had more favorable attitudes than those with long experience. Teachers' age did not have any effect on their attitudes. The study also revealed that teachers of Biology rarely applied competence-based approaches in their teaching and assessment processes of students’ learning. It was inferred that the usage of CBC approaches differed significantly among teachers from boarding and day schools. The usage of CBC assessment methods did not differ significantly among teachers. From the findings, it was concluded that CBC seems not to be effectively implemented in the lower secondary schools under the study. Consequently, a recommendation was made to facilitate Biology teachers in schools with in-service training for professional development.

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.