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.

The purpose of this paper is to report a part of a calculus research project, about the performance of a group of pre-service mathematics teachers on two tasks on limit and differentiation of the trigonometric sine function in which the unit of angle measurement was in degrees. Most of the pre-service teachers were not cognizant of the unit of angle measurement in the typical differentiation formula, and a number of participants recognized the condition on the unit of angle measurement but did not translate this to the correct procedure for performing differentiation. The result also shows that most of the participants were not able to associate the derivative formula with the process of deriving it from the first principle. Consequently, they did not associate it with finding  . In the process of evaluating this limit, the pre-service teachers exhibited further misconceptions about division of a number by zero.

The study examines the effectiveness of employing semiosis in the teaching and learning of the Quadratic Equation. The first goal is to compare results of De Saussure and Peirce models within the semiotic theory. The second goal is to determine the commonest effective semiotic objects student teachers mostly employ to solve for the roots in quadratic equations. This research method was mixed methods concurrent and adopted both quantitative and qualitative approach. The instruments for the study were teacher-made tests and interview guide structured on the likert scale. In the teacher-made tests, two sets of twenty questions were set and distributed to the respondents. The sets of questions were similar and each twenty questions were based on De Saussure and Peirce Semiotic Models. The analyses employed both quantitative and qualitative. In the quantitative analysis, three categorical independent variables were fixed on and Pierre and De Saussaure models, objects of Pierre and De Saussaure models, and diachronicity, trichronicity, categorization and quadratic equations, after satisfying normality and independent assumptions of t-test and ANOVA techniques. The qualitative analysis with ensured anonymity, confidentiality and privacy of respondents and transcribed responses from semi-structured interview guide. The results of the commonest semiotic objects improved significantly classroom interactions with Peirce model than with De Saussure model. They perceived the Peirce model as being broader, comprehensive, universal and ICT-compliant. We therefore recommended further quasi-experimental studies on semiotic objects to improve upon the use of cultural objects.

Research on students’ perceptions of scientists is ongoing, starting with early research by Mead and Metraux in the 1950s and continuing in the present. Continued research interest in this area is likely due to scholarship suggesting adolescents’ impressions of scientists are sourced in-part from media, which influence their interests in science and identity in becoming a scientist. A significant source of images, in which adolescents (or middle school students) view science and scientists, is in their science textbooks. A qualitative content analysis explored images of scientists in three of the major U.S.-based middle grade science textbooks published in the new millennium: sixth grade biology, seventh grade earth science, and eighth grade physical science. The Draw A Scientist Test (DAST) Checklist was employed to assess scientists’ images and the stereotypes therein. From nine textbooks, 435 images of scientists were coded and analyzed by publisher and grade level / area by DAST constructs of appearance, location, careers, and scientific activities. Statistical analyses showed significant variances between grade levels and textbook publishers of scientists. Despite scientists portrayed in active endeavors, traditional tropes of the scowling, older, solitary, white male scientist persist. This study offers insight in leveraging improved images of scientists in textbooks.

Learners bring prior knowledge to their learning environments. This prior knowledge is said to have an effect on how they encode and later retrieve new information learned. This research aimed at exploring ‘A’ level mathematics learners’ understanding of the determinant concept of 3×3 matrices. A problem-solving approach was used to determine learners' conceptions and errors made in calculating the determinant. To identify the conceptions; a paper and pencil test, learner interviews, and learner questionnaires were used. Ten learners participated in the research and purposive sampling was used to select learners who are doing the syllabus 6042/2 Zimbabwe School Examination Council (ZIMSEC). Data was analyzed qualitatively through an analysis of each learners' problem-solving performance where common themes were identified amongst the learners’ work. Results from the themes showed that Advanced level learners faced some challenges in calculating the determinant of 3×3 matrices. Learners were having challenges with the place signs used in 3×3 matrices, especially when using the method of cofactors. The findings reveal that learners had low levels of engagement with the concepts and the abstract nature of the concepts was the major source of these challenges. The study recommends that; teachers should engage learners for lifelong learning and apply some mathematical definitions in real-world problems. Teachers should address the issues raised in this research during the teaching and learning process. In addition, teachers should engage learners more through seminars where learners get to mingle with others from other schools.

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 focus of this action research was to adapt Bruner’s 3-tier theory to enhance conceptual knowledge of teacher trainees on integer operations. It looks into how learners' conceptual knowledge of integer operations changes over time, as well as their attitudes toward using the 3-tier model. Eighty-two (82) teacher trainees, who were in their first year semester one of the 2020/2021 academic year were purposely selected for the study. Data was collected using test and semi-structured interviews. The study found that using Bruner’s 3-tier theory contributed to substantial gains in conceptual knowledge on integers operations among learners.  It was also found that learners proffered positive compliments about the Concrete-Iconic-Symbolic (C-I-S) construct of lesson presentation and how it built their understanding to apply knowledge on integers operations. Learners also largely proffered positive image about C-I-S construct as it aroused interest and activated unmotivated learners. On these bases, the study concludes that lessons presentations should mirror C-I-S construct in order to alleviate learning difficulties encountered on integer operations. To do this, the study suggests that workshops on lesson presentation using C-I-S construct be organized for both subject tutors, mentors and lead mentors to re-equip their knowledge and to buy-in the idea among others.

This paper reports an exploratory study on the pre-service teachers’ content knowledge on school calculus. A calculus instrument assessing the pre-service teachers’ iconic thinking, algorithmic thinking and formal thinking related to various concepts in school calculus was administered to a group of pre-service mathematics teachers. Their performance on five of the items is reported in this paper. Other than their good performance in the iconic recognition of stationary points, their recognition on points of inflexion, differentiability and notion of minimum points was relatively poor. In addition, they appeared to lack the algorithmic flexibility in testing the nature of stationary points and the formal thinking about definition of an extremum point. The implications of the findings are discussed.  

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.

This study aims 1) to determine the effectiveness of the Mind-Mapping based Aptitude Treatment Interaction model towards creative thinking and 2) to explain the mathematical creative thinking process based on the creative level. The number of participants was 26 students who took the Multivariable Calculus course in the odd semester of 2020/2021. This research used the mixed-concurrent embedded method. The data collection techniques were validation, observation, creative thinking tests, and interviews. The results showed that 1) the Mind-Mapping based Aptitude Treatment Interaction model was effective in developing creative thinking, as indicated by the average creative thinking score of the experimental class, which was higher than the control class and 2) the characteristics of students mathematical creative thinking process varied following the creative thinking levels. The students mathematical creative thinking level consists of not creative (CTL 0), less creative (CTL 1), quite creative (CTL 2), creative (CTL 3), and very creative (CTL 4). Students at the CTL 2, CTL 3, and CTL 4 can meet the aspects of fluency, flexibility, and originality.

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.

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.

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.

Preservice elementary teachers have had a variety of experiences in their math classes which influence their willingness to engage in math as well as their confidence in doing so. This study examined the responses of two sets of preservice elementary teachers, in 2017 and in 2022, to questions about their "best" and "worst" experiences in math classes. Previous research has seldom asked preservice elementary teachers to examine what they do as students to create a better math experience and research is only now beginning on how COVID-19 may have affected student behavior. Inductive analysis revealed that the emotional intelligence of teachers greatly affected preservice elementary teachers' willingness to meaningfully engage in math. For example, a recurring theme in the data was a strong sense of not wanting to appear dumb, which prevented the students from asking questions or seeking help when needed. This study demonstrates that the classroom environment plays a significant role in preservice elementary teachers' success in math, confidence and comfort level with the subject, and, undoubtedly, how they will eventually teach math to their future students.

During the Covid-19 pandemic, this study investigated the role of metacognitive awareness as a mediator in the correlation between attitude and mathematical reasoning among undergraduates who are first year university students. These studies distribute mathematical reasoning assessments, metacognitive awareness questionnaires, and attitude surveys as research data. One hundred eighty-four undergraduate students from one public institution in Malaysia's Klang Valley area participated in the research. The impact of metacognitive awareness on attitude and mathematical reasoning was studied using Version 25 of the Statistical Packages for the Social Sciences. The findings indicated that undergraduate mathematics and science education students excelled in non-mathematics and science education students in mathematical reasoning capacity. According to the findings, undergraduate mathematics and science education students had good metacognitive understanding and used more approaches in mathematical reasoning assessment. Further study implies that more research should be conducted to assess different demographics, such as institute training teachers' metacognitive awareness and attitude towards mathematical reasoning.

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.

Reflection requires someone to think in deep and express the impression of a phenomenon or an event. Reflection can be defined as a mirror to look at and see the personal insights, feelings, motivation, or purposes of individuals within a particular context and practice in a realistic way. This study examined the nature of pre-service science teachers’ reflections during the last semester of the teacher education program. There were four cases as student-teachers attending science teacher education program in northwest region of Turkey. The qualitative data, written reflections and researcher field notes were utilized and analyzed through inductive methods. The results indicated that even though pre-service science teachers learned scientific practices and inquiry, they were not able to implement due to some constraints: mentor teachers forced them to teach on a traditional basis. They could only complete the required four-hour teaching practice. Student teachers reflected on their learning as becoming a science teacher, but their actions were restricted, and they could not find supportive community in school and classroom context.

The study investigated the impact of YouTube video assisted instructions (YVAI) on pre-service teachers’(PSTs) attitudes and academic performance in chemistry classroom. A quasi-experimental design was adopted for the study. One hundred and twenty (120) Pre-Service Teachers (PSTs) pursuing primary education programme constituted the participants of the study. Sixty (60) PSTs each were non-randomly assigned to the Experimental Group (EG) and Control Group (CG). Data on PSTs’ attitude and performance were collected with PSTAS and GCPT respectively. The SPSS software version 20 was used to analyse the data to generate descriptive and inferential statistics. A non-parametric analysis was used in the inferential statistics. The attitude means rank (MR=78.62) of EG (U = 713.000, Z=-6.924, p <.001) was statistically higher than CG (MR=42.38) (U = 713.000, Z=-6.924, p <.001) after treatment. The EG after treatment recorded a mean rank (80.86) statistically higher than CG (40.14), U = 578.500, Z = -6.441, p <.001 after treatment. YVAI was proven as an effective instructional strategy that enhances learners’ altitudinal changes and performance. The study recommended the use of YouTube technological-driven instructions to support classroom instructions.