Search results for: engineering mathematics

Authors: John E. Boberg, Steven J. Bourgeois

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The decline in student engagement and motivation through the middle years is well documented and clearly associated with a decline in mathematics achievement that persists through high school. To combat this trend and, very often, to meet high-stakes accountability standards, a growing number of parents, teachers, and schools have implemented various methods to incentivize learning. However, according to Self-Determination Theory, forms of incentivized learning such as public praise, tangible rewards, or threats of punishment tend to undermine intrinsic motivation and learning. By focusing on external forms of motivation that thwart autonomy in children, adults also potentially threaten relatedness measures such as trust and emotional engagement. Furthermore, these controlling motivational techniques tend to promote shallow forms of cognitive engagement at the expense of more effective deep processing strategies. Therefore, any short-term gains in apparent engagement or test scores are overshadowed by long-term diminished motivation, resulting in inauthentic approaches to learning and lower achievement. The current study focuses on the relationships between student trust, engagement, and motivation during these crucial years as students transition from elementary to middle school. In order to test the effects of controlled motivational techniques on achievement in mathematics, this quantitative study was conducted on a convenience sample of 22 elementary and middle schools from a single public charter school district in the south-central United States. The study employed multi-source data from students (N = 1,054), parents (N = 7,166), and teachers (N = 356), along with student achievement data and contextual campus variables. Cross-sectional questionnaires were used to measure the students’ self-regulated learning, emotional and cognitive engagement, and trust in teachers. Parents responded to a single item on incentivizing the academic performance of their child, and teachers responded to a series of questions about their acceptance of various incentive strategies. Structural equation modeling (SEM) was used to evaluate model fit and analyze the direct and indirect effects of the predictor variables on achievement. Although a student’s trust in teacher positively predicted both emotional and cognitive engagement, none of these three predictors accounted for any variance in achievement in mathematics. The parents’ use of incentives, on the other hand, predicted a student’s perception of his or her controlled motivation, and these two variables had significant negative effects on achievement. While controlled motivation had the greatest effects on achievement, parental incentives demonstrated both direct and indirect effects on achievement through the students’ self-reported controlled motivation. Comparing upper elementary student data with middle-school student data revealed that controlling forms of motivation may be taking their toll on student trust and engagement over time. While parental incentives positively predicted both cognitive and emotional engagement in the younger sub-group, such forms of controlling motivation negatively predicted both trust in teachers and emotional engagement in the middle-school sub-group. These findings support the claims, posited by Self-Determination Theory, about the dangers of incentivizing learning. Short-term gains belie the underlying damage to motivational processes that lead to decreased intrinsic motivation and achievement. Such practices also appear to thwart basic human needs such as relatedness.

Keywords: controlled motivation, student engagement, incentivized learning, mathematics achievement, self-determination theory, student trust

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Authors: Atara Shriki, Ilana Lavy

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Teaching for the first time an online course dealing with the history of mathematics, we were struggling with questions related to the design of a proper learning environment (LE). Thirteen high school mathematics teachers, M.Ed. students, attended the course. The teachers were engaged in independent reading of mathematical texts, a task that is recognized as complex due to the unique characteristics of such texts. In order to support the learning processes and develop skills that are essential for succeeding in learning online (e.g. self-regulated learning skills, meta-cognitive skills, reflective ability, and self-assessment skills), the LE comprised of three components aimed at “scaffolding” the learning: (1) An online "self-feedback" questionnaires that included drill-and-practice questions. Subsequent to responding the questions the online system provided a grade and the teachers were entitled to correct their answers; (2) Open-ended questions aimed at stimulating critical thinking about the mathematical contents; (3) Reflective questionnaires designed to assist the teachers in steering their learning. Using a mixed-method methodology, an inquiry study examined the learning processes, the learners' difficulties in reading the mathematical texts and on the unique contribution of each component of the LE to the ability of teachers to comprehend the mathematical contents, and support the development of their learning skills. The results indicate that the teachers found the online feedback as most helpful in developing self-regulated learning skills and ability to reflect on deficiencies in knowledge. Lacking previous experience in expressing opinion on mathematical ideas, the teachers had troubles in responding open-ended questions; however, they perceived this assignment as nurturing cognitive and meta-cognitive skills. The teachers also attested that the reflective questionnaires were useful for steering the learning. Although in general the teachers found the LE as supportive, most of them indicated the need to strengthen instructor-learners and learners-learners interactions. They suggested to generate an online forum to enable them receive direct feedback from the instructor, share ideas with other learners, and consult with them about solutions. Apparently, within online LE, supporting learning merely with respect to cognitive aspects is not sufficient. Leaners also need an emotional support and sense a social presence.

Keywords: cognitive and meta-cognitive skills, independent reading of mathematical texts, online learning environment, self-regulated learning skills

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Authors: Ozgul Kartal, Wade Tillett, Lyn D. English

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Despite its global significance in curricula, mathematical modeling encounters persistent disparities in recognition and emphasis within regular mathematics classrooms and teacher education across countries with diverse educational and cultural traditions, including variations in the perceived role of mathematical modeling. Over the past two decades, increased attention has been given to the integration of mathematical modeling into national curriculum standards in the U.S. and other countries. Therefore, the mathematics education research community has dedicated significant efforts to investigate various aspects associated with the teaching and learning of mathematical modeling, primarily focusing on exploring the applicability of modeling in schools and assessing students', teachers', and preservice teachers' (PTs) competencies and engagement in modeling cycles and processes. However, limited attention has been directed toward examining potential resistance hindering teachers and PTs from effectively implementing mathematical modeling. This study focuses on how PTs, without prior modeling experience, resist and/or embrace mathematical modeling and its pedagogy as they learn about models and modeling perspectives, navigate the modeling process, design and implement their modeling activities and lesson plans, and experience the pedagogy enabling modeling. Model eliciting activities (MEAs) were employed due to their high potential to support the development of mathematical modeling pedagogy. The mathematical modeling module was integrated into a mathematics methods course to explore how PTs embraced or resisted mathematical modeling and its pedagogy. The module design included reading, reflecting, engaging in modeling, assessing models, creating a modeling task (MEA), and designing a modeling lesson employing an MEA. Twelve senior undergraduate students participated, and data collection involved video recordings, written prompts, lesson plans, and reflections. An open coding analysis revealed acceptance and resistance toward teaching mathematical modeling. The study identified four overarching themes, including both acceptance and resistance: pedagogy, affordance of modeling (tasks), modeling actions, and adjusting modeling. In the category of pedagogy, PTs displayed acceptance based on potential pedagogical benefits and resistance due to various concerns. The affordance of modeling (tasks) category emerged from instances when PTs showed acceptance or resistance while discussing the nature and quality of modeling tasks, often debating whether modeling is considered mathematics. PTs demonstrated both acceptance and resistance in their modeling actions, engaging in modeling cycles as students and designing/implementing MEAs as teachers. The adjusting modeling category captured instances where PTs accepted or resisted maintaining the qualities and nature of the modeling experience or converted modeling into a typical structured mathematics experience for students. While PTs displayed a mix of acceptance and resistance in their modeling actions, limitations were observed in embracing complexity and adhering to model principles. The study provides valuable insights into the challenges and opportunities of integrating mathematical modeling into teacher education, emphasizing the importance of addressing pedagogical concerns and providing support for effective implementation. In conclusion, this research offers a comprehensive understanding of PTs' engagement with modeling, advocating for a more focused discussion on the distinct nature and significance of mathematical modeling in the broader curriculum to establish a foundation for effective teacher education programs.

Keywords: mathematical modeling, model eliciting activities, modeling pedagogy, secondary teacher education

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Authors: Juan Torralba

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Student digital artifacts were investigated, utilizing a qualitative exploratory research design to understand the ways in which students represented their knowledge of seventh-grade proportionality concepts as they participated in maker-based activities that culminated in the creation of digital 3-dimensional models of their dream homes. Representations of the geometric and numeric dimensions of proportionality were analyzed in the written, verbal, and visual data collected from the students. A directed content analysis approach was utilized in the data analysis, as this work aimed to build upon existing research in the field of maker-based STEAM Education. The results from this work show that students can represent their understanding of proportional reasoning through open-ended written responses more accurately than through verbal descriptions or digital artifacts. The geometric and numeric dimensions of proportionality and their respective components of attributes of similarity representation and percents, rates, and ratios representations were the most represented by the students than any other across the data, suggesting a maker-based instructional approach to teaching proportionality in the middle grades may be promising in helping students gain a solid foundation in those components. Recommendations for practice and research are discussed.

Keywords: learning through making, maker-based education, maker education in the middle grades, making in mathematics, the maker movement

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Authors: Natalia Podkhodova, Olga Sheremeteva, Mariia Soldaeva

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Creating favorable conditions for students’ comprehension of mathematical content is one of the primary problems in teaching mathematics in secondary school. Psychology research has demonstrated that positive comprehension becomes possible when new information becomes part of student’s subjective experience and when linkages between the attributes of notions and various ways of their presentations can be established. The fact of comprehension includes the ability to build a working situational model and thus becomes an important means of solving mathematical problems. The article describes the implementation of a holistic approach to teaching mathematics designed to address the primary challenges of such teaching, specifically, the challenge of students’ comprehension. This approach consists of (1) establishing links between the attributes of a notion: the sense, the meaning, and the term; (2) taking into account the components of student’s subjective experience -emotional and value, contextual, procedural, communicative- during the educational process; (3) links between different ways to present mathematical information; (4) identifying and leveraging the relationships between real, perceptual and conceptual (scientific) mathematical spaces by applying real-life situational modeling. The article describes approaches to the practical use of these foundational concepts. Identifying how proposed methods and technology influence understanding of material used in teaching mathematics was the research’s primary goal. The research included an experiment in which 256 secondary school students took part: 142 in the experimental group and 114 in the control group. All students in these groups had similar levels of achievement in math and studied math under the same curriculum. In the course of the experiment, comprehension of two topics -'Derivative' and 'Trigonometric functions'- was evaluated. Control group participants were taught using traditional methods. Students in the experimental group were taught using the holistic method: under the teacher’s guidance, they carried out problems designed to establish linkages between notion’s characteristics, to convert information from one mode of presentation to another, as well as problems that required the ability to operate with all modes of presentation. The use of the technology that forms inter-subject notions based on linkages between perceptional, real, and conceptual mathematical spaces proved to be of special interest to the students. Results of the experiment were analyzed by presenting students in each of the groups with a final test in each of the studied topics. The test included problems that required building real situational models. Statistical analysis was used to aggregate test results. Pierson criterion was used to reveal the statistical significance of results (pass-fail the modeling test). A significant difference in results was revealed (p < 0.001), which allowed the authors to conclude that students in the study group showed better comprehension of mathematical information than those in the control group. Also, it was revealed (used Student’s t-test) that the students of the experimental group performed reliably (p = 0.0001) more problems in comparison with those in the control group. The results obtained allow us to conclude that increasing comprehension and assimilation of study material took place as a result of applying implemented methods and techniques.

Keywords: comprehension of mathematical content, holistic approach to teaching mathematics in secondary school, subjective experience, technology of the formation of inter-subject notions

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Authors: Kamolrat Turner, Somporn Rakkwamsuk, Ladda Leungratanamart

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The aim of this descriptive study was to determine the perception of 21^st century skills among nursing professors and nursing students at Boromarajonani College of Nursing, Chonburi. A total of 38 nursing professors and 75 second year nursing students took part in the study. Data were collected by 21^st century skills questionnaires comprised of 63 items. Descriptive statistics were used to describe the findings. The results have shown that the overall mean scores of the perception of nursing professors on 21^st century skills were at a high level. The highest mean scores were recorded for computing and ICT literacy, and career and leaning skills. The lowest mean scores were recorded for reading and writing and mathematics. The overall mean scores on perception of nursing students on 21^st century skills were at a high level. The highest mean scores were recorded for computer and ICT literacy, for which the highest item mean scores were recorded for competency on computer programs. The lowest mean scores were recorded for the reading, writing, and mathematics components, in which the highest item mean score was reading Thai correctly, and the lowest item mean score was English reading and translate to other correctly. The findings from this study have shown that the perceptions of nursing professors were consistent with those of nursing students. Moreover, any activities aiming to raise capacity on English reading and translate information to others should be taken into the consideration.

Keywords: 21st century skills, perception, nursing instructor, nursing student

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Authors: G. S. Androulakis, G. Deli, M. Kaisari, N. Mihos

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Teaching practices at the university level have changed and developed during the last decade. Implementation of inverted classroom method in secondary education consists of a well-formed basis for academic teachers. On the other hand, distance learning is a well-known field in education research and widespread as a method of teaching. Nonetheless, the new pandemic found many Universities all over the world unprepared, which made adaptations to new methods of teaching a necessity. In this paper, we analyze a model of an inverted university classroom in a distance learning context. Thus, the main purpose of our research is to investigate students’ difficulties as they transit to a new style of teaching and explore their learning development during a semester totally different from others. Our teaching experiment took place at the Business Administration department of the University of Patras, in the context of two courses: Calculus, a course aimed at first-year students, and Statistics, a course aimed at second-year students. Second-year students had the opportunity to attend courses in the university classroom. First-year students started their semester with distance learning. Using a comparative study of these two groups, we explored significant differences in students’ learning procedures. Focused group interviews, written tests, analyses of students’ dialogues were used in a mixed quantity and quality research. Our analysis reveals students’ skills, capabilities but also a difficulty in following, non-traditional style of teaching. The inverted classroom model, according to our findings, offers benefits in the educational procedure, even in a distance learning environment.

Keywords: distance learning, higher education, inverted classroom, mathematics teaching

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Authors: Alhassan Dramani Yakubu

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The primary purpose of this study was to analyze effects that participating in sporting activities has on academic performance among students at Yaa Asantewaa Girls’ Senior High School. To dig out the main objective of the study, descriptive survey design was employed. The study used 45 respondents comprising of 25 student – athletes and 20 non-student – athletes. The purposive sampling and stratified random sampling technique were used to sample population of 455 students involved. The academic performance of sports participants is compared with those of non – participants in terms of their outcomes in the form of grades from mathematics. Data was obtained from the sample by the use of questionnaire which was self - administered. The questionnaire sought information on level of student’s participation in sports and importance of sports participation to students. Results revealed that participation in sporting activities is associated with higher grades among students. The analysis reinforces the idea that apart from their health benefits for participants, sporting activities lead to the attainment of the performance goals to which higher institutions aspire. The findings also implies that, mathematics teachers and other subject teachers should not fend off students from participating in sporting activities with the trepidation that participating in sports inflame academic performance. This study recommend that, educational programs about sports should be provided for students’ through the educational system to bring about positive academic performance.

Keywords: physical activity, physical education, intra mural, extra mural

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Authors: Alice D. Dioquino, Olivia N. Buzon, Emilio F. Aguinaldo, Ruel Avila, Erwin R. Callo, Cristy Ocampo, Malvin R. Tabajen, Marla C. Papango, Marilou M. Ubina, Josephine Tondo, Cromwell L. Valeriano

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The main purpose of this study was to develop, evaluate and validate courseware on Selected Topics in Mathematics, Science, and the English Language. Specifically, it aimed to: 1. Identify the appropriate Instructional Systems Design (ISD) model in the development of the courseware material; 2. Assess the courseware material according to its: a. Content Characteristics; b. Instructional Characteristics; and c. Technical Characteristics 3. Find out if there is a significant difference in the performance of students before and after using the tutorial CAI. This research is developmental as well as a one group pretest-posttest design. The study had two phases. Phase I includes the needs analysis, writing of lessons and storyboard by the respective experts in each field. Phase II includes the digitization or the actual development of the courseware by the faculty of the ICT department. In this phase it adapted an instructional systems design (ISD) model which is the ADDIE model. ADDIE stands for Analysis, Design, Development, Implementation and Evaluation. Formative evaluation was conducted simultaneously with the different phases to detect and remedy any bugs in the courseware along the areas of content, instructional and technical characteristics. The expected output are the digitized lessons in Algebra, Biology, Chemistry, Physics and Communication Arts in English. Students and some IT experts validated the CAI material using the Evaluation Form by Wong & Wong. They validated the CAI materials as Highly Acceptable with an overall mean rating of 4.527and standard deviation of 0 which means that they were one in the ratings they have given the CAI materials. A mean gain was recorded and computing the t-test for dependent samples it showed that there were significant differences in the mean achievement of the students before and after the treatment (using CAI). The identified ISD model used in the development of the tutorial courseware was the ADDIE model. The quantitative analyses of data based on ratings given by the respondents’ shows that the tutorial courseware possess the characteristics and or qualities of a very good computer-based courseware. The ratings given by the different evaluators with regard to content, instructional, and technical aspects of the Tutorial Courseware are in conformity towards being excellent. Students performed better in mathematics, biology chemistry, physics and the English Communication Arts after they were exposed to the tutorial courseware.

Keywords: CAI, tutorial courseware, Instructional Systems Design (ISD) Model, education

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Authors: Mpofu Vongai, Vhurumuku Elaosi

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Many African countries, such as Zimbabwe and South Africa, have curricula reform agendas that include incorporation of Indigenous Knowledge and Nature of Science (NOS) into school Science, Technology, Engineering and Mathematics (STEM) education. It is argued that at high school level, STEM learning, which incorporates understandings of indigenization science and NOS, has the potential to provide a strong foundation for a culturally embedded scientific knowledge essential for their advancement in Science and Technology. Globally, investment in STEM education is recognized as essential for economic development. For this reason, developing countries such as Zimbabwe and South Africa have been investing into training specialized teachers in natural sciences and technology. However, in many cases this training has been detached from the cultural realities and contexts of indigenous learners. For this reason, the STEM curricula reform has provided implementation challenges to teachers. An issue of major concern is the teachers’ pedagogical content knowledge (PCK), which is essential for effective implementation of these STEM curricula. Well-developed Teacher PCK include an understanding of both the nature of indigenous knowledge (NOIK) and of NOS. This paper reports the results of a study that investigated the development of 3 South African and 3 Zimbabwean in-service teachers’ abilities to integrate NOS and NOIK as part of their PCK. A participatory action research design was utilized. The main focus was on capturing, determining and developing teachers STEM knowledge for integrating NOIK and NOS in science classrooms. Their use of indigenous games was used to determine how their subject knowledge for STEM and pedagogical abilities could be developed. Qualitative data were gathered through the use dialogues between the researchers and the in-service teachers, as well as interviewing the participating teachers. Analysis of the data provides a methodological window through which in-service teachers’ PCK can be STEMITIZED and their abilities to integrate NOS and NOIK developed. Implications are raised for developing teachers’ STEM education in universities and teacher training colleges.

Keywords: indigenous knowledge, nature of science, pedagogical content knowledge, STEM education

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Authors: Jin Koo

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During the coronavirus pandemic, there has been a further increasing demand for computer-based tests (CBT), and now it has become an important test mode. The main purpose of this study is to investigate the comparability of student scores obtained from computerized-based formats of a standardized test in the two subject areas of reading and mathematics. Also, this study investigates whether there is an interaction effect between test modes of CBT and paper-based tests (PBT) and gender/ability level in each subject area. The test used in this study is a multiple-choice standardized test for students in grades 8-11. For this study, data were collected during four test administrations: 2015-16, 2017-18, and 2020-21. This research used a one-factor between-subjects ANOVA to compute the PBT and CBT groups’ test means for each subject area (reading and mathematics). Also, 2-factor between-subjects ANOVAs were conducted to investigate examinee characteristics: gender (male and female), ethnicity (African-American, Asian, Hispanic, multi-racial, and White), and ability level (low, average, and high-ability groups). The author found that students’ test scores in the two subject areas varied across CBT and PBT by gender and ability level, meaning that gender, ethnicity, and ability level were related to the score difference. These results will be discussed according to the current testing systems. In addition, this study’s results will open up to school teachers and test developers the possible influence that gender, ethnicity, and ability level have on a student’s score based on whether they take the CBT or PBT.

Keywords: ability level, computer-based, gender, paper-based, test

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Authors: Karen Koellner, Nanette Seago, Jennifer Jacobs, Helen Garnier

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Although studies of teacher professional development (PD) are prevalent, surprisingly most have only produced incremental shifts in teachers’ learning and their impact on students. There is a critical need to understand what teachers take up and use in their classroom practice after attending PD and why we often do not see greater changes in learning and practice. This paper is based on a mixed methods efficacy study of the Learning and Teaching Geometry (LTG) video-based mathematics professional development materials. The extent to which the materials produce a beneficial impact on teachers’ mathematics knowledge, classroom practices, and their students’ knowledge in the domain of geometry through a group-randomized experimental design are considered. In this study, we examine a small group of teachers to better understand their interpretations of the workshops and their classroom uptake. The participants included 103 secondary mathematics teachers serving grades 6-12 from two states in different regions. Randomization was conducted at the school level, with 23 schools and 49 teachers assigned to the treatment group and 18 schools and 54 teachers assigned to the comparison group. The case study examination included twelve treatment teachers. PD workshops for treatment teachers began in Summer 2016. Nine full days of professional development were offered to teachers, beginning with the one-week institute (Summer 2016) and four days of PD throughout the academic year. The same facilitator-led all of the workshops, after completing a facilitator preparation process that included a multi-faceted assessment of fidelity. The overall impact of the LTG PD program was assessed from multiple sources: two teacher content assessments, two PD embedded assessments, pre-post-post videotaped classroom observations, and student assessments. Additional data was collected from the case study teachers including additional videotaped classroom observations and interviews. Repeated measures ANOVA analyses were used to detect patterns of change in the treatment teachers’ content knowledge before and after completion of the LTG PD, relative to the comparison group. No significant effects were found across the two groups of teachers on the two teacher content assessments. Teachers were rated on the quality of their mathematics instruction captured in videotaped classroom observations using the Math in Common Observation Protocol. On average, teachers who attended the LTG PD intervention improved their ability to engage students in mathematical reasoning and to provide accurate, coherent, and well-justified mathematical content. In addition, the LTG PD intervention and instruction that engaged students in mathematical practices both positively and significantly predicted greater student knowledge gains. Teacher knowledge was not a significant predictor. Twelve treatment teachers were self-selected to serve as case study teachers to provide additional videotapes in which they felt they were using something from the PD they learned and experienced. Project staff analyzed the videos, compared them to previous videos and interviewed the teachers regarding their uptake of the PD related to content knowledge, pedagogical knowledge and resources used.

Keywords: teacher learning, professional development, pedagogical content knowledge, geometry

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Authors: Mounir Adal, Baalal Azeddine, Afifi Moulay Larbi

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Numerical analysis is a branch of mathematics devoted to the development of iterative matrix calculation techniques. We are searching for operations optimization as objective to calculate and solve systems of equations of order n with time and energy saving for computers that are conducted to calculate and analyze big data by solving matrix equations. Furthermore, this scientific discipline is producing results with a margin of error of approximation called rates. Thus, the results obtained from the numerical analysis techniques that are held on computer software such as MATLAB or Simulink offers a preliminary diagnosis of the situation of the environment or space targets. By this we can offer technical procedures needed for engineering or scientific studies exploitable by engineers for water.

Keywords: numerical analysis methods, obstacles solving, engineering, simulation, numerical modeling, iteration, computer, MATLAB, water, underground, velocity

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Authors: Wilma Coetzee

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Statistics lecturers experience that many students who are taking a service course in statistics do not like statistics. Students in these courses tend to struggle and do not perform well. This research takes a look at the student’s perspective, with the aim to determine how to change the teaching of statistics so that students will enjoy it more and perform better. Questionnaires were used to determine the perspectives of first year service statistics students at a South African university. Factors addressed included motivation to study, attitude toward statistics, statistical anxiety, mathematical abilities and tendency to procrastinate. Logistic regression was used to determine what contributes to students performing badly in statistics. The results show that the factors that contribute the most to students performing badly are: statistical anxiety, not being motivated and having had mathematical literacy instead of mathematics in secondary school. Two open ended questions were included in the questionnaire: 'I will enjoy statistics more if…' and 'I will perform better in statistics if…'. The answers to these questions were analyzed using qualitative methods. Frequent themes were identified for each of the questions. A simulation study incorporating bootstrapping was done to determine the saturation of the themes. The majority of the students indicated that they would perform better in statistics if they studied more, managed their time better, had a flare for mathematics and if the lecturer was able to explain difficult concepts better. They also want more active learning. To ensure that students enjoy statistics more, they want an active learning experience. They want fun activities, more interaction with the lecturer and with one another, more computer based problems, and more challenges. They want a better understanding of the subject, want to understand the relevance of statistics to their future career and want excellent lecturers. These findings can be used to direct the improvement of the tuition of statistics.

Keywords: active learning, performance in statistics, statistical anxiety, statistics education

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Authors: Aliya Kamilyevna Salahova

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This study examines the effectiveness of the Kids Science Labs intervention program, based on STEM, in fostering independent thinking among preschool and elementary school children and its influence on their academic achievement. Through a comprehensive methodology involving interviews, surveys, observations, case studies, and statistical tests, data were collected from various sources to accurately analyze the program's effects. The findings indicate a significant positive impact on children's independent thinking abilities, leading to improved academic performance in mathematics and science, enhanced learning motivation, and a propensity to critically evaluate problem-solving approaches. This research contributes to the theoretical understanding of how STEM activities can foster independent thinking and academic success in young children, providing valuable insights for the development of educational programs. Introduction: The goal of this study is to investigate the influence of the Kids Science Labs intervention program, grounded in STEM, on the development of independent thinking skills among preschool and elementary school children. By addressing this objective, we aim to explore the program's potential to enhance academic performance in mathematics and science. The study's findings have theoretical significance as they shed light on the ways in which STEM activities can foster independent thinking in young children, thus enabling educators to design effective learning programs that promote academic success. Methodology: This study employs a robust methodology that includes interviews, surveys, observations, case studies, and statistical tests. These methods were carefully selected to collect comprehensive data from multiple sources, such as documents and records, ensuring a thorough analysis of the program's effects. The use of diverse data collection and analysis procedures facilitated an in-depth exploration of the research questions and yielded reliable results. Results: The results indicate that children participating in the Kids Science Labs program experienced a sustained positive impact on their independent thinking abilities. Moreover, these children demonstrated improved academic performance in mathematics and science, displaying higher learning motivation and the capacity to critically evaluate problem-solving methods and seek optimal solutions. Theoretical Importance: This study contributes significantly to the existing theoretical knowledge by elucidating how STEM activities can foster independent thinking and enhance academic success in preschool and elementary school children. The findings have practical implications for educators, empowering them to develop learning programs that stimulate independent thinking, leading to improved academic performance in young children. Discussion: The findings of this research affirm that the Kids Science Labs intervention program is highly effective in fostering independent thinking among preschool and elementary school children. The program's positive impact extends to improved academic performance in mathematics and science, highlighting its potential to enhance learning outcomes. Educators can leverage these findings to develop educational programs that promote independent thinking and elevate academic achievement in young children. Conclusion: In conclusion, the Kids Science Labs intervention program has been found to be highly effective in fostering independent thinking among preschool and elementary school children. Furthermore, participation in the program correlates with improved academic performance in mathematics and science. The study's outcomes underscore the importance of developing educational initiatives that stimulate independent thinking in young children, thereby enhancing their academic success.

Keywords: STEM in preschool, STEM in elementary school, kids science labs, independent thinking, STEM activities in early childhood education

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Authors: Veronica Diaz Quezada

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In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

Keywords: engineering education, errors, limits, mathematics competences, problem solving

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Authors: Pascal Roubides

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The presentation proposed herein describes a research case study of a hybrid application of the competency-based education model best exemplified by Western Governor’s University, within the general temporal confines of an accelerated (8-week) term of a College Algebra course at the author’s institution. A competency-based model was applied to an accelerated online College Algebra course, built as an Open Educational Resources (OER) course, seeking quantifiable evidence of any differences in the academic achievement of students enrolled in the competency-based course and the academic achievement of the current delivery of the same course. Competency-based learning has been gaining in support in recent times and the author’s institution has also been involved in its own efforts to design and develop courses based on this approach. However, it is unknown whether there had been any research conducted to quantify evidence of the effect of this approach against traditional approaches prior to the author’s case study. The research question sought to answer in this experimental quantitative study was whether the online College Algebra curriculum at the author’s institution delivered via an OER-based competency-based model can produce statistically significant improvement in retention and success rates against the current delivery of the same course. Results obtained in this study showed that there is no statistical difference in the retention rate of the two groups. However, there was a statistically significant difference found between the rates of successful completion of students in the experimental group versus those in the control group.

Keywords: competency-based learning, online mathematics, online math education, online courses

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Authors: Nursel Bektas

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The purpose of this study is to investigate the roles of teaching assistants (TAs) working in reception classes through practitioners’ perspectives. The study has two major purposes; firstly to explore the general roles of TAs, and secondly to identify their roles in supporting children for mathematics. A small-scale case study approach was adopted for this study. The research was carried out in two reception classes within a primary school in London. The qualitative data were gathered through observations and semi-structured interviews with four reception class practitioners, comprising two teachers and two TAs. The results show that TAs consider their role to be more like a teacher, whereas classroom teachers do not corroborate this and they generally believe that the role of TAs depends on their personal characteristics and skills. In regard to the general role of TAs, the study suggests that reception class TAs are deployed both at the classroom level to provide academic support for children’s learning and development, and at the school level they are deployed as support staff such as Midday Meal Supervisor or assistants. In terms of the pedagogical roles of TAs, it was found that TAs have a strong teaching role in literacy development, with notable autonomy if conducting their own phonics sessions without teacher direction, but a negligible influence in numeracy/ math’s. In addition, the results show that the TA role is perceived to be quite limited in planning and assessment processes. Linked to their limited roles in such processes, all participants agree that all the responsibility regarding the children’s learning and development, planning and assessment lies with the teacher. Therefore, data suggest that TAs’ roles in these areas depend on TAs’ their own initiatives.

Keywords: early years education, reception classes, roles, teaching assistants

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Authors: Veronica Diaz Quezada

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The society of the 21st century requires training of engineers capable of solving routine and non-routine problems in applications of the limit of real functions, as part of the course Calculus I. For this purpose, research was conducted with a methodological design that combines quantitative and qualitative procedures and that aims, to identify and to characterize the types of problems according to their nature and context, through the application of a mathematics test; to know— through a questionnaire— the opinion of difficulties in their solution, previous and missing knowledge of some students of three engineering careers of a state university in Chile. This research is completed with three case studies. The results favor the performance of students in solving problems of a fantasist and realistic context, but these do not guarantee mathematical skills which are necessary to solve non-routine problems of limit applications. In conclusion, through this research, it became clear that the students of the three engineerings do not have all the necessary skills to solve problems of application of the limit of a function of the real variable.

Keywords: case studies, engineering program, limits, problem solving

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Authors: Shafaq Rubab

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One of the biggest reasons of dropouts from schools is lack of motivation and interest among the students, particularly in mathematics. Many developing countries are facing this problem and this issue is lowering the literacy rate in these developing countries. The best solution for increasing motivation level and interest among the students is using tablet game-based learning. However, a pedagogically sound game required a well-planned instructional design model to enhance learner’s attention and confidence otherwise effectiveness of the learning games suffers badly. This research aims to evaluate the impact of the pedagogically sound instructional design model on students’ motivation by using tablet game-based learning. This research was conducted among the out-of-school-students having an age range from 7 to 12 years and the sample size of two hundred students was purposively selected without any gender discrimination. Qualitative research was conducted by using a survey tool named Instructional Material Motivational Survey (IMMS) adapted from Keller Arcs model. A comparison of results from both groups’ i.e. experimental group and control group revealed that motivation level of the students taught by the game was higher than the students instructed by using conventional methodologies. Experimental group’s students were more attentive, confident and satisfied as compared to the control group’s students. This research work not only promoted the trend of digital game-based learning in developing countries but also supported that a pedagogically sound instructional design model utilized in an educational game can increase the motivation level of the students and can make the learning process a totally immersive and interactive fun loving activity.

Keywords: digital game-based learning, student’s motivation, instructional design model, learning process

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Authors: Anne Marie Morrin

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This paper will focus on the design, delivery and assessment of a transdisciplinary STEAM (Science, Technology, Engineering, Arts, and Mathematics) education initiative in a college of education in Ireland. The project explores a transdisciplinary approach to supporting STEAM education where the concepts, methodologies and assessments employed derive from visual art sessions within initial teacher education. The research will demonstrate that the STEAM Education approach is effective when visual art concepts and methods are placed at the core of the teaching and learning experience. Within this study, emphasis is placed on authentic collaboration and transdisciplinary pedagogical approaches with the STEAM subjects. The partners included a combination of teaching expertise in STEM and Visual Arts education, artists, in-service and pre-service teachers and children. The inclusion of all stakeholders mentioned moves towards a more authentic approach where transdisciplinary practice is at the core of the teaching and learning. Qualitative data was collected using a combination of questionnaires (focused and open-ended questions) and focus groups. In addition, the data was collected through video diaries where students reflected on their visual journals and transdisciplinary practice, which gave rich insight into participants' experiences and opinions on their learning. It was found that an effective program of STEAM education integration was informed by co-teaching (continuous professional development), which involved a commitment to adaptable and flexible approaches to teaching, learning, and assessment, as well as the importance of continuous reflection-in-action by all participants. The delivery of a transdisciplinary model of STEAM education was devised to reconceptualizatise how individual subject areas can develop essential skills and tackle critical issues (such as self-care and climate change) through data visualisation and technology. The success of the project can be attributed to the collaboration, which was inclusive, flexible and a willingness between various stakeholders to be involved in the design and implementation of the project from conception to completion. The case study approach taken is particularistic (focusing on the STEAM-ED project), descriptive (providing in-depth descriptions from varied and multiple perspectives), and heuristic (interpreting the participants’ experiences and what meaning they attributed to their experiences).

Keywords: collaboration, transdisciplinary, STEAM, visual arts education

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Authors: A. Schuchter, M. Promegger

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The outbreak of the COVID-19 pandemic has shown us that online education is so much more than just a cool feature for teachers – it is an essential part of modern teaching. In online math teaching, it is common to use tools to share screens, compute and calculate mathematical examples, while the students can watch the process. On the other hand, flipped classroom models are on the rise, with their focus on how students can gather knowledge by watching videos and on the teacher’s use of technological tools for information transfer. This paper proposes a co-educational teaching approach for coding and engineering subjects with the help of drone-building to spark interest in technology and create a platform for knowledge transfer. The project combines aspects from mathematics (matrices, vectors, shaders, trigonometry), physics (force, pressure and rotation) and coding (computational thinking, block-based programming, JavaScript and Python) and makes use of collaborative-shared 3D Modeling with clara.io, where students create mathematics knowhow. The instructor follows a problem-based learning approach and encourages their students to find solutions in their own time and in their own way, which will help them develop new skills intuitively and boost logically structured thinking. The collaborative aspect of working in groups will help the students develop communication skills as well as structural and computational thinking. Students are not just listeners as in traditional classroom settings, but play an active part in creating content together by compiling a Handbook of Knowledge (called “open book”) with examples and solutions. Before students start calculating, they have to write down all their ideas and working steps in full sentences so other students can easily follow their train of thought. Therefore, students will learn to formulate goals, solve problems, and create a ready-to use product with the help of “reverse engineering”, cross-referencing and creative thinking. The work on drones gives the students the opportunity to create a real-life application with a practical purpose, while going through all stages of product development.

Keywords: flipped classroom, co-creational education, coding, making, drones, co-education, ARCS-model, problem-based learning

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Authors: Keng Keh Lim, Zaleha Ismail, Yudariah Mohammad Yusof

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This paper aims to find out how students using convergent and divergent thinking in creative problem solving to solve mathematical problems creatively. Eight engineering undergraduates in a local university took part in this study. They were divided into two groups. They solved the mathematical problems with the use of creative problem solving skills. Their solutions were collected and analyzed to reveal all the processes of problem solving, namely: problem definition, ideas generation, ideas evaluation, ideas judgment, and solution implementation. The result showed that the students were able to solve the mathematical problem with the use of creative problem solving skills.

Keywords: convergent thinking, divergent thinking, creative problem solving, creativity

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Authors: Gülcan Taşkıran, Ayla Bayık Temel

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Background: Florence Nightingale, the modern founder of the nursing, is most famous for her role as a nurse. But not so much known about her contributions as a mathematician and statistician. Aim: In this conceptual article it is aimed to examine Florence Nightingale's statistics education, how she used her passion for statistics and applied statistical data in nursing care and her scientific contributions to statistical science. Design: Literature review method was used in the study. The databases of Istanbul University Library Search Engine, Turkish Medical Directory, Thesis Scanning Center of Higher Education Council, PubMed, Google Scholar, EBSCO Host, Web of Science were scanned to reach the studies. The keywords 'statistics' and 'Florence Nightingale' have been used in Turkish and English while being screened. As a result of the screening, totally 41 studies were examined from the national and international literature. Results: Florence Nightingale has interested in mathematics and statistics at her early ages and has received various training in these subjects. Lessons learned by Nightingale in a cultured family environment, her talent in mathematics and numbers, and her religious beliefs played a crucial role in the direction of the statistics. She was influenced by Quetelet's ideas in the formation of the statistical philosophy and received support from William Farr in her statistical studies. During the Crimean War, she applied statistical knowledge to nursing care, developed many statistical methods and graphics, so that she made revolutionary reforms in the health field. Conclusions: Nightingale's interest in statistics, her broad vision, the statistical ideas fused with religious beliefs, the innovative graphics she has developed and the extraordinary statistical projects that she carried out has been influential on the basis of her professional achievements. Florence Nightingale has also become a model for women in statistics. Today, using and teaching of statistics and research in nursing care practices and education programs continues with the light she gave.

Keywords: Crimean war, Florence Nightingale, nursing, statistics

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Authors: Jaya Bishnu Pradhan

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Weaving mat is one of the common activities performed in different community generally in the rural part of Nepal. Mat weavers’ practice mathematical ideas and concepts implicitly in order to perform their job. This study is intended to uncover the mathematical ideas embedded in mat weaving that can help teachers and students for the teaching and learning of school geometry. The ethnographic methodology was used to uncover and describe the beliefs, values, understanding, perceptions, and attitudes of the mat weavers towards mathematical ideas and concepts in the process of mat weaving. A total of 4 mat weavers, two mathematics teachers and 12 students from grade level 6-8, who are used to participate in weaving, were selected for the study. The whole process of the mat weaving was observed in a natural setting. The classroom observation and in-depth interview were taken with the participants with the help of interview guidelines and observation checklist. The data obtained from the field were categorized according to the themes regarding mathematical ideas embedded in the weaving activities, and its possibilities in teaching learning of school geometry. In this study, the mathematical activities in different sectors of their lives, their ways of understanding the natural phenomena, and their ethnomathematical knowledge were analyzed with the notions of pluralism. From the field data, it was found that the mat weaver exhibited sophisticated geometrical ideas in the process of construction of frame of mat. They used x-test method for confirming if the mat is rectangular. Mat also provides a good opportunity to understand the space geometry. A rectangular form of mat may be rolled up when it is not in use and can be converted to a cylindrical form, which usually can be used as larder so as to reserve food grains. From the observation of the situations, this cultural experience enables students to calculate volume, curved surface area and total surface area of the cylinder. The possibilities of incorporation of these cultural activities and its pedagogical use were observed in mathematics classroom. It is argued that it is possible to use mat weaving activities in the teaching and learning of school geometry.

Keywords: ethnography, ethnomathematics, geometry, mat weaving, school pedagogy

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Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: Madina Tynybayeva, Sanya Zhumazhanova, Saltanat Kozhakhmetova, Merey Mussabayeva

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One of the leading indicators of the education quality is the level of students’ educational achievements. The processes of modernization of Kazakhstani education system have predetermined the need to improve the national system by assessing the quality of education. The results of assessment greatly contribute to addressing questions about the current state of the educational system in the country. The monitoring of students’ educational achievements (MEAS) is the systematic measurement of the quality of education for compliance with the state obligatory standard of Kazakhstan. This systematic measurement is independent of educational organizations and approved by the order of the Minister of Education and Scienceof Kazakhstan. The MEAS was conducted in the regions of Kazakhstanfor the first time in 2022 by the National Testing Centre. The measurement does not have legal consequences either for students or for educational organizations. Students’ achievements were measured in three subject areas: reading, mathematics and science literacy. MEAS was held for the first time in April this year, 105 thousand students from 1436 schools of Kazakhstan took part in the testing. The monitoring was accompanied by a survey of students, teachers, and school leaders. The goal is to identify which contextual factors affect learning outcomes. The testing was carried out in a computer format. The test tasks of MEAS are ranked according to the three levels of difficulty: basic, medium, and high. Fourth graders are asked to complete 30 closed-type tasks. The average score of the results is 21 points out of 30, which means 70% of tasks were successfully completed. The total number of test tasks for 9th grade students – 75 questions. The results of ninth graders are comparatively lower, the success rate of completing tasks is 63%. MEAS participants did not reveal a statistically significant gap in results in terms of the language of instruction, territorial status, and type of school. The trend of reducing the gap in these indicators is also noted in the framework of recent international studies conducted across the country, in particular PISA for schools in Kazakhstan. However, there is a regional gap in MOES performance. The difference in the values of the indicators of the highest and lowest scores of the regions was 11% of the success of completing tasks in the 4th grade, 14% in the 9thgrade. The results of the 4th grade students in reading, mathematics, and science literacy are: 71.5%, 70%, and 66.9%, respectively. The results of ninth-graders in reading, mathematics, and science literacy are 69.6%, 54%, and 60.8%, respectively. From the surveys, it was revealed that the educational achievements of students are considerably influenced by such factors as the subject competences of teachers, as well as the school climate and motivation of students. Thus, the results of MEAS indicate the need for an integrated approach to improving the quality of education. In particular, the combination of improving the content of curricula and textbooks, internal and external assessment of the educational achievements of students, educational programs of pedagogical specialties, and advanced training courses is required.

Keywords: assessment, secondary school, monitoring, functional literacy, kazakhstan

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Authors: Eyasu Gemech, Kassa Michael, Mulugeta Atnafu

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A non-equivalent group's quasi-experiment research was conducted at Wolkite University to investigate MATLAB supported learning and students' conceptual understanding in learning Applied Mathematics II using four different comparative instructional approaches: MATLAB supported traditional lecture method, MATLAB supported collaborative method, only collaborative method, and only traditional lecture method. Four intact classes of mechanical engineering groups 1 and 2, garment engineering and textile engineering students were randomly selected out of eight departments. The first three departments were considered as treatment groups and the fourth one 'Textile engineering' was assigned as a comparison group. The departments had 30, 29, 35 and 32 students respectively. The results of the study show that there is a significant mean difference in students' conceptual understanding between groups of students learning through MATLAB supported collaborative method and the other learning approaches. Students who were learned through MATLAB technology-supported learning in combination with collaborative method were found to understand concepts of functions of two variables better than students learning through the other methods of learning. These, hence, are informative of the potential approaches universities would follow for a better students’ understanding of concepts.

Keywords: MATLAB supported collaborative method, MATLAB supported learning, collaborative method, conceptual understanding, functions of two variables

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Authors: Gurcharan Singh Buttar

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It has been discovered that although these two areas, statistics, and information theory, are independent in their nature, they can be combined to create applications in multidisciplinary mathematics. This is due to the fact that where in the field of statistics, statistical parameters (measures) play an essential role in reference to the population (distribution) under investigation. Information measure is crucial in the study of ambiguity, assortment, and unpredictability present in an array of phenomena. The following communication is a link between the two, and it has been demonstrated that the well-known conventional statistical measures can be used as a measure of information.

Keywords: probability distribution, entropy, concavity, symmetry, variance, central tendency

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Authors: Oláh Gál Róbert, Veress Bágyi Ibolya

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The scientific public has relatively little knowledge about the Hungarian János Bolyai, one of the greatest thinkers of all times. Few people know that apart from being the founder of the non-Euclidean geometry he was also interested in sociology, philosophy, epistemology and linguistics. According to the renowned Hungarian psychoanalytic Imre Hermann, who lives in France, János Bolyai was mentally deranged. However, this is incorrect. The present article intends to prove that he was completely sane until the moment of his death.

Keywords: Imre Hermann, insane, János Bolyai, mathematics, non-Euclidean geometry, psyphoanalytic

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