Search results for: mathematics laboratory

Authors: S. Rawashdi, D. Bshouty

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This paper aimed at discussing how to urge middle and high school Arab students in Israel to be aware of the importance of and investing in learning mathematics. In the first phase of the study, three questionnaires were passed to two nine-grade classes, one on Awareness, one on Awakeness and one on Learning. One of the two classes was an outstanding class from a public school (PUBS) of 31 students, and the other a heterogeneous class from a private school (PRIS) with 31 students. The Learning questionnaire which was administrated to the Awareness and Awareness topics was passed to PRIS and the Awareness and Awareness Questionnaires were passed to the PUBS class After two months we passed the post-questionnaire to both classes to validate the long-term impact of the study. The findings of the study show that awakeness and awareness processes have an effect on the math learning process, on its context in students' daily lives and their growing interest in learning math.

Keywords: awakeness, awareness, learning mathematics, pupils

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Authors: Jay-R. Hosana Leonidas, Jayson A. Lucilo

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The K-12 Curriculum in the Philippines shed light to mathematics education as it recognizes the use of smartphones/mobile phones as appropriate tools necessary in teaching mathematics. However, there were limited pieces of evidence on the use of these devices in teaching and learning process. This descriptive study developed lessons integrating the use of mobile phone applications with basis on low-level competencies of students in Precalculus and determined its effects on students’ conceptual understanding, procedural skills, and attitudes towards Precalculus. Employing Bring Your Own Device (BYOD) scheme in the study, lessons developed were conducted among Grade 11 Science, Technology, Engineering, and Mathematics (STEM) students at Central Bicol State University of Agriculture for the academic year 2018-2019. This study found that there is a significant difference between the competency levels of students along conceptual understanding and procedural skills prior to and after the conduct of lessons developed. Also, it disclosed that the use of mobile phone applications had positive effects on students’ attitudes towards Precalculus. Thus, the use of mobile phone applications in teaching Precalculus can enrich students’ understanding of concepts and procedural skills (solving and graphing skills) and can increase students’ motivation, self-confidence, and enjoyment in dealing with Precalculus.

Keywords: bring your own device, mathematics education, mobile phone applications, senior high school

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Authors: A. Giannakopoulos, S. B. Buckley

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Problem solving in any field is recognised as a prerequisite for any advancement in knowledge. For example in South Africa it is one of the seven critical outcomes of education together with critical thinking. As a systematic way to problem solving was initiated in mathematics by the great mathematician George Polya (the father of problem solving), more detailed and comprehensive ways in problem solving have been developed. This paper is based on the findings by the author and subsequent recommendations for further research in problem solving and critical thinking. Although the study was done in mathematics, there is no doubt by now in almost anyone’s mind that mathematics is involved to a greater or a lesser extent in all fields, from symbols, to variables, to equations, to logic, to critical thinking. Therefore it stands to reason that mathematical principles and learning cannot be divorced from any field. In management of knowledge situations, the types of problems are similar to mathematics problems varying from simple to analogical to complex; from well-structured to ill-structured problems. While simple problems could be solved by employees by adhering to prescribed sequential steps (the process), analogical and complex problems cannot be proceduralised and that diminishes the capacity of the organisation of knowledge creation and innovation. The low efficiency in some organisations and the low pass rates in mathematics prompted the author to view problem solving as a product. The authors argue that using mathematical approaches to knowledge management problem solving and treating problem solving as a product will empower the employee through further training to tackle analogical and complex problems. The question the authors asked was: If it is true that problem solving and critical thinking are indeed basic skills necessary for advancement of knowledge why is there so little literature of knowledge management (KM) about them and how they are connected and advance KM?This paper concludes with a conceptual model which is based on general accepted principles of knowledge acquisition (developing a learning organisation), knowledge creation, sharing, disseminating and storing thereof, the five pillars of knowledge management (KM). This model, also expands on Gray’s framework on KM practices and problem solving and opens the doors to a new approach to training employees in general and domain specific areas problems which can be adapted in any type of organisation.

Keywords: critical thinking, knowledge management, mathematics, problem solving

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Authors: Idha Novianti, Suci Nurhayati, Puryati, Elang Krisnadi

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Community service activities are activities of the academic community in practicing and cultivating science, knowledge, and technology to advance the general welfare and educate the nation's life as described in the Higher Education Law. Training activities on the use of GeoGebra software are an option because GeoGebra software is software that is easy to operate and complete in the presentation of graphic design. The training activity was held for 3 hours online via teams and 3 hours offline. Involving 15 junior high school mathematics teachers located around south Tangerang. As a result, all teachers were satisfied with the activity, and they had additional new knowledge and skills to teach mathematics in the topic of geometry and algebra. The existence of new knowledge made the participants increase their confidence in developing mathematical science for students at school.

Keywords: geogebra, Ms. teams, junior high school teacher, mathematics

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Authors: Mustafa Akpolat, Baha Vural Kök

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Using a waste material such as crumb rubber (CR) obtained by waste tires has become an important issue in respect to sustainability. However, the CR modified mixture also requires high manufacture temperature as a polymer modified mixture. For this reason in this study, it is intended to produce a CR modified mixture with warm mix asphalt additives in the same mixture. Asphalt mixtures produced by pure, 10%CR, 10%CR+3% Sasobit and 10%CR+0.7% Evotherm were subjected to aging procedure in the laboratory and the field. The indirect tensile repeated tests were applied to aged and original specimens. It was concluded that the fatigue life of the mixtures increased significantly with the increase of aging time. CR+Sasobit modified mixture aged at the both field and laboratory gave the highest load cycle among the mixtures.

Keywords: crumb rubber, warm mix asphalt, aging, fatigue

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Authors: J. Shamash

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The high-school curriculum in algebra deals mainly with the solution of different types of equations. However, modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. A question then arises: What might be the relevance and contribution of an abstract algebra course for developing expertise and mathematical perspective in secondary school mathematics instruction? This is the focus of this paper. The course Algebra: From Equations to Structures is a carefully designed abstract algebra course for Israeli secondary school mathematics teachers. The course provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. In other words, algebraic structures grew out of a need to solve certain problems, and proved to be a much more fruitful way of viewing them. This theorems in both group theory and field theory. Along the historical ‘journey’, many other major results in algebra in the past 150 years are introduced, and recent directions that current research in algebra is taking are highlighted. This course is part of a unique master’s program – the Rothschild-Weizmann Program – offered by the Weizmann Institute of Science, especially designed for practicing Israeli secondary school teachers. A major component of the program comprises mathematical studies tailored for the students at the program. The rationale and structure of the course Algebra: From Equations to Structures are described, and its relevance to teaching school algebra is examined by analyzing three kinds of data sources. The first are position papers written by the participating teachers regarding the relevance of advanced mathematics studies to expertise in classroom instruction. The second data source are didactic materials designed by the participating teachers in which they connected the mathematics learned in the mathematics courses to the school curriculum and teaching. The third date source are final projects carried out by the teachers based on material learned in the course.

Keywords: abstract algebra , linking abstract algebra and school mathematics, school algebra, secondary school mathematics, teacher professional development

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Authors: Itumeleng Phage

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Students’ comprehension of graphs may be affected by the characteristics of the discipline in which the graph is used, the type of the task as well as the background of the students who are the readers or interpreters of the graph. This research study investigated these aspects of the graph comprehension of 152 first-year undergraduate physics students by comparing their responses to corresponding tasks in the mathematics and physics disciplines. The discipline characteristics were analysed for four task-related constructs namely coordinates, representations, area and slope. Students’ responses to corresponding visual decoding and judgement tasks set in mathematics and kinematics contexts were statistically compared. The effects of the participants’ gender, year of school completion and study course were determined as reader characteristics. The results of the empirical study indicated that participants generally transferred their mathematics knowledge on coordinates and representation of straight line graphs to the physics contexts, but not in the cases of parabolic and hyperbolic functions or area under graphs. Insufficient understanding of the slope concept contributed to weak performances on this construct in both mathematics and physics contexts. Discipline characteristics seem to play a vital role in students’ understanding, while reader characteristics had insignificant to medium effects on their responses.

Keywords: kinematics graph, discipline characteristics, constructs, coordinates, representations, area and slope

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Authors: Meziane Belkacem

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We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: Sukriti Sabharwal, Sonali Bhattar, Shikhar Saxena

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Introduction: COVID-19 molecular diagnostic laboratory is the cornerstone of the COVID-19 disease diagnosis as the patient’s treatment and management protocol depend on the molecular results. For this purpose, it is extremely important that the laboratory conducting these results adheres to the quality management processes to increase the accuracy and validity of the reports generated. We started our own molecular diagnostic setup at the onset of the pandemic. Therefore, we conducted this study to generate our quality management data to help us in improving on our weak points. Materials and Methods: A total of 14561 samples were evaluated by the retrospective observational method. The quality variables analysed were classified into pre-analytical, analytical, and post-analytical variables, and the results were presented in percentages. Results: Among the pre-analytical variables, sample leaking was the most common cause of the rejection of samples (134/14561, 0.92%), followed by non-generation of SRF ID (76/14561, 0.52%) and non-compliance to triple packaging (44/14561, 0.3%). The other pre-analytical aspects assessed were incomplete patient identification (17/14561, 0.11%), insufficient quantity of samples (12/14561, 0.08%), missing forms/samples (7/14561, 0.04%), samples in the wrong vials/empty VTM tubes (5/14561, 0.03%) and LIMS entry not done (2/14561, 0.01%). We are unable to obtain internal quality control in 0.37% of samples (55/14561). We also experienced two incidences of cross-contamination among the samples resulting in false-positive results. Among the post-analytical factors, a total of 0.07% of samples (11/14561) could not be dispatched within the stipulated time frame. Conclusion: Adherence to quality control processes is foremost for the smooth running of any diagnostic laboratory, especially the ones involved in critical reporting. Not only do the indicators help in keeping in check the laboratory parameters but they also allow comparison with other laboratories.

Keywords: laboratory quality management, COVID-19, molecular diagnostics, healthcare

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Authors: J. Miranda, D. Chavarría-Barrientos, M. Ramírez-Cadena, M. E. Macías, P. Ponce, J. Noguez, R. Pérez-Rodríguez, P. K. Wright, A. Molina

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Higher education methods need to evolve because the new generations of students are learning in different ways. One way is by adopting emergent technologies, new learning methods and promoting the maker movement. As a result, Tecnologico de Monterrey is developing Open Innovation Laboratories as an immediate response to educational challenges of the world. This paper presents an Open Innovation Laboratory for Rapid Realization of Sensing, Smart and Sustainable Products (S³ Products). The Open Innovation Laboratory is composed of a set of specific resources where students and teachers use them to provide solutions to current problems of priority sectors through the development of a new generation of products. This new generation of products considers the concepts Sensing, Smart, and Sustainable. The Open Innovation Laboratory has been implemented in different courses in the context of New Product Development (NPD) and Integrated Manufacturing Systems (IMS) at Tecnologico de Monterrey. The implementation consists of adapting this Open Innovation Laboratory within the course’s syllabus in combination with the implementation of specific methodologies for product development, learning methods (Active Learning and Blended Learning using Massive Open Online Courses MOOCs) and rapid product realization platforms. Using the concepts proposed it is possible to demonstrate that students can propose innovative and sustainable products, and demonstrate how the learning process could be improved using technological resources applied in the higher educational sector. Finally, examples of innovative S³ products developed at Tecnologico de Monterrey are presented.

Keywords: active learning, blended learning, maker movement, new product development, open innovation laboratory

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Authors: Zhanna Dedovets

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Fostering a mathematical style of thinking is crucial for cultivating intellectual personalities capable of thriving in modern society. Intuitive thinking stands as a cornerstone among the components of mathematical cognition, playing a pivotal role in grasping mathematical truths across various disciplines. This article delves into the exploration of leveraging search activities rooted in students' intuitive thinking, particularly when tackling geometric problems. Emphasizing both student engagement with the task and their active involvement in the search process, the study underscores the importance of heuristic procedures and the freedom for students to chart their own problem-solving paths. Spanning several years (2019-2023) at the Physics and Mathematics Lyceum of Dushanbe, the research engaged 17 teachers and 78 high school students. After assessing the initial levels of intuitive thinking in both control and experimental groups, the experimental group underwent training following the authors' methodology. Subsequent analysis revealed a significant advancement in thinking levels among the experimental group students. The methodological approaches and teaching materials developed through this process offer valuable resources for mathematics educators seeking to enhance their students' learning experiences effectively.

Keywords: teaching of mathematics, intuitive thinking, heuristic procedures, geometric problem, students.

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Authors: R. M. Kashim

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The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching.

Keywords: conceptual knowledge, primary school teachers, procedural knowledge, rational numbers

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Authors: Nazir Amir

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Teaching approaches to present science and mathematics content amongst academically-low-achieving students may need to be different than approaches that are adopted for the more academically-inclined students, primarily due to the different learning needs and learning styles of these students. In crafting out lessons to motivate and engage these students, teachers need to consider the backgrounds of these students and have a good understanding of their interests so that lessons can be presented in ways that appeal to them, and made relevant not just to the world around them, but also to their personal experiences. This presentation highlights how the author worked with a Professional Learning Community (PLC) of teachers in crafting out fun and feasible classroom teaching approaches to present science and mathematics content in ways that are made Relevant, Appealing, and Personal (RAP) to groups of academically-low-achieving students in Singapore. Feedback from the students and observations from their work suggest that they were engaged through the RAP-modes of instruction, and were able to appreciate the role of science and mathematics through a variety of low-cost design-based STEM (Science, Technology, Engineering, and Mathematics) activities. Such results imply that teachers teaching academically-low-achieving students, and those in under-resourced communities, could consider infusing RAP-infused instructions into their lessons in getting students develop positive attitudes towards STEM subjects.

Keywords: STEM Education, STEAM Education, Curriculum Instruction, Academically At-Risk Students, Singapore

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Authors: Martin Pumera

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Graphene materials are being widely used in electrochemistry due to their versatility and excellent properties as platforms for biosensing. Here we present current trends in the electrochemical biosensing of pesticides and other toxic compounds. We explore two fundamentally different designs, (i) using graphene and other 2-D nanomaterials as an electrochemical platform and (ii) using these nanomaterials in the laboratory on chip design, together with paramagnetic beads. More specifically: (i) We explore graphene as transducer platform with very good conductivity, large surface area, and fast heterogeneous electron transfer for the biosensing. We will present the comparison of these materials and of the immobilization techniques. (ii) We present use of the graphene in the laboratory on chip systems. Laboratory on the chip had a huge advantage due to small footprint, fast analysis times and sample handling. We will show the application of these systems for pesticide detection and detection of other toxic compounds.

Keywords: graphene, 2D nanomaterials, biosensing, chip design

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Authors: Guorong Sui, Xingwei Jia, Chenhui Yin, Xiumin Gao

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In the processing of camera-based high precision and non-contact measurement, the geometric-optical aberration is always inevitably disturbing the measuring system. Moreover, the aberration is different with the different focal length, which will increase the difficulties of the system’s calibration. Therefore, to understand the relationship between the focal length as a function of aberration properties is a very important issue to the calibration of the measuring systems. In this study, we propose a new mathematics model, which is based on the plane calibration method by Zhang Zhengyou, and establish a relationship between the focal length and aberration coefficient. By using the mathematics model and carefully modified compensation templates, the calibration precision of the system can be dramatically improved. The experiment results show that the relative error is less than 1%. It is important for optoelectronic imaging systems that apply to measure, track and position by changing the camera’s focal length.

Keywords: camera calibration, aberration coefficient, vision measurement, focal length, mathematics model

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Authors: Eugenia Vomvoridi-Ivanovic

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It is broadly assumed that participation in field experiences will help pre-service teachers (PSTs) bridge theory to practice. However, this is often not the case since PSTs who are placed in classrooms with large numbers of students from diverse linguistic, cultural, racial, and ethnic backgrounds (culturally diverse students (CDS)) usually observe ineffective mathematics teaching practices that are in contrast to those discussed in their teacher preparation program. Over the past decades, the educational research community has paid increasing attention to investigating out-of-school learning contexts and how participation in such contexts can contribute to the achievement of underrepresented groups in Science, Technology, Engineering, and mathematics (STEM) education and their expanded participation in STEM fields. In addition, several research studies have shown that students display different kinds of mathematical behaviors and discourse practices in out-of-school contexts than they do in the typical mathematics classroom since they draw from a variety of linguistic and cultural resources to negotiate meanings and participate in joint problem solving. However, almost no attention has been given to exploring these contexts as field experiences for pre-service mathematics teachers. The purpose of this study was to explore how participation in a community based after-school field experience promotes understanding of the content pedagogy concepts introduced in elementary mathematics methods courses, particularly as they apply to teaching mathematics to CDS. This study draws upon a situated, socio-cultural theory of teacher learning that centers on the concept of learning as situated social practice, which includes discourse, social interaction, and participation structures. Consistent with exploratory case study methodology, qualitative methods were employed to investigate how a cohort of twelve participating pre-service teacher's approach to pedagogy and their conversations around teaching and learning mathematics to CDS evolved through their participation in the after-school field experience, and how they connected the content discussed in their mathematics methods course with their interactions with the CDS in the after-school. Data were collected over a period of one academic year from the following sources: (a) audio recordings of the PSTs' interactions with the students during the after-school sessions, (b) PSTs' after-school field-notes, (c) audio-recordings of weekly methods course meetings, and (d) other document data (e.g., PST and student generated artifacts, PSTs' written course assignments). The findings of this study reveal that the PSTs benefitted greatly through their participation in the after-school field experience. Specifically, after-school participation promoted a deeper understanding of the content pedagogy concepts introduced in the mathematics methods course and gained a greater appreciation for how students learn mathematics with understanding. Further, even though many of PSTs' assumptions about the mathematical abilities of CDS were challenged and PSTs began to view CDSs' cultural and linguistic backgrounds as resources (rather than obstacles) for learning, some PSTs still held negative stereotypes about CDS and teaching and learning mathematics to CDS in particular. Insights gained through this study contribute to a better understanding of how informal mathematics learning contexts may provide a valuable context for pre-service teacher's learning to teach mathematics to CDS.

Keywords: after-school mathematics program, pre-service mathematical education of teachers, qualitative methods, situated socio-cultural theory, teaching culturally diverse students

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Authors: Irvan Adhin Cholilie, Susinggih Wijana, Yusron Sugiarto

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The aim of this research is to compare the results of black grass jelly produced using laboratory scale and double scale. In this research, the production from the laboratory scale is using ingredients of 1 kg black grass jelly added with 5 liters of water, while the double scale is using 5 kg black grass jelly and 75 liters of water. The results of organoleptic tests performed by 30 panelists (general) to the sample gels of grass black powder produced from both of laboratory and double scale are not different significantly in color, odor, flavor, and texture. Proximate test results conducted in both of grass black jelly powder produced in laboratory scale and double scale also have no significant differences in all parameters. Grass black jelly powder from double scale contains water, carbohydrate, crude fiber, and yield in the amount of 12,25 %; 43,7 %; 5,89 %; and 16,28 % respectively. The results of the energy efficiency analysis by boiling, draining, evaporation, drying, and milling processes are 85,11 %; 76,97 %; 99,64 %; 99,99% and 99,39% respectively. The utility needs including water needs for each batch amounted 0.1 m3 and cost Rp 220,5 per batch, the electricity needs for each batch is 20.01 kWh and cost Rp 18569.28 per batch, and LPG needs for each batch is 30 kg costed Rp 234,000.00 so that the total cost spent for the process is Rp 252,789.78 .

Keywords: black grass jelly, powder, mass balance, energy balance, cost

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Authors: Onesimus Bulus Shiaki

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The study investigated the effect of cooperative learning strategy on mathematics achievement and retention among senior secondary school students of different abilities in Taraba State Nigeria. Cooperative learning strategy could hopefully contribute to students’ achievement which will spur the teachers to develop strategies for better learning. The quasi-experimental of pretest, posttest and control group design was adopted in this study. A sample of one hundred and sixty-four (164) Senior Secondary Two (SS2) students were selected from a population of twelve thousand, eight hundred and seventy-three (12,873) SS2 Students in Taraba State. Two schools with equivalent mean scores in the pre-test were randomly assigned to experimental and control groups. The experimental group students were stratified according to ability levels of low, medium and high. The experimental group was guided by the research assistants using the cooperative learning instructional package. After six weeks post-test was administered to the two groups while the retention test was administered two weeks after the post-test. The researcher developed a 50-item Mathematics Achievement Test (MAT) which was validated by experts obtaining the reliability coefficient of 0.87. Mean scores and standard deviations were used to answer the research questions while the Analysis of Co-variance (ANCOVA) was used to test the hypotheses. Major findings from the statistical analysis showed that cooperative learning strategy has a significant effect on the mean achievement of students as well as retention among students of high, medium and low ability in mathematics. However, cooperative learning strategy has no effect on the interaction of ability level and retention. Based on the results obtained, it was therefore recommended that the adoption of the use of cooperative learning strategy in the teaching and learning of mathematics in senior secondary schools be initiated, maintained and sustained for the benefit of senior secondary school students in Taraba State. Periodic Government sponsored in-service training in form of long vacation training programme, workshops, conferences and seminars on the nature, scope, and use of cooperative learning strategy should be organized for senior secondary school mathematics teachers in Taraba state.

Keywords: ability level, cooperative learning, mathematics achievement, retention

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Authors: Esmaeil Ahmadinia, Frank Bullen, Ron Ayers

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Many concerns have been raised in recent years about the adequacy of existing creep test methods for evaluating rut-resistance of asphalt mixes. Many researchers believe the main reason for the creep tests being unable to duplicate field results is related to a lack of a realistic confinement for laboratory specimens. In-situ asphalt under axle loads is surrounded by a mass of asphalt, which provides stress-strain generated confinement. However, most existing creep tests are largely unconfined in their nature. It has been hypothesised that by providing a degree of confinement, representative of field conditions, in a creep test, it could be possible to establish a better correlation between the field and laboratory. In this study, a new methodology is explored where confinement for asphalt specimens is provided. The proposed methodology is founded on the current Australian test method, adapted to provide simulated field conditions through the provision of sample confinement.

Keywords: asphalt mixture, creep test, confinements, permanent deformation

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Authors: Cristina-Maria Păcurar

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The paper presents an original Python-based application that outlines the advantages of combining some elementary notions of mathematics with the study of a programming language. The application support refers to some of the first lessons of analytic geometry, meaning conics and quadrics and their reduction to a standard form, as well as some related notions. The chosen programming language is Python, not only for its closer to an everyday language syntax – and therefore, enhanced readability – but also for its highly reusable code, which is of utmost importance for a mathematician that is accustomed to exploit already known and used problems to solve new ones. The purpose of this paper is, on one hand, to support the idea that one of the most appropriate means to initiate one into programming is throughout mathematics, and reciprocal, one of the most facile and handy ways to assimilate some basic knowledge in the study of mathematics is to apply them in a personal project. On the other hand, besides being a mean of learning both programming and analytic geometry, the application subject to this paper is itself a useful tool for it can be seen as an independent original Python package for analytic geometry.

Keywords: analytic geometry, conics, python, quadrics

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Authors: G. Quiroga-Cubides, A. Díaz, M. Gómez

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The genus Azotobacter has been widely used as bio-fertilizer due to its significant effects on the stimulation and promotion of plant growth in various agricultural species of commercial interest. In order to obtain significantly viable cellular concentration, a scale-up strategy for a liquid fermentation process (SmF) with two strains of A. chroococcum (named Ac1 and Ac10) was validated and adjusted at laboratory and pilot scale. A batch fermentation process under previously defined conditions was carried out on a biorreactor Infors®, model Minifors of 3.5 L, which served as a baseline for this research. For the purpose of increasing process efficiency, the effect of the reduction of stirring speed was evaluated in combination with a fed-batch-type fermentation laboratory scale. To reproduce the efficiency parameters obtained, a scale-up strategy with geometric and fluid dynamic behavior similarities was evaluated. According to the analysis of variance, this scale-up strategy did not have significant effect on cellular concentration and in laboratory and pilot fermentations (Tukey, p > 0.05). Regarding air consumption, fermentation process at pilot scale showed a reduction of 23% versus the baseline. The percentage of reduction related to energy consumption reduction under laboratory and pilot scale conditions was 96.9% compared with baseline.

Keywords: Azotobacter chroococcum, scale-up, liquid fermentation, fed-batch process

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Authors: Han Hyuk Cho, Hanik Jo

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In recent years, coding education has been globally emphasized, and the Free Semester System and coding education were introduced to the public schools from the beginning of 2016 and 2018 respectively in Korea. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this paper aims to design ‘Coding Environment’ and Minecraft-like Turtlecraft in which learners can design and construct mathematical objects through mathematical symbolic expressions. Students can transfer the constructed mathematical objects to the Turtlecraft environment (open-source codingmath website), and also can print them out through 3D printers. Furthermore, we design learnable mathematics and coding curriculum by representing the figurate numbers and patterns in terms of executable expression in the coding context and connecting them to algebraic symbols, which will allow students to experience mathematical patterns and symbolic coding expressions.

Keywords: coding education, computational thinking, mathematics education, TurtleMAL and Turtlecraft

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Authors: Sibawu Witness Siyepu

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This study explores the effects of instructional design using blended learning in the learning of radian measures among Engineering students. Blended learning is an education programme that combines online digital media with traditional classroom methods. It requires the physical presence of both lecturer and student in a mathematics computer laboratory. Blended learning provides element of class control over time, place, path or pace. The focus was on the use of Khan Academy to supplement traditional classroom interactions. Khan Academy is a non-profit educational organisation created by educator Salman Khan with a goal of creating an accessible place for students to learn through watching videos in a computer assisted computer. The researcher who is an also lecturer in mathematics support programme collected data through instructing students to watch Khan Academy videos on radian measures, and by supplying students with traditional classroom activities. Classroom activities entails radian measure activities extracted from the Internet. Students were given an opportunity to engage in class discussions, social interactions and collaborations. These activities necessitated students to write formative assessments tests. The purpose of formative assessments tests was to find out about the students’ understanding of radian measures, including errors and misconceptions they displayed in their calculations. Identification of errors and misconceptions serve as pointers of students’ weaknesses and strengths in their learning of radian measures. At the end of data collection, semi-structure interviews were administered to a purposefully sampled group to explore their perceptions and feedback regarding the use of blended learning approach in teaching and learning of radian measures. The study employed Algebraic Insight Framework to analyse data collected. Algebraic Insight Framework is a subset of symbol sense which allows a student to correctly enter expressions into a computer assisted systems efficiently. This study offers students opportunities to enter topics and subtopics on radian measures into a computer through the lens of Khan Academy. Khan academy demonstrates procedures followed to reach solutions of mathematical problems. The researcher performed the task of explaining mathematical concepts and facilitated the process of reinvention of rules and formulae in the learning of radian measures. Lastly, activities that reinforce students’ understanding of radian were distributed. Results showed that this study enthused the students in their learning of radian measures. Learning through videos prompted the students to ask questions which brought about clarity and sense making to the classroom discussions. Data revealed that sense making through reinvention of rules and formulae assisted the students in enhancing their learning of radian measures. This study recommends the use of Khan Academy in blended learning to be introduced as a socialisation programme to all first year students. This will prepare students that are computer illiterate to become conversant with the use of Khan Academy as a powerful tool in the learning of mathematics. Khan Academy is a key technological tool that is pivotal for the development of students’ autonomy in the learning of mathematics and that promotes collaboration with lecturers and peers.

Keywords: algebraic insight framework, blended learning, Khan Academy, radian measures

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Authors: Abraham Motlhabane

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This research analysed the written views of science education students regarding the teaching of laboratory work using the online mode. The research adopted the qualitative methodology. The qualitative research was aimed at investigating small and distinct groups normally regarded as a single-site study. Qualitative research was used to describe and analyze the phenomena from the student’s perspective. This means the research began with assumptions of the world view that use theoretical lenses of research problems inquiring into the meaning of individual students. The research was conducted with three groups of students studying for Postgraduate Certificate in Education, Bachelor of Education and honors Bachelor of Education respectively. In each of the study programmes, the science education module is compulsory. Five science education students from each study programme were purposively selected to participate in this research. Therefore, 15 students participated in the research. In order to analysis the data, the data were first printed and hard copies were used in the analysis. The data was read several times and key concepts and ideas were highlighted. Themes and patterns were identified to describe the data. Coding as a process of organising and sorting data was used. The findings of the study are very diverse; some students are in favour of online laboratory whereas other students argue that science can only be learnt through hands-on experimentation.

Keywords: online learning, laboratory work, views, perceptions

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Authors: Joanne Hardman

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South Africa’s crisis in mathematics attainment is well documented. To meet the need to develop students’ mathematical performance in schools the government has launched various initiatives using computers to impact on mathematical attainment. While it is clear that computers can change pedagogical practices, there is a dearth of qualitative studies indicating exactly how pedagogy is transformed with Information Communication Technologies (ICTs) in a teaching activity. Consequently, this paper addresses the following question: how, along which dimensions in an activity, does pedagogy alter with the use of computer drill and practice software in four disadvantaged grade 6 mathematics classrooms in the Western Cape province of South Africa? The paper draws on Cultural Historical Activity Theory (CHAT) to develop a view of pedagogy as socially situated. Four ideal pedagogical types are identified: Reinforcement pedagogy, which has the reinforcement of specialised knowledge as its object; Collaborative pedagogy, which has the development of metacognitive engagement with specialised knowledge as its object; Directive pedagogy, which has the development of technical task skills as its object, and finally, Defensive pedagogy, which has student regulation as its object. Face-to-face lessons were characterised as predominantly Reinforcement and Collaborative pedagogy and most computer lessons were characterised as mainly either Defensive or Directive.

Keywords: computers, cultural historical activity theory, mathematics, pedagogy

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Authors: Joel S. Mtebe, Aron Kondoro, Mussa M. Kissaka, Elia Kibga

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Sub-Saharan Africa is described as the second fastest growing mobile phone penetration in the world more than in the United States or the European Union. Mobile phones have been used to provide a lot of opportunities to improve people’s lives in the region such as in banking, marketing, entertainment, and paying various bills such as water, TV, and electricity. However, the potential of using mobile phones to enhance teaching and learning has not been explored. This study presents an experience of developing and delivering SMS quizzes questions that were used to assess mastery of the subject content knowledge of science and mathematics secondary school teachers in Tanzania. The SMS quizzes were used as a follow up support mechanism to 500 teachers who participated in a project to upgrade subject content knowledge of science and mathematics subjects. Quizzes of 10-15 questions were sent to teachers each week for 8 weeks and the results were analyzed using SPSS. The results showed that chemistry and biology had better performance compared to mathematics and physics. Teachers reported some challenges that led to poor performance, invalid answers, and non-responses and they are presented. This research has several practical implications for those who are implementing or planning to use mobile phones for teaching and learning especially in rural secondary schools in sub-Saharan Africa.

Keywords: mobile learning, elearning, educational technolgies, SMS, secondary education, assessment

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Authors: Josephine Shamash, Stuart Smith

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We examine reasons for introducing definitions in teaching mathematics in a number of different cases. We try to determine if, where, and when to provide a definition, and which definition to choose. We characterize different types of definitions and the different purposes we may have for formulating them, and detail examples of each type. Giving a definition at a certain stage can sometimes be detrimental to the development of the concept image. In such a case, it is advisable to delay the precise definition to a later stage. We describe two models, the 'successive approximation model', and the 'model of the extending definition' that fit such situations. Detailed examples that fit the different models are given based on material taken from a number of textbooks, and analysis of the way the concept is introduced, and where and how its definition is given. Our conclusions, based on this analysis, is that some of the definitions given may cause discontinuities in the learning sequence and constitute obstacles and unnecessary cognitive conflicts in the formation of the concept definition. However, in other cases, the discontinuity in passing from definition to definition actually serves a didactic purpose, is unavoidable for the mathematical evolution of the concept image, and is essential for students to deepen their understanding.

Keywords: concept image, mathematical definitions, mathematics education, mathematics teaching

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Authors: Murray Olowa

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This article examines the studies investigating the Mathematical Knowledge for Teaching (MKT) of secondary preservice teachers in Papua New Guinea based on probabilities. This research was conducted due to the continuous issues faced in the country in both primary and secondary education, like changes in curriculum, emphasis on mathematics and science education, and a decline in mathematics performance. Moreover, the mathematics curriculum doesn’t capture Pedagogical Content Knowledge (PCK) or Subject Matter Knowledge (SMK). The two main domains that have been identified are SMK and PCK, which have been further sub-divided into Common Content Knowledge (CCK), Specialised Content Knowledge (SCK) and Horizon Content Knowledge (HCK), and Knowledge of Content and Students (KCS), Knowledge of Content and Teaching (KCT) and Knowledge of Content and Curriculum (KCC), respectively. The data collected from 15-_year-_ ones and 15-_year-_fours conducted at St Peter Chanel Secondary Teachers College revealed that there is no significant difference in subject matter knowledge between year one and year four since the P-value of 0.22>0.05. However, it was revealed that year fours have higher pedagogical content knowledge than year one since P-value was 0.007<0.05. Finally, the research has proven that year fours have higher MKT than year one. This difference occurred due to final year preservice teachers’ hard work and engagement in mathematics curriculum and teaching practice.

Keywords: mathematical knowledge for teaching, subject matter knowledge, pedagogical content knowledge, Papua New Guinea, preservice teachers, probability

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Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

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Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

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Authors: Farhaz Amyn Rajabali, Collins Odour

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Mathematics has been there for over 4000 years and has been one of the very first educational topics explored by human civilization. Throughout the years, it has become a complex study and has derived so many other subjects. With advancements in ICT, most of the computation in mathematics is done using powerful computers. In many different countries, the children in primary and secondary schools face difficulties in learning mathematics, and this has many reasons behind it, one being the students don’t engage much with the mathematical concepts hence failing to understand them deeply. The objective of this system is to help the students understand this mathematical concept interactively, which in return will encourage the love for learning and increase thorough understanding of many concepts. Research was conducted among a group of samples and about 50% of respondents replied that they had never used an augmented reality application before. This means that the chances for this system to be accepted in the market are high due to its innovative idea. Around 60% of people did recommend the use of this system to learn mathematics. The study also showed several challenges in an educational system, including but not limited to lack of resources which was chosen by 30% of respondents, the challenge to read from textbooks (34.6%) and how hard it is to visualize concepts (46.2%). The survey question asked what benefits the users see using augmented reality to learn mathematics. The responses that were picked the most were increased student engagement and using real-world examples to understand concepts, both being 65.4% and followed by easy access to learning material at 61.5%, and increased knowledge retention at 50%. This shows that there are plenty of issues with an education system that can be addressed by software applications; now that the newer generation is so enthusiastic about electronic devices, it can actually be used to deliver good knowledge and skills to the upcoming students and mitigate most of the challenges faced currently. The study concludes that the implementation of the system is a best practice for the educational system especially leveraging a new technology that has the ability to attract the attention of many young students and use it to deliver information. It will also give rise to awareness of new technology and on multiple ways it can be implemented. Addressing the educational sector in developing countries using information technology is an imperative task since these kids studying now is the future of the country and will use what they learn and understand during their childhood will help them to make decisions about their lives in the future which will not only affect them personally but also affect the whole society in general.

Keywords: AR, mathematics, system development, augmented reality

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