Images of Undergraduate Mathematics Curriculum: A Critical Self-Reflection

Higher education practices in Nepal have been playing an important role to train and develop pre-service school teachers. This paper critically reflects on the curricular and pedagogical practices of mathematics education based on the first author's experiences of learning at the undergraduate level from the perspective of mathematics curriculum images and pedagogical implications. Subscribing to autoethnography as a research methodology, we analysed the first author's experiences as an undergraduate student in one of the public campuses in Nepal which point to two major images of mathematics curriculum: curriculum as a prescription and curriculum as a cultural reproduction. Considering Habermasian Knowledge Constitutive Interest as a theoretical referent, the paper concludes that the transformation of curricular and pedagogical practices in teacher education is essential. The transformative practice in teacher education is insightful to improve pre-service and in-service school teachers' pedagogical and content knowledge in Nepal.

Elementary Algebra on Vedic Mathematics

The South Asian region has a long history of discovering new ideas, ideologies, and technologies. Since the Vedic period, the land has been known as a fertile place for innovative discoveries. The Vedic technique used by Bharati Krishna Tirthaji is unique among South Asian studies. The focus of this study was mostly on algebraic topics, which are typically taught in our school level. The study also looked at how Vedic Mathematics solves issues of elementary algebra using Vedic techniques such as Paravartya Yojayet, Sunyam Samyasamuccaye, Anurupye Sunyamanyat, Antyayoreva and Lopanasthapanabhyam. The comparison and discussion of the Vedic with the conventional techniques indicate that the Vedic Mathematics and its five unique formulas are more beneficial and realistic to those learners who are experiencing problems with elementary level algebra utilizing conventional methods.

Teachers’ Perception and Challenges of Using ICT in Teaching Mathematics at Secondary Level

The main objectives of this study were to identify the teachers’ perceptions and challenges of using ICT tools in the mathematics classroom at the secondary level in Kathmandu. The major tool of the study was a closed-ended questionnaire consisting of 19 items. The quantitative descriptive survey design was used in this study. The researcher selected 158 teachers by using simple random method from 261 government teachers who teach compulsory mathematics at grade X of Kathmandu district in Nepal. The standardized questionnaire was administered to the sample teachers. The SPSS-25 version database was used to analyze and interpret the collected data. Teachers’ perception of using ICTs in the mathematics classroom was positive with insignificant difference in terms of gender. There were some challenges: lack of knowledge, confidence, enough experience, training, interest and access to ICT tools, lack of technical support, lack of genuine ICT Software and unstable and unreliable internet connection at the schools. Due to these challenges, teachers did not use ICT in the classroom. Therefore, teachers should learn more to improve their knowledge and skills in ICT. The government should focus on management strategies and policies to reduce the challenges faced by teachers in mathematics classrooms. By these policies, they can use the ICT tools in the classroom.

Exploring Project-Based Teaching for Engaging Students' Mathematical Learning

The declining interest of learners in mathematics in the learning process has resulted in poor achievement (Yeh et al., 2019). To get rid of these poor achievements, we explored project-based teaching in four topical areas (e.g., mathematical concepts of coordinate geometry, trigonometry, sequence, and series) in the school mathematics. This paper results from observing changes in engagement of learners in learning mathematics by motivating them through the project-based learning (PBL) guided by two theories – knowledge constitutive interests (Habermas, 1972), and collaborative and cooperative learning under the paradigms of interpretivism and criticalism. In this ethos, PBL is an “engaging and learner-directed approach that provides equal opportunities for students to explore their knowledge and understanding” (Thomas, 2000, p. 12). More specifically, we adopted the 'action research' method with the secondary level students (Grade IX) of one of the institutional schools in their classrooms. The information was collected by observing and recording the changes seen in consecutive seventeen days. The research landed that project-based learning is an appropriate pedagogy for engaged learning. The study revealed that the students were motivated while they got opportunities to interact in the projects. Moreover, the findings show that PBL is helpful to engage the learners through questioning, pair/group discussion, discovery learning, and concept mapping.

Predicting Logarithm of Real Numbers to any Real Number Base

This paper aims to propose an algorithm that can predict the values of logarithmic function for any domain and for any bases with minimum possible error using basic mathematical operations. It talks about a univariate quadratic function that overlaps with the graph of the common logarithmic function to some extent, and using this resemblance to fullest advantage. It proposes a formula and certain algorithms based on the same formula.

Engaged Mathematics Learning as/for a Transformative Praxis

Engaged learning in mathematics is essential to students' success and has a significant role in creating a transformative path in mathematics education. Considering this, this editorial attempts to highlight the role of behavioural, cognitive, affective and agentic aspects of engaged learning. It is impossible to bring all aspects of this complex and multidimensional construct in this short editorial; however, we try to open a new avenue by bringing the issue of engaged learning into pedagogical practices of mathematics in the context of Nepal. The discourse opens up how disengaged learning creates a mathematical Othering and its detrimental effects on mathematics education. Moreover, this discourse binds with the major features of classroom engagement, conceptualize and the impact of engaged learning on students' success. The editorial ends with a brief overview of the issue.

What are possible Sources of Common and Persistent Student Errors in Algebra and Calculus?

Research shows that college students make numerous algebra and other prerequisite content-related errors in Calculus courses. Most of these errors are common, persistent, and often observed in simple mathematical tasks. This qualitative study is an attempt to identify the potential sources of such errors. Based on our observations of student errors, we wrote a Precalculus and a Calculus test and administered them in twelve sections of four different undergraduate mathematics courses for which either Precalculus, Calculus I or both were a prerequisite. The tests were announced on the first day of the class and administered the following week. All the questions on the test were True or False questions. Based on our experience as college mathematics instructors, we assumed that many students would perceive the True answers as False and the False as True. Therefore, if students’ selected a given answer, mathematical statement, process or solution as True, they were asked to justify why that was not False and vice-versa. They were instructed to provide logical explanations and avoid plugging in numbers to check for correctness. Analysis of data using grounded theory approach resulted in the following three possible external sources of common and persistent student errors: a) Difficulty with symbols and/or lack of attendance to the meaning of those symbols, b) Instructional practices, and c) Lack of knowledge. We will provide examples to illustrate how such errors could have originated from these sources.

Dynamic Analysis of Prey-Predator Model with Harvesting

Employing the Lotka -Voltera (1926) prey-predator model equation, the system is presented with harvesting effort for both species prey and predator. We analyze the stability of the system of ordinary differential equation after calculating the Eigen values of the system. We include the harvesting term for both species in the model equation, and observe the dynamic analysis of prey-predator populations by including the harvesting efforts on the model equation. We also analyze the population dynamic of the system by varying the harvesting efforts on the system. The model equation are solved numerically by applying Runge - Kutta fourth order method.

Emerging ICT Tools, Techniques and Methodologies for Online Collaborative Teaching and Learning Mathematics

Emerging ICT tools, techniques and methodologies (TTM), which might be helpful for pedagogical practices, for a synchronous and asynchronous mode of teaching and learning mathematics in online and distance mode of education. This action research reported from the underpinning practices of the authors as trainers, course facilitators, educational researchers and innovative practitioner-the possible uses of emerging ICT tools, techniques and methodologies for teaching and learning mathematics. This article highlights some key strengths with possible integration of emerging ICT tools, techniques and methodologies to facilitate online and offline task(s) and assessment(s) of the learners, and trainees in a collaborative manner. Epistemologically, our experiences reflected that the learning experiences of the learners and trainees would be better by incorporating emerging ICT tools, techniques and methodologies in day to day practices in online classes specifically more in this present context. We have concluded the paper by highlighting the effectiveness of use of emerging ICT tools, techniques and methodologies as a new innovative virtual teaching and learning platform.

Common Fixed Point Theorems Using Compatible Mappings of Type (R) in Semi-metric Space

In this paper, we establish a common fixed point theorem for three pairs of self mappings in semi-metric space using compatible mappings of type (R) which improves and extends similar known results in the literature.