International conference on mathematics and mathematics education 2025

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Status of secondary level mathematics education in selected schools in kalmunai education zone, sri lanka
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Farzan, M.C.; Chathuranga, K.M.N.M.; Dewasurendra, M.T.M.
This study investigates the status of secondary-level Mathematics education in selected schools within the Ampara District of Sri Lanka, with a focus on students’ performance, teaching methodologies, and the challenges faced by both students and teachers. Employing a mixed-methods approach, the sample consisted of 200 students (grades 10 and 11), 25 Mathematics teachers, and 8 trainee teachers from three selected schools in the Kalmunai Education Zone. The test assessed students' knowledge and skills in key areas of Mathematics, while the questionnaires gathered insights into students' learning experiences, teachers' teaching practices, and the availability of teaching resources. The test results revealed that a significant majority of students scored below satisfactory levels, with 36% scoring below 20%. Only 10% of the students achieved scores above 75%. The majority of the students performed below satisfactory levels, particularly struggling with Set Theory and Probability. Key challenges identified include, insufficient instructional time, a lack of modern teaching aids, and limited use of innovative teaching strategies. Students reported dissatisfaction with teachers’ ability to clarify doubts, while teachers cited difficulties in syllabus completion and engaging with students effectively. These findings align with consistently low Mathematics scores in national examinations. The study recommends the integration of modern teaching aids, the provision of remedial classes for underperforming students, and enhanced professional development for teachers. Establishing well-equipped Mathematics classrooms and promoting student-centered instructional methods are essential steps toward improving secondary-level Mathematics education in the Kalmunai Education Zone.
Factors affecting mathematics performance of grade 10 students in division 2 schools at Hatton educational zone
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Sutharshini, V.; De Silva, T.H.K.R.
The General Certificate of Education (Ordinary Level) (G.C.E. (O/L)) examination is an important public examination in Sri Lanka. Mathematics plays a key role in this examination, and passing mathematics is a fundamental requirement for students to advance to advance higher level classes. Grade 10 is the foundational year for the G.C.E. (O/L), and this study aims to identify the factors influencing the mathematics performance of Grade 10 students in schools within the Hatton Division 2. The study explores how four main themes: interest for mathematics, home environment, parents' education level, and the type of school attended, affect students' performance in mathematics. Under these themes, we examined the relationship between students' performance in mathematics and the factors; private tuition attendance, homework completion, time spent on self-studying mathematics per week, parental conflict at home, paternal alcoholism, education level of both parents, the location of the school (urban or rural), and the category of the school (1AB, 1C, Type 2). The data for this study were collected from 125 students and 6 teachers from schools in the Hatton Educational Zone Division 2. A convenience sampling method was used to select schools, ensuring representation from 1AB, 1C, and Type 2 schools in both urban and rural areas. Data were gathered through a structured questionnaire and semi-structured interviews. The Chi-square test and Cramér's V rule were applied for data analysis using SPSS software. The results show that the amount of time spent on self-studying mathematics per week is strongly associated with students' mathematics performance in Grade 10. Additionally, completing assigned homework, father being an alcoholic, the relationship between parents, the education levels of both parents, the location of the school, and the type of school attended all show a moderate association with students' mathematics performance. The study also revealed that attending private tuition classes does not have a significant relationship with students' mathematics performance in Grade 10.
Determinants of mathematics achievement among GCE (O/L) students: a study in the Kalmunai education zone
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Sanjeevan, A.; Dewasurendra, M.T.M.; Chathuranga, K.M.N.M.
This study investigates the factors influencing mathematics achievement among G.C.E. (O/L) students in the Kalmunai Education Zone, Sri Lanka. The research explores the impact of socio-economic background, school infrastructure, teacher quality, student motivation, and parental involvement on students' mathematics performance. Data was collected from 96 teachers across various schools using proportionate random sampling technique. Structured questionnaires were administered through direct distribution and collection method. Data analysis was conducted using SPSS software, employing correlation analysis and one-way ANOVA tests at p < 0.05 significance level. Correlation analysis revealed that student motivation is the strongest positive correlation with mathematics achievement (r = 0.70), and ANOVA results showed significant differences across all factor categories. The study concludes that all identified factors significantly influence mathematics achievement, with student motivation and parental involvement showing the strongest impact. A multi- faceted approach, which addresses these determinants, can substantially improve mathematics achievement in the Kalmunai Education Zone. The findings of this study highlight the complex interplay of factors that contribute to the academic achievement of students in mathematics. To improve students' performance, a multi-dimensional approach is required, focusing on enhancing socio-economic conditions, improving school infrastructure, investing in teacher quality, fostering motivation, and encouraging parental involvement.
Characterization of inner toral polynomials via finite blaschke products
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Senadeera, A.T.; Wijesooriya, U.D.
A finite Blaschke product is a product of finitely many automorphisms on the unit disc. These complex-valued functions are bounded and analytic on the unit disc. An inner toral polynomial is a polynomial in ℂ[z, w] such that its zero set is contained in 𝔻² ∪ 𝕋² ∪ 𝔼², where 𝔻 is the open unit disc, 𝕋 is the unit circle, and 𝔼 is the exterior of the closed unit disc in ℂ. Finite Blaschke products generate inner toral polynomials in the following way; given a finite Blaschke product B(z), the numerator of wᵐ − B(z) is an inner toral polynomial. Previous work has shown that every inner toral polynomial of the form q(z)wᵐ − αr(z), where α ∈ℂ \ {0}, m ∈ ℕ and r(z), and q(z) are polynomials in z with deg (q(z)) ≥ deg (r(z)), is also generated by a finite Blaschke product. This study generalizes previous results by considering inner toral polynomials generated by two finite Blaschke products. It is proved that for given two finite Blaschke products B₁(z) and B₂(w), the numerator of B₁(z) − B₂(w) is an inner toral polynomial. Furthermore, under certain limitations, a partial converse is also proved. If p(z, w) = αr₁ (z)q₂(w) − q₁(z)r₂(w), where α ∈ ℂ \ {0}, and r₁(z), q₁(z), are polynomials in z, and r₂(w), q₂(w) are polynomials in w, with degree one is inner toral, then p(z, w) can be written as the numerator of the difference of two finite Blaschke products. These findings further deepen the understanding of the relationship between finite Blaschke products and inner toral polynomials, providing new insights into the structure of distinguished varieties and their generation in multivariable complex analysis.
An innovative statistical approach to restricted transportation problems
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Dhananjalee, S.B.R.D.; Ekanayake, E.M.U.S.B.
The transportation problem, which aims at minimizing the total transportation cost while delivering goods from multiple sources to various destinations, is a fundamental optimization problem. Classical methods, such as the Least Cost Method, Vogel's Approximation Method, Row Minima Method, Column Minima Method, and North-West Corner Method, are frequently used to find an initial basic feasible solution. To achieve the optimal solution, techniques like the Stepping Stone Method and the Modified Distribution Method are typically employed. This research focuses on the restricted transportation problem, which arises when certain routes are restricted due to regulatory, safety, or logistical constraints. First, the balance of the given transportation problem is examined. If it is unbalanced, a dummy row or column with zero transportation costs is added to ensure that the total supply equals the total demand. Subsequently, the arithmetic mean and the standard deviation of the cost matrix are calculated, excluding the large costs assigned to restricted routes and all zero-cost entries. Next, each valid cost is transformed into its corresponding cumulative distribution function (CDF) value of the log-normal distribution. Then, the geometric mean for each row and column is computed, excluding zero-cost values. Afterwards, the row or column is identified with the lowest geometric mean, and the maximum possible quantity is allocated to the cell with the lowest CDF value in that row or column. Thereafter, the corresponding supply and demand are updated by eliminating any fully satisfied row or column. After that, the CDF matrix is revised accordingly, and the allocation process is repeated until all supply and demand requirements are met. Finally, the total transportation cost is determined using the original cost matrix and the final allocation plan. Benchmark instances validate the effectiveness of the proposed method in minimizing transportation costs while satisfying restricted conditions. A comparative analysis is performed with traditional approaches to demonstrate the superior accuracy of this statistical approach.
Generalization of the symmetricity properties of polynomials defining distinguished varieties on the open unit bidisk
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Perera, G.R.A.R.; Wijesooriya, U.D.
Let 𝔻 be the open unit disk, 𝕋 be the unit circle, and 𝔼 be the exterior of the closed unit disk in ℂ. A polynomial p(z, w) is said to define a distinguished variety on 𝔻², if Z(p) = { (z, w) ∊ ℂ²∶ p(z, w) = 0 } ⊆ 𝔻²∪𝕋² ∪ 𝔼². For such polynomials, the zero set Z(p) inside 𝔻²is called a distinguished variety on 𝔻². For a polynomial p(z, w) with two variables having bidegree (n, m), the reflection is defined by p̃(z, w) = zⁿwᵐp (Mathematical Formula)). A polynomial p ∊ ℂ[z, w] is essentially 𝕋² −symmetric if p(z, w) = c p̃(z, w) for some c ∊ 𝕋. In 2010, Greg Knese introduced the concept of symmetricity for polynomials defining distinguished varieties on 𝔻2 and has shown that a polynomial p defining a distinguished variety on 𝔻² is essentially 𝕋² −symmetric. In this study, this concept of symmetricity is generalized for polynomials defining distinguished varieties on open unit polydisk 𝔻ⁿ, by considering polynomials with n variables. A polynomial p(z₁, z₂, ... , z(n)) is said to define a distinguished variety on 𝔻ⁿ, if Z(p) = { (z₁, z₂, ... ,z(n)) ∊ ℂⁿ∶ p(z₁, z₂, ... , z(n)) = 0 } ⊆𝔻ⁿ ∪ 𝕋ⁿ ∪ 𝔼ⁿ. For such polynomials, the zero set Z(p) inside 𝔻ⁿ is called a distinguished variety on 𝔻ⁿ. For a polynomial p(z₁, z₂, ... , z(n) with n variables having degree (m₁, m₂, ... , mn), the reflection is introduced by p̃(z₁, z₂, ... , z(n)) =z₁ᵐ¹z₂ᵐ² ... z(n)ᵐⁿp (Mathematical Formula)). We defined a polynomial p ∊ ℂ[z₁, z₂, ... , z(n)] to be essentially 𝕋ⁿ −symmetric if p(z₁, z₂, ... , z(n)) = cp̃(z₁, z₂, ... , z(n) ) for some c ∊ 𝕋. This study proves that a polynomial p defining a distinguished variety on 𝔻ⁿ is essentially 𝕋ⁿ −symmetric for any 2 ≤ n < ∞. Future studies can focus on proving properties that already exist for two variable polynomials in the case of polynomials with n variables.
Mathematical modeling of the effect of warfarin on blood clotting in patients with prosthetic heart valves
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Rathnayake, R.P.T.A.; Chandrasiri, A.M.P.; De Silva, T.H.K.R.
Warfarin is an important anticoagulant in use to prevent thromboembolic complications in patients with prosthetic heart valves. The effectiveness of warfarin therapy is monitored using the International Normalized Ratio (INR), with a target range of 2.0–3.5, to minimize the risks of thrombosis and bleeding. However, maintaining INR within this therapeutic range is challenging due to warfarin’s narrow therapeutic window, significant inter-individual variability, and complex pharmacokinetics (PK) and pharmacodynamics (PD), which depend on individual patient characteristics. This study develops a mechanistic PK/PD model to describe warfarin dynamics including absorption, distribution, metabolism, elimination, and its effects on clotting factors and INR dynamics, particularly, in patients with prosthetic heart valves. The PK component models the drug’s disposition in the body, while the PD component accounts for its inhibition of vitamin K-dependent clotting factors. The formulated model is solved using Python programming and some model parameters were estimated using clinical data, while the other parameters were obtained from existing literature. The model was validated using data from an additional 12 consecutive days. Further, a sensitivity analysis was performed to identify key parameters influencing INR stability and therapeutic outcomes. Furthermore, the model demonstrates how different warfarin dosing scenarios affect INR stabilization. Regular dosing achieves therapeutic INR (2-3.5) in approximately 4.31 days. Missed doses delay stabilization to 5.04 days, increasing thrombosis risk, while extra doses stabilize INR faster in about 2.45 days with quick spikes. However, extra doses increase the risk of excessive anticoagulation and bleeding. This model serves as a valuable tool for predicting individual responses to therapy and for optimizing personalized dosing strategies, ultimately improving patient care and enhancing the safety and efficacy of anticoagulation therapy.
Topological data analysis of financial market volatility: a study of persistence diagrams
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Dinanjalee, D.G.J.N.; Amarasinghe, A.K.; Ratnayake, J.K.
Financial markets are known for their volatility, making it challenging to predict stock price movements using traditional methods. This study explores the application of Topological Data Analysis (TDA) to analyse financial time series data, focusing on identifying persistent topological features that correlate with periods of high volatility. To detect structural changes over time, each stock’s closing price series was segmented into windows of 252 data points (equivalent to one trading year), and for each window, Takens’ embedding method was applied to transform the time series into high-dimensional point clouds, which were then analysed using persistent homology to identify topological features. The most persistent features are structures as connected components (0-dimensional holes, detected via H₀) and loops (1- dimensional holes, detected via H₁), which persisted across a wide range of scales in the persistence diagram. From each diagram, the most persistent H₁ feature was extracted, and the overall maximum persistent point across all windows was identified along with its corresponding time series segment. The analysis was applied to major stock indices, including the S&P 500, the Dow Jones Industrial Average, Apple Inc., and Tesla. The emergence of persistent H₁ after high volatility indicates a return to structural regularity in the market, suggesting that after chaotic fluctuations, financial systems tend to reorganise into more stable configurations. Furthermore, computing market volatility using a rolling standard deviation supports this trend. This suggests that TDA can capture meaningful and stable market structures that arise after periods of instability, offering a novel perspective on market dynamics. Future research will focus on integrating machine learning models with TDA to enhance time series forecasting in financial markets.
A utility-based equilibrium framework for weather index insurance
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Harischandra, K.H.A.S.; Karunathunge, G.N.
Climate change and extreme weather events pose significant risks to farmers' livelihoods, increasing the need for effective risk management tools. Weather Index Insurance (WII) has emerged as a cost-effective solution, offering timely payouts based on predefined weather indices. By facilitating quicker recovery from crop losses and reducing loan default risks, WII enhances financial stability for farmers, particularly in rural areas vulnerable to climate-related disruptions. Despite the numerous advantages of WII, its uptake among farmers remains low due to high premiums and unreliable compensation. This study proposes a utility-based equilibrium model that analyses the supply, demand, and risk preferences of farmers and insurers. The model is based on mean-variance utility theory and assumes non-homogeneous farmers, whose revenues and benefit payouts follow a normal distribution. A simulation is conducted using 100 synthetic farmers, grouped by weather index exposure and assigned varying risk aversion coefficients, to explore how insurance demand responds to risk preferences and the introduction of premium subsidies. The market equilibrium is determined by farmers who purchase a positive amount of insurance, balancing aggregate demand with supply. Demand for WII increases with higher farmer risk aversion and is also influenced by the insurer’s risk preferences; lower risk aversion on the insurer’s side leads to greater willingness to supply, increasing overall demand. The inclusion of premium subsidies further shows that individual farmer demand is shaped not only by personal characteristics but also by the behaviour of other farmers in the market. The model assumes non-homogeneous farmers with normally distributed revenues and benefit payments, which future studies are encouraged to relax.
Mathematical optimization and computational geometric packing algorithms for maximizing material utilization in wood processing
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Madhuwanthi, E.A.T.; Nanayakkara, N.G.S.S.; Nandani, E.J.K.P.
Optimizing the use of timber resources is essential for ensuring sustainable forestry practices and maximizing wood utilization. The primary challenge in wood processing is to achieve the highest possible usable yield while minimizing waste, particularly when it comes to heartwood, which is stronger and more valuable than sapwood. The conventional wood-cutting technique, known as the plain (flat) sawn method, follows a straightforward approach but often results in significant wastage. This study specifically focuses on Jack wood, highlighting the importance of optimization tailored to the wood type. The primary objective is to reduce cutting waste and maximize usable wood by strategically positioning prioritized rectangular cuts within the heartwood. Data were collected from the State Timber Corporation (STC) in Sri Lanka, with each log of wood measured by its length and girth. Each timber log is assumed to be in a perfectly cylindrical shape, with no internal damage. The heartwood is assumed to occupy 70% of the timber log’s radius, and its cross-sectional area was calculated accordingly. The study framework combines geometry-based optimization with spatial algorithms. The arrangement of rectangular shapes on the cross-sectional area is prioritized (3” x 4”) first, then followed by prioritizing larger areas defined by lengths with widths of 28 mm, 31 mm, and 38 mm for the remaining area. An optimization model was formulated to maximize the utilization of the heartwood area under some constraints regarding total heartwood area, rectangular area, non- overlapping and rotation. Compared to plain sawn method, the optimized approach improved material utilization by up to 18% in area and 13% in volume, with a noticeable reduction in remaining usable material. The results of this study show the effectiveness of the optimized cutting method in maximizing material utilization and minimizing wastage compared to the commonly used plain-sawn method. These findings emphasize the benefit of wood-type- specific optimization in enhancing yield and reducing waste in industrial applications.
A novel cryptographic scheme based on radio mean labelling
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Weerasinghe, G.H.S.N.; Perera, A.A.I.
Graph theory and cryptography have long been intertwined, offering powerful techniques for securing information across disciplines such as computer science, engineering, and biology. This study introduces a novel encryption and decryption algorithm that integrates Radio mean labelling of cycle graphs with a polyalphabetic cypher, aiming to bolster cryptographic security. Graph labelling assigns labels to graph elements, facilitating efficient data representation and manipulation. A radio labelling ƒ of graph G assigns positive integers to the vertices of G such that |ƒ(u) − ƒ(v)| ≥ diam(G) + 1 − d (u , v), where u, v ∈ V (G), diam(G) represents the diameter of the graph, and d(u, v) denotes the distance between vertices u and v. This definition is modified as ⌈(ƒ(u) + ƒ(v)) ⁄ 2 ⌉ ≥ diam(G) + 1 − d(u, v), which is called the Radio Mean Labelling (RML) of G. The Radio Mean number of ƒ, rmn(ƒ), is the maximum number assigned to any vertex of G. The Radio Mean number of G, rmn(G), is the minimum value of rmn(ƒ) taken over all RMLs of G. In this approach, the plaintext is transformed into cyphertext using an alternative RML method applied to odd cycle graphs, specifically C₂(n)₊₁, combined with a polyalphabetic structure. The method assigns labels sequentially to odd cycles with odd or even diameters, selecting vertices from zero at maximum distance. Each label satisfies the Radio Mean condition relative to all previous labels, shaping the cypher. Decryption is achieved by utilizing two keys: the odd cycle graph and a keyword, enabling the accurate restoration of the original message. The polyalphabetic table is constructed using a shifting value, k, derived from the Radio mean number of the cycle graph and the length of the keyword. This method effectively enhances data security by integrating graph-based transformations with traditional encryption techniques. Future research will focus on extending this approach by incorporating different cycle graph structures and alternative graph labelling techniques to further improve encryption strength.
A Mathematical model to describe the behaviour of mite population in scabies
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) De Silva, N.H.M.A.; De Silva, T.H.K.R.
Scabies is a highly contagious skin disease caused by the microscopic mite Sarcoptes scabiei. The female mite burrows into the skin to lay eggs, leading to intense itching, and rashes with pimple-like bumps or burrow tracks. While Nodular Scabies involves fewer mites, Crusted Scabies is a severe form characterized by thick crusts and thousands of mites. This study develops a mathematical model to examine the population dynamics of mites and the spread of rashes due to human scabies infestation. The model captures the four developmental stages of the mite: egg, larva, nymph and adult, and considers male and female mites separately. Mite mortality is influenced by natural lifespan, immune response, and medications, particularly with permethrin 5%. The model consists of sixteen parameters, where values of eleven parameters were obtained from existing literature, and the values of the other five parameters were assumed based on biological reasoning. In this model, four key assumptions are made: individuals get infectious when carrying fertilized female mites, permethrin 5% exhibits equal effectiveness against both larval and nymph stages, a uniform immune response with a constant effectiveness rate of 5% is applied across all developmental stages of the mites, and adult mites emerge in equal proportions of males and females. The model is solved both analytically and numerically, using Python, and the results were validated by comparing with the existing literature. Simulation results show that without treatment, mite populations grow rapidly, leading to Crusted Scabies. A 7-day treatment reduces mites, but does not eliminate them, while a 14- to 20-day treatment ensures complete clearance. Early and continuous treatment is crucial, as delays or early discontinuation leads to rapid regrowth. These findings are consistent with medical observations, supporting the validity of the proposed model.
Product cordial labelling of lattice of helm graphs
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Fernando, C.L.R.; Perera, A.A.I.; Senadeera, A.T.
Graph labelling is a widely studied concept in graph theory, involving the assignment of integers to vertices, edges, or both under specific constraints. One such labelling, cordial labelling, was introduced by Ibrahim Cahit in 1987 as a generalization of graceful and harmonious labelling. A particular variant, known as product cordial labelling, is defined for a graph G = (V(G), E(G)) as a function ƒ: V(G) → {0,1}, where each edge uv receives a label determined by the product ƒ(u)ƒ(v). The labeling must satisfy two conditions: the absolute difference between the number of vertices labeled 0 and those labeled 1 should be at most 1, and the absolute difference between the number of edges labeled 0 and those labeled 1 should also not exceed 1. If a graph can be labelled in this manner, it is classified as product cordial. The concept of product cordial labelling was introduced by R. Ponraj, M. Sivakumar, and M. Sundaram, and since then, many authors have worked on this product cordial labelling and have identified many types of graphs as product cordial. The helm graph H(n) is the graph obtained from an n-wheel graph by adjoining a pendant edge at each node of the cycle, which can be used in real world situations like controlling systems, networking, etc. This study presents that helm graphs are product cordial, and introduce the product cordial labelling for any such graph depending on whether its cycles have odd or even number of vertices. Furthermore, the product cordiality of lattices of helm graphs is studied by combining a finite number of copies of helm graphs with or without bridging edges.
An Optimization technique to assembly line balancing in apparel industry
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Salay, M.I.; Senarathne, B.D.S.N.; Dissanayake, D.M.P.S.; Rajarathne, P.M.K.; Jayarathna, D.V.M.; Kularathna, A.P.; Kahadawa, J.D.; Daundasekera, W.B.
Balancing the assembly line in the apparel industry, which is crucial for maximizing production efficiency, requires effective assignments of machine operators (MOs) based on their skills and availability to reduce production delays. This study aims to increase the production rate by developing an optimization model as a two-phase Integer Linear Programming Model (ILPM). In the first phase, based on the MOs’ efficiency, an ILPM is implemented to increase the total production rate by assigning them to operations while identifying bottleneck operations which contribute to lower the production rate. In the second phase, the total skill level of the assembly line is minimized. The predetermined bottleneck production rate is used as an indicator, ensuring that the production rate which is maximized in the first phase is kept fixed. The reassignment of the remaining MOs is based on their skill levels, while the bottleneck operations and operators are isolated in the second phase. The proposed method assigns MOs to maximize the production. Sequentially, it seeks to minimize the overall skill usage to ensure efficient utilization of operator skills. The bottleneck operation, identified in the first phase, ensures that the most efficient MOs are assigned where needed, while other operations are conducted by MOs based on a compromise solution between their skill levels and availability. This approach guarantees that the maximum production rate remains intact while optimizing operator efficiency. This proposed method offers flexibility in assigning operators with an optimum production rate and identifies the optimum number of MOs needed to perform the set of operations. Isolating bottleneck operations in the second phase minimizes their negative effect on the production efficiency and allows to reallocate resources to less critical operations. This two-phase approach compromises between production rates and skill levels, and ensures a balanced and efficient workflow. This approach can be adopted to any production line with the necessary modifications.
Product cordial labelling of generalized helm graphs
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Senadeera, A.T.; Fernando, C.L.R.; Perera, A.A.I.
Graph labelling is the process of assigning integers to the vertices, edges, or both, under specific constraints. In 1987, Ibrahim Cahit introduced cordial labelling as a more flexible alternative to graceful and harmonious labellings. A specialized form, product cordial labelling, was later introduced by R. Ponraj, M. Sivakumar, and M. Sundaram in 2012, leading to further research on different classes of graphs that exhibit this property. Product cordial labelling is defined as a function ƒ: V(G) → {0,1}, where each edge uv is assigned the label ƒ(u)ƒ(v). A graph is said to be product cordial if the absolute difference between the number of vertices labeled 0 and 1 is at most 1, and the absolute difference between the number of edges labeled 0 and 1 does not exceed 1. This labelling method provides insights into graph structures and their combinatorial properties, making it a useful tool in network theory, coding, and other applied fields. In this study, the existence of product cordial labelling for helm graphs H(n), obtained by attaching a pendant edge to each vertex of the cycle in an n-wheel graph, is shown. A structured approach is presented for labelling these graphs based on whether the cycle has an odd or even number of vertices. Furthermore, this study extends the analysis to a generalized version of helm graphs, such as those with additional pendant attachments, and explores conditions under which these graphs maintain product cordiality. These findings contribute to the broader study of graph labellings and their applications in discrete mathematics and theoretical computer science.
Examining the interaction of motivation, self-efficacy, and academic emotions in shaping mathematics learning outcomes: a study on undergraduate students in management science in Sri Lanka
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Kumara, H.C.T.
This study investigates the influence of motivation components, effort, self-efficacy, and worry, on the mathematics learning outcomes of Sri Lankan undergraduate students in Management Science, with a sample of 384. Using a validated questionnaire, these components were measured in relation to gender and academic performance. Results show high overall motivation with 72.7% demonstrating strong effort, while self-efficacy is moderate with 47.1%. Female students scored significantly higher in motivation than males, particularly in self-efficacy and effort. Students with higher cumulative grade point averages (CGPA) exhibited stronger motivation, specifically in the range of 3.00-3.49 CGPA showing the highest scores. Significant positive correlations emerged between motivation components and academic achievement: effort (r = .152, p < .01), self-efficacy (r = .175, p < .01), and overall motivation (r = .214, p < .01). Moderate worry levels correlated with better performance, suggesting some anxiety may be motivational, which should be investigated further. Both male and female students demonstrated overall higher levels of motivation, while no visible differences were observed in terms of gender. The study contributes to understanding the influence of motivation on learning Mathematics.
Effects of mathematics recitation sessions on course success and its equitable impact on college calculus
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Corchado, C.
To combat a prevalent low success rate as college STEM majors take courses in the Calculus sequence, recitation support sessions focusing on group work and discussion were introduced at a public university. This research studies the effects of this implementation in Precalculus, Calculus I, and Calculus II courses by investigating failure rates and course success. Discussing the qualitative student-reported perceptions of recitation sessions and quantitative ordinal linear regression analysis of course outcomes helps bridge the gap between how research views these sessions versus the experiences of the impacted students. The probability of earning an F (versus a D or above) in Precalculus without recitation is 47.37%, while it is 12.28% with recitation. Calculus I students had a 17.36% probability of failing the course without recitation, and 9.91% with. Calculus II students had a 15.25% chance of failing the course without recitation and a 13.04% chance with. Students overall had lower rates of earning lower course grades. Of the students surveyed, 86% agreed that they interact with their peers during recitations. This allows greater opportunity for collaboration and a leveling of understanding throughout the lecture sections. This is reflected in the 73% of students who agreed that recitations help them understand mathematics concepts better. In recitation sessions, small learning communities of problem solvers are formed, and students can enter a safe space to practice mathematics content. Diving into the setbacks and successes of recitations offers an example of how to catalyze change in the classroom. Since the odds and probabilities of earning lower scores significantly decrease as recitations are introduced, this data indicates that students are more likely to not only pass their course but also receive higher grades. Although this study focuses on undergraduate students, the ideas for the sessions and strategies can be utilized in almost any academic environment. Showcasing researched recitation sessions and their effects could offer insight into other supplemental courses or recitation-like classroom setups.
The Impact of cohort experiences on students’ sense of belonging, academic performance, and career readiness
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Michel - Carrillo, Itzel
Mathematics is widely regarded as one of the most challenging academic disciplines, and many students struggle to complete their degrees within the typical four-year timeline in the USA. This study explores how cohort affiliation and shared experiences influence mathematics majors’ sense of belonging, academic performance, and preparedness to become high school teachers. A significant number of undergraduates in mathematics in the state of California pursue the Teaching Option or the Integrated Credential Option with the goal of entering the teaching profession. Traditionally, aspiring mathematics educators in the USA complete a four-year mathematics degree followed by a one-year credential programme. However, the Integrated Credential Programme allows students to complete both their degree and credential within four years. This research focuses on the academic success of undergraduate students pursuing the Teaching and Integrated Credential Options who participated in structured cohort experiences, compared to those who did not engage in such programmes. The cohort programmes examined Mentoring Mathematics Scholars with Success (M2S2), Building Opportunities through Networks of Discoveries (BOND), and the NOYCE Scholarship Programme. Both M2S2 and NOYCE are federally funded programmes that offer financial support and cohort-based learning experiences. The NOYCE programme also provides teaching seminars, content mentoring, and opportunities to attend professional conferences. Using a mixed-methods approach, this study compares the sense of belonging and academic outcomes of students in cohort programmes with those of other mathematics majors. Data sources include institutional performance metrics (GPA and graduation rates), surveys, and interviews. The quantitative dataset includes 766 mathematics majors who entered the university between 2018 and 2024, comprising both first-time freshmen and transfer students from community colleges. Additionally, 43 survey responses and five interviews were collected and analyzed quantitatively. A pooled two- sample t-test is used to identify significant differences in outcomes between the groups. Preliminary findings indicate that students involved in cohort programmes demonstrate higher retention rates, a stronger sense of belonging, and increased career readiness in mathematics education. These insights can inform the development of academic programmes that enhance student success and effectively prepare future educators for the teaching profession.
Statistical analysis of engineering undergraduates' performance across formative and summative assessments in calculus module
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Nawarathne, N.G.S.A.; Malake, K.A.P.; Premalal, U.S.R.; Nawarathne, N.G.R.M.
A collection of 199 undergraduates from the Faculty of Engineering, General Sir John Kotelawala Defence University (KDU), was selected for the study using convenience sampling. The calculus module for engineering undergraduates is designed with various essential and complex concepts for advanced engineering problems and is offered in the second academic semester. To fulfil the formative assessment category, five in-class assignments were conducted to cover all learning outcomes. For the analysis, the weighted average marks of the formative assessments were considered, and the end-semester examination was considered as the summative assessment. A descriptive analysis was performed to identify the relationship between the summative assessment marks of the calculus module and the formative assessment marks. The significant gap between the weighted average of formative and summative assessment marks suggests that end-semester examinations are considerably more challenging than continuous assessments. Shapiro-Wilk normality test results indicated that the formative assignment marks slightly differ from normality, and the end-semester examination marks are normally distributed. Pearson and Spearman Rank correlation tests were performed in the analysis. Statistically significant moderate positive correlations indicate that students who perform well in formative assessment tend to perform better in summative assessment in the calculus module. A simple linear regression model was fitted to strengthen the results, revealing that formative assessment marks significantly predict summative assessment performance (R2 = 0.327). The residual analysis shows that the model's error terms are normally distributed with relatively constant variance across the range of predicted values. Although, the correlation improved slightly upon the removal of influential outliers, the fundamental relationship between the assessments remained consistent with the regression model, explaining approximately 33% of the variance in summative assessment performance.
Building on prior knowledge and making connections: case of teaching complex numbers
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Jayakody, G. N.; Perera, S.
This study explores the role of mathematical connections in the teaching of complex numbers at the upper-secondary level. Drawing on the Extended Theory of Mathematical Connections (ETMC), we examine how teachers establish links between prior knowledge and new concepts to promote conceptual understanding. Through the analysis of video-recorded lessons from 10 teachers of G.C.E. (A/L) Combined Mathematics, we identify instances of Instruction-Oriented Connections (IOC), Different Representations (DR), and Part-Whole Relationships (PWR). Additionally, our findings reveal two previously unclassified types of connections: Extensional Connections (6), where new concepts are framed as extensions of prior knowledge, and Structural Connections (4), which highlight similarities in mathematical structures. Results emphasize the importance of these connections in fostering deeper comprehension and suggest their applicability across broader mathematical domains. This study contributes to the ongoing discourse on mathematical pedagogy by providing practical insights for educators to enhance student learning through purposeful connections.

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