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Articles 1 - 30 of 562
Full-Text Articles in Mathematics
Double-Scoring: Reliable Extraction Of Strong Lottery Tickets, Bryce Christopherson, Jack Baretz, Darian Colgrove, Salah Dandan
Double-Scoring: Reliable Extraction Of Strong Lottery Tickets, Bryce Christopherson, Jack Baretz, Darian Colgrove, Salah Dandan
Mathematics Faculty Publications
The lottery ticket hypothesis proposes that large random neural networks contain sparse subnetworks that can match the performance of dense models after compara- ble training. A stronger version asserts that sufficiently overparameterized random networks contain subnetworks that are already accurate before any weight training. Existing theory establishes that such strong lottery tickets exist, but reliable ex- traction remains difficult. We revisit edge-popup, a frozen-weight score-training method for extracting strong tickets, and identify layerwise sparsity selection as a central bottleneck. We introduce double-scoring, an augmented score-space parameterization that replaces a layerwise sparsity search with optimization over enlarged score tensors. We prove …
Adaptive Control For A Robotic Bipedal Device Using A Hybrid Discrete-Continuous Reinforcement Learning Strategy, Karla Rincon-Martinez, Wen Yu, Isaac Chairez
Adaptive Control For A Robotic Bipedal Device Using A Hybrid Discrete-Continuous Reinforcement Learning Strategy, Karla Rincon-Martinez, Wen Yu, Isaac Chairez
Mathematics Faculty Publications
This research develops and implements a novel reinforcement learning (RL) architecture to address the trajectory-tracking problem in bipedal robotic systems under articulated-joint constraints. The proposed RL framework extends previously designed adaptive controllers characterized by state-dependent gain structures. The learning mechanism comprises two hierarchical adaptation layers: the first employs an adaptive dynamic programming (ADP) formulation to approximate the Bellman value function using a class of continuous-time dynamic neural networks. In contrast, the second uses an iterative optimization scheme based on the deep deterministic policy gradient (DDPG) algorithm. The resulting control strategy minimizes a robust performance index defined over the tracking trajectories …
Alexander Duals Of Symmetric Simplicial Complexes And Stanley-Reisner Ideals, Ayah Almousa, Kaitlin Bruegge, Martina Juhnke-Kubitzke, Uwe Nagel, Alexandra Pevzner
Alexander Duals Of Symmetric Simplicial Complexes And Stanley-Reisner Ideals, Ayah Almousa, Kaitlin Bruegge, Martina Juhnke-Kubitzke, Uwe Nagel, Alexandra Pevzner
Mathematics Faculty Publications
Given an ascending chain (In)n∈N of Sym-invariant squarefree monomial ideals, we study the corresponding chain of Alexander duals (In∨)n∈N. Using a novel combinatorial tool, which we call avoidance up to symmetry, we provide an explicit description of the minimal generating set up to symmetry in terms of the original generators. Combining this result with methods from discrete geometry, this enables us to show that the number of orbit generators of In∨ is given by a polynomial in n for sufficiently large n. The same is true for …
The Fermat Quartic X4 + Y4 = 2m In Quadratic Number Fields, Jayanth Athipatla
The Fermat Quartic X4 + Y4 = 2m In Quadratic Number Fields, Jayanth Athipatla
Mathematics Faculty Publications
In this paper, we generalise to the family of Fermat quartics X4+Y4=2m,m∈Z, a result of Aigner [‘Über die Möglichkeit von x4+y4=z4 in quadratischen Körpern’, Jahresber. Deutsch. Math.-Ver. 43 (1934), 226–228], which proves that there is only one quadratic field, namely Q(−7−−−√), that contains solutions to the Fermat quartic X4+Y4=1. The m≡0(mod4) case is due to Aigner. The m≡2(mod4) case follows from a result of Emory [‘The Diophantine equation X4+Y4=D2Z4 in quadratic fields’, Integers 12 (2012), Article no. A65, 8 pages]. This paper focuses on the two cases m≡1,3(mod4), classifying for m≡1(mod4) the infinitely many quadratic number fields that contain solutions, …
(A,B,C) Tilings With Prescribed Symmetry Groups From Regular Triangle Or Hexagon Tiling, Mark D. Tomenes, Ma. Louise Antonette N. De Las Penas
(A,B,C) Tilings With Prescribed Symmetry Groups From Regular Triangle Or Hexagon Tiling, Mark D. Tomenes, Ma. Louise Antonette N. De Las Penas
Mathematics Faculty Publications
A tiling T of the Euclidean plane (E2) is a countable collection of closed topological disks called tiles T = {Ti : i ∈ N} that is a covering (Ui Ti = E2) as well as a packing (Int(Ti) ∩ Int(Tj) = ∅ if i ̸= j, Int(T) denotes the interior of tile T). One of the problems of interest in discrete geometry is the classification of tilings based on transitivity properties of their vertices, edges and tiles. This talk presents a family of tilings whose vertices, edges and tiles have exactly a, b and c orbits, respectively, under the …
The Mathematical Experience Museum: Breathing Life Into Theorems And Formulas, Jin Akiyama, Jude Buot, Mark Anthony C. Tolentino
The Mathematical Experience Museum: Breathing Life Into Theorems And Formulas, Jin Akiyama, Jude Buot, Mark Anthony C. Tolentino
Mathematics Faculty Publications
No abstract provided.
Comparing Two Psychometric Approaches: The Case Of Item Analysis For A Classroom Test In Mathematics, Mark Lester B. Garcia, Kevin Carl P. Santos, Catherine P. Vistro-Yu
Comparing Two Psychometric Approaches: The Case Of Item Analysis For A Classroom Test In Mathematics, Mark Lester B. Garcia, Kevin Carl P. Santos, Catherine P. Vistro-Yu
Mathematics Faculty Publications
Multiple-choice and constructed-response item formats are widely used in Philippine classrooms where tests are primarily summative. Conducting item analysis provides teachers the professional possibility to independently improve their test items while also allowing them to make informed decisions about test improvement and ensure that their assessments provide meaningful scores. Comparisons of item analysis approaches have been extensively used in standardized tests but not so much in small-scale testing such as classroom assessments. Hence, this research reports an empirical study where a summative test for classroom use is analyzed using psychometric techniques from the Classical Test Theory (CTT) and the Item …
Identities For Whitehead Products And Infinite Sums, Jeremy Brazas
Identities For Whitehead Products And Infinite Sums, Jeremy Brazas
Mathematics Faculty Publications
Whitehead products and natural infinite sums are prominent in the higher homotopy groups of the n-dimensional infinite earring space En" role="presentation"> and other locally complicated Peano continua. In this paper, we derive general identities for how these operations interact with each other. As an application, we consider a shrinking wedge of finite (n−1)" role="presentation">-connected CW-complexes and compute the infinite-sum closure W2n−1(X)" role="presentation"> of the set of Whitehead products [α,β]" role="presentation"> in π2n−1(X)" role="presentation"> where α,β∈πn(X)" role="presentation"> are represented in respective sub-wedges that meet only at the basepoint. In particular, we show that W2n−1(X)" role="presentation"> is canonically isomorphic to …
Impartial Geodetic Building Games On Graphs, Bret J. Benesh, Dana C. Ernst, Marie Meyer, Sarah K. Salmon, Nándor Sieben
Impartial Geodetic Building Games On Graphs, Bret J. Benesh, Dana C. Ernst, Marie Meyer, Sarah K. Salmon, Nándor Sieben
Mathematics Faculty Publications
A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the set. The convex hull of a set of vertices is the smallest convex set containing the set. We study variations of two games introduced by Buckley and Harary, where two players take turns selecting previously-unselected vertices of a graph until the convex hull of the jointly-selected vertices becomes too large. The last player to move is the winner. The achievement game ends when the convex hull contains every vertex. In the avoidance game, the …
Vanishing Of Local Cohomology With Applications To Hodge Theory, Scott Hiatt
Vanishing Of Local Cohomology With Applications To Hodge Theory, Scott Hiatt
Mathematics Faculty Publications
Let H = ((H, F •), L) be a polarized variation of Hodge structure on a smooth quasi-projective variety U . By M. Saito’s theory of mixed Hodge modules, the variation of Hodge structure H can be viewed as a polarized Hodge module M ∈ HM (U ). Let X be a compactification of U , and j : U ↪→ X is the natural map. In this paper, we use local cohomology with mixed Hodge module theory to study j+M ∈ DbM HM (X). In particular, we study the graded pieces of the de Rham complex GrF p DR(j+M) …
Enhancing Mathematical Models For Covid-19 Pandemic Response: A Philippine Study, Timothy Robin Teng, Elvira De Lara-Tuprio, Ma. Regina Justina Estuar, Christian Pulmano, Lu Christian S. Ong, Zachary Pangan, Lenard Paulo V. Tamayo, Jasper John V. Segismundo, Mark Anthony C. Tolentino, Alyssa Nicole N. Ty
Enhancing Mathematical Models For Covid-19 Pandemic Response: A Philippine Study, Timothy Robin Teng, Elvira De Lara-Tuprio, Ma. Regina Justina Estuar, Christian Pulmano, Lu Christian S. Ong, Zachary Pangan, Lenard Paulo V. Tamayo, Jasper John V. Segismundo, Mark Anthony C. Tolentino, Alyssa Nicole N. Ty
Mathematics Faculty Publications
Mathematical models supported by a robust automated data pipeline proved to be useful tools for a data-driven and science-based response and policy-making during the COVID-19 pandemic in the Philippines. In the first year of the pandemic, FASSSTER (Feasibility Analysis on Syndromic Surveillance using Spatio-Temporal Epidemiological modeleR) used a compartmental model to generate scenario-based projections of COVID-19 cases. The emergence of the Delta variant, however, and the administration of vaccines over the second half of 2021 caused significant changes in the Philippine pandemic landscape. This necessitated making adjustments to the model to better capture the local disease transmission dynamics and address …
Noncrystallographic Tail-Triangle C-Groups Of Rank 4 And Interlacing Number 2, Mark L. Loyola, Nonie Elvin S. Leyrita, Ma. Louise Antonette N. De Las Peñas
Noncrystallographic Tail-Triangle C-Groups Of Rank 4 And Interlacing Number 2, Mark L. Loyola, Nonie Elvin S. Leyrita, Ma. Louise Antonette N. De Las Peñas
Mathematics Faculty Publications
This work applies the modular reduction technique to the Coxeter group of rank 4 having a star diagram with labels 5, 3, and k = 3,4,5, or 6. As moduli, we use the primes in the quadratic integer ring Z[τ], where τ = (1+√5)/2, the golden ratio. We prove that each reduced group is a C-group, regardless of the prime used in the reduction. We also classify each reduced group as a reflection group over a finite field, whenever applicable.
A Quotient Of Fomin-Kirillov Algebra And Q-Lucas Polynomial, Sirous Homayouni
A Quotient Of Fomin-Kirillov Algebra And Q-Lucas Polynomial, Sirous Homayouni
Mathematics Faculty Publications
We introduce a quotient of the Fomin-Kirillov algebra F K(n) denoted by F KCn (n), over the ideal generated by the edges of a complete graph on n vertices that are missing in the n-cycle graph Cn. In this quotient algebra, we establish a one-to-one correspondence between the basis elements and the set of matchings in an n-cycle graph. We prove that the Hilbert series of F KCn (n) corresponds to the q-Lucas polynomials, and the dimension of this quotient algebra is equal to the Lucas number Ln. We also find the character map of this quotient algebra over the …
An Em-Based Likelihood Inference For Degradation Data Analysis Using Gamma Process, Lochana Palayangoda, N. Balakrishnan
An Em-Based Likelihood Inference For Degradation Data Analysis Using Gamma Process, Lochana Palayangoda, N. Balakrishnan
Mathematics Faculty Publications
The gamma process is widely used for the lifetime estimation of highly reliable products that degrade over time. Typically, incomplete likelihood is used to estimate the model parameters and the reliability estimates for the first passage time distribution of the gamma process; however, it (i.e., pseudo method) does not consider interval censoring and right censoring information of the degradation data. In this work, the expectation-maximization algorithm-based method (EM method) is developed for the estimation of the gamma process model parameters and the reliability estimates incorporating interval censoring and right censoring. The asymptotic variance–covariance matrix and the asymptotic confidence intervals for …
Leveraging International Large-Scale Assessments: Insights From An Item-Writing Professional Development Program For High School Mathematics Teachers, Mark Lester B. Garcia, Catherine P. Vistro-Yu
Leveraging International Large-Scale Assessments: Insights From An Item-Writing Professional Development Program For High School Mathematics Teachers, Mark Lester B. Garcia, Catherine P. Vistro-Yu
Mathematics Faculty Publications
The Philippine Department of Education, despite seeing minimal improvements in the country’s score and rankings in the recent cycles of international large-scale assessments (ILSAs) such as TIMSS and PISA, maintained that it shall continue to participate in ILSAs to monitor the progress of educational effectiveness and benchmark with other countries by observing and adopting commendable practices. While legislators and other stakeholders push for increased financial resources in the education sector as part of the country’s preparations for upcoming ILSAs, one crucial aspect that is largely overlooked is teacher training. This paper presents a viable yet contentious way of upskilling teachers …
Resonant Solutions Of The Non-Linear Schrödinger Equation With Periodic Potential, Arein Duaibes, Yulia Karpeshina
Resonant Solutions Of The Non-Linear Schrödinger Equation With Periodic Potential, Arein Duaibes, Yulia Karpeshina
Mathematics Faculty Publications
The goal is construction of stationary solutions close to non-trivial combinations of two plane waves at high energies for a periodic non-linear Schrödinger Equation in dimension two. The corresponding isoenergetic surface is described for any sufficiently large energy k2. It is shown that the isoenergetic surface corresponding to k2 is essentially different from that for the zero potential even for small potentials. We use a combination of the perturbative results obtained earlier for the linear case and a method of successive approximation.
Designing Learning Trajectory To Support Preservice Mathematics Teachers' Skills In Creating And Implementing Realistic Mathematics Tasks, Veronika Fitri Rianasari, Angela Fatima H. Guzon
Designing Learning Trajectory To Support Preservice Mathematics Teachers' Skills In Creating And Implementing Realistic Mathematics Tasks, Veronika Fitri Rianasari, Angela Fatima H. Guzon
Mathematics Faculty Publications
In mathematics teaching and learning, mathematics tasks embedded in realistic contexts are crucial for developing mathematical concepts, procedures, and the application of mathematical knowledge. Despite this, mathematics teachers often encounter challenges in designing and implementing such realistic mathematics tasks. Therefore, this study aims to construct a learning trajectory to enhance preservice mathematics teachers' abilities to create and implement Realistic Mathematics Tasks (RMTs). Employing a design research methodology, the study comprises three phases: preliminary design, teaching experiment, and retrospective analysis. The data presented in this article are from the first cycle, encompassing all three phases. The research involved four fourth-year preservice …
Differentiated Instruction In Geometry Using Low Floor, High Ceiling Mathematical Tasks, Franklin R. Falculan, Maria Alva Q. Aberin
Differentiated Instruction In Geometry Using Low Floor, High Ceiling Mathematical Tasks, Franklin R. Falculan, Maria Alva Q. Aberin
Mathematics Faculty Publications
This study investigated the effects of using Low Floor High Ceiling (LFHC) mathematical tasks on students’ conceptual understanding and procedural fluency in seventh-grade Geometry by closely examining pre-test and posttest results. Two intact classes composed of thirty-two grade 7 students in each class participated in the study. The control group was taught and had practice using conventional, algorithmic tasks while the experimental group was taught and had practice using LFHC mathematical tasks. Data analysis revealed that, as compared to students exposed to algorithmic problems, students exposed to LFHC activities were much more mathematically proficient in Geometry, at the very least …
Representations Of Solutions Of Time-Fractional Multi-Order Systems Of Differential-Operator Equations, Sabir Umarov
Representations Of Solutions Of Time-Fractional Multi-Order Systems Of Differential-Operator Equations, Sabir Umarov
Mathematics Faculty Publications
This paper is devoted to the general theory of systems of linear time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order is known through the matrix-valued Mittag-Leffler function. Multi-order (incommensurate) systems with rational components can be reduced to single-order systems, and, hence, representation formulas are also known. However, for arbitrary fractional multi-order (not necessarily with rational components) systems of differential equations, the representation formulas are still unknown, even in the case of fractional-order ordinary differential equations. In this paper, we obtain representation formulas for the solutions of arbitrary fractional multi-order …
How Generative Ai Models Such As Chatgpt Can Be (Mis)Used In Spc Practice, Education, And Research? An Exploratory Study, Fadel M. Megahed, Ying-Ju (Tessa) Chen, Joshua A. Ferris, Sven Knoth, L. Allison Jones-Farmer
How Generative Ai Models Such As Chatgpt Can Be (Mis)Used In Spc Practice, Education, And Research? An Exploratory Study, Fadel M. Megahed, Ying-Ju (Tessa) Chen, Joshua A. Ferris, Sven Knoth, L. Allison Jones-Farmer
Mathematics Faculty Publications
Generative Artificial Intelligence (AI) models such as OpenAI's ChatGPT have the potential to revolutionize Statistical Process Control (SPC) practice, learning, and research. However, these tools are in the early stages of development and can be easily misused or misunderstood. In this paper, we give an overview of the development of Generative AI. Specifically, we explore ChatGPT's ability to provide code, explain basic concepts, and create knowledge related to SPC practice, learning, and research. By investigating responses to structured prompts, we highlight the benefits and limitations of the results. Our study indicates that the current version of ChatGPT performs well for …
Commognitive Conflicts In A Virtual Learning Environment: Exploring The Affordances Of Mobile Learning For Discourse Analysis, Mark N. Cumayas, Maria Alva Q. Aberin
Commognitive Conflicts In A Virtual Learning Environment: Exploring The Affordances Of Mobile Learning For Discourse Analysis, Mark N. Cumayas, Maria Alva Q. Aberin
Mathematics Faculty Publications
This paper explores the affordances of mobile learning in developing frameworks for discourse analysis. Specifically, this paper examines the commognitive analysis of classroom discourses in virtual learning environments (VLEs) and how it resolves the challenges of discourse analysis in face-to-face (F2F) settings. With the ongoing social turn of mathematics education research comes the widespread adoption of discourse analysis in educational research. The shift towards virtual learning technologies necessitated by the recent COVID-19 crisis has led to the development of various tools and processes that enable the teaching-learning process to occur in the virtual environment. While the initial drive to adapt …
Geogebra Applets For Fostering Conceptual Understanding In Algebra, Ma. Louise Antonette N. De Las Penas, Mark Anthony C. Tolentino, Maria Alva Q. Aberin, Agnes D. Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Debbie Marie B. Verzosa
Geogebra Applets For Fostering Conceptual Understanding In Algebra, Ma. Louise Antonette N. De Las Penas, Mark Anthony C. Tolentino, Maria Alva Q. Aberin, Agnes D. Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Debbie Marie B. Verzosa
Mathematics Faculty Publications
This paper discusses two GeoGebra applets, Radical and Parabola, that are designed to strengthen the conceptual understanding of specific topics in algebra. The design and pedagogical basis of the applets are presented. The integration of the applets in teaching Grade 9 mathematics in a partner high school in the Philippines is then discussed. Finally, we report feedback gathered from students and teachers during this integration. Their feedback indicates the potential of these applets for improving students’ learning of algebra.
Cognitive Load Scale In Learning Formal Definition Of Limit: A Rasch Model Approach, Rina Oktaviyanthi, Ria Noviana Agus, Mark Lester B. Garcia, Kornkanok Lertdechapat
Cognitive Load Scale In Learning Formal Definition Of Limit: A Rasch Model Approach, Rina Oktaviyanthi, Ria Noviana Agus, Mark Lester B. Garcia, Kornkanok Lertdechapat
Mathematics Faculty Publications
Constructing proofs for the limit using the formal definition induces a high cognitive load. Common assessment tools, like cognitive load scales, lack specificity for the concept of limits. This research aims to validate an instrument tailored to assess cognitive load in students focused on the formal definition of limits, addressing the need for diverse strategies in education. The research employs a quantitative survey design with a Rasch model approach, utilizing a data collection instrument in the form of a questionnaire. Subsequently, the data are analyzed by focusing on three aspects: (1) item fit to the Rasch model, (2) unidimensionality, and …
Tight Bounds For The N2-Chromatic Number Of Graphs, Arnold Eniego, Ian June L. Garces, Jose Rosario
Tight Bounds For The N2-Chromatic Number Of Graphs, Arnold Eniego, Ian June L. Garces, Jose Rosario
Mathematics Faculty Publications
Let G be a connected graph. A vertex coloring of G is an N2-vertex coloring if, for every vertex v, the number of different colors assigned to the vertices adjacent to v is at most two. The N2-chromatic number of G is the maximum number of colors that can be used in an N2vertex coloring of G. In this paper, we establish tight bounds for the N2-chromatic number of a graph in terms of its maximum degree and its diameter, and characterize those graphs that attain these bounds.
Additive Energies Of Subsets Of Discrete Cubes, Xuancheng Shao
Additive Energies Of Subsets Of Discrete Cubes, Xuancheng Shao
Mathematics Faculty Publications
For a positive integer n ≥ 2, define tn to be the smallest number such that the additive energy E (A) of any subset A ⊂ {0, 1, · · · , n − 1}d and any d is at most |A|tn . Trivially, we have tn ≤ 3 and tn ≥ 3 − logn 3n3 2n3 + n by considering A = {0, 1, · · · , n − 1}d. In this note, we investigate the behaviour of tn for large n and obtain the following non-trivial bounds: 3 − (1 + on→∞(1)) logn 3√3 4 ≤ tn …
A Geometric Model For Syzygies Over 2-Calabi–Yau Tilted Algebras Ii, Ralf Schiffler, Khrystyna Serhiyenko
A Geometric Model For Syzygies Over 2-Calabi–Yau Tilted Algebras Ii, Ralf Schiffler, Khrystyna Serhiyenko
Mathematics Faculty Publications
In this article, we continue the study of a certain family of 2-Calabi–Yau tilted algebras, called dimer tree algebras. The terminology comes from the fact that these algebras can also be realized as quotients of dimer algebras on a disk. They are defined by a quiver with potential whose dual graph is a tree, and they are generally of wild representation type. Given such an algebra B, we construct a polygon S with a checkerboard pattern in its interior, which defines a category Diag(S). The indecomposable objects of Diag(S) are the 2-diagonals in S, and its morphisms are certain pivoting …
Id Numbers Of Lobster Graphs, Mark Anthony C. Tolentino, Luis Silvestre Jr, Richwell T. Chan Sim, Amir Jann Erikson Diga, Althea Julia R. Loyola
Id Numbers Of Lobster Graphs, Mark Anthony C. Tolentino, Luis Silvestre Jr, Richwell T. Chan Sim, Amir Jann Erikson Diga, Althea Julia R. Loyola
Mathematics Faculty Publications
No abstract provided.
Can't We Just Use Computers? Initial Efforts On Technology-Enhanced Learning Of Operations Research In A Philippine University, Lester Hao, Jeric C. Briones, Mark Anthony C. Tolentino
Can't We Just Use Computers? Initial Efforts On Technology-Enhanced Learning Of Operations Research In A Philippine University, Lester Hao, Jeric C. Briones, Mark Anthony C. Tolentino
Mathematics Faculty Publications
Operations Research (OR) is a required course in any applied math program in the Philippines. It involves complex and computation-heavy algorithms to guide and improve decision-making in organizations and relevant contexts. Despite the advent of software that have automated the computations or the implementation of algorithms, the teaching and learning of OR may still be rife with procedures being performed manually by hand. In this paper, we report on our initial progress on a research project that aims to revise the OR syllabi in one Philippine university, by integrating more technological tools in the teaching and learning of OR for …
A Mathematical App For The Conceptual Understanding Of Area And Perimeter, Jumela F. Sarmiento, Debbie Marie B. Verzosa, Maria Alva Q. Aberin, Ma. Louise Antonette De Las Penas, Agnes D. Garciano, Juan Carlo F. Mallari, Mark Anthony C. Tolentino
A Mathematical App For The Conceptual Understanding Of Area And Perimeter, Jumela F. Sarmiento, Debbie Marie B. Verzosa, Maria Alva Q. Aberin, Ma. Louise Antonette De Las Penas, Agnes D. Garciano, Juan Carlo F. Mallari, Mark Anthony C. Tolentino
Mathematics Faculty Publications
This paper discusses an app that was developed to build a strong understanding of the concepts of area and perimeter in students. An important feature of the app is the three-component feature which highlights progressive learning: Explore, designed for the learning of the conceptual understanding of area and perimeter; Apply, where area and perimeter concepts are applied; and Create intended for constructing representations to develop higher order thinking skills. The pedagogical basis for the creation of the app, the game design elements employed in the app as well as the integration of the app in the classroom will be presented.
A Visualization App On Proving Geometric Concepts, Ma. Louise Antonette N. De Las Peñas, Debbie Marie B. Verzosa, Maria Alva Q. Aberin, Agnes D. Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Juan Carlo F. Mallari
A Visualization App On Proving Geometric Concepts, Ma. Louise Antonette N. De Las Peñas, Debbie Marie B. Verzosa, Maria Alva Q. Aberin, Agnes D. Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Juan Carlo F. Mallari
Mathematics Faculty Publications
This paper discusses the description, design and pedagogical basis of a mathematical app called Two Column Proof which provides students a framework for writing proofs of geometric statements. The app focuses on proving concepts on: properties of parallelograms, conditions that determine when a quadrilateral is a parallelogram, properties on trapezoids and kites for high school mathematics. It employs visual representations for students to understand the statement or reason of each given line in the proof, strengthening their logical and mathematical knowledge needed in the proof construction.