Education Commons^™

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 …

Deployment Of Mathematical Resources To A Philippine High School Through A Community Lte Network, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Verzosa

Mathematics Faculty Publications

In the Philippines, one challenge that continues to be faced by the Department of Education in bringing educational content in a blended learning modality is the lack of internet access of the learners. This paper discusses the distribution, through a community LTE network, of mathematical resources for Grades 7 to 10 to teachers and students of a particular high school in the Philippines. It also gives details on particular technological tools (mathematical applications) that were created to help the mathematical learning of students in a remote setting.

Pre-Service Secondary Mathematics Teachers' Definitions Of Mathematics Terms In Their Video-Lesson Presentations: A Deductive Content Analysis, Art Walden A. Dejoras, Catherine P. Vistro-Uy

Mathematics Faculty Publications

Taking into account the nature of mathematics as an exact science and the essential role of mathematics teachers’ knowledge of fundamental mathematics definitions; the authors investigated the pre-service secondary mathematics teachers (PSMTs) knowledge of a good mathematics definition in their group video-lesson presentations related to algebra; geometry; descriptive statistics; and number theory. The quality of their definitions can provide a glimpse of their preparedness to teach mathematics at the secondary level. Drawing on Leikin and Zazkis’ (2010) framework to analyze teacher- generated definitions; and Borasi’s (1992) characterizations of a good definition; the authors developed an analytical framework to analyze a …

Faith, Family, And Friends As Integral Factors In Student Resilience In The Ateneo De Manila School Of Science And Engineering, Queena N. Lee-Chua

Mathematics Faculty Publications

What makes Filipino students resilient in times of crises such as the COVID-19 pandemic? Even as some students succumb to anxiety and despair and lose motivation to learn; others actively take charge of their learning and remain hopeful and strong amid severe trials. What keeps them going; and what can we learn from them? 25 professors of the Ateneo de Manila School of Science and Engineering selected 92 college undergraduate and graduate students whom they observed to display resilience in learning and prodded them to reflect on how they overcame challenges in and out of the classroom. Whatever their circumstances; …

Development Of An App And Videos To Support The Fraction Learning Trajectory From Grades 1-7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Juan Carlo F. Mallari, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Lack of procedural fluency in fractions impedes access to advanced mathematical courses and limits opportunities for entry into STEM-related fields. This paper describes the design and pedagogical basis of the Moving Fractions app and supplementary fraction videos for promoting fraction learning. Moving Fractions utilizes game-design factors to draw students through a trajectory of fraction learning from part-whole comparisons to a more robust understanding of the measurement concept of fractions. The supplementary video immerses students in a broad range of fraction representations. The app and video are intended to form a fraction learning package for distribution in Philippine schools. Future work …

Development Of A Gamified Number Line App For Teaching Estimation And Number Sense In Grades 1 To 7, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Fraction knowledge is known to be a gatekeeper to more advanced mathematical learning. On the basis of the literature on early number learning; a number line mobile application called Catch the Carrot was designed to develop students’ knowledge of whole number and fraction magnitude. This paper aims to describe the design of the Catch the Carrot app and discusses the rationale for using number lines as representational scaffolds for developing children’s understanding of numbers; particularly their estimation and number sense skills. The gamification features of the app; as well as strategies for integration in a classroom are also presented. This …

Designing Performance Tasks In Mathematics Using Technological Tools, Ma. Louise Antonette N. De Las Peñas, Debbie Marie Versoza, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

In the Philippines, the performance task is one of the major summative assessments in the K to 12 curriculum. This paper discusses how performance tasks may utilize mathematical apps within the context of blended learning. Guidelines on designing performance tasks; as well as the GRASPS framework; are discussed. Performance tasks that cut across various grade levels and strands of mathematics are presented. These involve divisibility (Numbers); integer and polynomial operations (Algebra); triangle centers (Geometry); and statistics (Statistics). The performance tasks described in this paper can provide an initial idea for the design of other summative assessments and contribute to the …

Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

The problem of rote-based learning in mathematics is well documented. Mobile technology can provide a potential solution, especially when application (app) design is based on sound pedagogical principles and gamification elements. However, an inventory of available mobile apps for mathematics reveals that many of the available apps are guided by a behaviorist perspective that favors repetition over meaningful learning. This paper reports on the design of mobile mathematics apps that harness gamification techniques to promote higher-order thinking skills (HOTS) even in basic elementary school concepts such as number comparison, and addition and subtraction. The integration of these apps in the …

Development Of A Gamified Number Line App For Teaching Estimation And Number Sense In Grades 1 To 7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Fraction knowledge is known to be a gatekeeper to more advanced mathematical learning. On the basis of the literature on early number learning, a number line mobile application called Catch the Carrot was designed to develop students’ knowledge of whole number and fraction magnitude. This paper aims to describe the design of the Catch the Carrot app and discusses the rationale for using number lines as representational scaffolds for developing children’s understanding of numbers, particularly their estimation and number sense skills. The gamification features of the app, as well as strategies for integration in a classroom are also presented. This …

Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

The problem of rote-based learning in mathematics is well documented. Mobile technology can provide a potential solution; especially when application (app) design is based on sound pedagogical principles and gamification elements. However; an inventory of available mobile apps for mathematics reveals that many of the available apps are guided by a behaviorist perspective that favors repetition over meaningful learning. This paper reports on the design of mobile mathematics apps that harness gamification techniques to promote higher-order thinking skills (HOTS) even in basic elementary school concepts such as number comparison; and addition and subtraction. The integration of these apps in the …

Development Of A Mobile Ten Frames App For Philippine K-12 Schools, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

This paper reports on the Quick Images app, whose design framework is informed by research on ten-structured thinking and gamification principles. Inclusivity was also a major consideration, especially in the context of a developing country. Thus, the app was made freely available and required only moderate system requirements. Pilot studies revealed that the app has the potential to promote children’s ability to see two-digit numbers in relation to tens and ones, which is a major goal of elementary school mathematics. Collaborations with the Philippine Department of Education to ensure the app’s sustained use are also discussed.

Designing Mobile Apps To Promote Numeracy And Statistical Reasoning, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Versoza

Mathematics Faculty Publications

Developing countries typically do not perform well in international benchmarks of mathematics achievement. This may be partially explained by students’ immersion in classrooms characterized by superficial strategies or rote-learning methods. This paper reports on the design of mobile applications (apps) developed by the authors as part of an ongoing project funded by a national government agency and intended to promote structural thinking and statistical reasoning. It describes the general features of the apps, as well as the pedagogical principles upon which the apps’ designs were anchored on. These principles are grounded on research and established practices on number sense and …

Digital Simulations For Grade 7 To 10 Mathematics, Ma. Louise Antonette N. De Las Peñas, Debbie Marie Verzosa, Maria Alva Q. Aberin, Len Patrick Dominic M. Garces, Flordeliza F. Francisco, Evangeline P. Bautista, Mark Anthony C. Tolentino, Winfer C. Tabares

Mathematics Faculty Publications

This article describes a Department of Science and Technology – Philippine Council for Industry, Energy and Emerging Technology (DOST-PCIEERD) project aimed to facilitate the implementation of the mathematical objectives raised by the Department of Education’s (DepEd) K to 12 program in the Philippines through the use of innovative digital technologies. In particular, a selection of application software (“apps”) were created for Grade 7 to 10 mathematics that covered topics indicated in the five strands outlined in the K to 12 program – namely (1) number, (2) geometry, (3) measurement, (4) patterns and algebra, and (5) statistics and probability. The design …

Relationships Between Mathematics Teacher Preparation And Graduates' Analyses Of Classroom Teaching, James Hiebert, Emily Miller, Dawn Berk

Mathematics Faculty Publications

The purpose of this longitudinal study was to investigate the relationships between mathematics teacher preparation and graduates’ analyses of classroom teaching. Fifty three graduates from an elementary teacher preparation program completed 4 video-based, analysis-of-teaching tasks in the semester before graduation and then in each of the 3 summers following graduation. Participants performed significantly better on the 3 tasks focused on mathematics topics studied in the program than on the task focused on a mathematics topic not studied in the program. After checking several alternative hypotheses, we conclude that a likely explanation for the performance differences is the mathematical knowledge for …

Discovering New Tessellations Using Dynamic Geometry Software, Ma. Louise Antonette N. De Las Peñas, Eduard C. Taganap

Mathematics Faculty Publications

In this paper we use dynamic geometry software to investigate a class of tilings called k-uniform tilings or tessellations. A tiling consisting of regular polygons whose vertices belong to k-transitivity classes under the action of its symmetry group (vertex-k-transitive) is said to be k-uniform. We also present constructions of tilings consisting of irregular polygons that are vertex-k-transitive.

Going For Gold In The International Math Olympiad, Queena N. Lee-Chua

Mathematics Faculty Publications

In July 2016, two high school students in the Philippine team garnered gold at the 57th International Mathematics Olympiad (IMO) in Hong Kong, capping a three-decade long quest for the top prize in the most prestigious high school math competition in the world. The four other team members also brought home honors, boosting our country to its highest rank ever, 17th out of 109 countries. This article discusses the history of the Philippine participation in the IMO, and examines the critical factors that have led to the victory. For Philippine team participants in general, these include: institutionalized and refined search …

Mathematics Without Calculations – It’S A Beautiful Thing!, Jason J. Molitierno

Mathematics Faculty Publications

All students should have the opportunity to do mathematics in a meaningful way for the sheer fun of it. Such experiences, if well designed, improve students’ effective thinking skills, increase their appreciation of the beauty and utility of mathematics, and prepare them to be mathematically-literate members of society. This session invites talks on how we can engage the liberal arts student through courses specifically designed for them. We welcome presentations on innovative course design, pedagogy, projects, or activities, as well as talks on tools used to assess such courses. Presentations should include a research basis for the design or pedagogical …

Have Gender Gaps In Math Closed? Achievement, Teacher Perceptions, And Learning Behaviors Across Two Ecls-K Cohorts, Joseph R. Cimpian, Sarah T. Lubienski, Jennifer D. Timmer, Martha B. Makowski, Emily K. Miller

Mathematics Faculty Publications

Studies using data from the Early Childhood Longitudinal Study–Kindergarten Class of 1998–1999 (ECLS-K:1999) revealed gender gaps in mathematics achievement and teacher perceptions. However, recent evidence suggests that gender gaps have closed on state tests, raising the question of whether such gaps are absent in the ECLS-K:2011 cohort. Extending earlier analyses, this study compares the two ECLS-K cohorts, exploring gaps throughout the achievement distribution and examining whether learning behaviors might differentially explain gaps more at the bottom than the top of the distribution. Overall, this study reveals remarkable consistency across both ECLS-K cohorts, with the gender gap developing early among high …

Teaching Beyond The Assessment, Daniel R. Ilaria

Mathematics Faculty Publications

This paper discusses how students can learn mathematics assessed on standardized testing in a way that promotes deeper thinking about the mathematics. While potential assessments aligned to the Common Core Content Standards drive the focus of the curriculum, technology can provide a way for delving into conceptual understanding. Using two standardized test questions, this paper provides examples of how technology can promote deeper thinking about mathematical concepts than what is supposed to be assessed in the questions.

Horizon Content Knowledge In The Work Of Teaching: A Focus On Planning, Nick Wasserman, Julianna Connelly Stockton

Mathematics Faculty Publications

Horizon content knowledge, one component of Ball et al.’s mathematical knowledge for teaching framework (e.g., Ball, Thames, & Phelps, 2008), has yet to reach adequate clarity and consensus in the field. Recently, various scholars have worked to further conceptualize and describe the mathematical horizon (e.g., Jakobsen, Thames & Ribeiro, 2013; Figueiras et al., 2011; Zazkis & Mamolo, 2011). In this communication, we identify some limitations in the ways such knowledge has thus far been described and offer an additional form of potential impact of horizon content knowledge on the work of teaching.

Color Models As Tools In Teaching Mathematics, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

In this paper we discuss various situations how color models and patterns can be used to simplify the study of abstract mathematics and serve as tools in understanding mathematical ideas. We illustrate the realization of such models through the development of advanced computer technology. In particular, we present how a computer algebra software such as Mathematica, or a dynamic geometry environment, can be utilized to facilitate the study of transformation geometry and group theory.

Instructor Use Of Tablet Pcs In A College Pre-Calculus Course: Implementation & Assessment, Julianna Connelly Stockton, Peter Gregory

Mathematics Faculty Publications

A group of six math instructors used tablet PCs to teach their individual sections of a high enrollment gateway Pre-Calculus course in a diverse urban four-year college. Student performance in the experimental sections were compared to those in 31 other sections in terms of student retention, pass rates, and score on the department-wide standardized final exam. Student performance was higher in Tablet PC sections across all three measures, although in some cases the improvement was not substantial enough to improve students’ overall course grades. Surveys of students and faculty in classes using a Tablet PC reflected overall positive impressions of …

Undergraduate Students' Self-Reported Use Of Mathematics Textbooks, Aaron Weinberg, Emilie Wiesner, Bret Benesh, Timothy Boester

Mathematics Faculty Publications

Textbooks play an important role in undergraduate mathematics courses and have the potential to impact student learning. However, there have been few studies that describe students' textbook use in detail. In this study, 1156 undergraduate students in introductory mathematics classes were surveyed, and asked to describe how they used their textbook. The results indicate that students tend to use examples, instead of the expository text, to build their mathematical understanding, which instructors may view as problematic. This way of using the textbook may be the result of the textbook structure itself, as well as students' beliefs about reading and the …

Mathematical Competitions In Hungary: Promoting A Tradition Of Excellence & Creativity, Julianna Connelly Stockton

Mathematics Faculty Publications

Hungary has long been known for its outstanding production of mathematical talent. Extracurricular programs such as camps and competitions form a strong foundation within the Hungarian tradition. New types of competitions in recent years include team competitions, multiple choice competitions, and some exclusively for students who are not in a special mathematics class. This study explores some of the recent developments in Hungarian mathematics competitions and the potential implications these changes have for the very competition-driven system that currently exists. The founding of so many new competitions reflects a possible shift in the focus and purpose of competitions away from …

Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee

Mathematics Faculty Publications

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, …

Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti

Mathematics Faculty Publications

This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.

Tilings, Patterns And Technology, Ma. Louise Antonette N. De Las Peñas, Angela Fatima H. Guzon

Mathematics Faculty Publications

In this paper we discuss various situations where tilings and patterns, with the aid of technology, facilitate the teaching of mathematics and serve as tools in understanding and developing new mathematical ideas. We also illustrate how technology makes possible cultural connections in the study of mathematics using Islamic tilings and patterns.

Education Of Mathematically Talented Students In Hungary, Julianna Connelly Stockton

Mathematics Faculty Publications

Hungary is famous for its production of large numbers of highly talented mathematicians and physicists. This study explores the Hungarian system for educating mathematically talented secondary school students with the goal of identifying successful features that may be applicable to education in the United States. Highlights of the Hungarian approach include an emphasis on problem solving, problem posing, detailed explanation or proof for solutions, and development of mathematical creativity through the search for multiple solution paths.

Hungary And The United States: A Comparison Of Gifted Education, Julianna Connelly Stockton

Mathematics Faculty Publications

There is a lot that can be learned about a country based on the programs and provisions it has for mathematically talented students. While it is difficult to identify a single U.S. "program" or "approach" for gifted education, in general the trend is to put mathematically talented students through the standard mathematics sequence, just starting at an earlier age. In Hungary, on the other hand, the focus is on enrichment over acceleration. This paper explores how some very different historical, cultural, and political forces have shaped these two countries’ different approaches to educating mathematically talented students.

Hungary, Slovakia, And Romania: International Relations Examined Through Minority Language Education, Julianna Connelly Stockton

Mathematics Faculty Publications

The Hungarians in Romania and Slovakia are not just ethnic minorities but also linguistic minorities whose language has almost no linguistic similarity to their host nations’ language. One aspect of life in which linguistic minority issues arise most frequently is that of education. Should minority linguistic groups be forced to learn the national language in order to attend school or participate in official functions or should the government provide or allow for education in their native language?

The ethnic Hungarian minorities did not, for the most part, emigrate from Hungary to these other countries by choice the way most immigrants …