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Articles 1 - 24 of 24
Full-Text Articles in Education
Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett
Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett
Journal of Humanistic Mathematics
Mathematics can be used as a tool to question and critique society and, in doing so, give us more information about the world around us and how it operates. This however, is not a common perspective that is conveyed to students during their undergraduate mathematics coursework. This paper contributes to the understanding of how undergraduate mathematics students question and critique society via mathematical modeling tasks. In two courses at two universities, 27 mathematics majors and secondary preservice teachers engaged in the modeling process situated in authentic contexts to learn specific concepts and make mathematical connections across domains and disciplines. Both …
Blue Whale And Krill Populations Modeling, Li Zhang
Blue Whale And Krill Populations Modeling, Li Zhang
CODEE Journal
We present an intriguing topic in an undergraduate mathematical modeling course where predator-prey models are taught to our students. We describe modeling activities and the use of technology that can be implemented in teaching this topic. Through modeling activities, students are expected to use the numerical and graphical methods to observe the qualitative long-term behavior of predator and prey populations. Although there are other choices of predators and prey, we find that using blue whales and krill as predator and prey, respectively, would be most beneficial in strengthening our students' awareness of protecting endangered species and its impact on climate …
Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change, Victor J. Donnay
Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change, Victor J. Donnay
CODEE Journal
How does mathematics connect with the search for solutions to the climate emergency? One simple connection, which can be explored in an introductory differential equations course, can be found by analyzing the energy generated by solar panels or wind turbines. The power generated by these devices is typically recorded at standard time intervals producing a data set which gives a discrete approximation to the power function $P(t)$. Using numerical techniques such as Euler’s method, one can determine the energy generated. Here we describe how we introduce the topic of solar power, apply Euler’s method to determine the energy generated, and …
Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist
Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist
CODEE Journal
In this paper, I discuss two environmentally-focused writing assignments that I developed and implemented in recent integral calculus and differential equations courses. These models of carbon storage and PCB’s in a river provide interesting applications of one-compartment mixing problems. The assignments were intended to focus student attention on sustainability concerns while also developing other essential skills. I discuss these assignments and their effect on my students’ technical writing and environmental awareness. Detailed introductory instructions and mostly complete solutions to these assignments appear in the appendices, to include sample student work.
The Diagnostic Value Of Attributes From An Optimum Set Of Variables For Explaining An Outcome In Powerlifting At The Junior Level, Lukasz Plociennik, Igor Rygula, Tomasz Dancewicz, Krzysztof Łukaszuk
The Diagnostic Value Of Attributes From An Optimum Set Of Variables For Explaining An Outcome In Powerlifting At The Junior Level, Lukasz Plociennik, Igor Rygula, Tomasz Dancewicz, Krzysztof Łukaszuk
Baltic Journal of Health and Physical Activity
The sport of powerlifting has been extensively studied, but there is lack of information on an optimum list of features that explain performance in 19–20-years-old contestants. Therefore, the study aimed at two research objectives: (1) to determine a minimum set of attributes contributing the most information to an outcome; (2) to develop a biometric model describing the sport result. The study group (n = 30) consisted of athletes (aged 19.38 ±0.84) competing in powerlifting. Two methods for collecting information were used: observation and a diagnostic survey. Analytical methods comprised the multiple regression and Hellwig’s method. An analysis revealed that the …
تحليل مهارات التفكير فوق المعرفي أثناء عمليات النمذجة الرياضية في بيئة تكنولوجية لدى طالب - معلم الرياضيات في جامعة الخليل. Analysis Of Metacognitive Thinking Skills During Mathematical Modeling Processes In A Technological Environment Among Student-Teacher Of Mathematics At Hebron University, إبراهيم إبراهيم أبو عقيل
Association of Arab Universities Journal for Education and Psychology
هدف هذا البحث إلى معرفة مستوى مهارات التفكير فوق المعرفي من خلال عمليات النمذجة الرياضية في بيئة تكنولوجية لدى طلبة الرياضيات في جامعة الخليل، وتم اختيار عينة عشوائية قوامها (48) طالبا وطالبة قسموا إلى عشر مجموعات تحوي كل مجموعة على (4-6) طلاب قاموا بعمليات النمذجة في بيئة تكنولوجية، واستخدم الباحث المنهج التحليلي، وتم اعداد بطاقة ملاحظة لتحليل مهارات التفكير فوق المعرفي، وأظهرت النتائج أن المجموعات المشاركة تشابهت في عمليات ومراحل النمذجة، وقد اشتملت هذه العمليات على تفسيرات منطقية وعمليات حسابية ومهارات تفكير متنوعة، وكشفت النتائج أيضا أن مستوى مهارات التفكير فوق المعرفي التي يمكن تحليله من خلال عمليات النمذجة الرياضية …
Competence Of Computer Modeling In The Context Of Modern Education, Sarvar Djumaboev, Sodik Usmonov, Ulugbek Ergashev
Competence Of Computer Modeling In The Context Of Modern Education, Sarvar Djumaboev, Sodik Usmonov, Ulugbek Ergashev
Mental Enlightenment Scientific-Methodological Journal
The study of computer modeling at various stages of the educational process - from school to university is considered, competencies acquired by students in the study of computer mathematical modeling are formulated and the need for further development of competencies acquired at school is substantiated. A new approach to teaching students of mathematical directions is proposed preparation of mathematics and computer science by means of computer modeling. This technique is built on the principles of the competence approach, interdisciplinary connections of the educational disciplines of mathematics and computer science, contributes to the formation of research competence.
Three Questions From Cctm Teachers About Mathematical Modeling, Robyn Stankiewicz-Van Der Zanden, Rachel Levy
Three Questions From Cctm Teachers About Mathematical Modeling, Robyn Stankiewicz-Van Der Zanden, Rachel Levy
Colorado Mathematics Teacher
This article shares three questions and answers about mathematical modeling in the classroom from an April 2020 online conversation with participants of a CCTM webinar. We hope that the answers to these questions will motivate teachers to embrace the value of implementing math modeling tasks, help students see the math all around them in the world, and empower future professionals to reach for the mathematical tools in their pockets to make data-driven decisions.
A Mathematical Model Of Pancreatic Cancer Growth And Response To Treatment, Allison Cruikshank
A Mathematical Model Of Pancreatic Cancer Growth And Response To Treatment, Allison Cruikshank
Honors Theses
Pancreatic cancer is one of the leading causes of death due to cancer in the United States. Analyzing the effects of radiation is extremely valuable in determining when a patient is allowed surgical resection, which is, presently, the only potentially curative treatment for pancreatic cancer. This study examines pancreatic tumor growth and shrinkage to predict tumor response and change of resectability for pancreatic cancer patients undergoing radiation therapy. This is done using ordinary differential equations as a mathematical model. Mathematical models have increasingly been applied to various biological systems/processes to analyze the principles involved. In our project, a population dynamical …
Modeling The Ecological Dynamics Of A Three-Species Fish Population In The Chesapeake Bay, Iordanka N. Panayotova, Maila B. Hallare
Modeling The Ecological Dynamics Of A Three-Species Fish Population In The Chesapeake Bay, Iordanka N. Panayotova, Maila B. Hallare
CODEE Journal
We present an inquiry-based project that is designed for a mathematical modeling class of undergraduate junior or senior students. It discusses a three-species mathematical model that simulates the biological interactions among three important fish species in the Chesapeake Bay: the prey Atlantic menhaden and its two competing predators, the striped bass and the non-native blue catfish. The model also considers the following ecological issues related to these three species: the overfishing of menhaden, the invasiveness of the blue catfish, and the harvesting of blue catfish as a method to control the population. A series of modeling scenarios are considered based …
Mathematical Modeling: Part 1 Of Series, Catherine Martin
Mathematical Modeling: Part 1 Of Series, Catherine Martin
Colorado Mathematics Teacher
The Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME), released in April 2016, provides specific guidance and support to teachers as they incorporate the practice of mathematical modeling into classroom instruction.
Going Beyond Promoting: Preparing Students To Creatively Solve Future Problems, Kristin M. Arney, Kayla K. Blyman, Jennifer D. Cepeda, Scott A. Lynch, Michael J. Prokos, Scott Warnke
Going Beyond Promoting: Preparing Students To Creatively Solve Future Problems, Kristin M. Arney, Kayla K. Blyman, Jennifer D. Cepeda, Scott A. Lynch, Michael J. Prokos, Scott Warnke
Journal of Humanistic Mathematics
While we cannot know what problems the future will bring, we can be almost certain that solving them will require creativity. In this article we describe how our course, a first-year undergraduate mathematics course, supports creative problem solving. Creative problem solving cannot be learned through a single experience, so we provide our students with a blend of experiences. We discuss how the course structure enables creative problem solving through class instruction, during class activities, during out of class assessments, and during in class assessments. We believe this course structure increases student comfort with solving open-ended and ill-defined problems similar to …
Modeling Where It Matters: Redesigning Mathematics Education With Adolescent Girls Of Color, Kara L. Imm
Modeling Where It Matters: Redesigning Mathematics Education With Adolescent Girls Of Color, Kara L. Imm
Dissertations, Theses, and Capstone Projects
Mathematical modeling is not a new idea for mathematicians, scientists, and engineers. But until recently it remained largely outside of the purview of most K-12 math educators. With the adoption of the Common Core State Standards for Mathematics (Common Core State Standards Initiative, 2010) modeling gained a more prominent place within math curriculum and instruction. An iterative form of problem solving, which supports students to make generalizable models instead of single-use solutions, modeling is now poised to be taken up as a practice in classrooms across the country. The purpose of this research—a design study—is to understand how a carefully …
Examining Students’ Covariational Reasoning Through Mathematical Modeling Activities Embedded In The Context Of The Greenhouse Effect, Debasmita Basu
Examining Students’ Covariational Reasoning Through Mathematical Modeling Activities Embedded In The Context Of The Greenhouse Effect, Debasmita Basu
Theses, Dissertations and Culminating Projects
The greenhouse effect is one of the most pressing environmental as well as social issues of the present age. In news media and weather reports, most of the essential information about the phenomenon is expressed in forms of graphs and pictures. However, the interpretation of such graphs is challenging for students; they often focus on the shape of the graphs, overlooking the covariational relationships between the concerned quantities. Building on the framework of critical mathematics literacy and social justice mathematics, in this study I aimed to explore the power of dynamic mathematical modeling activities for engaging students in covariational reasoning …
Testing The Psychometric Properties Of The Modeling Self-Efficacy Scale, Anu Sharma, Stephen J. Pape, Jonathan Templin
Testing The Psychometric Properties Of The Modeling Self-Efficacy Scale, Anu Sharma, Stephen J. Pape, Jonathan Templin
Journal of Educational Research and Practice
The Modeling Self-Efficacy Scale was developed to measure middle and high school students’ confidence in understanding and solving modeling tasks. The scale was administered to 225 eighth- and ninth-grade students. Participants read modeling tasks adapted from Programme for International Student Assessment’s 2003 problem-solving assessment and rated their confidence on a 100-point self-efficacy scale. Confirmatory factor analysis indicated that modeling self-efficacy is a unidimensional construct, best elicited by a repeated-measures-style survey design in which participants responded to the same self-efficacy items across multiple modeling problems. The omega reliability coefficient for the scale was .88. The findings suggest that the Modeling Self-Efficacy …
Elementary Preservice Teachers’ Perceptions Of Modeling As A Tool For Instruction, Ginger S. Watson, Mary Enderson
Elementary Preservice Teachers’ Perceptions Of Modeling As A Tool For Instruction, Ginger S. Watson, Mary Enderson
Teaching & Learning Faculty Publications
As the standards movement continues to gain momentum in U.S. schools, preservice and in-service teachers need greater knowledge in mathematical modeling to engage PK-12 students in such practices. This case-based research study investigated the perceptions and understandings of modeling for 76 entry-level, preservice elementary teachers enrolled in a mathematics methods course at a mid-Atlantic university. Participants were prompted to define modeling and its application to classroom instruction through open-response questions administered in an online survey. A case-based, phenomenological method was used to code and analyze responses. Most preservice teachers expressed a very limited definition or understanding of modeling or how …
Building Conceptual Understandings Of Equivalence, Kelli Rich
Building Conceptual Understandings Of Equivalence, Kelli Rich
Boise State University Theses and Dissertations
The equal sign is prevalent at all levels of mathematics however many students misunderstand the meaning of the equal sign and consider it an operational symbol for the completion of an algorithm (Baroody & Ginsburg, 1983; Rittle-Johnson & Alibali, 1999). Three constructs were studied through the lens of the Developing Mathematical Thinking (Brendefur, 2008), Relational Thinking, Spatial Reasoning and Modes of Representation. A review of literature was conducted to examine the effects of mathematics instruction on the development of students’ conceptual understanding of equivalence through the integration of spatial reasoning and relational thinking. The Developing Mathematical Thinking (DMT) curricular resources …
Effects Of The Instruction With Mathematical Modeling On Pre-Service Mathematics Teachers’ Mathematical Modeling Performance, Gulzade Karaci Yasa, Ilhan Karatas
Effects Of The Instruction With Mathematical Modeling On Pre-Service Mathematics Teachers’ Mathematical Modeling Performance, Gulzade Karaci Yasa, Ilhan Karatas
Australian Journal of Teacher Education
The purpose of the study was to investigate the effects of the instruction with mathematical modeling on pre-service mathematics teachers’ mathematical modeling performance. The participants were 24 pre-service elementary mathematics teachers. A mixed method approach was used to conduct the research. Each week, the participants were given two mathematical modeling problems and solved them as a group. After that, each group shared their solutions with the class so that there was an opportunity to focus on different solution methods. The data was collected via a pre and a post mathematical modeling test. SPSS package program was utilized in order to …
Implementing The Constructed Scaffold Model: Hands-On Activity Units For Advanced Placement Calculus, Susan Scott
Implementing The Constructed Scaffold Model: Hands-On Activity Units For Advanced Placement Calculus, Susan Scott
Theses and Dissertations
The purpose of the present action research study is to describe a hands-on activity model, named the Constructed Scaffold Model (CSM), used in an Advanced Placement Calculus class in a southeastern United States suburban high school. Data were collected over an 8-week period during the spring 2017 semester. The teacher-researcher developed a pretest and posttest to describe the CSM’s impact on 10 student-participants in her Advanced Placement classroom. Repeated measures t-tests were used to determine the effect of the CSM on the student-participants’ test scores. Additional qualitative data were collected from field notes, student surveys, a focus group, and student …
Supporting Teachers’ Learning About Mathematical Modeling, June L. Gastón, Barbara A. Lawrence
Supporting Teachers’ Learning About Mathematical Modeling, June L. Gastón, Barbara A. Lawrence
Publications and Research
In the United States, one of the Standards for Mathematical Practice of the Common Core Curriculum (Common Core State Standards Initiative, 2010) is Model with mathematics. This standard requires that students be taught in a manner that will enable them to ―apply the mathematics they know to solve problems arising in everyday life, society, and the workplace‖ (p. 7). However many prospective and practicing teachers acquire a pedagogical style that does not support this standard. To promote higher levels of student thinking associated with mathematical modeling, teachers must thus be taught not only what mathematical modeling is, but how it …
A Primer For Mathematical Modeling, Marla A. Sole
A Primer For Mathematical Modeling, Marla A. Sole
Publications and Research
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school with the mathematics they will use outside of school. Instructors have found mathematical modeling difficult to teach. To successfully incorporate modeling activities I believe that curricular changes should be accompanied by professional development for curriculum developers, classroom teachers, and higher education professionals. This article serves as an introduction to modeling by …
Affinity Learning In Mathematics, Arthur I. Zygielbaum, Neal Grandgenett
Affinity Learning In Mathematics, Arthur I. Zygielbaum, Neal Grandgenett
Teacher Education Faculty Proceedings & Presentations
Teaching complex subjects such as mathematical modeling is intrinsically challenging. It is more so in a typical classroom setting. In this paper, we explore the use of technology to provide an electronic tutor that interacts with both teacher and student to provide a personalized and focused learning experience. Affinity Learning is an environment that captures the skills of a master teacher in a dynamic but simple technical embodiment and presents lessons and assessments online to a student. Initial results not only indicate that learning has occurred, but also distinguish male from female performance and give interesting insight into the learning …
Using Web Pages To Teach Mathematical Modeling: Some Ideas And Suggestions, Elliott Ostler, Neal Grandgenett
Using Web Pages To Teach Mathematical Modeling: Some Ideas And Suggestions, Elliott Ostler, Neal Grandgenett
Teacher Education Faculty Proceedings & Presentations
Mathematical modeling can perhaps be best defined as “the process of scientific inquiry” for mathematics. This is obviously a comfortable mode for teachers of science, but is rarely seen in the mathematics classrooms of today. This paper explores the possibilities of using interactive web pages to help facilitate an understanding of practical applications based mathematics. Because the scientific process is emphasized as the general operating framework, situations where students can hypothesize and experiment, and create data tables are most valuable. Special emphasis is placed on the fact that students and teachers both need to re-conceptualize effective mathematics instruction in order …
Mathematical Modeling Within A Technology Based Learning Environment: Some Principles For Adaptive Instruction, Neal Grandgenett, Elliott Ostler, Arthur I. Zygielbaum, Scott Henninger, Char Hazzard
Mathematical Modeling Within A Technology Based Learning Environment: Some Principles For Adaptive Instruction, Neal Grandgenett, Elliott Ostler, Arthur I. Zygielbaum, Scott Henninger, Char Hazzard
Teacher Education Faculty Proceedings & Presentations
This paper describes a set of research based instructional plans being developed by a multidisciplinary team of researchers at the University of Nebraska within a National Science Foundation Proof-of-Concept Grant. The project is seeking to establish a prototype effort for teaching mathematical modeling within a technology based learning environment, which includes components of adaptive instruction for the student. Seven curriculum based design principles for the adaptive instruction that are being followed in the development of the project are described in the paper as they relate to research on effective mathematics instruction, and in particular the enhancement of mathematical modeling activities.