Conference Session

Mathematics Division Technical Session 5: From Functions to Big Data–A Hands-on Challenge

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Jeffrey Lloyd Hieb, University of Louisville; Campbell R. Bego, University of Louisville

Tagged Divisions

Mathematics

through controlled implementations of evidence-based practices in the classroom. Dr. Bego has an undergraduate Mechanical Engineering degree from Columbia University, a Professional Engineering license in the state of NY, and a doctorate in Cognitive Science. American c Society for Engineering Education, 2020 Turning the Tables on Partial Credit: Computer Aided Exam with Student Reflection for Partial Credit (CAESR4PC)AbstractThis full-length research paper describes a new type of exam, the Computer Assisted Exam withStudent Reflection for Partial Credit (CAESR4PC). CAESR4PC combines the automatic gradingof computer

Conference Session

Mathematics Division Technical Session 3

Collection

2019 ASEE Annual Conference & Exposition

Authors

Norha M. Villegas, Universidad Icesi, Colombia - University of Victoria, Canada; Stephanie Celis Gallego, Universidad Icesi; Ivonne María Suárez, Universidad Icesi; Juliana Jaramillo JJO, Universidad Icesi; Angelica Burbano, Universidad Icesi; Alvaro Pachon, Universidad Icesi; Diego Antonio Bohorquez, Universidad Icesi; Lina Marcela Quintero P.E., Universidad Icesi; Isabel Echeverri, Universidad Icesi; Lady K. Castillo; Cesár Augusto Cuartas Rodríguez, Universidad Icesi

Tagged Divisions

Mathematics

Paper ID #26882Professor Critical Reflection and its Impact on Learning Environments: ACase Study Applied to a First-year Mathematics Course in EngineeringDr. Norha M. Villegas, Universidad Icesi, Colombia - University of Victoria, Canada Norha M- Villegas is an Associate Professor in the Department of Information and Communication Tech- nologies, Director of the Software Systems Engineering Bachelor Program at Universidad Icesi, Cali, Colombia, an Adjunct Assistant Professor of the Department of Computer Science, University of Victoria, in Canada, and an IEEE Senior Member. Her research interests include engineering

Conference Session

Mathematics Division Technical Session 3

Collection

2017 ASEE Annual Conference & Exposition

Authors

Bailey Braaten, The Ohio State University; Arnulfo Perez, The Ohio State University

Tagged Divisions

Mathematics

appendix. The teachers were able to engage in the unit asstudents and were given time for reflection and discussion after each lesson within the unit. Teachers were first introduced to a multi-meter and were asked to measure the voltage ofseveral batteries. The unit had an inquiry-based focus; instead of telling the teachers how to use amulti-meter they were allowed to explore and discover how to measure voltage on their own. Asthe unit progressed, the teachers were introduced to each separate component of a circuit in asimilar way. After the battery was the resistor, then the LED, then the switch and finally thebreadboard. As each component was introduced the teachers were given a loosely structuredactivity that allowed them to explore the

Conference Session

Mathematics Division Technical Session 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Rebecca Bourn, University of Wisconsin - Milwaukee; Sarah Baxter, University of St. Thomas

Tagged Divisions

Mathematics

Calculus, which most certainly covers this topic, but the problem“feels” different to students in the later course because the notation and setting have changed andthe purpose is specific to statistics rather than the more abstract concepts of the area of a two-dimensional region and anti-derivatives.Previous WorkIn recent years the authors have been exploring ways to reframe course assignments to provide agreater variety of application and visualization avenues to enhance critical thinking and promptstudent reflection. The objective is to provide multiple levels of connections that promotestudents’ cognitive retention. Preliminary work1 presented a methodology for using large scale,Fermi-type estimation problems to try to encourage students to

Conference Session

Mathematics Division Technical Session 1: Best Practices in Engineering Math Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

JaCoya Thompson, Northwestern University ; Sally P.W. Wu, Northwestern University; Jacob Mills, Evanston Township High School

Tagged Divisions

Mathematics

project focuses on helping high school teachers integrate computer science principles into their mathematics or science classrooms. She received her PhD from University of Wisconsin-Madison in Educational Psychology-Learning Sciences. Her research broadly examines how to help students learn complex visual-spatial content in introductory STEM courses through the design of technology-enhanced interventions for the classroom. Her work thus far has investigated the effects of drawing, collaboration, reflection, and other active learning strategies in undergraduate chemistry and electrical engineering.Mr. Jacob Mills, Evanston Township High School American c

Conference Session

Mathematics Division Technical Session 2: Poster Presentations

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Anibal Sosa, Universidad Icesi, Colombia; Norha M. Villegas, Universidad Icesi, Colombia; Stephanie Celis Gallego, Universidad Icesi, Colombia; Diego Antonio Bohórquez, Universidad Icesi, Colombia

Tagged Divisions

Mathematics

that the national education system does not focus on thedevelopment of STEM competencies. As a result, the motivation of engineering students inmathematics courses is continuously hampered because of deficiencies in prerequisites.The case study presented in this paper is part of a wider project conducted at our institution.The project involved several math courses taken by first and second year engineeringstudents. The main objective of this project was to support mathematics instructors in theprocess of contributing to improve student learning, by continuously reflecting on theeffectiveness of the pedagogical practices that are applied inside and outside the classroom,while adopting a continuous improvement culture that benefits student

Conference Session

Mathematics Division Technical Session 1

Collection

2015 ASEE Annual Conference & Exposition

Authors

Angela Minichiello, Utah State University; Ted Campbell, Utah State University; Jim Dorward, Utah State University; Sherry Marx, Utah State University

Tagged Divisions

Mathematics

engineering calculus course taught via synchronous broadcast at a mid-size,Western, public university. The instructional innovation required first year calculus students toparticipate in an asynchronous, online discussion forum for graded credit. Data, consisting ofwritten reflections and transcribed interviews, were gathered from three STEM faculty memberswho each played a different role in the change process: a mathematics instructor implementingthe online forum within his course; an engineering faculty peer-mentor assisting with theimplementation of the online forum; and a STEM education faculty member evaluating theimplementation and observing the process of change. Situated within the interpretive researchparadigm, this study uses exploratory

Conference Session

Engineering and Math Potpouri

Collection

2008 Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University; Jean Hodges, VCU\Qatar Campus

Tagged Divisions

Mathematics

expand upon rotations, reflections, andtranslations. In addition, the course begins with mathematical formulas that speak to the issue ofgeometric shapes, followed by an intense development of the Fibonacci sequence and several of Page 13.1184.3its properties illustrating the utility of the sequence in the “real world.” In the current study,students were shown some past student projects submitted as partial fulfillment in the previousMATH 131 courses to introduce each new topic visually and were required to complete a muchmore comprehensive project component (hence the term Implementing Techniques for Project-Directed Mathematics). The students

Conference Session

Changing the Classroom Environment in Mathematics Education

Collection

2014 ASEE Annual Conference & Exposition

Authors

Rebecca Bourn, Tribeca Flashpoint Media Arts Academy; Sarah C. Baxter, University of South Carolina

Tagged Divisions

Mathematics

way that promotes and encourages reflective and analytical thinking. The idea is toengage students in a context-rich problem, through the use of a driving question, to guide themthrough active learning modules exploring core concepts, and to lead them to a solutionmethodology. The production of a final report serves as a mechanism that allows them to revisetheir original solution based on a synthesis of the knowledge and understanding gained throughthe learning modules.The developmental framework for instructors using EFFECTs begins with the identification ofthe concepts to be studied; in general these are difficult concepts. Next, these concepts areassociated with active learning activities; each concept could be associated with a single

Conference Session

Innovative Instructional Strategies and Curricula

Collection

2010 Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University Qatar Branch; Jean Hodges, Virginia Commonwealth University Qatar Branch

Tagged Divisions

Mathematics

fororganizing experience and substantially strengthened the idea of using cross-curricularexpressive writing (in which the writer captures, investigates, and reflects upon his/her ideas) toenhance students’ learning (pp. 57-58).10 Throughout the 1980s and 1990s, Emig’s and Britton’swork became the basis for recognizing writing as a primary learning method. (For a morecomplete discussion of WAC history, refer to Chapter 5, “Writing to Learn,” of Reference Guideto Writing Across the Curriculum, by Charles Bazerman, et al.10)Three major goals for incorporating VCUR’s WAC program into VCUQatar’s project-directedapproach became • to develop students’ metacognition about their learning and thinking processes, • to convince students that using knowledge

Conference Session

Mathematics Division Technical Session 3

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Emre Tokgoz, Quinnipiac University; Elif Naz Tekalp; Hasan Alp Tekalp

Tagged Divisions

Mathematics

. APOS theory is initiated with Piaget’stheory of reflective abstraction [17] and got expanded to K16 mathematics education and RUME in recent years. Itwas applied in 1997 to mathematical topics for analyzing combined math knowledge of a student in a specificsubject [1]. Action, process, object, and schema are the mental structures proposed as a part of the APOS theory tofollow developmental stages of the learners. The main goal of this theory is to observe and categorize mentalstructures through observations of learners’ mental mechanisms; it is important to understand the totality ofknowledge and its’ reflection in applications.In the relevant APOS literature, learners’ conceptual view of the function was studied in [3] by relying on

Conference Session

Mathematics Division Technical Session 4

Collection

2018 ASEE Annual Conference & Exposition

Authors

Gianluca Guadagni, University of Virginia; Hui Ma, University of Virginia; Lindsay Wheeler, University of Virginia

Tagged Topics

Diversity

Tagged Divisions

Mathematics

participant in the course.Below we describe the course and modifications we have made through our second iteration.Pilot ULA course The class provides tools and support for UTAs to reflect on the several aspectsof their activity, from the most effective teaching practices, such as student-centered and inquirybased, to relevant educational methods, grading techniques, and including tips to improveinterpersonal skills. Topics covered include: Constructivism, Motivation, Problem solving,Engaging with Groups, Grading and Feedback, and Metacognition (see Appendix A for fullcourse syllabus)These topics are organized around three main modules during the semester. The first one is basedon understanding the learning process as an elaborated process where

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Aaron Brakoniecki, Boston University; Michael Ward, Boston University; Gretchen Fougere, Boston University

Tagged Divisions

Mathematics

of the reflection when theengineering students and the beginning teachers reflected on the engineering design process theyimplemented during the activity. They compared this to the mathematical practice standards theyare expected to implement throughout their classrooms. What occurred during this discussionwere many connections among the different aspects of these two descriptions. They sawconnections between the mathematical expectations to make sense of the problem and theengineering process of identifying the needs and constraints. They linked the mathematicalstandards of reasoning abstractly and constructing viable arguments to the engineering processesof developing possible solutions and selecting promising solutions. With the

Conference Session

Mathematics Division Technical Session 4

Collection

2016 ASEE Annual Conference & Exposition

Authors

Eliza Gallagher, Clemson University; Lisa Benson, Clemson University; Geoff Potvin, Florida International University

Tagged Divisions

Mathematics

qualitative in nature, and our chosen research methods reflectthat. Rather than conduct a quasi-experimental design with a selection of GTAs participating incase analysis and others not, we instead used mixed qualitative and quantitative methods tocollect and analyze data solely from participants who experienced the use of case analysis in theirfirst semester of graduate school. This paper focuses in particular on two quantitative measures(survey data and student performance) and on two qualitative measures (case discussion recordsand reflective writings). We give a summary of the data within each of those four categoriesseparately. However, the nature of the research questions is such that a more significant analysisinvolves integration of those

Conference Session

Mathematics Division Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Eliud Quintero, Tecnologico de Monterrey (ITESM); Patricia Salinas, Tecnologico de Monterrey (ITESM)

Tagged Topics

Diversity

Tagged Divisions

Mathematics

described by text or bya graphic. Application of the instrument lead us to reflect that, once the appropriation is achievedthrough the motion context, it could be easier for students to apply it without connection with areal context. It also reveals the difficulties for interpreting graphical information based on thederivative function. These findings are part of the overall results of a doctoral dissertationconcerning with the use of digital technologies for the learning of Calculus.Keywords: Calculus learning, digital technologies, linear motion, real context, mediation.BackgroundDigital technologies are important tools in our daily activities, and it looks easy to use them inclassroom to support learning. According to Hillman1, a lot of research

Conference Session

Computers and Software in Teaching Mathmatics

Collection

2011 ASEE Annual Conference & Exposition

Authors

Cheri Shakiban, University of St. Thomas; Michael P. Hennessey, University of St. Thomas

Tagged Divisions

Mathematics

“line groups,” that visually correspond to what are commonly known as frieze patterns.Translations, half-turns, vertical reflections, horizontal reflections, vertical & horizontalreflections, glide reflections, and vertical reflections & glide reflections with half-turns constitutea practical visual manner in which to identify them (Table 7). Throughout our travels in Peru,students were on the lookout for examples of all 7 types. Table 7 Frieze patterns and their categorization Basic visual coding of all 7 types of frieze patterns using letters of the alphabet. Eight different Incan frieze patterns (top

Conference Session

Mathematics in Transition

Collection

2007 Annual Conference & Exposition

Authors

Sandra Linder, Math Out of the Box; Donna Gunderson, Math Out of the Box/Clemson University

Tagged Divisions

Mathematics

development model where they wereimmersed in tasks in which the facilitator supported an inquiry-based learning environment. The professional development model consisted of two full days of inquiry experience anda half-day at the end of implementation dedicated to reflection of practice. The first day ofprofessional development focused mainly on Algebra concepts and was given prior toimplementing any of the Math Out of the Box lessons. After teachers implemented the tenlessons relating to Algebra, they returned for the second day of professional development dealingprimarily with data concepts. Teachers were also given the opportunity to reflect on the Algebralessons and discuss issues relating to implementation with their peers. Topics such as

Conference Session

Innovative Instructional Strategies

Collection

2009 Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University Qatar Branch; Jean Hodges, Virginia Commonwealth University Qatar Branch

Tagged Divisions

Mathematics

students’responses revealed sudden engagement with the mathematical concepts as students discovered a Page 14.1382.8relationship to their interests and passions. Some students reported really struggling with some ofthe concepts and repeatedly seeking additional outside help or conducting online research.In her discussion of symmetry, one student chose the capital letter H to illustrate symmetry,rotation, and glide reflections. As she concluded her answer, her enthusiasm became evident: Overall, the letter H in Helvetica has tons of different kinds of symmetry. A nice re-design I see for this where it would still be very

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Leszek Gawarecki, Kettering University; Yaomin Dong, Kettering University; Gina Rablau, Kettering

Tagged Divisions

Mathematics

Faculty, and Campus Environment. In our work we targeted the theme of AcademicChallenge, which includes four engagement indicators: Higher-Order Learning, Reflective andIntegrative Learning, Learning Strategies, and Quantitative Reasoning. We attempted to improvein our students taking calculus courses the Higher-Order Learning component: Applying facts,theories, or methods to practical problems or new situations, the Reflective and IntegratingLearning component: Combining ideas from different courses when completing assignments,and the Quantitative Reasoning component: Reaching conclusions based on own analysis ofnumerical information.Following the revised Boom’s taxonomy of educational objectives, we targeted levels three –Applying, and four

Conference Session

First-Year Programs Division - Visualization and Mathematics

Collection

2018 ASEE Annual Conference & Exposition

Authors

Kristen L. Sanford Bernhardt P.E., Lafayette College; Mary Roth P.E., Lafayette College

Tagged Divisions

First-Year Programs, Mathematics

dynamics course [4], and student preconceptions in anintroductory transportation engineering course [5], among other applications.In a pilot project [1], students were asked to develop a concept map on the first day of class inresponse to the prompt, “What is engineering” (Figure 1 shows the assignment) and were askedto construct a new map using the same prompt on the last day of class. The authors then used acommon rubric focused on desired student learning outcomes to evaluate changes between theinitial and final concept maps and created radar plots to display the results. Both authors werestruck by differences in what we had expected to see and what students actually reported, as wellas by how strongly students reflected some of what we tried

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Sarah Maor, Technion-Israel Institute of Technology; Igor Verner, Technion-Israel Institute of Technology

Tagged Divisions

Mathematics

, algorithmic analysis, and reflection were selected. Through integrating them with the ideas given by the architects we developed the concepts of learning activities in the course.Data on learning outcomes and students’ reflections were collected by:• Design project portfolios The design assessment criteria were based on the existing practice of studio evaluation and referred to the three following aspects: concept, planning/detailing, and representation/expression. The mathematics assessment criteria were: perception of mathematical problems, solving applied problems, precision in drawing geometrical objects, accuracy of calculations and parametric solutions. Frequencies and correlations of grades in design vs. mathematics evaluation grades

Conference Session

Mathematics Division Technical Session 2

Collection

2015 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

step-by-step instructions on how to perform the operation... Process: When an action is repeated and the individual reflects upon it, he or shecan make an internal mental construction called a process which the individual can think ofas performing the same kind of action, but no longer with the need of external stimuli... Object: An object is constructed from a process when the individual becomes awareof the process as a totality and realizes that transformations can act on it... Schema: Individuals collection of actions, processes, objects, and other schemaswhich are linked by some general principles to form a framework in individual’s mind... In APOS theory, concepts are constructed on different concepts and schemas

Conference Session

Project and Model-Based Mathematics

Collection

2007 Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University; Jean Hodges, Virginia Commonwealth University Qatar

Tagged Divisions

Mathematics

mathematical text6 that expand upon rotations, reflections, andtranslations. In addition, the course begins with mathematical formulas that speak to this issue ofgeometric shapes, followed by an intense development of the Fibonacci sequence and several ofits properties illustrating the utility of the sequence in the “real world.” In this study, studentswere shown some past student projects submitted as partial fulfillment in the previous MATH131 courses to introduce each new topic visually and were required to complete a much morecomprehensive project component (hence the term Project-Directed Mathematics). The studentswere very much impressed by the past projects and wanted to compete with each other to findnew projects that illustrate mathematical

Conference Session

Mathematics Division Technical Session 2

Collection

2017 ASEE Annual Conference & Exposition

Authors

Angeles Dominguez, Tecnologico de Monterrey, Monterrey, Mexico, and Universidad Andres Bello, Santiago, Chile; Genaro Zavala, Tecnologico de Monterrey, Monterrey, Mexico, and Universidad Andres Bello, Santiago, Chile; Maria Elena Truyol, Universidad Andrés Bello, Santiago, Chile

Tagged Topics

Diversity

Tagged Divisions

Mathematics

first day of class (text in black) and follow-up process during the entire semester (text in green). Adapted from [11].The PD process (Figure 2) is called a cycle because it consists of a few elements that arerepeated11. The description of each element is taken from Ho et al (2001, p.147)12:  Self-reflections: Instructors “undergo self-reflection and clarify personal conceptions.” In this study, all three reflections occurred prior to the first day of class.  Exposures: Workshop facilitators “provide a direction and a model for improvement.” Exposure 1 and Exposure 2 occurred prior to the first day of class, whereas Exposure 3 occurred during the semester.  Confrontations: Instructors “are brought to realize

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Muteb M. Alqahtani, Rutgers University; Arthur Belford Powell, Rutgers University

Tagged Divisions

Mathematics

Foundation, DRK-12 program, under awardDRL-1118888. The findings and opinions reported are those of the authors and do not necessarily reflect the viewsof the funding agency.For example, a line segment can be used as a radius to create a circle. These objects can bedragged around the screen, which allows the users to observe the consequences of their draggingto understand the relations among the different objects. Users act on geometric objects and DGEsreact to their actions in a manner that corresponds to engineered infrastructure that responds tothe theory of geometry [8, 9]. This co-active relationship between the environment and usersallows users to monitor and reflect on their activity. In an instrument-mediated activity in DGE,the environment

Conference Session

Mathematics Division Technical Session 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Guenter Bischof, Joanneum University of Applied Sciences; Thomas Singraber B.Sc., Joanneum University of Applied Sciences; Christian J. Steinmann, HM&S IT-Consulting; Marton Szabo-Kass B.Sc., Joanneum University of Applied Sciences; Stefan Woerndl B.Sc., Joanneum University of Applied Sciences

Tagged Divisions

Mathematics

oppositedirections. Then the simulation was started within the highest-order integration scheme andthe positions of the particles were stored after each time step. From these data a movie wascreated as described above. In the following figures (Figures 10 to 14) snapshots are shown,which were taken at different evolutionary phases of wave phenomena that occurred in thecourse of the numerical simulation.The snapshot in Figure 10 shows two wave fronts that have already established and propagatetowards each other. Both regions confined by the wave fronts show already a rich internalstructure that is caused by several reflections at the boundaries (Dirichlet boundary conditionsproduce fixed end wave reflections) and by interference.Figure 10: Array of 261206

Conference Session

Mathematics Division Technical Session 2

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Emre Tokgoz, Quinnipiac University; Samantha Eddi Scarpinella , Quinnipiac University; Michael Giannone, Quinnipiac University

Tagged Divisions

Mathematics

reflects upon an action when the action is repeated and he or she can make an internal mental construction called a process by which the individual can think of as performing the same kind of action without an external support...  An object is results from individual’s awareness of the process’ totality and realizes that transformations can act on it...  A schema is a linkage of collected actions, processes, objects, and other schemas that help to form a framework by using general principles in individual’s mind...APOS theory can be appropriately applied to the collected research data due to the involvementof certain mathematical concepts such as limits, derivatives, and asymptotes. The participants ofthis

Conference Session

Mathematics Division Technical Session 2

Collection

2015 ASEE Annual Conference & Exposition

Authors

Patricia Salinas, Tecnologico de Monterrey (ITESM); Eliud Quintero, Tecnologico de Monterrey (ITESM); Pablo Guillermo Ramirez, Tecnologico de Monterrey (ITESM); Eduardo González Mendívil, Tecnologico de Monterrey (ITESM)

Tagged Divisions

Mathematics

the development of adidactic toolkit AR_Dehaes that aim to improve spatial ability in freshmen engineering students.These authors state that spatial ability is something that cannot be taught but instead needstraining (development and improvement). Within these considerations, testing of tool promise itsrelease.Our perspective in Mathematics Education, always grounded in the classroom as a collegeteachers, makes us aware of the difficulties when dealing with spatial visualization. The teachingof solids of revolution in Calculus II has been a crucial issue in this reflection. When teaching inCalculus I the graphs of functions of a single real variable, graphs visualization stays in a 2Dplane perception. These curves, compelled in 2D, could be

Conference Session

Mathematics Division Technical Session 1

Collection

2015 ASEE Annual Conference & Exposition

Authors

Janet Callahan, Boise State University; Judith A. Garzolini, Boise State University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

levelwhich significantly exceeded the fall, 2013 female STEM enrollment figure (26.5%). In addition,13.4% of awards went to underrepresented minority students. These also significantly exceededthe fall, 2013 URM STEM enrollment figures which reflect a student body consisting of 9.2%URM. When awards were evaluated in terms of student enrollment category we found that 40%of awards went to first-time, full-time students, 28% went to transfer students, 22% to returningstudents and 10% to second degree seeking students.When the retention of FTFT students who received awards was examined, we found that 71.4%of awardees were retained in STEM one year later, and 81.6% were retained here in any major.This favorably compares with STEM FTFT retention figures

Conference Session

Mathematics Division Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University; Gabriela C. Gualpa, Quinnipiac University

Tagged Divisions

Mathematics

operation... • When an action is repeated and the individual reflects upon it, he or she can make an internal mental construction called a process which the individual can think of as performing the same kind of action, but no longer with the need of external stimuli... • An object is constructed from a process when the individual becomes aware of the process as a totality and realizes that transformations can act on it... • A schema is a ... individuals’ collection of actions, processes, objects, and other schemas which are linked by some general principles to form a framework in individual’s mind...In this theory, every concept can be constructed on different concepts and schemas. For example,if a researcher