Suofei+Lu



Having spent a decade of my life in Tennessee, I have grown to enjoy listening to country music. My name is Suofei Lu, a Chinese-Canadian graduate student at the University of Cincinnati. I have always liked mathematics and will be pursuing an M. Ed. degree in Curriculum and Instruction with a specialization in Secondary Mathematics Education. In my coming days, I hope to share my love for the subject with my prospective students.

There are a couple of websites that I visit often, sometimes for resource, other times for leisure. They include [|Wolfram|Alpha] and.[|HowStuffWorks].

Reflection I: Jonassen's and Cronje's Research on Objectivism versus Constructivism and Paradigmatic Integration

In the second half of the last century, academics in the educational field underwent a paradigm shift from objectivism to constructivism. As the two approaches differ in origin, researchers have regarded objectivism and constructivism as separate entities. In epistemology, the first is in line with the Lockean empiricist tradition, and the latter was derived from Cartesian mentalist tradition. While, in psychology, objectivism has its basis in B. F. Skinner’s behaviorism, constructivism is founded in Piagetian cognitive development. Hence, for some time, people tended to view the two as opposite and contradictory assumptions. However, through time, people have started to rethink these two assumptions from another point of view for the sake of instructional practicality. The summary, application, and evaluation of Jonassen’s and Cronje’s research provide insights into what needs to be done in education in order to maximize learning potential.

To summarize the main idea of Jonassen’s and Cronje’s writings, I claim that it is about the debate of two extreme schools of thought and the change which needs to take place shifting from objectivistic methods of thinking to more constructivistic ways of learning. According to Jonassen, objectivism is defined by the knowing and learning process of representing and mirroring reality, while, constructivism means the process of actively interpreting and constructing individual knowledge representations (1991, p.5). In other words, objectivistic thinking is inductively oriented, but constructivistic thinking refers to deductive reasoning. In a visual sense, Cronje illustrates the two paradigms on a straight line with the two on opposite ends of the continuum, with the pendulum swinging either in one extreme direction or the other. However, shifting completely from objectivism to constructivism is problematic in that learning is a collaboration of experience and cognition. Therefore, Jonassen does not conclude with vehement certainty that there should be a new philosophical paradigm (1991, p. 13). Cronje attempts to modify what used to be thought of as a straight line or continuum of polar paradigmatic opposites to a matrix of objectivism on the x-axis and constructivism on the y-axis. Within this representation, four quadrants are divided into Integration, Construction, Immersion, and Injection (described in a counter-clockwise direction). Construction is designed in such a way that learners instrinsically construct their own meaning by building on their previous knowledge and experiences (Cronje, 2006, p. 397). Immersion is defined by giving the learner no environment or necessary tools to learn, generating chaos inside the mind of the learner. Integration scores high on the objectivist and constructivist scale, because according to Cronje, it is the combination of instruction and construction in appropriate conditions (2006, p. 398). The concept of Injection in education, much like medical injections, is pre-organized with set outcomes. Cronje continues with Jonassen’s findings on objectivism versus constructivism and bends the two extremes into a uniform idea. Their observations also apply to teaching in an actual classroom.

Applying the two researchers’ writings to the real world of teaching stems from how objectivistic and constructivistic learning translate into thinking skills. For instance, Benjamin Bloom’s taxonomy of cognitive domains classifies learning or thinking skills into four strata. The first three strata, knowledge, comprehension, and application, are considered lower-order skills of thinking. The fourth stratum contains three skills of equal rigor, analysis, synthesis, and evaluation. These three skills are of higher-order thinking. In the objectivistic mode, lower-order thinking skills are involved, because the observation of knowing, understanding, and applying a concept can be externally measured. Higher-order thinking skills, on the other hand, pertain to constructivistic learning, in that analyzing, synthesizing, and evaluating are internal processes using critical thinking. As a prospective secondary mathematics teacher, I would like to use more constructivist approaches in teaching. For example, pose questions that begin with the words how and why. Also, letting students discover what they are learning is key to building self-sufficiency and confidence. There are aspects of these two articles that excluded variables which may affect a student’s learning process. What is the student’s attitude toward learning? Is he willing to learn? What are his motivations toward learning? Not only is student attitude unmentioned in the research, at what age does one start to utilize constructivist methods of teaching?

In addressing this polarities dilemma, Cronje raised the question, “What kind of model might permit us to integrate objectivism and constructivism into a complementary and harmonious whole?” (2006, p. 393). With the perception that the two approaches could be set at opposite ends of a straight line as a continuum and after the argument that these two approaches are complementary rather than oppositional, he proposed a model that integrates the two approaches to instructional design. In this model, the two approaches are plotted at a right angle, producing four quadrants which are named Injection, Construction, Integration, and Immersion. With the two axes indicating two continuums against one another, four quadrants with varying degrees of integration emerge. In order to show how learning events can mingle both objectivist and constructivist elements, the article presented and analyzed two learning programs. After that the article displayed a discussion of comments that were received from members of a prominent instructional technology mailing list about the feasibility of the model. Finally the article presented two case studies. The first described a two-day workshop that was designed to be high on both axes, while the second showed how the model could be used as a decision-making tool. According to the article, initial findings suggested that it was both feasible and useful to plot objectivism and constructivism at right angles to one another rather than at opposite ends of a continuum.

In addressing this polarities dilemma with respect to objectivist or constructivist approach to instructional design, Cronje’s question and his “2 Axes – 4 Quadrants” model do shed a bright light on instructional design in coping with the issue of objectivism and constructivism, which has a great implication to future instructional design and teaching. Besides the model that can be one of the guidelines to experiment in teaching activities, the pedagogical dimensions synthesized by the author is lucid and can make the terms of objectivism and constructivism more comprehensible and discernible for the reader to understand the differences of the two opposite “isms”. However, this model has not been tried in the real instructional setting and needs to be tested by more practitioners.

Works Cited

Jonassen, D. H. (1991). Objectivism versus constructivism: Do we need a new philosophical paradigm? Educational Technology Research and Development, 39(3), 5-14.

Cronje, J. (2006). Paradigms regained: Toward integrating objectivism and constructivism in instructional design and the learning sciences. Educational Technology Research and Development, 54(4), 387-416.

Reflection II: On Chaika's and Anderson's Writings

Even with the fast evolution of today’s technology, not enough resources of educational technology are canvassing the school districts of this country and abroad. To ensure each student is as privileged as the rest of his peers become an unlikely reality. Therefore, based on individual classrooms, teachers should make the decision whether to incorporate technology into their teaching daily, weekly, or occasionally. With this situation, there raise questions of class/classroom organization, strategies of classwork and activities that enhance student-learning.

Because this is a prevalent issue, teachers and parents alike have collaborated to make the “one-computer classroom” as effective as having a computer for every student in the classroom.

To organize a class of students with one computer in the classroom seems a fairly simple task, in that only one computer needs a place to rest. In actuality, it is a challenge. Teachers, in coping with this challenge, have conjured up a few methods to resolve the issue. In Chaika’s article, she mentions Joan Peebles, a technology coordinator who says to put the lone computer in an easily accessible and supervised location without having any direct sunlight, water, magnets, or chalk dust present. Even though the computer is now in a safe environment, organizing student usage of the computer may be a challenge. Both Chaika and Anderson recommend different approaches to avoid chaos among students during activity time. As an example, dividing a class of students into groups then asking them to rotate around the room in completing various activities (with one of the activities being to use the computer for research or reinforcement) is an execution of fairness. Every student has had a chance to use the computer for himself. A computer with software for skills reinforcement is an advantageous addition to a classroom. However, unless a student has prior knowledge of doing research on a topic, the computer may not serve its full purpose. Search engines are not the only on-line methods of research. Therefore, students need to reach a certain maturity level in order to accomplish what is quality research.

The “one-computer classroom” is a good model in involving technology into the classroom. Teachers have been implementing this model in their classroom activities for a long time. As a prospective secondary mathematics teacher, I feel this model will enrich my classroom activities, as well.

In applying strategies in using the computer to learn in the classroom, teachers offer to magnify a single computer screen onto a projector or a larger monitor. In this way, even though learning may be passive (Anderson), students are all getting an equal opportunity to view the essences of a teacher’s lesson. To make this an active lesson, I shall ask each group of students in the class to solve the problems seen on the monitor. Then, a representative from each group could explain to the entire class how he came to the solution of a selected problem. This could be done each day until all of the students have had a turn.

Given the financial circumstances of various school districts across the nation and Canada, the “one-computer classroom” is the epitome of the lack of educational resources in creating effective strategies and activities that enhance student-learning. The “one-computer classroom” is an answer to the shortage of technological resources. However, what are ways to improve the “one-computer classroom” setting even further? Teachers could use the one computer to demonstrate an application, such as inserting a function into Microsoft Excel and creating a table and a graph, then ask his students to practice this application with a different function while at home. How can this kind of environment benefit the students’ disciplinary levels? They all learn to share with one another a mutually valuable tool and acknowledge the importance of time with respect to another individual. As one can see, one aggravation can end in elation.

<span style="font-family: 'Arial','sans-serif';">Works Cited

<span style="font-family: 'Arial','sans-serif';">Chaika, G. (2003). How to Thrive -- Not to Survive -- in a One-Computer Classroom. Education world. Retrieved from []

<span style="font-family: 'Arial','sans-serif';">Anderson, W. (2002). That’s not a drinking fountain or how to survive in a one computer classroom. North Central Regional Technology in Education Consortium. Retrieved from []

<span style="font-family: Arial,sans-serif; line-height: 1.5;">Reflection V: Digital Gaming Media

<span style="font-family: 'Arial','sans-serif';">The transition from the Industrial Age to the Digital Age of learning is occurring presently in the world. Knowing the importance of technology in the workforce has led academicians and digital game developers to collaborate and to generate a digital product that would help with utilizing twenty-first century skills. These are the thoughts of the minds described in the articles written by Hong et al. (2009) and Sardone et al. (2010).

<span style="font-family: 'Arial','sans-serif';">Twenty-first century skills, as given by Sardone et al. (2010), are abilities to be creative and innovative, to be able to think critically and to solve problems, and to communicate and collaborate well with others. The task and challenge are to implement these characteristics of effective skills into digital gaming software. Hong et al. (2009), in their article, laid out a procedural framework for how a digital game is analyzed and finalized. Then, in the article written by Sardone et al. (2010), she put the finalized product through tests with pre-service teachers to see their reactions. Hong et al. (2009) and Sardone et al. (2010) were able to prove successfully their findings on the topic of digital games for education.

<span style="color: black; font-family: 'Arial','sans-serif';">As a prospective, secondary mathematics teacher in the twenty-first century, it is vital for me to accustom myself in learning and adapting to using digital gaming software for the benefit of my students’ learning and social growth. In a face-to-face environment where there is teacher-student interaction, I would let the students experiment with the software, so that they are learning by doing, instead of by direct instruction. This way, as a part of their homework, they are able to learn effectively through an evolutionary contest game logical thinking skills (Hong et al., 2009, p. 425), which is highly utilized in STEM courses.

<span style="color: black; font-family: 'Arial','sans-serif';">The two articles provide valid points in advocating digital gaming media into education. They also warned that the playing of on-line games alone will not benefit a child’s intellectual growth. However, in my opinion, there should be a balance of Industrial Age habits with Digital Age achievements. The writing instrument, for example, lets people practice with their motor skills, which should not be lost. In this way, history will be preserved until a new era comes into being in which the legacies of the Industrial and Digital Ages should be remembered.

<span style="color: black; font-family: 'Arial','sans-serif';">How can the technologies of the future be attained without sacrificing or disregarding what was achieved in the past? What could be done in the past that we no longer can duplicate in the present? These questions are ones to be pondered.

<span style="color: black; font-family: 'Arial','sans-serif';">Works Cited

<span style="color: black; font-family: 'Arial','sans-serif';">Hong, et al. (2009). Assessing the educational values of digital games. Journal of Computer Assisted Learning. 25, 423-437.

<span style="color: black; font-family: 'Arial','sans-serif';">Sardone, N. & Devlin-Scherer, R. (2010). Teacher candidate responses to digital games: 21st-century skills development. Journal of Research on Technology in Education. 42(4), 409-425.

<span style="font-family: 'Arial','sans-serif';">Reflection VI: iPod Touch and the Interactive Whiteboard

<span style="color: black; font-family: 'Arial','sans-serif';">The articles written by Banister and Armstrong et al. both focus on integrating technology into the classroom. Banister wrote about theoretical applications of iPod Touch, along with other MacIntosh (Apple) devices, while Armstrong et al. researched and analyzed the results of the use of Interactive Whiteboards (IWBs) in the classroom. In the latter article, Armstrong et al. first recognized “that IWBs <span style="font-family: 'Arial','sans-serif';">are not necessarily used interactively and can actually reinforce teacher-centred styles of delivery <span style="color: black; font-family: 'Arial','sans-serif';">” (Armstrong et al., 2005, p. 456). Therefore, there was room for research as to how capable IWBs are in reaching student-learning and interactivity in the classroom. The research demonstrated via three case studies of three teachers that their perceptions of the IWB can affect how they use the technology, and in turn, cause student-learning either to rise or fall. Sarah Curran, the teacher in the first case study, took the IWB in her classroom as a gaming device. In teaching her class a science lesson on fish and their survival rate, she developed the lesson in such a way that the student with the last fish to survive won, which was totally irrelevant. Sarah later learned that she took in the IWB “at face value” (2005, p. 461). To contrast with Sarah’s experience, Ian Thompson, the teacher in the third case study, though he was a novice user of the IWB, was able to engage one of his more challenging students in productive work as the proofreader of a class-written story. This student discovered the usefulness of the IWB, while learning to correct the plot of a story with the assistance of his teacher and peers. The Interactive Whiteboard is a multi-faceted tool that can be integrated into the classroom in many ways.

<span style="color: black; font-family: 'Arial','sans-serif';">In applying the writings of Banister and Armstrong et al. into my teaching, I would utilize the first standard set by the <span style="font-family: 'Arial','sans-serif';">National Educational Technology Standards for Students (NETS-S) and its sub-standards into my prospective classroom. Because I will be teaching secondary mathematics, the application of the IWB in showing a real-world word problem would be useful and supplemental to the lesson. For instance, if I were to ask my students to solve a proportion problem in relating an individual’s height to the height of a tree, it would be helpful for the students to visualize this scenario on the IWB. As for using the iPod Touch in secondary mathematics, I could use applications, such as GraFunc, to introduce the concept of functions in algebra by showing examples and non-examples of it. In brainstorming further, how can the IWB be used to accomplish more advanced mathematics problems that could be used in Calculus I, for example?

<span style="color: black; font-family: 'Arial','sans-serif';">The findings provided in the article by Armstrong et al. were valid, in that they were based from research conducted scientifically over a two-year period. However, the validity of Banister’s article struck as superficial. I refer to this term, because even though, it was organized into categories and sub-categories, her findings were untested. Therefore, there could be a highly likely chance that many of the applications purchased or found on the iPod Touch may not be relevant for class teaching or learning. As written by the author herself, “ <span style="font-family: 'Arial','sans-serif';">Caution must be taken, as the management and implementation of these devices in the K–12 environment bring risks and challenges” (Banister, 2010, p. 129). With the pool of iPod Touch applications being so vast, what are some ways to narrow this pool and to organize the applications into the most essential to be used in the Humanities and STEM courses? Could the applications from iPod Touch and other similar devices be esteemed for use in higher educational settings? If so, how would this take place?

Works Cited

Armstrong, V. et al. (2005). Collaborative research methodology for investigating teaching and learning: The use of interactive whiteboard technology. Educational Review. 57(4), 455-468.

Banister, S. (2010). Integrating the iPod Touch in K–12 education: Visions and vices. Computers in the Schools. 27, 121-131.

Reflection VII: Virtual Reality and Second Life

<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">A virtual reality is an alternate world that mimics the real world. In this virtual reality, computer simulations of real-life objects are present and processes occur in real time. “Computer simulations are computer-generated versions of real-world objects (for example, a skyscraper or chemical molecules) or processes (for example, population growth or biological decay)” (Strangman & Hall, 2003, p. 2). These new technologies are usually associated “with science fiction, high-tech industries, and computer games; few associate these technologies with education” (Strangman & Hall, 2003, p. 2). In their writings, Strangman and Hall and Baker et al. offer to expose readers to how virtual realities with computer simulated objects and processes can assist students in learning. Virtual reality software have been used by elementary, junior high, and high school students. These tools “support a constructivist approach to learning. Students can learn by doing rather than, for example, reading. They can also test theories by developing alternative realities” (Strangman & Hall, 2003, p.3). Because of the commonalities between the virtual and real worlds, an unsurprising fact is that virtual reality software are more geared to the mathematics and sciences. The humanities subjects, such as history and reading, have little associations with this technology. However, “students can encounter abstract concepts directly, without the barrier of language or symbols and computer simulations and virtual environments are highly engaging” (Strangman & Hall, 2003, p.3), making humanities applications having the same positive outlook on this technology as the STEM applications. Within Second Life (SL), an on-line virtual world used by “more than one hundred universities in the United States and other countries” (Baker et al., 2009, p. 60), instructors hold lectures or meetings and interact with the avatars of their students. Virtual musical performances, health clinics, faculty offices with office hours are all available on SL. However, the virtual world thus far cannot completely replace real world interactions.

<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Universities that use SL have to allow a certain amount of annual budget in order to keep it running. This cost is not low. Older faculty members who are not technologically savvy but who teach a STEM course may find him or herself in a dilemma whether to use SL or not. Along with their reluctance, “instructors might need to develop new class management techniques. For example, discussions in SL can become complicated at times due to the delay incurred while participants type out comments and responses. Multiple overlapping conversations can occur simultaneously, which can become confusing. Instructors need to formulate procedures for managing group discussions in SL” (Baker et al., 2009, p. 62). Thus, virtual reality software still need fast progression in order to reach the growing real world.

<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">The quality of research and writing in Strangman and Hall’s article is very sound. Even though they are advocating the use of virtual reality software in the K-12 classroom, they still pose issues that may hinder its growth in the education realm. Strangman and Hall considered many aspects as to how the virtual reality software may or may not be successful with students, such as student grade level, student characteristics, and teacher training and support. These are all valid thoughts to ponder as to the development of virtual reality software in education.

<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">As for the article written by Baker et al., they were also consistent with their research and writing. Because this article was included in a journal about psychology, Baker et al. did not write enough about how Second Life (SL) can benefit the study of psychology. They did write extensively on how SL contributes to education in general.

<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Because I will be a prospective teacher in the STEM fields, I am willing to test the use of virtual reality software in a geometry course, for example. The study of three-dimensional shapes and the calculations of their surface area and volume may be hard to visualize in a two-dimensional format. According to the National Educational Technology Standards (NETS), virtual reality software would help students clarify conceptual understanding and thinking, planning, and creative processes. With virtual reality software, I can teach students to visualize spatially and to have a clearer scope of the significance of geometry in our lives. The most important thing to realize, in my opinion, is a balance between the virtual and the real worlds. If we relied entirely on a virtual world, such as Second Life, to learn, then what is the use of teachers in the real world? Following on with that, can virtual realities duplicate then replace our real world with the advancement of technology in its current pace?

<span style="font-family: 'Arial','sans-serif'; font-size: 13px;"> Works Cited

<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Strangman, N. & Hall, T. (2003). Virtual reality/computer simulations. National Center on Accessing the General Curriculum. 1-21.

<span style="font-family: Arial,sans-serif; line-height: 1.5;">Baker, Suzanne C., Wentz, Ryan K. and Woods, Madison M. (2009) Using Virtual Worlds in Education: Second Life® as an Educational Tool, Teaching of Psychology, 36: 1, 59 — 64