Maths

Another Look Around You special, as promised!

Technological Pedagogical Content Knowledge (TPCK)

The Technological Pedagogical Content Knowledge (TPCK) model is an extension of the Pedagogical Content Knowledge (PCK) model proposed by Shulman. There are, of course, strengths and weaknesses found within the bounds of the model—resulting in comprehensive gains in creating technology-based instruction and design as well as presenting difficulties in application (Mishra et al.).

 
The TPCK model can be useful in creating technology-based instruction by placing strong emphasis on interweaving not only technology with content, nor only technology with pedagogy, nor only content with pedagogy, but rather technology with content with pedagogy together. It requires facilitators of technology-based instruction to consider appropriate infusion of the target content within the confines of research-based pedagogy via technological environments.

 
The model adds a level of critique to the design of instruction which may not have been present—at least to this degree—in past considerations. Rather than focusing on technology as a means for delivery of content alone, the TPCK model calls for a rigorous exploration of the pedagogical components interwoven within. It allows one to consider whether the absence of technology would be as effective as the incorporation thereof. It is a complex model enabling designers and creators of instruction to more fully consider the effectiveness of technological tools and how they impact delivery.

 
In application, the TPCK model can be daunting due to the dynamic connectedness of each component. For example, that which one component lacks, the others may take upon themselves in order to preserve the woven nature of the triad. Additionally, technology changes at such a rate as to make even the freshest of today’s technologies stale by tomorrow. Finally, no matter how skilled an instructor may be in the art of using technology, it is likely that the instructor is no match for teaching with that technology. It is far easier to incorporate technology in “edutainment” than to wield it in such a way as to engage students in “playful learning” or other learning processes (Mishra et al., Resnick).

 
Perhaps one of the biggest strengths of the TPCK model is its ability to provide us with an analytical framework by which we may judge educational technological tools. It allows us to break down technological applications so we may individually evaluate the effectiveness and goals of the content, pedagogy, and technology:

The framework allows us to view the entire process of technology integration as being amenable to analysis and development work. Most importantly the TPCK framework allows us to identify what is important and what is not in any discussions of teacher knowledge around using technology for teaching subject matter (Mishra et al.).

There are several weaknesses within the TPCK model. Let’s imagine you have a child entering middle school. If you were to choose between a teacher who was able to expertly balance content knowledge with pedagogical awareness and a teacher who was balancing content knowledge with pedagogical awareness while focusing on technological implementation, which would you choose? On the surface, you might take the latter because they are balancing more on their plate, so to speak. But then again, maybe that’s a problem. Perhaps the educator focused on delivering content using sound pedagogical principles through the use of technology is actually more focused on using the vehicle (technology) than on the PCK alone. For this reason, you may end up choosing the educator who could deliver the content using sound pedagogical principles because their time and effort is being poured into those two critical components alone. In other words, perhaps by adding the “T” to PCK, educators are spreading their dedication to education too thin (Mishra et al.).

 
Furthermore, it can be argued that technology is merely a vehicle, and if it were to be added it to the PCK model, we might as well be adding components such as curriculum knowledge, educational context knowledge, morality (read David Patterson’s When Learned Men Murder), individual/classroom management knowledge, etc. In this way we could achieve a truly complex, quantum approach to considering every possible element of the learning process. While comprehensive, this idea could prove futile because the most important of these components (content and pedagogy) would be reduced in order to compensate for divided attention toward the others:

…technologies are merely vehicles that deliver instruction, but do not themselves influence student achievement…learning is influenced more by the content and instructional strategy in the learning materials than by the type of technology used to deliver instruction (Ally).

While strengths and weaknesses exist and difficulties in application encountered with regard to the TCPK model, it has been and will continue to be useful in creating and designing technology-based instruction.

 
 
Works Cited

Ally, Mohamed. “Foundations of Educational Theory for Online Learning.” 2004. Athabasca University. 19 April 2009. http://cde.athabascau.ca/online_book/contents.html

Mishra, Punya, and Matthew J. Koehler. “Technological Pedagogical Content Knowledge: A New Framework for Teacher Knowledge.” Teachers College Record.

Resnick, Mitchel. “Computer as Paint Brush: Technology, Play, and the Creative Society.” MIT Media Laboratory.

Limit the Children

Maybe you think young ones are a good thing.

Speaking in generalities, maybe you’re right.

Also speaking in generatlities, you may be horribly wrong.

Here’s a wonderful little ad which could use some reruns…

Stereotypes and Diversity in Technology

It’s important to break the stereotypes associated with technology–especially in today’s global climate. The stigma surrounding sexes and ethnicities must be realized and dealt with if we hope to succeed as a nation (Chapman).

We should be diligent to recognize opportunities to engage students from all backgrounds with regard to technology. If we can find a “hook” which will catch the interest of today’s youth (in art, technical drawing, music, photography, web design, programming, science, etc.), then perhaps we will enable members of all social groups to grab technology by the horns and use it fluently within the context of their lives (Pinkett).

A huge remedy to these challenges could be to create Community Technology Centers (CTCs), which would foster not only the technological skills needed, but would do so by using the “hooks” which appeal to our diverse youth populations. In this way, boredom can be transformed into something useful, causing accidental learning everywhere (Chapman)!

Works Cited

Chapman, Robbin. “Redefining Equity: Meaningful Uses of Technology in Learning Environments.” 2001. Position paper on Equity and Education Technologies. 9 April 2009.

Pinkett, Randall. “Strategies for Motivating Minorities to Engage Computers: Position Paper for the Carnegie Mellon Symposium on Minorities and Computer Science.” MIT Media Laboratory. Cambridge, MA. 1999.

Linking Sexuality and Learning

I’m confused as to why we, as educators, are concerned that students are heterosexual when considering learning abilities. This needs to be left out of the academic educational sphere (except to deal with any resulting bullying). Why? Because while sexuality is a part of human behavior, it is just that–a behavior. Gender, ethnicity, and socio-economic status are all unrelated to an individual’s behavior. If we begin talking about heterosexual/homosexual tendencies within the classroom, then perhaps we must begin considering solo sexuality, fantasies, sports preferences, what the children have eaten as after-school snacks, and tissue brand preference.

These examples are matters of behavioral preferences (some of which are inappropriate to the academic setting) and ought not to be attributed as classifications to the students we teach. Could you imagine if we identified someone as an upper-middle class, able-bodied, Caucasian, Puffs-blower, chocolate-covered-pretzel-after-school-snacker male? While perhaps these attributions are true, it is unnecessary for educators to classify based on behavior in such an inappropriate way, no matter how public students may be about such preferences.

From an educationally researched standpoint, how are we to truly incorporate consideration of something like sexuality within the bounds of reviewing an educational software package? Do people learn differently because they prefer a particular type of sexuality? Any sensitivity toward sexual preferences with regard to educational software would be disasterous because there should be NOTHING suggestive of that nature within our technological tools. Even if we included a picture of a family with two mommies (in an attempt toward sensitivity), it would detract from the learning process as the learner’s attention would be immediately diverted toward an image of something that is uncommon rather than being focused on the academic content involved. In this way, the content of the software has become more sexually explicit than necessary.

In mixed-sex classrooms, especially, the use of information technology to reach sexually explicit or risqué text and material provides a high-tech medium for teasing, harassment, and embarrassment. From the teachers’ perspective, the introduction of this material disrupts learning and weakens their confidence in being able to manage technology in the classroom (“Tech-Savvy”).

While perhaps advantageous from a political standpoint due to any normalization attempted by the software, it has no place within the academic educational sphere.

It’s not that I advocate insensitivity toward topics and situations which present themselves; I do not believe it is the place of educators to carry out political agendas to popularize human preferences–especially those pertaining to subjects which are banned to those younger than 18 years of age in media such as magazines, television programming, filmography, and websites. It is, however, appropriate and necessary for educators to guard against inappropriate material and any bullying resulting from students’ professed preferences within the academic environment. If significant educational research presents itself concerning the differences in learning abilities within groups of people who have preferences [seemingly] unrelated to education, I will certainly change this tune.

Works Cited:

“Tech-Savvy: Educating Girls in the New Computer Age.” April 2000.  AAUW Educational Foundation. 9 April 2009.

Who’s Driving the Learning?

There is a delicate balance between allowing students to drive their own learning and allowing federal mandates determine what you teach. The standards certainly provide a good skeletal structure for what needs to be taught in certain grades, but standards alone have no flesh and blood. Likewise, student interest provides some direction in the content which is taught (call it the flesh and blood), but without a skeletal structure is a rather useless heap.

While there are certain content areas which need to be addressed in each grade level, the “appropriateness” can be determined somewhat by the level of inquiry which has been developed within the students as well as by their obvious maturity level (for example, we wouldn’t give young students—if any—a car battery, stripped wires, and a light bulb in order to explore electric circuits), their zone of proximal development, as well as their developmental stage (as defined by Piaget).

By using appropriate and varied forms of assessment, I will also be able to uncover misconceptions. Through determining questions the students have, providing opportunity to confront misconceptions by comparing them to observation, providing proper information and allowing them to practice, I will be able to change their misconceptions.

Method for Science

Children learn science best by experiencing it hands-on. Personal, hands-on experimentation and exploration yields the greatest amount of learning—and it is through this fun, engaging method that a “good” science program can be born and implemented effectively. In our science programs, we should incorporate not only a hands-on, active approach, but also encourage different types of questioning in order to engage their minds as they work hands-on (otherwise it would just be a set of fun activities). The proper methods, if implemented properly, will allow a science program to operate smoothly and effectively in order to produce students who are inquiry-minded and ready to “do” science.

Look Around You: Water

We’ll be including several of these incredible Scientific videos…

be sure NOT to turn it off until you’ve watched at least 2 minutes of the video. If you’re anything like us or those we know well, you may experience difficulty restraining your laughter (maybe).

If you’re interested, keep an eye out for future Look Around You videos (we’ll post more in good time, we promise!)

Applying Piaget to Adult Learning

Although Piaget describes the stages as they relate to specific age ranges of children, much of his theory can, in my opinion, be applied to all age groups with regard to a wide array of topics.

For example, an adult learner might not understand how a particular computer program works. Despite any given modeling by an instructor, the learner is able to do nothing more than make guesses as to what is happening on the screen, and may not even understand why some visuals are appearing and disappearing again (sensorimotor).

As the instructor continues to work with the learner, the learner begins to manipulate parts of the program, though needs constant guidance from the instructor (preoperational).

As time passes and instruction builds, the learner is eventually able to work independently within the bounds of the program, manipulating variables in order to solve given problems (concrete operations).

Finally, the learner “gets it” when the ability to describe to someone how the particular program may be used to solve hypothetical situations without ever turning a computer on is mastered (formal operations) (Llorente, “Piaget”).

In this light, Piaget becomes more relevant to the cognitive process at all ages of human development rather than pinning his theories to ages 0-15.

Works Cited

“Piaget.” Funderstanding. 4 April 2009. http://www.funderstanding.com/content/piaget

Llorente, Juan Carlos. “Researching Adults’ Knowledge Through Piagetian Clinical Exploration…” 2000. Metapress. 4 April 2009. http://resources.metapress.com/pdf-preview.axd?code=q7wj1471r3174g61&size=largest

Abraham Maslow: Learning Theorist?

Maslow is a bit tricky. I would question whether or not he is a theorist with regard to learning. Undoubtedly, his pyramid is simple and pretty and, on the surface, seems to make sense, but when it comes to applying it to human behavior it works, at best, sometimes.

First, Maslow arbitrarily picked who he thought were self-actualized people and interviewed them in an attempt to understand and make conclusions about self-actualization itself (Boerre).

Second, much of Maslow’s research was based on responses from educated white males. It would be nice if someone who wanted to validate his hierarchy could perform a cross-cultural study (Illeris).

Finally, Maslow does not attempt to describe the learning process, he safely lists attributes which need to be met in order for other attributes to be built on top. Nowhere does he explain how learning occurs (“About Learning”).

What would we say of martyrs like Joan of Arc or “starving artists” or of those imprisoned for their beliefs or of those historical figures who spent the majority of their lives in solitude, arguably wanting of any sense of belongingness yet who still exhibit strong self-esteem and, perhaps, actualization? Were they not able to accomplish and live for that which they felt called or destined? Were they unable to learn in hostile environments or where they lacked nourishment?

While it doesn’t explicitly address any ideas about learning, I find Maslow’s hierarchy useful to keep in mind when I consider a child’s aptitude in learning environments. I often realize that they are dealing with some of these very issues at home (physiological, safety, belongingness) and, therefore, I am more sensitive to what they may need within the confines of my classroom, and try to provide for those which a child may lack when I am able.

Works Cited:

Boeree, George C. “Abraham Maslow.” 2006. Shippensburg University. 4 April 2009. http://webspace.ship.edu/cgboer/maslow.html

Illeris, Knud. “How We Learn: Learning and non-learning in school and beyond.” 2007. Routledge. 4 April 2009. http://books.google.com/books?id=41pWdwCrAx0C&printsec=copyright&dq

“About Learning.” 2008. Funderstanding. 4 April 2009. http://www.funderstanding.com/content/about-learning