Nucleus Learning - The Heart of Creative Education

Teacher Pay Scale Across Canada

bogusia — Tue, 02 Sep 2008 12:21:54 -0600

I couldn't believe it. I was in shock when I actually looked it up. This last year, I was making $30,000 less in Quebec than if I was working as a teacher in Alberta. I used to live in Alberta, and therefore I can't believe that I am worth so much less, just by living a few provinces down; and this doesn't even include the huge taxes that are taken off here in Quebec as opposed to Alberta.

Previously, I wrote a post about salaries in Canada and how they compare to test scores. Higher Teacher Salary = Better Education. In that post I was stunned at how correlated those two values were. But it seemed like the pay scale were somewhat comparable (plus or minus a 5 thousand dollars). But I was comparing statistics from 2001. Not now! Just a few years later and now there's a HUGE difference in the salaries.

Since it was not so easy for me to look up the most recent salary grids for all the provinces (a lot of clever internet searching, including emailing some schools for first hand information), I thought I would post all the provinces' teaching salary scales here (as a comparison), for future reference, for myself and anybody else that wants to know.

Just a few guidlines:

In most provinces, the salary is not the same in all cities / districts, but within 10% of each other. I'll therefore take a sample of a city I wouldn't mind living in (usually smaller cities can't attract as many teachers, so they pay more than the big cities). Also, the salaries usually depend on the amount of years of university/college, and years of teaching experience. I will use my university years (6 years - 4 yrs undergrad, 2 yrs ed. after-degree) and teaching experience (8 years) as an example. If you want to check for yourself, I give links to the actual sites from which I got the information, thus you can check the salary for you specifically.

Enjoy:

Province	Salary	Year	Link
British Columbia (Vancouver Island)	$72,242	2008	Vancouver Island North Payscale
Alberta (Calgary)	$74,299	2007	Collective agreement - ATA
Saskatchewan	$67,293	2007	Collective Agreement - STF
Manitoba (Winnipeg)	$74,317	2008	Collective Bargaining - MTS
Ontario (Toronto)	$75,688	2007	Collective Agreement - OSSTF
Quebec	$46,341	2007	Collective Agreement - QPAT
New Brunswick	$57,126	2008	None - negotiations under way.
Nova Scotia (Halifax)	$67,277	2007	Collective Agreement - NSTU
P.E.I.	$60,296	2008	PEITF Handbook
Newfoundland	$61,899	2007	Collective Agreement -NLTA

I's not only Alberta! Most provinces are on par with Alberta. It's Quebec - as if it was in Medieval times. What is up with that? This can't last long. If in Ontario and New Brunswick (the two neighbouring provinces) are $10,000 to $30,000 higher than here in Quebec, there is no way Quebec will not have to catch up with the salary - It's risking a major shortage of teachers in the next few years. Next year, I'm looking for a job in Ontario (I'm only a half hour away... I might as well move that half hour away, to save on taxes also). I cannot believe Quebec... where are these enormous taxes going to? - not the teachers, that's for sure!

Also see: Are Teachers Worth the Money?

If you enjoyed this article, please fill in the quick and anonymous Salary Survey, so I can compile a set of real teacher salary data and post the results here at a later time. Thanks in advance.

Are Teachers Worth the Money?

MathMentor — Sun, 14 Feb 2010 19:09:24 -0700

Judging from the comments from the article Teacher Pay Scale Across Canada, many people covet the schedule of a teacher and believe that they are paid too richly for simply reading textbooks. I think that teachers are not paid enough!

At the most abstract and philosophical, people get paid for value. How much would you pay me for a map to a long-lost gold nugget worth $1,000 that was buried in your backyard? Unless you have a logic deficiency, it would be some amount under $1,000. You might think it fair to split it 50/50 and offer me $500.

Hey! I have an MBA! I went to university for 6 years. Furthermore I invested 500 hours searching the old library archives to piece together the location of that lost nugget. My education entitles me to $50/hour, so for the 500 hours I'm going to need $25,000. You're lucky I'm not a lawyer at a big firm otherwise you'd be paying me $125,000 for that map.

That argument is ridiculous, yet it is the same type of argument that people use to grumble about the income and workload of teachers compared to their own. Investment bankers and lawyers work long hours, movers lift heavier things, and farmers never get time off. Nearly everyone thinks they should be paid more than a teacher. After all, teachers only babysit for about 6 hours a day because their marketable skills consist mostly of photocopying. They get months of holidays and never work overtime. If that's what you believe then the per hour and per unit of skill payrate of teachers is astronomical. So you grumble.

Generally, I think that the value of the teaching profession is tough to figure. It isn't like the gold nugget example because we don't really know how much we're getting from the teacher. I am, however, sure that it is a tremendous amount. Have a look at the mission statements and mandates of various provincial and state education departments. You'll read about preparing young people for participation in the global economy, about ensuring a country's leadership in this or that area, about building success and just generally creating high quality people.

It almost sounds like education departments think that they are delivering the future success of a society! Can we argue against that? Success in a society depends quite heavily on creating smart and ambitious people, which is pretty much what teachers should be doing. While we're at it, what is more valuable than the entire future of our society? If we look at it from “what value are we getting”, we would theoretically pay an almost unlimited amount.

Another reason people get paid a lot in the real world is because they have a lot of responsibility. A train engineer gets paid more than a truck driver because the train is worth many times more than the truck. A late train costs a lot more than a late truck and a crashed train could be a huge disaster. Railroads pay locomotive engineers a lot, and they expect only a few things: Be on time and don't cause an accident.

What responsibilities do teachers have? They only take care of human beings. Not just take care of them, but masterfully assembling the knowledge they'll need and trying to tease their personalities in being decent, healthy, achievers. Oh, there is also that whole future success of society thing. Over the years and decades, if teachers do a bad job, we could have generations of stupid and lazy people. That sounds like a potential train wreck to me! Many of the same people who think that a teachers job is worth little also think that young people are getting dumber. Maybe they're related.

Compare that responsibility to other jobs. Lawyers are responsible for what, really? Making sure that a contract leaves no loophole for the other party to run away? An MBA like myself is responsible for making sure that the detailed page 2 adds up to the number on page 1. Accountants need to be sure that money coming in ends up under the revenue column, and money going out under the expense column. Factory workers need keep up with assembly line. Landscapers dig holes deep enough for the roots. Fashion models need to keep their weight down and movie stars squeeze out tears on demand. None of those sound anywhere near as much responsibility as THE FUTURE OF SOCIETY!

So teachers have one of the highest levels of responsibility we can imagine, and produce an immeasurable amount of value for us. As a society, we really need to get behind them. When we underpay teachers, like we are here in Quebec where I live, it is saying that we expect a lot less from them. You couldn't pay a locomotive engineer $5/hour and expect precision timing with zero accidents; the employee simply wouldn't take you seriously and they wouldn't care. Paying them $120,000 per year is going to get their attention and respect.

Teachers are exactly the same. Their bosses mouth off about preparing future generations of people, but pay them like they're preparing hamburgers. Teachers can't take that seriously. Eventually, many teachers begin to care as much about their jobs as a hamburger cook cares about getting that pickle slice exactly in the middle of the patty. Everything becomes “pretend”. Teachers pretend they are highly skilled professionals, principals and education departments pretend they are chasing the lofty goals, and we all pretend we value our children and the future. The kids see this and they pretend all the way through school, getting out the other side with mainly self-taught cell-phone skills. It becomes a self-fullfiling prophecy.

Instead of playing around like that, let's just decide for sure what we want. I want a professional teacher, who is an expert in the topic she's teaching and the techniques of teaching. I want her to be motivated to make our kids tops in the world. I want her to be measured on performance, paid well for good performance, and fired for poor performance. I want our next generation of kids to be inventors, famous scientists, engineers, business people. Hard working with great values and enough resources to take care of me in my old age without grumbling, and to raise their own next generation in the same way. Teachers are the key to all that. We need to respect them, and to pay them, and demand performance.

I think teachers should be among the most highly paid segments of society.

Teacher Pay Scales Across Canada
Higher Teacher Salary = Better Education
Reader Comment: Teachers Working as Escorts to Top Up Earnings.
Improving Pay for Deserving Teachers

The Hydraulic Crane - a great science project!

bogusia — Sat, 13 Mar 2010 08:52:06 -0700

I had many requests for a step by step instruction of making the "Hydraulic Crane".

Although this wasn't my construction (one of my brilliant students did this one for a project that I assigned), I can figure out the basics from what I saw.

Note: The following is only meant as a start for anyone that wants to try this project. However, everyone has their own twist to every assignment, every design. Use your imagination to make the crane better, and your own!

Materials:

30 mL syringes (x8)
dialysis tubing (or any other kind of plastic tubing for connecting the syringes together)
wood (for crane construction and for base)
anchors (to hold the tubing in place)
bottle with water (or any other weight to counter balance the crane arm)
a scoop (any kind of shovel)
Screws / Nails / Nuts / Bolts
+ Other miscellaneous materials.

Procedure

Connect four stick of wood together so that they form a crane (as in the above picture). Connect them by drilling holes in both sticks of wood, and attach them with long bolts, securing them with nuts. Make sure the wood sticks rotate easily at the connections. (Think of these as hinges in a door.)
Attach the shovel / scoop to the end of one of the wooden sticks in the same way.
Secure this crane to a wooden base.
To counter balance the weight of the crane and scoop you need to hook on a weight (bottle with water) to the opposite side of the crane (see picture above).

Now for the hydraulics:

Connect four syringes with four pieces of flexible tubing. Make sure there are no leaks between the syringe and the tube connection. Make sure the tubing is long enough - similar length to your crane (see picture above to understand).
Fill in these syringe-tubing systems with water.
Attach another syringe to the other side of the tubing for each of the four syringe-tubing systems.

Now you should have four of these: syringe filled with water / flexible plastic tubing filled with water / empty syringe.

Next you need to attach these syringe/tubing/syringes to your crane. Each one of them is operating a motion up and down - so you should put them at the connections (the hinges).
Secure the syringes and tubing with u-type anchors (as in above picture).

You are done now. To operate, you push in the syringe with water, so that the connected empty syringe moves up the piston... this in turn pushes the wooden stick up. Depending which syringe you push makes that part of the crane move.

Hope this helps a bit. Have fun!

Conceptions of Force: Coherent Versus Fragmented

bogusia — Mon, 18 Jan 2010 11:27:49 -0700

Growing up, children have a plethora of experiences that have to do with the concept of force. Even before they start talking and knowing the word “force” they have an intuitive understanding of the concept of push and pull. It doesn’t take long for a child to figure out that pushing their brother will result in him moving in the same direction. Babies realize from very early on that things fall down. (A common game among babies and parents is the “baby drops toy – parent picks up toy – repeat many times until parent loses patience”.) This environmental input of the force of gravity acting on an object, thus accelerating it towards the earth gets absorbed by the child’s awareness, and becomes second nature to the child. Most children will ask a parent about these phenomena. The parent then tries to explain these phenomena in terms of sophisticated words such as force, gravity, energy, power, and push / pull. The adult might go in depth or just quickly dismiss the inquiry, depending on the adult’s actual knowledge of the phenomenon, the parent’s interest in scientific principles, or even the time and place of the question. Based on these explanations, and the instances of hearing the words of force or gravity in context, children start to associate what force actually means in terms of their world around them. Their understanding however might not be in alignment with the physicist’s definition.

A very similar example can be given in terms of the term work. In physics, work is very specifically defined as “the scalar product of the force acting on an object and the displacement caused by that force”. A person making hamburgers at McDonald’s is doing work, as well as a researcher reading an article. But this is not the same as doing work as defined in physics. Therefore the word work in the ordinary sense has to be understood as completely different from its meaning in Newtonian mechanics. I would call these two meanings of work polysemes (i.e. a polyseme is a word or phrase with multiple but related meanings.)

In the same way, the word force has a different meaning in the colloquial sense compared to the official meaning as described in Newtonian physics. But because language is so tightly bound to our knowledge, this creates misconceptions about how and why objects move, and the forces acting on them. This also creates a major obstacle in teaching mechanics, and why I found this topic so compelling.
Thus, in this thought paper, I investigate conceptual change as related to the concept of force. More specifically, I compare the two theories of initial (mis)conceptions: Knowledge in Pieces (diSessa, Gillespie, Esterly, 2004) and the Framework Theory model (Vosniadou & Brewer 1992) on the basis of two very similar experiments, related to the same domain and concept of force, yet resulting in two completely different interpretations.

Conceptual change deals with how students change their understandings and misconceptions into standardized understandings of ideas. Conceptual change contrasts with less problematic learning such as skill and fact acquisition, as the latter don’t have to compete with already established theories / explanations of concepts. The primary difficulty is that students must build new ideas in the context of old ones, instead of simple acquisition. It is well documented, that these prior ideas constrain learning of the new ones (diSessa, 2006). To realize conceptual change, one must first understand the misconceptions, or in other words the initial knowledge structures. This is where the perspectives from the two articles disagree.

The (chronologically) first study (Ionnides & Vosnidou, 2002) sets out to investigate the initial knowledge structures for the concept of force of children ranging from preschool to high school. The results overwhelmingly show that most of the children made use of a small number of relatively well-defined and internally consistent interpretations of force. This study supports the Framework Theory model of conceptual development, where children’s intuitive ideas about the physical world, rather than being inconsistent and fragmented, represent a few, possibly naïve, yet coherent models. According to Vosindou (1994) the framework theory of physics is established early on in infancy and forms the basis of individuals’ ontology and epistemology. These frameworks act as constraints on the way individuals interpret their observations and the information they receive from culture to construct specific theories about the physical world. The specific theories formed through this process are continuously enriched and modified. Some kinds of conceptual change require the simple addition of new information to an existing conceptual structure. Others are accomplished only when existing beliefs and presuppositions are revised.

According to this framework theory, misconceptions are interpreted as individuals’ attempts to assimilate new information into existing conceptual structures that contain information contradictory to the scientific view (Vosniadou, 1994). The results from the Ionnides and Vosindou (2002) support this view, as they demonstrated that even though the older students were exposed to the teachings of Newtonian mechanics at school, they did not fully reject their naïve theory of force, and only seemed to have a “hybrid” understanding of force, using both naïve and synthetic meanings.

The second study (diSessa, Gillespie, & Esterly, 2004), sets out to duplicate the empirical study of Ionnides & Vonidou of 2002, and extend it to illustrate the opposing theory of initial conceptions being fragmented as opposed to coherent models. This view, termed Knowledge in Pieces, envisions that intuitive physics is made up mostly of hundreds or thousands of self-explanatory schemata, typically abstracted from common situations, called phenomenological primitives (p-prims). DiSessa (1993) speculates that p-prims are explanatorily primitive, provide people with their sense of which events are natural, and need no explanation, which are surprising, and why. In a specific domain, p-prims are loosely organized, and sometimes highly contextual, so that the word “theory” is inappropriate (diSessa, 2006).

The results of the second study are very intriguing. Even though the intent of the authors was to replicate Ionnides’ & Vosnidou’s study, diSessa, Gillespie, and Esterly (2004) got conflicting results, even before the interpretation. In fact they found that children do not make use of a small number of relatively well-defined and internally consistent interpretations of force, as Ionnides & Vosnidou contended. Instead, they found that children have many, “fragmented” understandings of force.

Accordingly, the extension study found that when context and specification of a concept was introduced into the questions of the experimental design, the coherent models no longer existed (with even more fragmented results than in the quasi-replication of the study) (diSessa, Gillespie, & Esterly, 2004). For instance, when subjects were asked about forces in two different contexts (e.g. a ball travelling around in a circle in a tube compared to a ball travelling around in a circle held by a string), they saw the two situations as different in terms of what forces were present, yet in Newtonian physics, they would be considered equivalent. Also, when the specifications of the force concept were defined and probed, the differentiation of the responses rose significantly, and therefore supported the “fragmentation” hypothesis.

This debate is not inconsequential. Depending on the way we interpret misconceptions of force leads to different ways of teaching students Newtonian mechanics. The “coherence” view suggests the naive theory competes with the established scientific theory, thus the process involves the enrichment of the initial theories as well as their major reorganization (Ionnides & Vosnidou, 2002). On the other hand, the “fragmented” view suggests integration of p-prims into the theory, as collecting and systematizing the fragments of knowledge into consistent wholes (diSessa, 1993). Thus figuring out which side is the “true” theory, might lead to a resolution to overcoming the misconceptions when teaching Newtonian physics.

However, the comparison of these two articles also shows several other aspects not related to instruction or even physics misconceptions. First of all, it demonstrates an interesting debate in the open forum of the scientific knowledge building community. Initially, Ioannides and Voniadou (2002) put great emphasis on how their results directly contradict diSessa’s Knowledge by Pieces theory. This in turn triggered a reaction from diSessa and her colleagues. Yet seeing some merit to their argumentation and empirical results, diSessa, Gillespie, & Esterly, (2004), had to redefine and be more specific with certain aspects of their theory (e.g. the concept of “fragmentation” is redefined and presented in terms of contextualization and specification of the concept). Thus there is a refinement of ideas, and a fine-tuning of the theory. With every iteration, the theories improve.
Another interesting point is the fact that diSessa’s quasi-replication of Ioannides’ and Voniadou’s experiment yielded opposing results, even though the intention was to duplicate the experiment. DiSessa, Gillespie and Esterly (2004) state a few hypotheses for this discrepancy, namely: interviewing techniques, coding, instructional differences, and language (first study done in Greek the other in English). Yet from their elaboration on each of these possibilities, none of the differences should produce such significant outcomes. I find this extremely fascinating. Coming from a scientific background, replicability of an experiment is one of the most important features of science. So can these studies be considered scientifically valid? This brings back the question, whether it is appropriate to study humans, and their various practices such as learning, out of context, with traditional scientific methods? Possibly this failure to replicate the original results is a motivation to switch to design experiments instead of traditional experiments in the lab.

Finally, this comparison reveals how sensitive complex systems are to their initial variables. The few initial differences: the interviewing technique, the language, the desired result of the investigation, can completely change the outcome. This is a characteristic of chaos and any complex system, in which it is not possible to predict the outcome even knowing everything about the process that produces it. Also, this shows that the assumptions can unintentionally influence the results (i.e. in the second study, the questions were aligned to measure the differentiation in context and specification, and the results supported the researchers’ claims.)

This analysis of the two articles provides just a taste of the many issues that could be explored. The many questions raised in both articles were barely touched, and my own perspectives were hardly mentioned. Moreover, there are more than just the two theories mentioned of conceptual change and the initial knowledge structures. These other theories might shed more light onto the discussion and crystallize a resolution to the debate. Conceptual change is such an important concept to a physics teacher that I cannot conclude here. This thought paper therefore is just a launching point to explore these issues further.

References:

Ioannides, C., & Vosiniadou, S. (2002). The Changing Meanings of Force. Cognitive Science Quarterly, 2, 5 – 61

diSessa, A. A., Gillespie, N., & Esterly, J. (2004). Coherence vs. Fragmentation in the development of the concept of force. Cognitive Science, 28, 843 – 900.

Vosniadou, S. (1994). Capturing and Modeling the Process of Conceptual Change. Learning and Instruction, 4, 45 – 69.

diSessa, A. (1993). Toward an Epistemology of Physics. Cognition and Instruction, 10, 105-225

di Sessa, A. A. (2006). A history of conceptual change research: threads and fault lines. In. K. Sawyer (Ed.), The Cambridge Handbook of the Learning Sciences (pp. 265-282). MA: Cambridge University Press. Chan, C., Burtis, J., & Bereiter, C. (1997).

Knowledge building as a mediator of conflict in conceptual change. Cognition and Instruction, 15(1), 1-40

Conceptual Change in Force and Motion

bogusia — Tue, 23 Feb 2010 13:07:23 -0700

Introduction
Some things are easier to learn than others. Piaget, one of the fathers of the constructivist movement, talked about two types of learning: assimilation and accommodation (Atherton, 2009). Assimilation and accommodation are the two complementary processes through which awareness of the outside world is internalized (Atherton, 2009).
In assimilation, the perceptions of the outside world are incorporated into the internal world model without changing the structure of that model, but potentially at the cost of "squeezing" the external perceptions to fit (Atherton, 2009). In accommodation, the internal world model has to accommodate itself to the evidence with which it is confronted and thus adapt to it, which can be a more difficult and painful process (Atherton, 2009). Accommodation has everything to do with conceptual change, and is the starting point of the many theories concerned with misconceptions.
Constructivism tells us that learning has a lot to do with previous knowledge and experiences. A teacher must account for these preconceptions if she wants to influence the learning process. Most of the time, preconceptions are useful and, if accessed properly by the student, can help the student understand new concepts and fit them into the bigger picture, creating a shortcut to the new knowledge. Some preconceptions are incorrect and there may be great challenges in overcoming these misconceptions with correct knowledge. The process of modifying these naive misconceptions into scientifically acceptable concepts is called conceptual change (diSessa, 2006). This paper discusses conceptual change applied to teaching and learning about physical scientific principles; specifically learning about forces.
Learning scientists noticed there were many similar types of physics related misconceptions popping up in every classroom of the world. They are so universal that they seem a natural step through which most people pass. Researchers started recording the different types of misconceptions and, after over two decades of work and 3000 articles (Chi, 2005), researchers had a solid foundation for conceptual change research. The naive conceptions were readily observed, but were extremely hard to modify. Researchers started theorizing about how these misconceptions were organized by the student, and why they were so common and resistant to change. Were they all connected in a consistent network of conceptions or were they just disorganized fragments that only became connected when formal teaching of physics began? Perhaps they were simply caused by misunderstood terms; or were they evidence of an existing intuitive, but incorrect, model?
These questions are very relevant to learning theory and especially the practicality of teaching physics. Depending on the type of classification of the misconceptions, a physics teacher should approach teaching these conceptions in different ways. For instance, if the problem lies in the misalignment of the word “force” the teacher should focus on explaining to the students that their language is what's causing all the difficulty, and that their conception of force is actually momentum. If, on the other hand, the misconception is on a deeper level, and the idea of force for the novice is ingrained in a form of a complex knowledge system consisting of a network of beliefs and presuppositions (Vosniadou, 2002), then the teacher must undermine the whole system, which could be a much larger and longer effort. Therefore, it is important to understand the organization of these misconceptions. Unfortunately there is no overall consensus on this topic in the learning sciences community. Many studies have been done to try to confirm or negate each theory of misconception structure, but this issue is tough to measure. In one case, diSessa, Gillespie and Esterly (2004) tried to duplicate an experiment by Ioannides and Vosniadou (2002) and were unsuccessful in repeating similar results. The following section is a review of some of the main theories of misconceptions and a few methodological attempts of conceptual change.

Literature Review

Theories of Misconceptions

Medieval and Intuitive Beliefs
Historically, the scientific understanding of force and how things move has evolved. Nersessian and Resnik (1989) explore the parallels between historical pre-Newtonian explanations of motion and those used intuitively by students and even adults. In the article, the authors develop an extensive model of the medieval belief structure and conceptual structure of motion and then compare the many studies investigating misconceptions of motions of intuitive physics. They sum up historical beliefs of motion into six main misconceptions (Nersessian & Resnik, 1989):
1) All motion requires a causal explanation.
2) Motion is caused by a mover.
3) Continuing motions is sustained by impetus (impetus - a stored-up force that is the property of the object, imparted to it by the mover).
4) Carrying does not convey impetus.
5) Downward motion is natural.
6) Heavier objects fall faster.
They then compiled a list of conceptions of naive physics about motion from the numerous studies of the 1970 and 1980. The authors notice that the naive conceptions about motion are almost identical to the beliefs gathered from historical records, calling them intuitive beliefs, because they come naturally to so many of us, without training, by self-explaining the world around us.
An important difference between intuitive beliefs and the Newtonian view is that all motion requires an explanation, while Newton states that motion, or constant velocity, is a state and that only a change of state, or acceleration, requires an explanation. Nersessian and Resnik (1989) also propose a conceptual structure of medieval theory of motion, linking all the beliefs together, and then hypothesized on the possible structure of intuitive physics. They demonstrate the striking similarity between intuitive and medieval conceptual / belief structures. Therefore, by comparing intuitive physics with historical pre-Newtonian physics, Nersessian and Resnik (1989) confirm that there could be an underlying structure of naive conceptions that generates intuitive explanations of certain types of motions.

Framework Theory
Vosniadou (2002) also rationalizes that the force and motion misconceptions are organized in a form of a coherent yet a narrow sort of internal theory. Vosniadou chooses to use the word framework as opposed to theory to describe her view of the organization of preconceptions in order to separate these internal, quasi-coherent explanatory systems from real scientific theories. Vosniadou (2002) believes conceptual change takes a long time and is a difficult process as it requires undermining an array of intuitive beliefs that are deep-seeded along with their complex interconnections. These frameworks act as constraints on the way individuals interpret environmental inputs to conjecture about the physical world. Specific theories formed through this process are continuously enriched and modified. Some kinds of conceptual change require the simple addition of new information to an existing conceptual structure. Others can only be accomplished when existing beliefs and presuppositions are revised.
The empirical study (Ionnides & Vosniadou, 2002) tries to probe the initial knowledge structures for the concepts of force and motion of children ranging from preschool to high school. The authors’ aim is to empirically support Vosniadou’s Framework theory. The results appear to support the Framework theory and that most of the children made use of a small number of relatively well-defined and internally consistent interpretations of force (Ionnides & Vosniadou, 2002). Also this cross sectional study gives rise to a progression of the different intuitive beliefs about motion. In particular, it seems that in their earlier years, children see force as an internal property of physical objects related to their weight. Then they metamorphose their view of force to be an acquired property of objects, similar to the impetus idea from historical accounts. Finally, when formal teaching of physics begins at school (around the age of 15), students start combining several different meanings of force, trying to assimilate the notions of “gravity” and “force of push and pull” into their already set framework. This creates confusion in the internal model of force and motion and thus leads to increased fragmentation and a less cohesive framework (Ionnides & Vosniadou, 2002).

Force as a Property of a Substance
Alternatively, Reiner, Slotta, Chi and Resnik (2000) see misconceptions arising when people use their understanding of substances to explain motion and force. From their daily lives and their observations, people learn about objects and substances in general. They make connections and eventually create an internalized model of how substances behave; specifically, substances are pushable, are frictional, are able to be contained, can be consumed, have definite location, are able to move or be moved, are stable, have surface and volume, require force to move, and fall down when dropped (Reiner et al, 2000). Consequently misconceptions arise on the ontological level with a scientific concept such as force. The authors (Reiner et al, 2000) propose that intuitively understood force is associated with a substance ontology when in fact these two concepts belong to a process ontology; the novice sees force as a property of substances, instead of a process, making sense of the concept of force by appealing to their reliable understanding of the material world through a substance schema. In the case of the impetus misconception (described by Nersessian & Resnik, 1989), students often believe that the impetus object exerts a force on another material object, thus providing it with the potential to exert a force on a third object. This is consistent with the belief that the impetus-force is an extensive property of the first object, which may be transferred to the second, and then onto the third, or even that the force is an actual substance that is carried along by the first object and then transferred over to the second (Reiner et al, 2000). Therefore force is not considered a process of interaction but instead either a substance or a property of a substance. This misconception theory supports the claim that misconceptions are not fragmented but instead form an ontologically misaligned structure based on the substance intuitive model.

Direct versus Emergent Models of Force
In another more recent article (Chi, 2005), Chi changes her position on her view of misconceptions, and points to the evolution of her theory:
The current thesis has evolved over the last decade. Our prior analyses were incomplete in several ways and have metamorphosed several times. The metamorphosis is reflected in the various names we have used (many incorrectly) over the years to refer to emergent processes, ranging from “events” (Chi, 1992), to “acausal interaction processes” (Chi, 1993; Chi & Slotta, 1993), to “constraint-based interactions” (Chi, de Leeuw, et al., 1994; Slotta, Chi & Joram, 1995; Slotta & Chi, 1996), to “equilibration processes” (Chi, 1997a; Ferrari & Chi, 1998), to “complicated, abstract and dynamic concepts” (Chi, 2000a), and to “complex, dynamic processes” (Chi&Roscoe, 2002).The evolution of names reflects our improved understanding. More recently, we have used these ideas to discriminate between robust and non-robust misconceptions (Chi&Roscoe, 2002), as well as to apply some of these ideas to scientific discoveries (Chi & Hausmann, 2003). This article represents a more complete but still evolving exposition of this theoretical explanation. (Chi, 2005, pp 164)
In her 2005 version, Chi theorizes about why some misconceptions are so hard to change, calling them robust. She begins by explaining that in science there is a distinction between direct processes and emergent ones. Relations between objects produce emergent behaviours that are not apparent in the description of either the object or the relation (Leher & Schuable, 2006). For instance, the “V” shape of a bird flock is emergent: The birds fly according to what is most aerodynamically efficient for each individual bird. Flying behind and to the side of a bird is what is easiest for each bird, and the V shape is what emerges when all these individual birds do the similar thing. The bird is the component of the process; the pattern is the V shape that emerges.
Chi (2005) explains the difference between emergent and direct processes using two different flow mechanisms: circulation being a direct process and diffusion an emergent one. Direct and emergent processes are very different on the constituent level: In a direct process every element has distinct behaviours, has constrained interactions, is sequential, is dependent on each other, has terminating interactions, is said to be part of a subgroup or class, directly affects the pattern, corresponds to the overall pattern, and has global goal or is intentional. While in an emergent process every element behaves uniformly, is unconstrained, has simultaneous interactions, is independent of other elements, has continuous interactions, has non-direct effect on the overall pattern, has disjointed behaviour from the overall pattern, and has only local goals or unintentional (Chi, 2005). When Chi examined several responses of students about how diffusion occurs, it was evident that the students' explanations contained many attributes of a direct process rather than of an emergent one. Chi speculates that this would be the case in terms of any emergent process, with forces and motion included. She believes that students' commonsense ideas of process correspond more closely to a direct kind rather than emergent. They rely on their commonsense understanding of direct processes to interpret emergent ones causing these robust misconceptions (Chi, 2005). Although a very compelling theory, Chi realizes that there is yet not enough empirical data to support her thesis.

Knowledge in Pieces
On the other end of the spectrum is the theory of Knowledge in Pieces (diSessa, 1993). This view envisions that intuitive physics is made up mostly of hundreds or thousands of self-explanatory schemata, typically abstracted from common situations, called phenomenological primitives (p-prims). P-prims are loosely organized, and sometimes highly contextual, so that the word “theory” is inappropriate (diSessa, 2006). DiSessa argues that intuitive thinking is not developed sufficiently to constitute a theory, yet her opponents believe that intuitive thinking about motion can still have a structure and consistency across contexts (Vosniadou, 2002). To deny this claim, diSessa and her colleagues (diSessa, Gillespie, & Esterly, 2004) set out to replicate Ionannides and Vosniadou’s empirical study (2002), and to extend it to show the incompleteness of the original study. The authors took great care to discuss the theoretical issues of misconceptions and define the terminology used.
First, they explicitly state that context is the central concept in the debate between advocates of coherence versus fragmentation. After an extensive discussion of context and fragmentation, the authors present a new term to describe their model: Crowded-irregular knowledge systems entail many elements, overlapping contexts that are ad hoc in their specification, and have numerous instabilities(diSessa, Gillespie, & Esterly, 2004). The other relevant concept diSessa, Gillespie, & Esterly (2004) point to is specificity of an intuitive belief or misconception. They notice that in the Ionnides and Vosniadou’s study (2002) misconceptions were only recorded on the basis of existential aspect (i.e. answering the question: Does a force exist?). But what about the quantitative aspect (i.e. How much force in comparison is there?), the ontological aspect (i.e. What is the nature of the force?), the compositional aspect (i.e. Do forces combine or act on each other?), or even the causal aspect (i.e. What are the consequences of the existence of a force?). Hence, the authors decided to extend the original design of Ionannides and Vosniadou’s study to investigate more of these specifications.
DiSessa, Gillespie, & Esterly (2004) were not able to replicate the results of the original study. In fact, students in the study didn’t seem to have a “small number of relatively well-defined and internally consistent interpretations of force” as was the thesis of Ionannides and Vosniadou (2002). Moreover, their extension study, taking into account context and specificity, demonstrated that the concept of force is very diverse among different students and it doesn’t seem to be internally consistent as proposed by Vosniadou (2002).
Below is a visual representation of the main three misconception theories presented in this paper.

Conceptual Change Methodology
Given the possible ways misconceptions are organized in the naive physicists mind determines the appropriate methodology of instruction. If, for instance, we assume that diSessa is correct in saying that all knowledge is divided into numerous p-primes then the way to teach physics is to organize and systematize all of these fragments into something that resembles Newtonian mechanics (diSessa, 1993). On the other hand, if we assume that Vosniadou's Framework Theory is more correct, we would have to undermine the whole framework and replace it slowly with the scientifically appropriate theory. Vosniadou (2002) argues that conceptual change does not happen suddenly, because we are dealing with a complex knowledge system that consists of a network of beliefs or presuppositions that take a long time to change. But if we assume Reimer's, Slotta's, Chi's and Resnik (2000) perspective that the misconceptions are ontological in nature and that physicist neophytes see force as a property of a substance instead of a process, then the shift to the correct understanding would be abrupt, radical and would occur in a short amount of time. Finally, if we see the misconceptions as Chi’s (2005) most recent hypothesis, where the intuitive beliefs are ontologically misclassified, a re-representation or a conceptual shift across ontological kinds needs to occur. In this case, misconceptions of the emergent kind are robust (and therefore hard to modify) and such a shift requires that students know about the emergent nature of force and can overcome their predisposition to conceive of all processes as direct.
Therefore, depending on the theory assumed about misconceptions, the approach to overcome them should be different. However, while the debate rages on about the nature of misconceptions, and teachers still attempt to produce conceptual change in students. The following three studies show three different strategies that are very accessible to the average teacher. They require few resources and could be an addition (or partial replacement) to the traditional classroom. Small changes, as opposed to huge transformations of the classroom, are more realistic and are more likely to be adopted by teachers.

CSCL in the Physics Classroom
As an example, Tao and Gunstone (1999) used a computer-supported collaborative learning environment (CSCL) to undertake conceptual change in force and motion. Their research question was: (a) How effective is conceptual conflict in fostering conceptual change? (b) Is conceptual change realized as a development (addition), a replacement of alternative conceptions, the coexistence of a range of conceptions with each coming into play in a specific context, or some other process? Even though in their research questions there was no mention of CSCL, their method was primarily to use simulations and collaborative learning to confront student's conceptions. The assumption was that once students realized their original conception doesn't match with what actually happens physically, the student will reconsider their own beliefs and possibly accept the scientifically correct version. In the field study, students were grouped into pairs, and over a span of 10 weeks they worked with a computer simulation program called the Force and Motion Microworld. Each task required the students to: (1) Make a prediction about the consequences when certain changes were made to the program. (2) Explain their prediction. (3) Run the program to test their prediction. (4) Reconcile any discrepancy between their prediction and the observation in the Microworld.
Even though students were asked explicitly to predict what they would see, and then reflect on what they actually saw in the simulation, thus confronting their misconceptions, this didn't reflect in their reactions. The authors didn't observe any sighs of amazement or outbursts of conflict. It's as though they were going through the motions of the procedure of the CSCL activities but didn't understand nor care to delve deeper into the situation. It is therefore no surprise that few students increased their conceptual understanding of force and motion (decreasing their misconceptions). Through post study interviews with the students, Tao and Gunstone realized that some of the students had no opportunity to reflect on the conflict they encountered in the simulations due to ill-formed partnerships. In the interview, when confronted with the conflict, the students realized that their conception was false, and changed some of their ideas of force and motion. The researchers therefore concluded that conceptual conflicts were not enough to produce conceptual change. They asserted that cognitive engagement is an important factor: “For conflicts to lead to change, students need to reflect on and reconstruct their conceptions.” (Tao & Gunstone, 1999, pp 870).
Another interesting observation in the Tao and Gunstone (1999) study was that the misconceptions were very much context based. Three situations (and simulations) of the same physical principal were presented: one of a model car, one of a spaceship, one of a skydiver. After the CSCL intervention, the students were asked to discuss each situation. Even though physically the three situations were identical, more students had misconceptions about the model car situation as opposed to the spaceship and skydiver. The authors speculated that this was due to the students' familiarity of the car situation, thus the misconception being more profound and harder to change, yet the spaceship and the parachutist contexts were relatively new and not as developed, thus easier to change.
Finally, Tao and Gunstone (1999) also noted that for the students that were not at all motivated during the CSCL activity, absolutely no conceptual change occurred. Being off task, not motivated to participate in the collaborations with their partner, these students' prior conceptions remained untouched. Motivation, therefore, seems to be one of the most important indicators of whether any conceptual change will occur.

Class Discussions to Promote Conceptual Change
Eryilmaz (2002) used a different approach to produce conceptual change. He wanted to see what effect conceptual assignments and conceptual change discussions had on students' misconceptions of force and motion. Comparing traditional physics teaching versus regular teaching with inserted conceptual assignments and follow up classroom discussions on conceptual change, he found that the discussions were very advantageous in terms of producing conceptual change. Eryilmaz took a quantitative approach in his research, studying close to 400 students from 18 physics classes. Over a span of a term, half the teachers were to use their regular methods of teaching, and the other were instructed to use classroom discussions on conceptual change at least once a week. To control for the type of discussions occurring in the 9 separate classrooms, the teachers received training and guidelines to keep the discussions consistent over the many teachers participating. As in Tao and Gunstone's CSCL activity, Eryilmaz focused on conceptual conflict to attempt conceptual change. The core of the discussion was for students (1) to understand their own beliefs and conceptions about force and motion; (2) create a discrepant event, one that creates conflict between exposed preconceptions and some observed phenomenon that students cannot explain – let students become aware of this conflict; (3) let students reflect upon the conflict and show explicitly where and how their preconceptions and the accepted force and motion theories differed. In the end, the students from the conceptual change discussion classes and conceptual assignment classes outperformed the students from the traditional classes with respect to the reduction of force and motion misconceptions. Although significantly different from traditional teaching, the difference in lowering misconceptions from start to finish of the intervention was small (small effect size). This once again demonstrates how resistant misconceptions are to change.

Teaching by Example
In yet another attempt to produce conceptual change, a study compared types of examples and the way they were used in teaching (Brown, 1992). In this study, students were presented with two different types of text explaining Newton's Third Law (the law of action and reaction). The first explanation was basically a statement of Newton's Third Law followed by many examples of where and how it is applied, from pushing a finger against a rock, to legs pushing against the floor while walking, to recoil while shooting a gun, and finally to the specific example where a book is sitting on a table with the table exerting a force on the book. This type of explanation uses induction from examples to generate an understanding for Newton's Third Law, which in turn should be applied to new situations (the book on the table). The second text also stated Newton's Third Law, but then attempted to take the reader through a journey from a hand pushing on a spring and the spring pushing back on the hand (an anchoring situation), through progressively more similar situations to the final outcome of the book sitting on the table having a force being pushed up onto it (the target problem). Brown called this a bridging explanation. Within this bridging explanation, a mechanistic model was developed for the reader (compressing and/or bending of rigid objects on a microscopic scale) which now could be applied in a general sense. The results of this research show the power of the anchoring analogy followed by the bridging explanations in producing conceptual change. Not only did the students reading the second text overwhelmingly outperform on a follow-up misconceptions questionnaire with alternate contexts of Newton's Third, they also scored extremely high on “how much their answers made sense”, as compared to the students that read the induction from multiple examples type text (Brown, 1992).
This study supports Chi's (2005) recent theory on misconception organization, in the sense that the force and motion are ontologically misclassified as being of the direct nature. But if an emergent model of force is undeniably illustrated, conceptual change will happen radically and in a short amount of time. Unfortunately, this study investigated only a small amount of participants (only 14 students with the initial misconception of the table not pushing up on the book received the two different text explanations) and did not investigate long-term effects of the bridging explanation on conceptual change. However, it seems that the method of anchoring analogy followed by bridging explanations have great potential in influencing conceptual change and overcoming misconceptions in novice physicists.

Discussion and Conclusion

From the three presented methods of conceptual change, it appears that the best option was Brown's (1992) anchoring analogy followed by the bridging explanation. The other two seemed to follow the Piaget's idea of accommodation, yet they only had a slightly better effect at producing conceptual change as compared to traditional teaching. This, I believe, is because Brown's method (1992) tackled the underlying problem with these robust misconceptions: The mechanistic model gave a way for students to understand that force is not a direct process, but instead an emergent one. Once students understood the mechanistic model, their understanding of what is a force changed in an ontological way. They had a way to generalize each different situation, explain it with their model, and their naive misconceptions were instantly replaced. This process was radical and occurred in a short period of time. Since Brown's (1992) study was prior to Chi's (2005) ontological redefinition of her direct versus emergent model of robust misconceptions, he did not include her idea as part of his theoretical backing. But if Brown was to redo his study now after Chi's interpretation, I am certain he would have made the connection.
The other two methods of conceptual change (Eryilmaz, 2002; Tao & Gunstone, 1999) were both interested in confronting students with discrepant events that contradict their existing conceptions to produce disequilibration, as recommended by Piaget (Atherton, 2009). This, in theory, induces students to reflect on their conceptions as they try to resolve their conflict. I believe that this disequilibrium only works in a given context, possibly without transferring to other situations, and for sure without generalization. For instance a spaceship travelling through space with no force acting on it would continue travelling at the same rate, but in Tao & Gunstone's study (1999), this idea did not transfer to the model car situation. Students didn't see these two situations as the same: One is on earth - one is in space; one has an engine – the other does not; one is usually seen in a frictional environment, with model cars usually stopping after a set period of time, the other is set in space with no resistance. Using conflict to produce conceptual change therefore seems fruitless if we want the students to see a generalization of force and motion. We are not giving the students a model to replace their own. Instead we are telling them that they were wrong, and this is what actually happens in this particular situation. Since an alternative to their own explanation is not presented, their misconceptions will remain if only slightly modified. We assume students can see the similarity between contexts, as physicists do, but I believe, as does diSessa (diSessa 1993; diSessa 2006; diSessa,Gillespie, & Esterly, 2004) that this assumption is wrong. Until the students have a generalizable model that makes sense to them and is applicable to every type of situation of motion and force, conceptual change by confrontation and disequilibration is futile, only confronting one p-prim at a time.
I therefore offer a slightly modified version and combination of a theory of misconceptions. Evidently, when novices encounter physics phenomena, initially, students have a very context specific view. I hypothesize that this is because intuitively they see force and motion as direct processes and not emergent as they are. If force was a direct process, then possibly the situations presented and assumed to be equivalent would actually be different, not just in terms of context, but in terms of the processes. Therefore the wrong ontology (Chi, 2005) of force and motion makes the observer see the physical world as a huge array of many situations that have little to do with each other (Knowledge in Pieces: diSessa, 1993). However, the moment the person realizes the underlying structure at the molecular level and understands the emergent model of force, they will see how all the different fragmented phenomena are disguised versions of the same concept, as it happened in Brown's study (1992). In all the articles I read, diSessa's fragmented theory and Chi's ontological mis-categorization theory are always presented on opposite ends of the misconception theory spectrum. I, however, see these two theories complementary: one explaining the other.

References
Atherton, J. S. (2009) Learning and Teaching; Assimilation and Accommodation [On-line] UK: Available: http://www.learningandteaching.info/learning/assimacc.htm Accessed: 10 December 2009

Brown, D. E. (1992). Using Examples and Analogies to Remediate Misconception in Physics: Factors
Influencing Conceptual Change. Journal of Research in Science Teaching, 29(1), 17-34.

Chi, M. T. H. (2005). Commonsense Conceptions of Emergent Processes: Why Some Misconceptions
Are Robust. Journal of the Learning Sciences, 14(2), 161-199.

diSessa, A. (1993). Toward an Epistemology of Physics. Cognition and Instruction, 10, 105-225

diSessa, A. A. (2006). A history of conceptual change research: threads and fault lines. In. K. Sawyer
(Ed.), The Cambridge Handbook of the Learning Sciences (pp. 265-282). MA: Cambridge University Press.

diSessa, A. A., Gillespie, N., & Esterly, J. (2004). Coherence vs. Fragmentation in the Development of
the Concept of Force. Cognitive Science, 28, 843-900.

Gopnik, A., & Wellman, H. M. (1994). The Theory Theory. In L. A. Hirschfeld & S. A. Gelman (Eds.),
Mapping the Mind: Domain Specificity in Cognition and Culture (pp. 257-293). New York:
Cambridge University Press.

Eryilmaz, A. (2002). Effects of Conceptual Assignments and Conceptual Change Discussions on
Students' Misconceptions and Achievement Regarding Force and Motion. Journal of Research
in Science Teaching, 39(10), 1001-1015.

Ioannides, C. & Vosniadou, C. (2002). The Changing Meanings of Force. Cognitive Science
Quarterly, 2, 5-61.

Lehrer, R., & Schauble, L. (2006). Cultivating Model-Based Reasoning in Science Education. In. K.
Sawyer (Ed.), The Cambridge Handbook of the Learning Sciences(pp. 371-388). MA:
Cambridge University Press.

Neressian, N. J., & Resnick, L. B. (1989). Comparing Historical and Intuitive Explanations of Motion:
Does “Naive Physics” Have a Structure? Proceedings of the 11th Annual Conference of the
Cognitive Science Society (pp. 412-417). Hillsdale, NJ: Lawrence Erlbaum Associates.

Reiner, M., Slotta, J. D., Chi, M. T. H., & Resnick, L. B. (2000). Naive Physics Reasoning: A
Commitment to Substance-Based Conceptions. Cognition and Instruction, 18(1), 1-34.

Stahl, G., Koschmann, T. & Suthers, D.D. (2006). Computer-Supported Collaborative Learning. In. K. Sawyer
(Ed.), The Cambridge Handbook of the Learning Sciences (pp. 409-426). MA: Cambridge University Press.

Tao, P.-K., & Gunstone, R. F. (1999). The Process of Conceptual Change in Force and Motion during
Computer-Supported Physics Instruction. Journal of Research in Science Teaching, 36(7),
859-882.

Vosniadou, S. (2002). M. Limon & L. Mason (Eds.), Reconsidering Conceptual Change, Issues in
Thoery and Practice (pp. 61-76). Kluwer Academic Publishers.

Hydraulics and Pneumatics Projects

bogusia — Tue, 08 Jan 2008 19:36:09 -0700

At the beginning of December, I assigned my grade 8 students to build a machine / model using hydraulics or pneumatics. They are due this week, and some have already come in. So far I am extremely impressed.

At the end of the week, I'll take pictures of them all to show what projects they built, but so far there has been an excellent selection of machines. From the simple yet elegant dentist chair to a powerful crane to a digging machine, bridge, and a mechanical claw. I have all the projects displayed at the side of my classroom. Whenever other classes come by, they look, play around with the machines, and are all jelous that they weren't assigned this project. The students that didn't hand in the projects yet are all very inspired by the creations and some even have decided to scrap their original ideas/models to make better more complex designs.

An interesting observation:

The boys are more into this project than the girls. The stereotype continues... boys are the builders, the physicists, the engineers. Girls on the other hand did much better on the previous project on the cell organelles, when a presentation was involved. Even the "best girl students in the class" did simple models, nothing too challenging, nothing too complex. While the boy teams really went out of their way to create something extraordinary. I only teach 100 students, so maybe this is not the best statistical sample, but really, I am amazed at how obvious this is.

Actually I'm quite dissapointed in this outcome, because I am a "girl physicist" and I thought I would inspire the girls to be the same. It is possible that I did inspired my girl students to enjoy physics, however there might be something more innate in the female brain than I can inspire. Maybe girls just don't like machines, don't have the same 3-D visualization required to think of awesome, complex structures . For example I, myself, don't like to watch TV shows about construction projects / machines, while my husband is all about that. Am I only interested in physics because of the fun of the math? Or am I really interested in how things work?

I can't wait until the rest of the projects are handed in. Every project gives me hope that these children are actually interested in science, and that it's actually worth it to put in effort to continue to teach them, think of interesting ways of presenting the material. This time around, I can tell that the students really had fun doing SCIENCE!

UPDATE: Here are some pictures of the machines.

A Crane - One of the best projects! Click here for a description of how to make this one.

This was the best bridge - good design, didn't break easily, esthetically pleasing.

Dump Truck

Mechanical Hand - excellent design worked great initially, but started leaking. Most students loved this one!

Hair Salon Chair - very simple yet very well done.

A great site for learning physics - THE PHYSICS CLASSROOM.

bogusia — Mon, 15 Feb 2010 12:34:06 -0700

My grade 11 students have an ultra secret facebook group dedicated for studying physics and chemistry (their sciences). I don't actually know what goes on in this group... I tried to become a member of their group, but they rejected me (hahahaha). But they have my website as a link, so I guess I'm supposed to be a useful link to their studies. So maybe in a way I can influence them even though I'm not a member of their silly little group... (HEHEHEHE)

Here is an awesome website they (and anybody else who wants to) can use to study physics (that is if they don't have enough physics with me during regular school hours). It has great notes, interactive stuff, simulations, practice questions with answers, and many many more practical applications. The best part of it: It's FREE for anyone to use. I hope my students will go and visit this site and use it on a regular basis: THE PHYSICS CLASSROOM.

Draw a Person Test (DAP) - a great way to tell a kid's intelligence

bogusia — Fri, 07 Nov 2008 10:12:47 -0700

Recently I went to the doctor for my son's yearly check-up. Our doctor is fantastic, and I am so lucky that I was fortunate enough to get him. Everytime we go, I learn something very interesting, this time was no exception.

The Doctor started asking standard medical questions: Was Jakub seriously ill this past year? Any ear infections? etc. Then he turned to his mental, social and physical development. And he asked me:

"Does Jakub know how to draw a person?"

I answered that probably yes, because he draws dinosaurs all the time, but I can't remember any people he drew recently... So the doctor gives Jakub (my 4 year old son) a piece of paper and asks him: "Draw a person". After a bit of shock and shyness, Jakub complies and draws a person. He started with a head, then a body, arms, legs, some eyes and mouth on the head - in their proper positions, and then also some hair. Nothing artistically pleasing, but just a stick figure (unfortunately I couldn't take the picture with me, as the doctor wanted to keep it in his records - the picture above is also Jakub's picture, from February 2008 - he was 3 years and 10 months old). The doctor said that was interesting, and started explaining the theory behind the "draw a person" test to me.

He said that at the test is very universal. Many studies show that the results are similar in all the corners of the earth. The way the kids draw the person determines at what mental developmental stage they are at. You can pretty much test for intelligence with a simple drawing. At the age of 3 kids start to draw circles and lines, but usually can't really make a stick figure look like a person. At the age of 4, they are supposed to start drawing people more like we're used to: head, arms, legs. But at the age of 4 (mental age of 4) most kids draw the arms and legs coming out of their heads - no body. Jakub didn't do this. His picture had a body. Even in the picture above - drawn when he was 4 months shy of four, Jakub drew a body. The doctor said that this was an indication that his mental development stage is more like a 5 year old rather than a 4 year old (I always knew my son was smart :)). At the age of 5, children start drawing bodies, arms and legs coming from the bodies. Then, between 5 and 5.5, kids start to draw more detail, including 3 fingers (not 5), clothes, etc. The doctor didn't go into more than this - figuring I'm not interested past my son's age anyway.

But when I got home, I wanted to know more about this cool non-invasive test: the Draw a Person test. I actually didn't know it was called that until I researched it online. Supposedly this test has been around for a whole century, and it's been used everywhere in the world, for children of many ages (up to 13 as I've seen in the few studies I read through), and by psychologists to analyze not only intelligence but also emotional stability of kids. It is the perfect test, because it is very simple and non-invasive, yet so telling of the child.

As I understand it, the procedure to administer the test is to tell the child: "Draw a Person" with not much more explanation. After that, there is a series of points the psychologist can award, depending on the picture's details (is there a neck? clothing? proportions correct? size of picture? etc.). Then, based on the child's age and the points of the picture, a mental age equivalence can be given. Cool!

A few days after my appointement, after picking up Jakub from Pre-School, I found a picture of two stick figures in his school bag. The hands and legs were coming out of the head. I was shocked... Jakub drew this? Did he regress in just a few days? I asked him: "Did you draw this?" He said: "No, a Emily drew this picture for me." He was so proud that his friend drew a picture for him, and I was happy to see that the DAP test is for real.

If you want to see some real studies (not on my child but on a statistical level) on this DAP test, here are some good sites I found:

This one is based in Pakistan, but is in english and has many sample drawings of the children's drawings and the analysis of them. The author of this paper also links culture and mental stability into the DAP test. Very interesting: STANDARDIZATION OF DRAW-A-PERSON test

This one is an exerpt from a book. I think eventually I will purchase this book, because this stuff fascinates me, but for now, this will do: Using Drawings in Assessment and Therapy

More "How to Fail a Test" - again very funny

bogusia — Mon, 25 Jan 2010 10:26:42 -0700

If you liked these, check out The first post: Very Funny: "How To Fail a Test" examples.

Understanding Knowledge Building

bogusia — Thu, 14 Jan 2010 09:47:47 -0700

I was impressed from the very moment I read about Knowledge Building in the Cambridge Handbook of the Learning Sciences (Sawyer, 2006, pp. 97 - 115). As a science teacher, I see the enormous potential of this learning philosophy, and cannot wait to apply it to my existing teaching repertoire. In order to implement the principles of Knowledge Building, I must understand it fully and understand how to apply it. To this end, I am writing this thought paper with two articles on Knowledge Building as a backdrop. The first is “Learning to Work Creatively With Knowledge” by Carl Bereiter and Marlene Scardamalia (2003) and the second is “Student-Directed Assessment of Knowledge Building Using Electronic Portfolios” by Jan van Aalst and Carol K. K. Chan (2007). The first article serves as the theory portion of my understanding of Knowledge Building. The second article provides an example of Knowledge Building in practice and presents a possible way of implementing the innovative learning environment as well as assessing students in the collaborative Knowledge Building setting.

I see teaching science as having two different sides. The first side is teaching the basics, the processes, the structures of a lab report, the ways of solving a physics problem, the organization. Let’s call this the “alphabet” of the scientist. Without this, the students could not achieve any kind of success in the sciences. It is a way of communication in the scientific world, the building blocks of science. In the same way that a child cannot read a beautiful story without knowing the alphabet first, the scientist cannot see or understand the complex design of car without first understanding the mechanisms of the simple machines or the fuel combustion effects, or even the knowledge of the basic elements or simple kinematics. I would say that traditional teaching focuses on these basic skills. Teaching only these kinds of skills is equivalent to presenting knowledge in what Bereiter and Scardamalia (2003) call belief mode.

On the other hand, one cannot teach science without teaching creativity, innovation, doubting and confronting-authority. Without this, there would be no progress in science; people would see scientific knowledge as static and would not try to improve upon the ideas of others. Science, however, is based on innovation and on the progressive improvement of ideas. Isaac Newton famously remarked in a letter to his rival Robert Hooke dated February 5, 1676 that:
What Descartes did was a good step. You have added much several ways, and especially in taking the colours of thin plates into philosophical consideration. If I have seen a little further it is by standing on the shoulders of Giants. (trans. Maury, 1992)
This quote is the essence of science – the improvement of ideas of others to progress towards a better solution, better theory, better car design, better teaching. There is never an end in sight, no final solution. I find that Knowledge Building is the perfect mirror in teaching of this idea. Carl Bereiter and Marlene Scardamalia (2003) refer to this type of mode of dealing with knowledge as design mode.
I know how to teach the “alphabet” type of science - I can teach it blind folded. I know where students encounter difficulty, where students need more scaffolding, what type of scaffolding is best in what situation, and when students need to work out the problems on their own. I might not know why students prefer this method over another, but by trial and error and some self-reflection, I come to a pretty good scheme of what works for my physics instruction.

However, I can honestly say that I am completely incompetent at teaching the innovation in science, or in other words the desing mode. I have no idea how to even attempt teaching students good scientific creativity or how to teach them to build on each others’ ideas. Of course I let my students use some of their innovation in projects, group activities, lab design, and some basic explorations and discussions. But, even in these instances, I feel as if I cannot properly assess their learning.

I was happy to read in Learning to Work Creatively with Knowledge (Bereiter and Scardamalia, 2003), that I don’t stand alone. There seem to be no fool proof methods of teaching students how to be innovators, collaborators, knowledge builders. Bereiter and Scardamalia propose that the best alternative is immersion: “If you do not have an effective way of teaching a foreign language, then place the students in an environment where that is the dominant language and trust that their natural adaptive abilities will lead them to master the language”(2003, pp. 2 - 3). Therefore the authors’ discussion in the article is no longer about “how to teach students design mode?” but instead “what is the best environment for students to learn design mode?”
In my nine years as a teacher and the previous 18 years as a student, I had the opportunity to experience the three out of the four environments discussed in this article. The only type of environment I never experienced officially was Knowledge Building. The authors are the creators of Knowledge Building, and therefore have a bias towards their own idea, but I agree with the observations, comments, and criticisms of the other three approaches, in terms of what I experienced first hand.

I have not encountered Knowledge Learning environments first hand in my schooling or as a teacher, however, I can see the similarity of this learning environment to scientific research. The focus of idea improvement is at the core of scientific inquiry. As I already stated, without the exact intent of idea improvement in science, there would be no innovation, no improvement of scientific principles.
Another idea of Knowledge Building is the knowledge value to the community. Students' contribution to improving their collective knowledge in the classroom is the primary purpose of the Knowledge Building classroom and all individuals are invited to contribute to the knowledge advancement in the classroom. This again has a parallel principle in the scientific community, whereby scientists are invited to publish their research and discoveries, later available to the whole scientific community. Thanks to this idea, researchers build on others' knowledge and are not constantly rediscovering the same principles / ideas.

And just like in the scientific community, once in a while there is a conference, and the researcher needs to demonstrate their findings in a presentable fashion, Knowledge Building environments call for tangible goals and products such as reports or multimedia presentations. But these are not the central part of research or Knowledge Building. Also this is not the “end” of the research (as it is in the Project-Based Learning), just a way to share information. The idea improvement continues even after such presentations.
As a believer in the scientific method and scientific research, I feel a connection to the Knowledge Building idea. Here, I only discuss three principles (out of twelve) of Knowledge Building, and yet already I am persuaded by the authors and see the Knowledge Building environment as the best environment for students to learn in design mode. Becoming an innovative scientist, a creative thinker needs to be done in an appropriate environment, and Knowledge Building seems to be a good approximation of the real world environment of scientific innovation.
Discussing an idea is one thing, and believing that it is the best thing on earth is fine. However, implementing it into the classroom and actually seeing some results is another. Seeing how Knowledge Building works in practice is what I really needed to recognize how this environment could be useful in my grade 11 physics class.

As a practical application of Knowledge Building, Bereiter and Scardamalia propose Knowledge Forum® as the principle environment in which the collaborative work goes on. After going on the website to see this online software and samples of its output, it reminds me a lot of wikis. I agree and see how it could be a very powerful tool in the Knowledge Building scheme. The ability of different parties to edit entries, discuss at varying levels, link different views and comments, and thus improve the knowledge of the whole community, is at the core of Knowledge Building. This is how I see learning – not in a linear fashion of a textbook or a lecture series, but in a scattered set of ideas linked together, and improved upon time after time.
Knowledge Forum®, however, does not take into account the fact that teachers must assess students, evaluate their progress and tell their parents if they are on track. Even though evaluation is not the reason for students to learn and go to school, it is a major part of the teacher’s job description. It is a way to keep the students accountable for their work and learning as well as to keep the teachers accountable to the parents. And most importantly it is a way to measure where the student is on the continuum from novice to expert.
Should we have the students work in Knowledge Forum® and then assess them in an incompatible fashion? If so, I think only select few intrinsically motivated students would actually take this on, and the Knowledge Forum® would then remain largely untouched – defeating the purpose of the Knowledge Building implementation.

Should we therefore count the students’ responses / input and give the students a mark based on participation? This also does not make much sense, as students might not engage in deep learning, instead making sure they are adding to the forum without thought, or reading other students’ input. I have come across this difficulty in assessing group work projects. I still have not come back with a good strategy. It is common that only one student of the group puts in the effort. But evaluating students on participation is not the solution.

So how do we assess collaborative work on an individual level if there is supposed to be collaborative effort in Knowledge Building across the whole class? How do we see improvement in the knowledge of the one student, when the purpose of the Knowledge Building is to improve the knowledge of the whole class? An ingenious solution is presented in the second article: “Student-Directed Assessment of Knowledge Building Using Electronic Portfolios” (van Aalst and Chan, 2007). This article not only presents a reasonable way of assessing student progress in a Knowledge Building environment, it also demonstrates how Knowledge Building can be implemented into the classroom.

There are several things about the proposed electronic portfolios that ring true with my understanding of assessment. First of all, the electronic portfolios foster self-reflection. Reflection is essential for deep learning to take place. The portfolios force students to revisit their notes and responses to others on Knowledge Forum® and see how they affected the community knowledge building process as well as their own. This iterative process not only reinforces student understanding, but also compels students to return to their original ideas after an incubation period, and thus could impact another improvement on these original ideas. Therefore the electronic portfolios are truly an assessment, working towards a development of knowledge improvement and do not have a finality about them as do tests and other traditional evaluation processes.

Secondly, the assessment itself is clear and guides the Knowledge Building process. As the researchers pointed out, in one of the studies the students had access to the guidelines of the assessment only at the end, and in another study, the guidelines were present from the start. When the electronic portfolio guidelines were present from the start, the responses in the Knowledge Building environment were deeper and more appropriate. When asked how the portfolios may scaffold students engagement in deeper collaborative inquiry, a student replied that “these four principles not only help me choose the notes but also in creating new notes. In order to make good notes, we can follow the principles when we are raising questions, giving explanations, or drawing conclusions…” (van Aalst & Chan, 2007, pp. 200).

A bonus is that the electronic portfolios were significantly correlated with normative knowledge acquisition evaluations. This means that they are a good measure of the acquisition of knowledge, yet they have the added benefit that they correspond to the way knowledge is acquired. Pellegrino emphasizes that there needs to be a relationship between theories of learning and knowing and the process of assessment (2002). Therefore if we are teaching in a Knowledge Building environment, we must align our assessments with this type of environment. But the correlation of the new electronic portfolios method with normative methods, such as standardized tests, gives us the confidence that this new method actually measures what it is supposed to measure – i.e. the amount and depth of acquired knowledge.

Finally, it is important to point out that there was a greater concept knowledge acquisition by the students in the Knowledge Building classrooms as compared to the control classrooms. Procedural knowledge was not tested, but I assume this would not be greater, as procedures fall more into the belief mode of knowledge. As I said initially, I know how to teach procedures, it’s the concepts and the innovation that I need help with. This after all is the whole idea behind Knowledge Building, and according to the research of van Aalst and Chan, Knowledge Building complemented by electronic portfolios were exemplary at building concept knowledge.

The two articles on Knowledge Building complemented each other. The first gave me the theory base, and the other gave me practical implementation ideas and a way to assess students. Now I feel I can try to implement the theory into practice in my physics classroom, and by immersion my students will become not only proficient at solving physics problems but also become scientific innovators.

REFERENCES

Bereiter, C., & Scardamalia, M. (2003). Learning to work creatively with knowledge. In
E. De Corte, L. Verschaffel, N. Entwistle, & J. van Merriënboer (Eds.), Unravelling basic components and dimensions of powerful learning environments (pp. 55-68).EARLI Advances in Learning and Instruction Series. Available: http://ikit.org/fulltext/inresslearning.pdf [Accessed 2009-09-14].

Maury, Jean-Pierre (1992) Letter from Isaac Newton to Robert Hooke, 5 February 1676. Newton: Understanding the Cosmos. New Horizons

Pellegrino, J. (2002). Understanding how students learn and inferring what they know:
Implications for the design of curriculum, instruction and assessment. (1-18).
Washington, DC. Available: http://www.agiweb.org/education/nsf02/Pellegrinopaper.pdf [Accessed 2004-12-17].

Scardamalia, M, & Bereiter, C. (2006). Knowledge building: Theory, pedagogy, and
technology. In. K. Sawyer (Ed.), The Cambridge Handbook of the Learning
Sciences (pp. 97-115). Cambridge, UK: Cambridge University Press.

van Aalst, J., & Chan, C. K. K. (2007). Student-Directed Assessment of Knowledge
Building Using Electronic Portfolios. Journal of the Learning Sciences, 16(2 %R
doi:10.1080/10508400701193697), 175-220.