knowledge representations of energy and motion in high school ...

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KNOWLEDGE REPRESENTATIONS OF ENERGY AND MOTION IN HIGH SCHOOL CONCEPTUAL PHYSICS CLASSES Nicholas C. Wilson

Teachers College Columbia University MSTU 4133 Cognition and Computers Professor Black

2 Scientifically speaking, energy is an amazingly complex notion, from which nothing less than the universe itself was born. Yet, people use energy to describe simple ideas, such as how they feel (e.g., “I have a lot of energy today.”), how technological devices work (e.g., “It uses batteries for energy.”), or how biological phenomena exist (e.g., “Plants get their energy from the sun.”). In a physics classroom, energy is broken down into more scientific terms, abstract concepts, and sophisticated mathematical statements. Energy is used to describe how one object can affect another in a system of complex interactions. Indeed, it is used to describe how much “work” an object can do. To be able to describe the amount of energy an object has at any given moment, one must have an understanding of the object’s location and motion at that time. Once the initial conditions of that object’s properties have been established, one can begin to use various related concepts, qualitative and quantitative, to investigate the energy of the object. Careful instruction through the use of declarative (i.e., factual) knowledge, procedural rules and applications (practice), imagery, and mental modeling, can enhance a student’s understanding of these abstract concepts.

General Knowledge General discussion of energy in high school science classrooms revolves around a handful of major concepts: frame of reference, vectors, motion, forces, momentum, and work, usually in that order. These concepts make up the majority of what is normally considered “mechanics” in a typical high school physics classroom, and as such, will remain the focus of the knowledge structure discussed in this paper. Before the concept

3 of energy can be effectively approached, each of these concepts must first be described in general.

FRAME OF REFERENCE A frame of reference is a system of objects that are not moving with respect to each other. For instance, as car is driving down the road, its speedometer reads “50 miles per hour.” A car traveling in the opposite direction passes by the first car at the same speed. To each driver, the other car appears to be moving at 100 m.p.h., but to an observer standing on the side of the road, each car appears to move at only 50 m.p.h. The drivers and the observer have different frames of reference – this is why the speeds of the cars seem different to them. In discussing any physical phenomenon in a basic high school science class, establishing a frame of reference is the first goal in approaching a situation. VECTORS A vector is a quantity that has both a magnitude and a direction. The magnitude of a vector is given as an amount of something (e.g., size or length), while the direction is usually given as a combination of Cartesian and Polar coordinate systems (e.g., 30o North). Vectors are combined following the rules of vector addition; that is, adding the respective vector components (the magnitudes in the horizontal and vertical directions), and solving for the direction with trigonometric principles produces the “resultant vector.” Resultant vectors indicate the overall magnitude and direction of a combination of vector quantities. When combining vectors in different directions, it is useful to devise a coordinate plane to describe their directions in relation to one another. Typically, the

4 X-Y coordinate plane used by mathematicians in line-graphing is adopted for this purpose. For the purposes of this discussion, it will be assumed that students have knowledge of vector addition and are rehearsed in finding resultant vectors.

MOTION Once a frame of reference is chosen, one can make measurements of the motion of objects within that frame of reference. For the purposes of this discussion, only three measurements of motion – all of which are vector quantities – are relevant: displacement, velocity, and acceleration. All three quantities follow the same rules of combination as other vector quantities.

Displacement Displacement is a vector quantity describing the shortest distance (i.e. straight line) between the starting and ending points of an object. The displacement an object moves in a given amount of time is described as the object’s velocity.

Hence,

measurements of displacement have the same units as typical length measurements (meter, feet, miles, etc.)

Velocity As it is also a vector quantity (has both a magnitude and a direction), the velocity of an object changes when the object’s displacement changes. It is calculated by the relation: velocity =

!

change in displacement (meters) time (seconds)

5 (or, more simply)

v=

"d "t

Where “v” is the object’s velocity, “!d” is the change in displacement, and “!t” is the

! time taken to travel the given displacement.

Acceleration The rate at which an object’s velocity changes is called the acceleration of the object. Acceleration occurs if the object experiences a change in velocity, or if the direction of an object’s movement changes, or both. It can be calculated by the relation: acceleration =

change in velocity (m/s) time (s)

(or, in concise terms) !

a=

"v "t

Where “a” is the acceleration of the object, “!v” is the change in velocity, and “!t” is the

! time taken for the change in velocity to occur. Thus, by convention, one can describe the motion of an object within a frame of reference through measurement and manipulation of certain vector quantities. Displacement, velocity, and acceleration are related through three notorious kinematic equations. 1. v = at + v 0

!

1 2. d = v 0 t + at 2 2 3. v 2 = v 02 + 2ad

!

!

6 Where “d” represents the displacement of the object, “v” is the final velocity of an object, “v0” is the object’s initial velocity, “a” is the object’s acceleration, and “t” is the time of the action. These equations are derived from the fundamentals of calculus, which is outside of the scope of this knowledge structure, so their derivations will be overlooked for our purposes.

NEWTON’S LAWS OF MOTION (FORCES) Within a frame of reference, moving objects often interact with each other in ways that affect their respective motions. In his own groundbreaking studies, Sir Isaac Newton (1643-1727) deduced three universal laws governing an object’s motion.

Newton’s First Law of Motion Newton’s First Law of Motion states that if in a state of rest, an object will remain at rest, while an object moving along a straight line path at a constant velocity will remain moving along a straight line path at a constant velocity, unless acted upon by an outside force. This phenomenon is often referred to as “inertia,” or the tendency for an object to remain in a given state. Here, the term “force” is used to describe interactions between objects.

Newton’s Second Law of Motion According to Newton’s Second Law of Motion, the amount of force an object exerts on something is directly proportional to the object’s mass and acceleration:

Force = mass (kg) " acceleration (m/s2 ) (or more simply,)

!

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F = ma The mass of an object is a measurement of the amount of matter an object contains. ! Simply, “matter” is anything that has a mass and takes up space. In other words, matter is the presence of something (i.e., atoms). Thus, the more matter an object contains, the more massive the object, and therefore, the more inertia it has. In the International System of measurements, force is measure in units of “Newtons,” where one Newton is equal to 1 kgm/s2.

Newton’s Third Law of Motion Newton’s Third Law of Motion states that for every force that is exerted by one object on another object, there is an equal force exerted by the second object on the first, acting in the opposite direction. For instance, consider a man pushing on a wall. If he is pushing in a direction perpendicular to a wall, it is easy to imagine the direction of the force he is exerting. However, unless the man is stronger than the wall (an unlikely situation), the wall goes nowhere. The man is not moving, therefore he must not be accelerating. Since he is not accelerating, there must be an equal force acting on him in the opposite direction to cancel out the man’s force. Indeed, the wall supplies this second force. Thus, if an object exerts a force on another object, but experiences no acceleration, the sum of the forces (or the Net Force) acting on that object is equal to zero. If the Net Force acting on an object is not equal to zero, then the object must be accelerating (experiencing a force).

8 MOMENTUM Momentum is a property of any moving, massive object. Effectively, it can be described as the inertia of motion, as according to Newton’s First Law of Motion. An object’s momentum is directly proportional to its mass and velocity, and can be calculated as: momentum = mass (kg) " velocity (m/s)

or !

P = mv

Where “P” stands for momentum, “m” is for mass, and “v” is the velocity of the object.

! follows the same rules for combination as the other It is another vector quantity and vectors discussed above. Momentum and force are related in that a force is needed to change the momentum of an object. Indeed, a force is directly related to the rate of change of the momentum of an object. In other words, the amount of force required to change the amount of momentum an object has can be calculated by the equation:

F=

"P "t

Where “F” is the amount of force, “!P” is the change in momentum, and “!t” is the change in time.

!

In a closed system, the total momentum of all the objects is conserved. A closed system is a system in which no objects or forces enter or leave. For example, if we consider the system of two trains colliding, the trains interact with each other (they exert forces on each other), affecting each other’s momentum. However, the total momentum

9 before the collision will be the same after the collision. This phenomenon is referred to as the Law of Conservation of Momentum.

WORK If a force is applied to an object in the direction of the object’s movement (or if the force causes the object to move in the direction of the force), the force is doing Work on the object. Work is defined as the product of the force acting on an object and the displacement the object moves:

W = Fd Where “W” is the work done on the object, “F” is the force acting in the direction of the object’s movement, and “d” is ! the displacement of the object caused by the force.

KINETIC ENERGY When we consider the amount of work done on an object, it is apparent that we can substitute some values from out kinematic equations to approach work from a different perspective. Thus,

W = Fd becomes

!

W = mad

We can substitute further for the acceleration and displacement, whose product equals !! 1 2 2 (v " v 0 ) (from kinematic equation 3) to get 2

1 1 W = mv 2 " mv 02 2 2

!

!

10 The quantity

1 2 mv is called the object’s “Kinetic Energy.” So, we can see that the 2

amount of work done on an object is equal to the change in the object’s kinetic energy:

!

1 KE = mv 2 2

This relation is also known as the Work-Energy Theorem.

! GRAVITATIONAL POTENTIAL ENERGY In addition to his laws of motion, Newton studied the effects of gravity of different masses. He found that the gravitational force of the Earth causes freely-falling bodies to accelerate towards the center of the Earth’s mass at a rate of approximately 9.81m/s2.

If we consider an object held aloft at a height (or, vertical displacement) “h,” and calculate the amount of work that gravity does on the falling object, we get W = Fd = mad = mgh

Where “g” is the acceleration due to gravity (9.81m/s2). The quantity “mgh” is referred ! Energy of the object: to as the Gravitational Potential PE = mgh

It represents the amount of work an object can do from a given height. !

CONSERVATION OF ENERGY From the relations above, we can see that the amount of energy an object has is equal to the amount of work that object can do. Indeed, energy is often defined as the

11 ability to do work. The total amount of mechanical energy an object has is equal to the sum of its various energies. Thus, the total amount of energy, “E”

E = KE + PE is equal to the sums of the object’s Kinetic Energy (KE) and Potential Energy (PE).

!

1 E = mv 2 + mgh 2

The Law of Conservation of Energy states that energy cannot be created or destroyed, but

! form to another. For a closed system, this implies that the only transformed from one total amount of energy is always conserved, though it may take on different forms (i.e. Kinetic Energy, Gravitational Potential Energy, Chemical Potential Energy, Electrical Energy, Nuclear Energy, etc.) at any given time.

KNOWLEDGE REPRESENTATION OF FACTS (PROPOSITIONAL NETWORK) Figure A in the appendix demonstrates a propositional network of the general knowledge structure of the Newtonian Mechanics topics discussed above. The network has been formatted to show the nodes and relationships between nodes of the physical concepts involved in describing the motion and energy of a hypothetical object. Anderson (1996) proposed that declarative knowledge can be represented using semantic networks of knowledge “chunks” represented by the entities in the network and their relationships, as shown by the links to other entities. A controversial outcome of this representation of cognition, called “Adaptive Character of Thought (ACT-R),” is that the time required to traverse such a complex network of ideas increases as the number of

12 entities and relations involved in a particular concept increase. This type of interference is known as the “Fan Effect” (Anderson and Reder, 1999). As such, this representation of knowledge provides only a piecemeal account of the complex structure of cognition and does not incorporate knowledge that maybe be stored as images, procedures (production rules), or mental models.

KNOWLEDGE REPRESENTATION OF IMAGES A good mental image can incorporate the declarative knowledge of a topic and associated chunks of higher-order knowledge, and conveys a spatial understanding of the topic and its sub-regions (Black, notes). The following images allow a learner to infer the proper knowledge concepts and recognize the relationships between prepositions. Figure 2 is an illustration of a car moving in one dimension. The motion of the car is described using vectors, as demonstrates to the learner both the rules of vector combination and the concept of displacement.

Figure 2. Displacement of a Car as Shown by One-Dimensional Vectors. (Prentice Hall)

The same image could be used to demonstrate how displacement and velocity are related. Given a value for time (10 seconds, for instance), the learner can use the definition of velocity (the rate of displacement over time) to find the average velocity of

13 the car in conditions A and B ( 6km /10s = 0.6km /s , and 2km /10s = 0.2km /s , respectively).

! ! The next figure (Figure 3) shows how two velocity vectors (X and Y) are combined to find the resultant vector (Z).

Figure 3. Velocity Vector Addition in Two Dimensions (Prentice Hall)

Again, the propositional information is depicted, although in a way that suggests students need to infer that the resultant vector of a combination of individual vectors can take on many values, based on how the individual vectors are oriented. Figure 4 shows a rock being dropped down a well to illustrate how velocity changes due to the acceleration. The earth’s gravitational acceleration is constant – 9.81m/s2, but this information must be inferred by the student at each point along the rock’s path.

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Figure 4. Velocity and Location of a Freely Falling Body at Different Time Intervals (Prentice Hall)

Figure 5 is an image showing three conditions of collisions between objects to show how the momentum of a system in conserved.

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Figure 5. Conservation of Momentum of a System as Shown Through A Series of Collisions (Prentice Hall)

Figure 6 relates the different energies of a system at any given time, depending on the position and motion of the object(s) in the system.

Figure 6. Conservation of Energy as Described By the Sum of Kinetic and Potential Energies of a System (Prentice Hall)

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KNOWLEDGE REPRESENTATION OF PROCEDURES (PRODUCTION SYSTEM) In their studies of problem solving, Newell and Simon (1972) found that participants in problem-solving experiments used “operators” (procedural actions) to move from a Start State to a Goal State (i.e., solution). Participants chose operators to use under certain conditions, meaning that different types of problems (or situations) required the execution of certain procedures. Newell and Simon postulated that these procedural rules represented a form of knowledge to be employed when a person faced a “how to” scenario. In other words, procedural knowledge tells one how to do something under certain conditions. Newell and Simon adopted this theory to construct an artificial form of knowledge that computers could use when attempting problem-solving tasks.

This

approach to computer programming spawned the field of Artificial Intelligence, and yielded a structure for representing conditions and production rules that can be applied to human cognition, as well. Using this structure, the knowledge required for describing the energy and motion of an object of mass “m” might look like the following: IF GOAL is to describe ENERGY THEN SUBGOAL is to Find KINETIC ENERGY AND SUBGOAL is to Find POTENTIAL ENERGY SUBGOAL is ENERGY=KINETIC ENERGY+POTENTIAL ENERGY IF SUBGOAL is to Find KINETIC ENERGY AND OBJECT is moving AND VELOCITY is known 1 THEN KE = " MASS " VELOCITY 2 2

!

17 IF SUBGOAL is to Find KINETIC ENERGY AND OBJECT is moving AND VELOCITY is not known AND DISPLACEMENT!0 DISPLACEMENT THEN VELOCITY = TIME 1 2 THEN KE = " MASS " VELOCITY 2 ! is to Find KINETIC ENERGY IF SUBGOAL AND OBJECT is moving ! AND WORK DONE is known THEN KE=WORK DONE

IF SUBGOAL is to Find KINETIC ENERGY AND OBJECT is moving AND WORK DONE is not known AND FORCE!0 AND DISPLACEMENT!0 THEN WORK DONE = FORCE " DISPLACEMENT IF SUBGOAL is to Find KINETIC ENERGY AND OBJECT is moving AND WORK ! DONE is not known AND FORCE=0 THEN WORK DONE =0 THEN KE=0 IF SUBGOAL is to Find KINETIC ENERGY AND OBJECT is moving AND WORK DONE is not known AND FORCE!0 AND DISPLACEMENT=0 THEN WORK DONE =0 THEN KE=0 IF SUBGOAL is to find POTENTIAL ENERGY AND OBJECT is located at HEIGHT!0 THEN PE = MASS " ACCELERATION OF GRAVITY " HEIGHT IF SUBGOAL is to find POTENTIAL ENERGY ! ! AND OBJECT is located at HEIGHT=0 THEN PE=0

18 This type of production system could continue almost indefinitely, depending on the initial conditions of the problem in question. Obviously, many algebraic procedures could be borrowed into this system, and multiple scenarios could be addressed to demonstrate the complexities of the mathematical relationships between the entities. Yet, these scenarios are not needed to demonstrate the basic function of this production system.

KNOWLEDGE REPRESENTATION OF MECHANISMS (MENTAL MODEL) A mental model is a mental depiction of a system of production rules and mechanisms actively affecting the interacting entities of a concept. In other words, it is a functioning physical model of a system within one’s mind. Mental models can be used to test predictions of outcomes, to make inferences, or even to contrast entities of a system. A study done by Kay and Black (1990) revealed an interesting disparity between expert computer users and the creators of a test program, due to the mental models these groups had constructed.

The experts in the study constructed mental models based on an

incomplete understanding of the technical functionality of a word processing program. The creators of the program had a more thorough, complete understanding of the program, and thus a more efficient mental model of the program’s operating mechanisms. For the knowledge discussed in this paper, an appropriate mental model needs to show how the motion and position of an object affect its internal energy. Thus, based on the given initial conditions, a learner should be able to navigate her mental model and describe the energy of the system by following the rules and procedures for finding the

19 amount of work done on the object, the velocity of the object, the momentum of the object, etc. Figure B in the appendix depicts these relationships as prescribed by the general knowledge and procedures discussed above.

COGNITIVE TASK ANALYSIS

Prepositional Network A strong background of factual knowledge is an essential aspect of learning how to describe an object’s internal energy. In a typical high school physics class, half of the school year is devoted to learning how to relate an object’s motion and position to its energy; this topic of study is referred to as “Mechanics.” Much emphasis is often placed on the terminology of physics, and knowing how to correctly describe a situation using the correct jargon. As well, many mathematical equations are associated with these terms, and require extensive knowledge of the values and units used in calculating different physical characteristics. Concept maps provide an avenue for showing how these terms, equations, and properties are interrelated, and are fundamentally based on the creation of propositional networks. An educational benefit of grouping information into a propositional network or concept map is that it promotes the chunking of knowledge by the learner. A student can look at a concept map, see the specific entities, and draw relations between associated ideas. Knowledge chunking has been shown to decrease the load on working memory, and enhancing the transition of knowledge from working to long-term memory (Anderson, 1996). These chunks help the learner in learning the production rules of the topic.

20 Thus, an appropriate instructional strategy for conveying the necessary items and relationship underlying Newtonian Mechanics and Energy would be to have students construct their own concept maps as new concepts are covered. For example, after only a few weeks of class, students should be able to connect the three vector quantities associated with motion and describe the relationships between them (velocity is the rate of displacement and acceleration is the rate of change of velocity, etc). The relationships between entities are vitally important in that they convey how concepts are connected, such as Force and Momentum, or Work and Kinetic Energy, but ultimately represent a small fraction of the knowledge required to gain a complete understanding of Newtonian Mechanics. Production Systems As discussed earlier, chunking knowledge can help facilitate the learning of procedures and production rules (Anderson, 1996). When a student begins to understand the relationships between entities of knowledge, knowing how and under what conditions to apply that knowledge becomes easier (Anderson, Boyle, and Reiser, 1985). These condition-action rules make up that procedural knowledge. The production system described above shows a few examples of how a situation may be addressed under a given set of conditions. Rehearsing these procedures is a necessary task for transferring the knowledge of the entities and relations into one’s longterm memory. According to ACT Theory (Anderson, Corbett, Koedinger, and Pelletier, 1995), declarative knowledge can be learned through instruction, whereas procedural knowledge must be learned experientially. A typical approach of instruction is to present

21 students with problem sets, where a given set of initial conditions must be manipulated to describe an outcome state. For example, given that an object with a mass of 5kg is moving at a velocity of 10m/s, how much momentum does the object have? A common procedure to follow would be to simply multiply the mass and velocity ( 5kg "10m /s = 50kgm /s ), as connected by the relationships of the propositional network above. Through rehearsal of this type of procedure, a learner is making progress towards !

an effective mental model of the knowledge topic. The main disadvantage of relying on problem sets for the learning of production rules is that students learn to depend on mathematical equations for recall instead of focusing on the relationships learned in the declarative knowledge representation. A better solution might be to present problems that require a student access both types of knowledge, such as with the use of word problems or unstructured problems where students have to apply their knowledge of declarative relationships and procedural rules to describe a certain situation.

Mental Images A great aspect of physics education, from an instructional point of view, is that a teacher can effectively create appropriate images to accompany any concept or group of problems. Vectors drawings, graphical models, free-body diagrams, and even simple depictions of scenarios are easily manipulated to represent a given set of initial conditions. Naturally, an instructor needs to choose the appropriate images to connect certain ideas, or else students might fall back on prior, and sometimes incomplete, knowledge or generate new misconceptions of the topic at hand (van Lehn, 1990). A

22 somewhat gold-standard example of such a misconception arises when students first learn about freely falling bodies. Students often believe that when a body is given an initial vertical velocity by some force (the force of a cannon, for instance), the force continues to act on the object until it reaches the earth again. Students fail to realize that the only force acting on the object is due to the pull of the earth’s gravity, and are apt to miss a few key points in this demonstration. For instance, at its apex, the body’s velocity is 0m/s, despite the fact that it is still accelerating (the acceleration due to gravity is constant and acts on all freely falling bodies). Using an image to accompany this scenario allows students to employ their declarative and procedural knowledge more confidently to a somewhat confusing situation. For the condition of freely falling bodies, students can generate their own mental images through an example that allows them to recall the appropriate facts and procedures for calculating velocity, acceleration, kinetic energy, and potential energy, with a pictorial aid like the one seen in Figure 7.

Figure 7. Worksheet for Describing Location, Motion, and Energy of a Freely Falling Body

23 The first segments of the object’s trajectory are already described as far as velocity, acceleration, kinetic energy, and potential energy are concerned, but the remaining segments require that the student fill in the blanks, there by invoking the associated procedural and declarative knowledge. As well, students can “zoom in” on a specific point in the object’s trajectory and reflect on how the different energies are related to each other (as by the Law of Conservation of Energy), as well as the velocity and acceleration. This diagram allows for a “visual segmentation and interpretation strategy” (Black, notes) that allows students to visualize and manipulate the image at certain points.

Mental Models The creation of a mental model requires that a student can mentally manipulate the entities of a system and simulate the appropriate mechanisms involved. After the information of a topic is learned through the three previous methods of knowledge representation (propositional networks, production rules, and mental images), the culminating experience for the learner is an effective, accurate, and robust mental model of the system that includes all the associated concepts and ideas. As a student develops this mental model, the teacher-assisted scaffolding supporting it can be slowly faded until she has a complete understanding of the topic (Jackson, Krajcik, and Soloway). Computer programs present a promising venue for this type of learning, and have been proven to enhance a student’s understanding of the material, provided the programmers take into account a number of cognitive principles (Mayer and Chandler, 1997).

24 For learning ways to describe an object’s motion and relate that to its internal energy, a program should include ways of manipulating the initial conditions of a system and the properties of the object’s motion to see how each entity affects the others. The program first needs to present a scenario where the relevant concepts are easily identifiable, and then allows the user to explore the relations and conditions of the system. Maggie Chan of Teachers College has created an elementary example of such a program, where students are presented with a simple rollercoaster and can manipulate the position of the car to show how position affects the kinetic and potential energies of the system.

A more sophisticated program might include ways of adjusting a world’s

gravitational force, the mass of an object (or group of objects), and the initial velocity and position of the object(s) to see show how the given parameters of the system affect the momentum of the object(s) (before and after collisions), how much work is done by the gravitational force, how inertia and force are related, how displacement affects the potential energy, etc. This type of program needs to incorporate the right visual images to represent the scenario, as well as allow students to practice the procedures of calculating the different physical quantities of the system. As well, the scaffolding provided by the program should be faded as users develop better mental models of the topic (Jackson, Krajcik, Soloway).

Conclusion A good mental model is the culmination of all the knowledge representations discussed above.

As a learner develops expertise through rehearsal of declarative

knowledge and production rules, and then learns to associate those notions with mental

25 images, a clearer picture of the overall topic is achieved. A computer program that incorporates these representations into instruction would be a great benefit to students. Thorough practice of declarative knowledge through the use of concept mapping, proceduralilzation through repetition, and mental imagery through visuals, learners can develop accurate and flexible mental models of the knowledge structure used to describe energy.

26 REFERENCES Anderson, J. R., Boyle, C.F., Resier, B.J. (1985). "Intelligent tutoring systems." Science 228: 456-462. Anderson, J. R., Corbett, A.T., Koedinger, K.R., Pelletier, R. (1995). "Cognitive tutors: Lessons learned." The Journal of the Learning Sciences 4(2): 167-207. Anderson, J. R. (1996). "ACT: A simple theory of complex cognition." American Psychologist 51(4): 355-365. Anderson, J. R., and Reder, L.M. (1999). "The fan effect: New results and new theories." Journal of Experimental Psychology: General 128(2): 186-197. Black, J. The symbols and worlds (saw) cognitive architecture, Teachers College, Columbia University. Jackson, S. L., Krajcik, J., Soloway, E. The design of guided learner-adaptable scaffolding in interactive learning environments. Kay, and. Black, J. From Classnotes "Mental Models and Mechanisms". (Black) Van Lehn. (1990). From "Cognitive Design of Educational Technology" (Black). Mayer, R. E., and Chandler, P. (2001). "When learning is just a click away: Does simple user interaction foster deeper understanding of multimedia messages?" Journal of Educational Psychology 93(2): 390-397. Newell, A. a. S., H. (1972). Human problem solving. Englewood Cliffs, NJ, Prentice-Hall. Prentice-Hall (2006). Physical science: Concepts in action. Upper Saddle River, NJ, Pearson Prenice Hall.