Facets of Students' Thinking

by Jim Minstrell

with special acknowledgments
to D. Simpson, V. Stimpson and the students at Mercer Island HS;
to E. Hunt for technological assistance; and
to A. Arons, J. Clement, A. diSessa, and E. vanZee for their consultation

Codes for Strategic and Knowledge Facets

• 000 Reasoning in Science and Nature of Science
  
• 100 Getting Started, Measurement, & Number Analysis
  
• 200 Kinematics & Observational Astronomy
  
• 300 Nature of Gravity & Relative Motion
  
• 400 Dynamics: Forces & Interacting Bodies
  
• 500 Conservation: Energy & Momentum
  
• 600 Fields: Static Electricity & Magnetics
  
• 700 Current Electricity & Electromagnetics
  
• 800 Waves
  
• Epistemological, Developmental Facets

This coding scheme was begun in 1987. It is based on a "Knowledge in Pieces" perspective derived from our earlier attempts to construct frameworks to organize students' conceptual understanding and from a theoretical view developed by A. diSessa. The Facet codes are slight abstractions of what students say or do when confronted with a situation in which they are asked to predict or explain a physical phenomenon. Although our research has investigated students' conceptual understanding, many of the Facets have been identified in the research done by others. We can not possibly acknowledge all those researchers who have contributed. The Facet Codes are our attempt to organize the phenomena of students' conceptual understanding.

Within a Facet Cluster, the codes ending in 9 are associated with the Facets that seem to be the most problematic. They are typically the ideas we choose to address first in our instruction. The codes ending in 0 or 1 for the units digit representing u understandings that are probably "OK" at this introductory level. The others are roughly rank ordered between the 9 and 1. These facets are descriptions of characteristic understanding and reasoning and are not intended to be used directly as a numerical s coring scheme.

This list is not complete (7/96).

Reasoning in Science and Nature of Science

Facets about Defining Terms

• *001 Technical terms are defined in recipe like steps, using terms of prior common experience.
• 008 One term is not differentiated from other, perhaps related, but non-equivalent terms.
• 009 Technical terms are defined by the use of perceived synonymic words and phrases of colloquial use.

Explanations or Interpretations of Phenomena

• *050 Explanations or interpretations involve conceptual modeling of multiple related science or math concepts, using experimental evidence and rational argument to address questions of "how do you know..?" or "why do you believe..?" the results, observation, or prediction.
• *051 Explanation involves a mathematical modeling approach, incorporating principles subsumed under that model.
• 053 Explanation involves identifying possible mechanisms involving a single concept causing the result.
• 055 Explanation involves identifying and stating a relevant concept.
• 057 Explanation constitutes a description of procedures that led to the result.
• 059 Explanations or interpretations are given by repeating the observation or result to be explained.

Experimenting to Determine Relation Between Variables

• 060 Experimenting identifying potentially relevant variables by manipulating variables one at a time controlling others and noting the direction and magnitude of change in the dependent variable. Each hypothesized potentially relevant variable is tested for its correctional effects.
• 061 Experimenting is determining the quantitative relations between each independent variable (one at a time and controlling each other potentially relevant variable) and the dependent variable.
• 065 Experimenting is manipulating several variables and identifying one that has an effect without testing specifically for others.
• 068 Experimenting is changing things and seeing what happens.
• 069 Experimenting is just seeing what happens.

Getting Started, Measurement & Number Analysis

Best Value in Measurement

• *100 Use a procedure appropriate to the context to obtain a number representative of the possible measures one might get.
• *101 Measure the quantity several times (possibly using different scales) and take the average of the several measures (perhaps using appropriate rationale to eliminate extreme outliers) to determine a number that best represents the actual value.
• 105 Always averages all the measures obtained.(regardless of outliers)
• 106 Always eliminate the high and low values and average all the rest.
• 107 Average the highest and lowest measures.
• 108 "Mine" (measure made by the student doing the reporting) is the only valid measure.
• 109 Some one authority made one measurement and the student reports it as "the" actual, true value. Uncertainty in Measurement

• *110 Report the variability in the data in some way appropriate to the context.
• *111 Report the variability in the data by using the range or plus or minus an amount that covers most of the measures with the exclusion of outliers.
• 112 Report plus or minus an amount that covers all measures including outliers.
• 115 Report plus or minus the range as the uncertainty.
• 119 There is no uncertainty (zero error) in measurement if one is knowledgeable, uses a good instrument, and is careful.

Best Value in Calculations

• *120
• *121 Appropriately calculate the best value using the best values of the individual parts of the calculation.
• 124 Calculate the average of all the extremes, using the uncertainties for each measure involved.
• 125 Calculate the average of the two calculated extremes.
• 129 The value calculated from single measures of each involved quantity.

Uncertainty in Calculations

• *130 Report an appropriate uncertainty for the measures involved in the calculation.
• *131 Report the uncertainty associated with the maximum differences from the calculated best value to the extremes of calculation, using the uncertainty for each measure.
• 134 Perform the same operations on the uncertainties as one does with the best values (e.g. take the average of the uncertainties for each of the measures) to get the uncertainty in calculation.
• 135 Report the uncertainty as the sum of the uncertainties (in calculations involving multiplication or division).
• 136 Report the calculated uncertainty as the uncertainty of one of the measures involved in the calculation.
• 139 There is no uncertainty in the calculation.

Significant Figures

• *141 The last digit reported is the one about which there is some question.
• 148 All the digits given by a measurement instrument are significant and should be reported.
• 149 All the digits given by calculation are significant and should be reported.

Area differentiated from Perimeter and Volume

• *150 Area is differentiated from perimeter and from volume.
• *151 An operational definition of area includes a unit of surface, covering region with identical units, with no overlap, counting the units, reporting the number and units.
• 154 Area is a region of surface with no operational way of determining it.
• 155 Area is length X width.
• 158 Area is the general location of something.
• 159 Area is the amount of space something takes up, i.e. undifferentiated use of terms area, perimeter and volume. They all have to do with measuring how much space an object takes up.

Volume

• *160 Volume is the number of standard unit cubes which would just fill the space occupied by an object.
• 164 Volume is a region of space with no operational way of determining it.
• 165 Volume is length X width X height.
• 169 Volume is size, amount of stuff, or quantity of objects, undifferentiated from mass, weight, area, etc.

Density

• *170 For a uniform substance, the mass per unit of volume is the same, regardless of size or shape.
• *171 Density of an object is the number of units of mass associated with each unit of volume. D = m/vol
• 172 Relative densities compare the weights associated with equal volumes of material.
• 175 Density has to do with close packing, the number of things in a region of space.
• 179 Density is how heavy. Density is undifferentiated from weight or mass.

Floating and Sinking

• *180 An object floats if its total mass divided by its total volume is less than the average density of the surrounding medium.
• *181 An object made of uniform material will float if its density is less than that of the surrounding medium.
• 182 Float if the average of the densities of the parts is less than density of the medium it is in.
• 185 Focus on weight relative to surrounding medium. Things float if heavier than water and sink if lighter.
• 186 Object floats if it has a large area on the bottom (in contact with the medium on which it floats.
• 187 Things sink if they have holes in them.
• 188 Materials float if they are floating materials in that medium.
• 188-1 wood and styrofoam float in water.
• 188-2 hot air and helium balloons float in air.
• 189 Things float if they are made to float.
• 189-1 if they have air in them.
• 189-2 if they are boats or the like.

200 Kinematics & Astronomy Observations

Determining distance, displacement (x), or position (x).

• *210 distance traveled is the total accumulation of distance the object went [·( x) between successive changes in direction].
• *211-1 position is location relative to a distance scale traveled.
• *211-2 displacement is x = xf - xi.
• 215 Over generalize formula for distance or displacement (applied in appropriate context).
• 215-1 x = 1/2 a t2 (where vi ­ 0 ).
• 215-2 x = 1/2 a t2 (where a is not constant).
• 217 Change in position is not differentiated from change in rate
• 217-1 x = v
• 217-2 x = a
• 218 Not differentiating among position, distance, and displacement 218-1 position graph is a spatial map of locations
• 218-11 farthest position is always at end of trip
• 218-2 position = distance traveled (x = dist)
• 218-3 position = displacement (x = x).
• 218-4 displacement = distance (x = dist).
• 218-5 displacement = position (x = x).
• 218-51 displacement =·xi for every interval.
• 218-6 displacement = max. displacement from zero during the trip.
• 218-61 displacement = max. disp. from a nonzero beginning of trip.
• 218-21 distance is a position (i.e., not differentiated from position).
• 218-41 distance is displacement.
• 218-52 distance is ·xi for every interval.
• 218-7 distance = max. displacement from zero.
• 218-71 distance is max. dist from the non zero beginning of trip 218-72 distance is the max. extension in one direction to the max. extension in the other.
• 219 Not differentiated from a rate.
• 219-1 position = vinst.
• 219-2 position = ainst.
• 219-3 x = vi.
• 219-31 x = · vi for every interval.
• 219-4 x = average v.
• 219-5 distance = Vinst.

Average Speed or Average Velocity

• *220 avg. speed = (total distance covered)/(total amount of time).
• *221 avg. velocity = x/t (together with a direction).
• 225 Rate expression over generalized.
• 225-1 avg. v = vf + vi unless compensation lo hi occurs.
• 225-2 avg. v = xf / tf.
• 226 Rate expression misstated.
• 226-1 avg. v = t/x.
• 226-2 avg. v = v/2.
• 226-3 avg. v = vf/2.
• 226-4 avg. v = (vf+vi)/t.
• 228 Average rate not differentiated from another rate.
• 228-1 avg. v means constant velocity.
• 228-2 Velocity = speed.
• 228-3 avg. v = vf.
• 228-31 greatest avg. vel = greatest Vf during any part of trip.
• 228-4 avg. v = avg. a
• 228-5 avg. v = v or v/?
• 229 Average rate (speed/velocity) not differentiated from amount.
• 229-2 avg.v = pf.
• 229-21 avg.v = avg.p.
• 229-3 avg.v = p.

Instantaneous Speed or Velocity

• *230 sinst. = lim elapsed time -0 distance traveled elapsed time.
• *231 vinst. = lim t ->0 x / t.
• 233 Negative velocity always less than positive velocity when comparing speeds.
• 234 Over generalizations associated with v = 0.
• 234-1 Constant velocity = v=0.
• 234-2 Start and end = necessarily to zero vel.
• 234-3 v=0 implies stopped.
• 235 vf = xf or vinst. = xinst. tf tinst.
• 236 vinst. = v
• 238 Instantaneous velocity not differentiated from other rates.
• 238-1 vinst. = avg. v accumulated from start (unless it has always a const. vel.).
• 238-2 vinst. = ainst.
• 238-3 vinst. = v.
• 239 Instantaneous velocity not differentiated from position related ideas.
• 239-1 vinst. = xinst.
• 239-2 vinst. = x.

Change in Velocity

• *241 v = vf - vi.
• 244 v = just fluctuating.
• 248 change in rate is rate.
• 248-1 v = avg. v.
• 248-2 v = v.
• 248-3 v = avg. a.
• 249 change in rate is change in amount, v = x.

Acceleration (Average or Instantaneous)

• *250 The rate at which the velocity (speed and direction) is changing.
• *251 avg. a = v ainst = lim t ->0 v.
• 254 avg. a = v direction is a confusion. t
• 255 Average acceleration is not differentiated from other rates.
• 255-1 avg. a =vf
• 255-2 a = v with no attention to t x .
• 256 Misapplied formulas and average acceleration.
• 256-1 avg. a = vf + vi t
• 256-2 avg. a = vf + vi
• 256-3 ainst. = ai + af
• 258 average acceleration is instantaneous acc. avg. a = ainst.
• 258-1 greatest acceleration at an instant means greatest somewhere in trip.
• 258-2 greatest avg. a means greatest acc. somewhere in that interval.
• 258-3 average acceleration means constant acceleration.
• 259 acc. is not differentiated from displacement or velocity ideas.
• 259-1 a = x
• 259-2 avg. a = avg. v
• 259-3 avg.a = vinst
• 259-4 ainst = vinst

300 Gravitational Effects and Relative Motion

Separating Fluid Effects From Gravitational effects

• *310 Pushes from above and below by a surrounding fluid medium lend a slight support (net upward pressure due to differences in depth pressure gradient).
• *310-1 The difference between the upward and downward pushes by the surrounding air results in a slight upward support or buoyancy.
• *310-2 Pushes above and below an object in a liquid medium yield a buoyant upward force due to the larger pressure from below.
• 314 Surrounding fluids don't exert any forces or pushes on objects in them.
• 315 Surrounding fluids exert equal pressures all around an object in the medium.
• 315-1 Air pressure has no up or down influence (neutral).
• 315-2 Liquid presses equally from all sides regardless of depth.
• 316 Which ever surface has greater amount of fluid above or below the object has the greater push by the fluid on the surface.
• 317 Mediums exert an upward push only.
• 317-1 Air pressure is a big up influence (only direction).
• 317-2 Liquid presses up only.
• 317-3 Fluids exert bigger up forces on lighter objects.
• 318 Surrounding fluid mediums exert a net downward push.
• 318-1 Air pressure is a down influence (only direction).
• 318-2 Liquid presses (net press) down.
• 319 Weight of an object is directly proportional to medium pressure on it.
• 319-1 Weight is proportional to air pressure.
• 319-2 Weight is proportional to liquid pressure.

Differentiating Among Actions at a Distance

• *320 Differentiates actions at a distance from each other.
• 326 Not all decrease with distance.
• 327 Not all act across empty space (need a medium).
• 328 All act on same objects (undifferentiated effects).
• 329 Electricity = magnetism = gravity (undifferentiated actions).
• 329-1 Electricity = gravity
• 329-2 Magnetism = gravity
• 329-3 Electricity = magnetism

Factors Affecting Gravitational Pull (weight)

• *330 Affected by both masses (e.g. earth and object) involved. Weight is a relation that depends directly upon both of the masses involved and inversely upon the square of the distance between them.
• 333 Gravity greater on light objects.
• 334 Things that float don't weigh anything ,i.e. no Fe on floaters.
• 335 Gravitational force decreases with distance but not 1/d2.
• 336 Gravitational force is the same at any elevation above the earth.
• 337 Gravitational force is same magnitude on all objects near earth.
• 338 Weight depends upon everything (confusion of factors) (unable to identify relevant factors).
• 339 Weight is property of object.
• 339-1 Weight is undifferentiated from mass.

Falling Bodies

• *340 Fall time depends upon gravitational field strength and inversely upon fluid medium resistance
• *341 With no resistance by fluid medium, vertical fall near the earth's surface is at nearly constant acceleration of 10 m/sec2.
• 342 Gravitational pull and mass compensate with no accounting for air resistance.
• 343 Greater drag effects compensate for greater gravitational pull explaining equal accelerations.
• 344 Medium effects will exist even when there is no motion relative to fluid medium.
• 345 All things fall equally fast regardless of medium effects.
• 346 Vertical fall is at a constant velocity of 10 m/sec.
• 348 Heavier will hold back more (fall slower).
• 348-1 Larger fall substantially slower.
• 349 Heavier falls faster.
• 349-1 Larger falls faster.

Perception of Motion in Different Frames

• *360 Perception of motions in different frames.
• *361 Appropriate addition of motions with respect to each frame.
• 362 Component motions are added, but without discriminating accelerated motion from constant velocity motion.
• 369 Perceives motion in one frame only.

Sideways Motion Effects on Forward Motion and Horizontal Motion Effects on Vertical Motion

• *370 Motion in forward direction is independent of motion in sideways direction.
• *370.1 Vertical drop time is independent of horizontal motion.
• *371 Motions appropriately added vectorally.
• 373 Motions added by ordinary arithmetic.
• 374 Accelerated frame added backwards.
• 375 Accelerated frame added as constant velocity.
• 376 Sideways influence adds nothing but a change in direction (no extra speed).
• 377 Sideways influence adds nothing but a change in speed (no change in direction).
• 378 Sideways motion increases forward motion.
• 378.1 Horizontal motion makes object fall more quickly.
• 378.2 Removal of horizontal motion influence means all effects of horizontal are lost, i.e. the movement goes back to vertical only.
• 379 Sideways motion decreases forward motion.
• 379.1 Horizontal motion makes it fall more slowly.
• 379.2 Motion in x decreases motion in y.
• 379.3 Sideways motion viewed as active motion overcoming forward motion.
• 379.31 Overcoming forward motion all at once.
• 379.32 Overcoming gradually, wearing away the forward motion.
• 379.33 Overcoming right away but then going back to original forward motion.

Vertical Motion Effects on Horizontal Motion

• *380 Horizontal motion is not affected by vertical motion.
• *381 Appropriate vector addition of vertical to horizontal.
• 388 Vertical motion increases horizontal motion.
• 388-1 Vertical fall makes object go horizontally faster.
• 388-2 Removal of vertical motion active influence means all effects of vertical are lost, i.e. the movement goes back to horizontal only.
• 389 Faster it goes vertically decreases horizontal motion.
• 389-1 Vertical pull decreases horizontal motion.
• 389-2 Vertical motion is viewed as the only active motion and overcomes horizontal motion.
• 389-21 Overcoming all at once.
• 389-22 Overcoming gradually, wearing away the horizontal motion.

Dynamics: Forces & Interacting Bodies

Identifying Forces

• *400 Forces are exerted by anything touching the object and by actions at a distance.
• *401 Above is true even when object is touched by a medium.
• 402 Only the things touching exert forces.
• 403 Force of motion on anything that is moving.
• 404 No force unless motion.
• 405 Force is a willful or teleological influence.
• 406 Force is a property of material out of which object is made.
• 407 Surfaces can't exert sideways forces.
• 408 Passive objects can't exert forces.
• 409 Distant energy source is exerting the force on the object (or causal agent).

Forces to Explain the At Rest Situation

• *410 Balanced forces on an 'at rest' object (vector sum is zero).
• *411 At rest and constant velocity are relative.
• 412 "Balanced forces" can not apply to both constant velocity and constant position conditions of motion.
• 418 Constant position requires a bigger "preventer force."
• 418-1 Requires a bigger "hold back" force.
• 418-2 Requires a bigger "hold up" (support) force.
• 419 Constant position requires a bigger "hold to/hold down" force.

Forces to Explain Linear Accelerated Motion

• *420 acceleration is proportional to Fnet.
• *421 acceleration is inversely proportional to mass.
• 422 Objects don't have mass in space.
• 423 Objects don't have hold back inertia in the vertical.
• 424 Fnet depends upon potential (or on what's about to happen to it).
• 428 Constant acceleration requires a constant changing force.
• 429 Explaining accelerated condition with an excess force proportional to the velocity. Forces to explain constant velocity.
• *430 Balanced forces on an object moving with constant velocity.
• *431 At rest and constant velocity are relative.
• 432 "Balanced forces" can not apply to both constant velocity and constant position conditions of motion.
• 439 Explaining constant velocity requires an excess force proportional to the velocity.

Resistive Force by a Fluid Medium

• *440 Resistive force is in a direction to oppose motion of object relative to medium or surface in contact with medium.
• *441 Plowing resistance (drag) proportional v2 x area (cross) x medium density.
• 445 Drag depends on 'heft' regardless of size.
• 446 Drag depends on size (regardless of cross section exposed).
• 447 Drag is same regardless of speed.
• 448 Drag is same regardless of medium.
• 449 Resistance is greater on a lighter weight object.

Rubbing Resistance by a Surface

• *450 Rubbing resistance is parallel to the surface and in the direction opposite to the direction that the surface is moving relative to the surface causing the friction.
• *451 Rubbing resistance (friction) proportional to normal force and depends on type and condition of surfaces.
• 453 Friction depends upon surface area.
• 454 Friction depends upon speed of object.
• 455 Friction is equal to the normal force.
• 458 Direction of frictional force is problematic.
• 458-1 Friction opposes motion of object rather than the surface.
• 458-2 Friction is in direction of motion.
• 459 Friction is undifferentiated from other "hold back" tendencies.
• 459-1 Friction depends upon how 'hefty' object is.
• 459-2 Friction is gravity.

Vector Resolution of Forces

• *460 Appropriate directions of individual forces and direction of Fnet.
• *461 Appropriate quantitative resolution of forces.
• 465 Resolves force into perpendicular components, but neither is parallel to direction of actual or possible acceleration in situation.
• 466 Resolves the force as one of the perpendicular pieces of one of its components.
• 468 Resolution of forces without attending to appropriate magnitudes.
• 469 Resolution of forces without attending to directions.

Forces During Interactions

• *470 All interactions involve equal magnitude and oppositely directed action and reaction forces that are on the separate interacting bodies.
• 474 Effects (such as damage or resulting motion) dictate relative magnitudes of forces during interaction.
• 474-1 At rest, therefore interaction forces balance.
• 474-2 "Moves", therefore interacting forces unbalanced.
• 475 Equal force pairs are identified as action and reaction but are on the same object.
• 476 Stronger exerts more force.
• 477 One with more motion exerts more force.
• 478 More active/energetic exerts more force.
• 479 Bigger/heavier exerts more force.

Explaining Circular Motion

• *480 Fnet is centripetal and depends directly on mass, v2 and inversely on radius of the curve.
• *481 Acceleration is centripetal and depends directly on v2 and inversely on the radius of the curve.
• 483 Fc exists but with no dependence on R.
• 484 Fc is proportional to v (not v2).
• 485 Fc =0, if speed is constant (even if direction is changing).
• 487 A particular circular motion is a condition, it does not depend on factors of speed, radius, or mass.
• 488 Involves outward and inward balancing forces.
• 489 Circular motion involves outward, centrifugal force.

System and Subsystem Analysis of Force and Motion (e.g. Atwood or Modified Atwood Machine)

• *490 Fnet on each part of the system is proportional to the masses of the parts of the total system in a rigid system.
• *491 The acceleration of parts in a rigid system are equal to the acceleration of the whole system.
• 498 Analysis of the whole system without analysis of the parts.
• 499 Analysis of subsystem without analysis of system as a whole.

Conservation: Energy & Momentum

Work

• *500 Work depends on both parallel components of force applied on object and the distance through which the object moves while the force is being applied.
• *501 Work = Force X Distance (using the parallel components).
• 505 Work = Force X Distance (without taking only parallel components).
• 507 Work is proportional to (or undifferentiated from) a time interval during which force is applied (without control of other variables).
• 508 Work is proportional to (or undifferentiated from) distance through which the force is applied (without control of other variables).
• 509 Work is undifferentiated from (or proportional to) force.

Work and Simple Machines

• *510 Work without machine = Ideal F X D ˛ Work with machine = Actual F X D.
• 515 Applies Ideal Work relation in non-ideal situation.
• 516 Unable to represent the work/mechanical advantage relationship in a picture.
• 518 Perceives one (input or output) work relation in a situation, but not both (the input and output situations are not related to each other).
• 519 No appropriately associated F and D work relation perceived.

Work-energy Transfers

• 520
• 524 More KE if has greater mass.
• 525 More KE if going faster.

Energy-energy Transfers

• 530

Impulse

• 540
• 544.1 Impulse = F by earth X delta t, using gravitational force by earth rather than net force.

Momentum

• 550
• 554 More momentum if more mass.
• 555 More momentum if more speed.

Change in Momentum

• 560

Impulse-momentum Transfers

• 570
• 574
• 579 More Momentum if Force is Larger

Momentum Conservation

• 580

Conservation

• 590

Fields: Static Electricity & Magnetism

• 600
• 610

Neutral

• 620
• 621
• 622 Neutral objects don't react with anything.
• 623 Neutral object and charged object may repel.
• 624
• 625
• 626
• 627
• 628
• 629

Acquiring Electrical Charge

• 630
• 631
• 632 Pieces are charged without any direct or indirect influence.
• 633 Influencer at a distance puts excess same charges on object.
• 634 Influencer at a distance puts excess opposite charges on object.
• 635 Like charges attract.
• 636 Pieces touching each other don't share charge (even if metal or smeared).
• 637 If attract, then opposite charge.

Bring in Outside Influence

• 640
• 641
• 642
• 643
• 644 Conditions of leaves is condition for whole electroscope.
• 645 To influence charges on metal must share charges with the metal (transfer charges to the metal).
• 646 Neutral body touched will share neutrality but doesn't get charged in process.
• 647
• 648 Other objects "have an attraction for" the influencer.
• 649

Take Away Outside Influence

• 650
• 651
• 652
• 653
• 654 Take influences away takes all excess charge away.
• 655 Charges only are influenced by outside influences, no local influence of each other, e.g., Metal piece that has been polarized stays polarized when influences removed.
• 656
• 657
• 658
• 659

PD Related to Current and Resistance

• 660 PD depends on proportion of the total resistance of the route.
• 661
• 662 PD not differentiated from flow (current).
• 663 Relational Reasoning Mental Model, e.g., half circuit, half PD.
• 664 PD is reduced to the energy at one end (PD -> The potential energy).
• 665 The more resistors (things to affect) the more PD.
• 666 PD from one location to another depends directly on the number of resisters (V proportional R).
• 667 PD inversely proportional to total resistance PD confuse with power
• 668 PD proportional to current.
• 669 You don't have a PD influence unless you have an effect (MM).
• 670
• 680
• 690

700 Current Electricity & Electromagnetics

Circuit of Conducting Material

• 700 Need a source of potential difference and a complete circular path of conducting material but no short circuit to get continuous flow through the device.
• 701 Representation correct - apparently traced all continuous loops.
• 703 If not touching battery and a wire, device is not in loop.
• 704 See only one circuit possible, follow one loop only - miss other circuit(s).
• 705 Focus on local partial connection only - not using sequential checking all the way around the circuit.
• 706 Spatial organization of elements is same, then it is the same circuit, regardless of actual connections of the elements.
• 708 Receivers (bulbs, resistors, etc) draw (pull) electricity from the source. Devices are active pullers of the electricity from passive batteries.
• 709 Battery is source and bulb is receiver (source receiver mental model). Wire is the pipe from source to receiver.
• 710 Two endedness of each device in a circuit path, so flow must go through device.
• 711
• 712 A burned out bulb means flow can go through unresisted.
• 713
• 714
• 715 Unclear about how many terminals the device has or how to use terminals.
• 716 2 kinds: source-receiver, 2 terminals of device, one connected to +, one to - of a battery.
• 717 Complete circular path with device externally attached will run device.
• 718 Provide one terminal with two kinds of electricity (definite one endedness).
• 719 Source-Receiver, two kinds of electricity interact at bulb (interaction mental model) [See circuit as necessary for providing two kinds of electricity or opposite ends of two batteries can provide two kinds] no attention to two endedness.
• 720 The more resistance in line the greater the total (RT = R1 + R2 + ...+ Rn).
• 721 A short means very little resistance in that route.
• 722 A short means increase in flow.
• 723 More effect (heat/light) -> more resistance.
• 724 The more resistors, the more resistance (not attention to number of routes).
• 725 The more routes the less the resistance (no attention to amounts of resistance).
• 726 Total resistance = resistance down any one route.
• 727 The bigger the resistive device, the more resistance.
• 728 Resistance is proportional to voltage (regardless of current).
• 729 First resistor gets its electricity, next gets less, etc. (sequential mental model; attenuation mental model; downstream sequential reasoning). (down stream change does not affect up or side stream).
• 730 Current is the flow of electricity measured by the number of units of charge passing through some point for each one unit of time.
• 731 At branching more flow through less resistive route (current is inversely proportional to resistance).
• 732 Flow is how fast.
• 733 The more devices, the more current (devices 'draw' electric current).
• 734 The more routes, the more flow (no attention to resistance or route).
• 735 The more resistors the less flow ( no attention to number of routes).
• 736 Flow always divides equally at a branching.
• 737 Parallel out allows more flow than one route in (or vise versa) Words: parallel implies more flow.
• 738 Current proportional to potential difference regardless of resistance.
• 739 Electricity goes to each device and gets shared in equitable manner (sharing mental model) (good useful idea for electric energy/unit charge)

Push:

• 740 Potential difference is a comparison of relative energy per unit charge. PD depends on number of batteries in series.
• 741
• 742 No coordinated endedness of batteries; parallel and series batteries not differentiated.
• 743 The more effect (light/heat), the more push (no attention to changes in R as well).
• 744 The more or bigger batteries, the more push (potential difference).
• 745 More batteries will last longer (arrangement doesn't matter).
• 746 Batteries in series, less flow in a series circuit.
• 747 Batteries in parallel, get more flow in parallel circuit.
• 748 Batteries in parallel push against each other.
• 749 One battery always puts out same amount of electricity regardless of arrangement (Conservation of Source output mental model).
• 740 [also see 660 series]

  (+,-, means 'add, take away, or change')

Add, Delete, Change an Element

• 750 +, -, an element affects virtually all other elements.
• 751
• 752 short circuit will make everything go out.
• 753
• 754
• 755
• 756 (see 229 for down stream)
• 757 +,-, an element affects next element upstream in series only.
• 758 +,-, an element affects next element in parallel only.
• 759 +,-, an element affects that element only (Mental Model: Localized Reasoning).

Capacitors and Potential Difference

• 760 Charge movement is in response to a field.
• 761 Capacitor in series add PD, capacitor in parallel add.
• 762
• 763
• 764
• 765
• 766
• 767
• 768 Capacitor is a break, therefore there can be no flow in that route.
• 769 Charge flows from one end of battery to one plate (Mental model: sequential from source to blocker).

Inductance

• 770
• 771
• 772
• 773
• 774
• 775
• 776
• 777
• 778
• 779

First Right Hand Rule

• 780
• 781
• 782
• 783
• 784
• 785
• 786
• 787
• 788
• 789

Second Right Hand Rule

• 790
• 791
• 792
• 793
• 794
• 795
• 796
• 797
• 798
• 799

800 Wave Behavior (Springs, Water, Sound and Light)

• 810 Movement of Waves.
• 820 Movement of particles affected by wave.
• 830 Waves hitting barriers (reflection).
• 840 Waves encountering a new medium (refraction).
• 850 Waves encountering an open slit (diffraction).
• 860 Waves colliding (interference).
• 870 Wave length.

Epistemological, Developmental Facets

• Undifferentiated use of language:
  • to appropriately differentiated use of language.

• Truth is knowable and is absolute:
  • -to there are limitations on knowledge, K is context dependent
  • -to abstract principles apply universally, but multiple factors applied in the different context give differential effects

• Assume a transformer influence [association of influence with effect, but no intermediate mechanisms] "push top of tube makes diver go down.", "rubbing plastic makes it charged."
• Assumed direct [or inverse] proportional relation between variables.
• No justification of "complex" problem solution (perhaps where individual got answer wrong.
• Explanation is local, consider what happens to that object only.
• Assumed not necessary to consider initial conditions
• Effects are due to single cause only. Lack of control of other variables.
• Glitches in reading, copying, arithmetic, etc. that it is reasonable to expect virtually anyone who is not handicapped to be able to do.
• Quantities are conserved, but transfer among participants. Change means something is given from one participant to another.
• Application of facet is overgeneralized
  • -to apply facet appropriate to context.