How People Learn

transcript

How People Learn

Conclusion 1:

Henri Poincaré“We must, for example, use

language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all.”

“Birds,” said the frog mysteriously. “Birds!” And he told the fish about the birds, who had wings, and two legs, and many many colors.

“Cows,” said the frog. “Cows! They have four legs, horns, eat grass and carry pink bags of milk.”

“And people,” said the frog. “Men, women, children!” And he talked and talked until it was dark in the pond.

Force / Motion Concept Map

Given some forces

1. F 2. m

1. Motion: r,v,a 2. F

Motion: r,v,a

Determine unknown forces

Vectors and component resolution

ENGINE

F = ma 1. Draw Picture. 2. Isolate Bodies. 3. Draw FBD. 4. Choose Axes. 5. Apply Fx = max Fy = may

6. Solve 7. Check

Special Cases 1. Constant v a = 0 v = r / t 2. Constant a a = v / t = F/m Example: ax=0, ay=-9.8m/s2 3. Motion in a circle ar = v2/r at = dv/dt

Models 1. Ropes massless and don't stretch. 2. Pulleys massless and frictionless. 3. Weight: Fg = mg 4. Equilibrium: F = 0 5. Friction: fs sn fk = kn f along common plane n common plane dimensionless materials parameter

v is slope of x vs t a is slope of v vs t

1. Motion: r,v,a 2. m

F and individual forces

INPUTS OUTPUTS

Constant Acceleration Kinematics

vxf = vxi + axt x = (vxi+vxf)t/2 x = vxit + axt

2/2 vxf

2 = vxi2 + 2axx

Conclusion 2: Expert vs. Novice Learners

Conclusion 3: Metacognition or reflection

1600to1900

ClassicalPhysics

Mechanics

Thermodynamics

Electromagnetism

1900to1940

ModernPhysics

RelativityLarge speeds (108 m/s).

Quantum MechanicsVery small scales (10-10 m).

1940topresent

CurrentPhysics

Particle Physics

Cosmology

Ch1-1 Physics and the Laws of Nature

How Physics Works

Model / Theory

Observation / Experiment

Length [L] meter Distance traveled by light in vacuum in 1 / 299792458 seconds

Mass [M] kilogram Mass of a platinum-iridium alloy kept in France at the International Bureau of Weights and Measures

Time [T] second 919263177 times the period of vibration of radiation from the Ce-133 atom

Ch1-2 Units of Length Mass and TimeStandards

Ch1-2 Standards of Length Mass and Time Standards

A Force acts on a mass resulting in motion.

Distance from the Earth to the nearest large galaxy (the Andromeda Galaxy, M31)

2 x 1022 m

Diameter of our galaxy (the Milky Way) 8 x 1020 m

Distance from the Earth to the nearest star (other than the Sun)

4 x 1016 m

One light year 9.46 x 1015 m

Average radius of Pluto’s orbit 6 x 1012 m

Distance from Earth to the Sun 1.5 x 1011 m

Radius of Earth 6.37 x 106 m

Length of football field 102 m

Height of a person 2 m

Diameter of a CD 0.12 m

Diameter of the aorta 0.018 m

Diameter of the period in a sentence 5 x 10–4 m

Diameter of a red blood cell 8 x 10–6 m

Diameter of the hydrogen atom 10–10 m

Diameter of a proton 2 x 10–15 m

Ch1-2 Standards of Length Mass and Time Typical Lengths

Scales

Galaxy (Milky Way) 4 x 1041 kg

Sun 2 x 1030 kg

Earth 5.97 x 1024 kg

Space Shuttle 2 x 106 kg

Elephant 5400 kg

Automobile 1200 kg

Human 70 kg

Baseball 0.15 kg

Honeybee 1.5 x 10–4 kg

Red blood cell 10–13 kg

Bacterium 10–15 kg

Hydrogen atom 1.67 x 10–27 kg

Electron 9.11 x 10–31 kg

Ch1-2 Standards of Length Mass and Time Typical Masses

Ch1-2 Standards of Length Mass and Time Typical Times

Age of the universe 5 x 1017 s

Age of the Earth 1.3 x 1017 s

Existence of human species 6 x 1013 s

Human lifetime 2 x 109 s

One year 3 x 107 s

One day 8.6 x 104 s

Time between heartbeats 0.8 s

Human reaction time 0.1 s

One cycle of a high-pitched sound wave 5 x 10–5 s

One cycle of an AM radio wave 10–6 s

One cycle of a visible light wave 2 x 10–15 s

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

101 deka da

10–1 deci d

10–2 centi c

10–3 milli m

10–6 micro

10–9 nano n

10–12 pico p

10–15 femto f

Power Prefix Abbreviation

Ch1-2 Standards of Length Mass and Time Common Prefixes

Concept Question 1.1

(2.44 x 10-5) / (2 x 103) =

a. 2.44 x 10-8

b. 2.44 x 10-2

c. 1.22 x 10-8

d. 1.22 x 102

e. 1.22 x 108

Distance [L]

Area [L2]

Volume [L3]

Velocity [L]/[T]

Acceleration [L]/[T2]

Energy [M][L2]/[T2]

Quantity Dimension

Ch1-2 Standards of Length Mass and Time Dimensions of Some Common Physical Quantities

Ch1-3 Dimensional Analysis

Given the following definitions with their dimensions:

v = velocity (L/T)

a = acceleration (L/T2)

t = time (T)

Which of the following equations could be correct as far as dimensions are concerned?

A. v = at2/2

B. v = a/2t

C. v = at

D. v = a2t/2

E. v = a/t2

How does v depend on a and x?

P1.5 (p. 14) Suppose v2 = 2axp

What is p?

Ch1-3 Dimensional Analysis

Which statement is correct regarding significant figures?

A. 1.355 + 1.2 = 2.555

B. 1.478 – 1.3 = 0.18

C. 1.513 / 1.5 = 1.009

D. 1.5 x 10-3 + 0.1 = 0.1015

E. 0.1513 x 1.5 = 0.23

Ch1-4 Significant Figures

Do P1.12 (p. 14)

P = 2l + 2 w

Round-off: If next digit is 5, then round up.

Scientific Notation: Covered previously.

How many seconds in a 50 minute class period?

A. 1000

C. 3 x 10-3

D. 4500

E. 3 x 103

Ch1-5 Conversion of Units

Do P1.24 (p. 15)

Ch1-5 Conversion of Units

CT1.5 A. 500 B. 5,000 C. 50,000 D. 500,000

Ch1-6 Order-of-Magnitude Calculations

Shea Stadium holds about 55,000.

CT1.6 Donovan Bailey – Canada – 1996 Olympics

Who is in 0.1 s of Donovan? A. 2,3,4,5 B. 2,3,4 C. 2,3 D. 2

Donavan is roughly 2 meters tall and that gives the scale. Since they covered 100 m in 10 seconds, each meter takes about 0.1 seconds. The answer is c because they are within roughly 1 meter (half Donovan’s height).

Estimate how many barbers in Chicago?

I started by assuming a typical person gets a haircut every two months. Next I assumed that a barber could give about 4 haircuts/hr or 20/day or 100/week or 400/month or 800/every two months. I rounded this off to about 500/every two months since there may be times when the barber doesn't have customers. So a barber could take care of about 500 customers and then they would all come back again. There are about 3 million people in Chicago proper and 8 million in the metropolitan area so I picked an average of 5 million to represent Chicago. That means about 5x106 / 500 or 104 or 10,000 barbers. This is just an estimate and may be off by a factor of 10 either way given all the questionable assumptions!

A Google search listed 1711 barbers around Chicago.

Ch1-7 Scalars and Vectors

• A scalar is a pure number. What are some examples?

• A vector has magnitude (value) and direction. What are some examples?

• The magnitude of a vector could be considered a scalar.

Ch1-8 Problem Solving

• Read the problem carefully.• Sketch the system.• Visualize the physical process.• Strategize.• Identify appropriate equations.• Solve the equations.• Check your answer.• Explore limits and special cases.

Ch1-8 Problem Solving

Do P1.39 (p. 16) N = number of beatsB = beats/second T = time

Mechanics

Study of forces and energy and motion.

• Force is an agent of change.• Energy is a measure of change.

How People Learn

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