Seeing the Light:
What's so hard about teaching optics?

Edward F. Redish

University of Maryland

Outline

Physics Education Research (PER)

Building a community knowledge

Modeling the student

Problems learning about light

Overview

The basics

Waves

Photons

What can we do about it?

Introduction

Optics in one of the most interesting and challenging areas of physics to teach.

It relates directly to everyday experience.

It relates to topics of much interest to many students such as photography, movies, astronomy, and biology.

It’s a class of phenomena where physics
has developed a number of different models
of increasing sophistication — rays, waves, photons.

It’s an area where it has been demonstrated
that students are strongly resistant to learning
scientific reasoning.

How does science learn?
Builng a community consensus

How can we learn to teach effectively?
Building a community consensus

Learning About
Student Learning

Physics Education Research (PER)
is the subject in which we study
how students understand
(and fail to understand) physics in order to

help individual students get over
their difficulties in learning physics

develop curriculum and materials
that are more effective for many students.

The PER frame

Observe students carefully using

interviews

open-ended exam questions (explain…, show…)

Interpret student errors in terms of a model of learning.

Apply our understanding of student starting points to

not gloss over points which are difficult for students

use what students know as resources for their learning

focus our evaluations on the basic building blocks
instead of on superficial manipulations

A model of student learning
from a noted expert

A better model
from cognitive science

Learning is about building long-term memory

Long-term memory

contains data, procedures, and rules about when to use them

is productive / generative

is associative

is structured

The key structures are patterns of association

links may be weak or strong

both connections and reasoning are context dependent

Key implications

1. Learning is productive / constructive.

The brain tries to make sense of new input in terms of existing mental structures.

We learn by analogy / metaphor

-- New constructions tend to be based on the model of existing structures.

2. Cognitive response is context dependent.

The productive response depends on the context in which new input is presented, including the student’s mental state (expectations).

Students can use multiple models

-- Confusion about appropriate context can make it appear
as if students hold contradictory ideas at the same time

The trouble with light

Physicists ideas about light are difficult
to teach to novices for two reasons.

Sighted people have lots of experience with light.
As a result, they have strong associations
and interpretations that create barriers to learning.

Physicists’ use a variety of models (rays, waves, photons), sometimes hybridizing them in ways
that are difficult for students to make sense of.

There has been a lot of PER concerning learning about light at a variety of levels.

Major contributors

Most of the work I will talk about
has been done by physicists,
in particular, Lillian McDermott,
her collaborators, students,
and postdocs.

There has also been a lot of important work by education specialists around the world including Driver (England), Treagust (Australia), and Anderson (Sweden).

Some difficult items learning about light

The ray model

how we see

colors

straight line propagation

images made
by mirrors and lenses

The wave model

superposition

Huygen’s principle

interference and diffraction

Why can’t we just
tell them? show them?

When a student has a strong association with or interpretation of a phenomena, telling them — even showing them —
often has little effect.

Students often re-interpret what they hear
so that it makes sense in their personal
scheme of things.

Even when shown a phenomenon explicitly, students will often fail to interpret things
in the way we want them to.

How we see

Children’s view of how we see
has been studied in depth.

Piaget found that young children often made no connection between the eye and the object.

Many studies of high school students show that only about 1/3 of students know we see an object by light coming to our eye from it.

About 1/3 of high school students have no explanation for vision: “We see with our eyes” suffices.

"The results stated on the..."

The results stated on the previous slide
lead to problems with mirrors and lenses, even at the university level.

In this case, the critical interpretive fact
is that the image is determined
by what light comes to our eyes.

Images: Mirrors

Many students at the university level do not understand basic issues with mirrors. They think:

The image in a mirror lies on the surface of the mirror. (~30% pre instruction)

That the position of a mirror image changes
when the observer moves. (~30% post instruction)

If a mirror is too small to see all of yourself, you can step back and see more. (~70% post instruction)

Images: Lenses

Many students at the university level do not understand basic issues with lenses. If a lens is positioned to create a real image of a bulb on a screen they think:

removing the lens will make the image right-side up (~45% post instruction)

the image does not lie on the screen
(~75% post instruction)

covering half a lens will block half of the real image
it creates (~75% post instruction)

Sherwood’s Theorem

“Glass attracts light.”

We often show only the relevant “critical rays”, ignoring the fact that many students do not understand

that light scatters from every point on an object
in all directions and that image formation
arises from what rays make it into our eyes
(and how our eyes interpret them)

Wave Optics

Waves are particularly confusing for students.

They have trouble with functions of many variables.

They get deeply confused about superposition.

We carry out calculations of interference and diffraction using a hybrid wave / ray model.

Interference:
A sample problem

When monochromatic laser light is shone
on a pair of double slits, the pattern
shown below is produced on a distant screen.

What would happen to the pattern
if one of the slits were covered?
(Since the interference arises from the waves from the two slits interfering with each other, the pattern would go away and be replaced by an almost uniform brightness.)

Results

This question was posed to a class
of engineering physics students
before and after instruction.

More than half of the students expected part of the pattern would remain.

Some said the left half of the lines would remain.

Some said every other line would remain.

Photons

When students are asked
to incorporate the photon
idea into their previous
observations they construct
some bizarre models.

Some students suggest that
photons move in oscillatory
paths “along the sine wave.”

Some students suggest that diffraction occurs because
“the photons bounce off the edge of the slit.”

Some suggest diffraction occurs because “the E-field vector
won’t fit through the slit and gets cut off.”

Why do they do this?

Many of the problems arise from the fact that
students use common sense rather than reason using the physical principles they have learned.

Students use their natural and spontaneous responses based on experience and overly simplistic reasoning. (“I know how light [or motion {or electricity}] works. I don’t need to go through that confusing physics stuff to get the answers.”)

Most students do not spontaneously seek to build
the tight consistency and coherence required
by a scientific approach. It needs to be learned
(and taught).

How can we help them?

In the past decade, it has been demonstrated that instructional environments
can be constructed that are much more effective than traditional instruction.

They need to be built

with an awareness of students’ natural responses

with an understanding of what instructional techniques have a significant impact.

The PER instructional development process

The UW Tutorial Model

Tutorials replace recitations:

training session for TAs

group-learning sessions with research-
based worksheets
and facilitators

tutorial homework

exams have a tutorial question

Lectures (and labs) as usual.

Tutorials on interference and diffraction

A series of 4 one-hour tutorials on interference and diffraction

focus on qualitative reasoning

concentrate on difficulties know to exist from PER

use a cognitive conflict model to engage
student interest (predict / observe / resolve)

stress logical coherence

Results

Shown many graphs of the type
shown at the right, rank the
relative slit width and spacing.

What about problem solving?

Example:

Light with l = 500 nm is incident on two narrow slits separated by d = 30 mm. An interference pattern is observed on a screen a distance L away from the slits. The first dark fringe is found to be 1.5 cm from the central maximum. Find L.

Results at UMd

Conclusions

After mechanics, optics is that area of physics where the most is known about what difficulties students have learning it.

Modern research-based instructional methods have proven effective in substantially increasing the fraction of students who “get it.”

If we want to introduce modern topics by cutting out introductory ones, we might do so more efficiently by making careful observations of student responses and learning.

For more information

For more information about PER
in general check our our website at

http://www.physics.umd.edu/perg/

For references to the articles in PER on optics check out the AJP resource letter on PER
by McDermott and Redish (Oct. ’99)

http://www.physics.umd.edu/rgroups/
ripe/papers/rlpre.pdf


	Physics Education Research (PER)
		Building a community knowledge
		Modeling the student
	Problems learning about light
		Overview
		The basics
		Waves
		Photons
	What can we do about it?


	Optics in one of the most interesting and challenging areas of physics to teach.
		It relates directly to everyday experience.
		It relates to topics of much interest to many students such as photography, movies, astronomy, and biology.
		It’s a class of phenomena where physics has developed a number of different models of increasing sophistication — rays, waves, photons.
		It’s an area where it has been demonstrated that students are strongly resistant to learning scientific reasoning.


	Physics Education Research (PER) is the subject in which we study how students understand (and fail to understand) physics in order to
		help individual students get over their difficulties in learning physics
		develop curriculum and materials that are more effective for many students.


	Observe students carefully using
		interviews
		open-ended exam questions (explain…, show…)
	Interpret student errors in terms of a model of learning.
	Apply our understanding of student starting points to
		not gloss over points which are difficult for students
		use what students know as resources for their learning
		focus our evaluations on the basic building blocks instead of on superficial manipulations


	Long-term memory
		contains data, procedures, and rules about when to use them
		is productive / generative
		is associative
		is structured
	The key structures are patterns of association
		links may be weak or strong
		both connections and reasoning are context dependent


	1. Learning is productive / constructive.
		The brain tries to make sense of new input in terms of existing mental structures.
		We learn by analogy / metaphor
		-- New constructions tend to be based on the model of existing structures.
	2. Cognitive response is context dependent.
		The productive response depends on the context in which new input is presented, including the student’s mental state (expectations).
		Students can use multiple models
		-- Confusion about appropriate context can make it appear as if students hold contradictory ideas at the same time


	Physicists ideas about light are difficult to teach to novices for two reasons.
		Sighted people have lots of experience with light. As a result, they have strong associations and interpretations that create barriers to learning.
		Physicists’ use a variety of models (rays, waves, photons), sometimes hybridizing them in ways that are difficult for students to make sense of.
	There has been a lot of PER concerning learning about light at a variety of levels.


	Most of the work I will talk about has been done by physicists, in particular, Lillian McDermott, her collaborators, students, and postdocs.
	There has also been a lot of important work by education specialists around the world including Driver (England), Treagust (Australia), and Anderson (Sweden).


	The ray model
		how we see
		colors
		straight line propagation
		images made by mirrors and lenses
	The wave model
		superposition
		Huygen’s principle
		interference and diffraction


	When a student has a strong association with or interpretation of a phenomena, telling them — even showing them — often has little effect.
		Students often re-interpret what they hear so that it makes sense in their personal scheme of things.
		Even when shown a phenomenon explicitly, students will often fail to interpret things in the way we want them to.


	Children’s view of how we see has been studied in depth.
		Piaget found that young children often made no connection between the eye and the object.
		Many studies of high school students show that only about 1/3 of students know we see an object by light coming to our eye from it.
		About 1/3 of high school students have no explanation for vision: “We see with our eyes” suffices.


	The results stated on the previous slide lead to problems with mirrors and lenses, even at the university level.
	In this case, the critical interpretive fact is that the image is determined by what light comes to our eyes.


	Many students at the university level do not understand basic issues with mirrors. They think:
		The image in a mirror lies on the surface of the mirror. (~30% pre instruction)
		That the position of a mirror image changes when the observer moves. (~30% post instruction)
		If a mirror is too small to see all of yourself, you can step back and see more. (~70% post instruction)


	Many students at the university level do not understand basic issues with lenses. If a lens is positioned to create a real image of a bulb on a screen they think:
		removing the lens will make the image right-side up (~45% post instruction)
		the image does not lie on the screen (~75% post instruction)
		covering half a lens will block half of the real image it creates (~75% post instruction)


	“Glass attracts light.”
	We often show only the relevant “critical rays”, ignoring the fact that many students do not understand
		that light scatters from every point on an object in all directions and that image formation arises from what rays make it into our eyes (and how our eyes interpret them)


	Waves are particularly confusing for students.
		They have trouble with functions of many variables.
		They get deeply confused about superposition.
		We carry out calculations of interference and diffraction using a hybrid wave / ray model.


	When monochromatic laser light is shone on a pair of double slits, the pattern shown below is produced on a distant screen.


	What would happen to the pattern if one of the slits were covered? (Since the interference arises from the waves from the two slits interfering with each other, the pattern would go away and be replaced by an almost uniform brightness.)


	This question was posed to a class of engineering physics students before and after instruction.
	More than half of the students expected part of the pattern would remain.
		Some said the left half of the lines would remain.
		Some said every other line would remain.


	When students are asked to incorporate the photon idea into their previous observations they construct some bizarre models.
		Some students suggest that photons move in oscillatory paths “along the sine wave.”
		Some students suggest that diffraction occurs because “the photons bounce off the edge of the slit.”
		Some suggest diffraction occurs because “the E-field vector won’t fit through the slit and gets cut off.”


	Many of the problems arise from the fact that students use common sense rather than reason using the physical principles they have learned.
		Students use their natural and spontaneous responses based on experience and overly simplistic reasoning. (“I know how light [or motion {or electricity}] works. I don’t need to go through that confusing physics stuff to get the answers.”)
		Most students do not spontaneously seek to build the tight consistency and coherence required by a scientific approach. It needs to be learned (and taught).


	In the past decade, it has been demonstrated that instructional environments can be constructed that are much more effective than traditional instruction.
	They need to be built
		with an awareness of students’ natural responses
		with an understanding of what instructional techniques have a significant impact.


	Tutorials replace recitations:
		training session for TAs
		group-learning sessions with research- based worksheets and facilitators
		tutorial homework
		exams have a tutorial question
	Lectures (and labs) as usual.


	A series of 4 one-hour tutorials on interference and diffraction
		focus on qualitative reasoning
		concentrate on difficulties know to exist from PER
		use a cognitive conflict model to engage student interest (predict / observe / resolve)
		stress logical coherence


	Shown many graphs of the type shown at the right, rank the relative slit width and spacing.


	Example:
		Light with l = 500 nm is incident on two narrow slits separated by d = 30 mm. An interference pattern is observed on a screen a distance L away from the slits. The first dark fringe is found to be 1.5 cm from the central maximum. Find L.


	After mechanics, optics is that area of physics where the most is known about what difficulties students have learning it.
	Modern research-based instructional methods have proven effective in substantially increasing the fraction of students who “get it.”
	If we want to introduce modern topics by cutting out introductory ones, we might do so more efficiently by making careful observations of student responses and learning.


	For more information about PER in general check our our website at
		http://www.physics.umd.edu/perg/
	For references to the articles in PER on optics check out the AJP resource letter on PER by McDermott and Redish (Oct. ’99)
		http://www.physics.umd.edu/rgroups/ ripe/papers/rlpre.pdf