GainingMore From a’Modern’ Moore Method

Gaining More From a ’Modern’ Moore Method

M. Padraig M. M. McLoughlin

Department of MathematicsKutztown University of Pennsylvania

11 October 20142014 Fall Meeting of the MAA Seaway Section

Outline

The Moore Method

My take on the method: my modified Moore method (MMM)

Gaining more from the Moore method (Student)

Gaining more with the Moore method (Instructor)

Summary, conclusion, & thank you

M. Padraig M. M. McLoughlin (KUP) Gaining More From a ’Modern’ Moore Method11 October 20142014 Fall Meeting of the MAA

Outline

The Moore Method

Outline

The Moore Method

Outline

The Moore Method

Outline

The Moore Method

R. L. Moore (1882 - 1974)

The progenitor to inquiry-based learning (IBL);

in order to learn we must do; not simply read, listen, or watch.

the method was developed by R. L. Moore, H. S. Wall, and H. J.

Ettlinger.

The Moore Method

R. L. Moore (1882 - 1974)

He wrote over 70 research articles.

50 students completed a Ph.D. under R. L. Moore

including W. S. Mahavier, M. E. E. Rudin, R. H. Bing, E. E. Moise,

J. R. Kline, R. L. Wilder, G. T. Whyburn, F. Burton Jones, B. J. Ball, and

J. W. Rogers. 3,129+ students completed a Ph.D. under R. L.

Moore’s students or further (the ’descendants’).M. Padraig M. M. McLoughlin (KUP) Gaining More From a ’Modern’ Moore Method

11 October 20142014 Fall Meeting of the MAA/ 42

R. L. Moore & the Moore method

The only person who could or did teach via the Moore method

was Dr. Moore himself.

What we call the Moore method was developed by R. L. Moore,

H. S. Wall, and H. J. Ettlinger.

So, we are discussing is the ’Moore method’ developed by

R. L. M., H. S. W., and H. J. E. & modifications of it.

[It is] “a commitment to teaching by letting students discover the

power their own minds have.”1

Discovering one’s own mind.

1Ed Parker, Primus, vol. 2 (September 1992): 235-246.M. Padraig M. M. McLoughlin (KUP) Gaining More From a ’Modern’ Moore Method

R. L. Moore & the Moore method

The only person who could or did teach via the Moore method

was Dr. Moore himself.

What we call the Moore method was developed by R. L. Moore,

H. S. Wall, and H. J. Ettlinger.

So, we are discussing is the ’Moore method’ developed by

R. L. M., H. S. W., and H. J. E. & modifications of it.

[It is] “a commitment to teaching by letting students discover the

power their own minds have.”1

Discovering one’s own mind.

1Ed Parker, Primus, vol. 2 (September 1992): 235-246.M. Padraig M. M. McLoughlin (KUP) Gaining More From a ’Modern’ Moore Method

R. L. Moore Lineage

R. L. Moore << W. S. Mahavier (UT)

H. J. Ettlinger << D. H. Tucker<< D. Ford

M. F. M. Neff (UF)

J. K. Doyle (SU)

H. S. Wall << Coke S. Reed (UT)

H. S. W. << B. Fitzpatrick (UT)

R. L. M. << W. S. M. (UT) << Michel Smith (EU)

R. L. M. << J. W. Rogers (UT)

R. L. M. << J. L. O’Connor (UT) << J. H. Neel (UF)

The Moore Method

Inquiry-based learning (IBL).

The Moore method is “first order IBL.” Presentation of

definitions, axioms, and lemmas, theorems, corollaries, etc.

No books, no group work, and no collusion.

The Moore Method

∗ Competition between students;

∗ the focus is on the student created arguments;

∗ depth not breathe, and repeated attempts (try, try, again); and,

∗ the instructor is an arbitrator, guide, or mentor.

The Moore Method

Slow careful work through material organised by the instructor.

More challenging or less challenging material:

lemmas, examples, theorems, or corollaries (depending on

class).

the individual must be active in learning (not passive), and as a

consequent self-confidence and self-directedness is established

and builds within the individual.

I have confidence...

The Moore Method

Focus is on individuals – each student is important and each student

is encouraged.

No coddling; no ’burping and diapering;’

tell students little; encourage students much;

and, push students to excel beyond their

perceived expectations (definitely), limitations (hopefully), or

imaginations (optimistically).

The Moore Method

The Moore method is a fundamental philosophy of education.

The Moore Method

“That student is taught best who is told the least.”2

2Dr. Moore from Challenge in the Classroom, 1966M. Padraig M. M. McLoughlin (KUP) Gaining More From a ’Modern’ Moore Method

Modified Moore Methods

Judith Covington, LSU-Shreveport Michel Smith, Auburn

Ted Mahavier, Lamar Judy Kennedy, Lamar

Alex Meadows, College of St. Mary’s Lee May, Salisbury

John Neuberger, North Texas Ju Zhou, KUP

Perry Lee, KUP Stan Yoshinobu, Cal. Poly S.L.O.

Ryan Gantner, St. John Fisher Patrick Rault, SUNY Geneseo

Carol Schumaker, Kenyon David Clark, SUNY New Paltz

Ed Parker, James Madison Univ. Charles Coppin, Lamar

Incredible instructors

My Moore Methods

Address all by last names; treat each class like a conference;

frequent feed-back; no collaboration on open questions;

individual work; presentations by students;

instructor not the centre of attention;

students are apprentices (art, skilled profession, etc.);

politeness;

naming theorems, corollaries, and lemmas after students;

minimal grading system (non-’puffery’); and minimal lectures.

My Moore Methods

politeness;

My Moore Methods

politeness;

My Moore Methods

politeness;

My Moore Methods

politeness;

My Moore Methods

politeness;

My Moore Methods

politeness;

My Moore Methods

politeness;

My Moore Methods

∗ Student created arguments, depth and breathe, and repeated

attempts (try, try, again).

∗ The instructor is a facilitator, guide, counsel, or referee.

Not every claim is answered.

Definitions, axioms, etc. then examples, lemmas, theorems,

corollaries, etc.

Limited use of books,

No collaboration before student presentations,

No group work,

Competition to get to the board (but not the grade).

My Moore Methods

corollaries, etc.

No group work,

My Moore Methods

corollaries, etc.

No group work,

My Moore Methods

corollaries, etc.

No group work,

My Moore Methods

corollaries, etc.

No group work,

My Moore Methods

corollaries, etc.

No group work,

My Moore Methods

I contend students are inquisitive; but, attention ebbs and flows or

intermittently turns on or off much as a distributor cap distributes a

charge in an engine.

∗ Help is not giving solutions to a student; help exists by asking

students what has been done, where the student got ’stuck,’ etc.; or,

∗ help is given by asking a sequence of directed questions (based on

what the student has done).

My Moore Methods

Almost everything is in the form of

a claim (universal): to prove or disprove

or a construction of an example or counter-example (existential).

Learning takes place in class, out of class: at home, or in the

office.

The student is never condescended to, is treated in a manner

collegial, and the class is encouraged to do likewise with each

other – – we are a community of scholars.

Humour and humility are also integral.

My Moore Methods

office.

My Moore Methods

office.

My Moore Methods

office.

Gaining more from the Moore method(Student)

∗ Many students are not used to being treated collegially nor are

initially comfortable answering questions about their work.

∗ The ’good’ students tend to be just ’good’ or become thus over the

semestre getting better and better because of their effort

understanding material and thus gain recognition from peers and the

instructor.

∗ Moore methods help us find the ’good’ students rather than ’weed

out’ the mediocre.

Hakuna Matata

∗ Some simultaneous (same problems) presentations on different

boards (different methods or same to compare).

∗ Discussions on solved problems can include, is there another way

to approach the claim? A different way to prove or disprove said?

∗ It is critical not to interrupt a presenter doing an ’awkward’ proof or

example to show them a ’better’ way for

it disheartens the presenter and crushes innovation and enthusiasm.

Ergo, the instructor must make every effort to be patient

(a huge task at times).

∗ The Moore methods do not reward superficiality or non-contextual

rote memorisation.

∗ ’Bottled,’ ’busy work’ exercises do not suffice.

∗ We encourage understanding.

Note: It seems that much understanding from traditional methods is ’imitative:

problem ’A’ learn a technique; slight change in problem ’B’ apply technique from ‘A’

to ‘B.’

∗ Much responsibility is placed on students and it is more work for

students and the instructor than traditional methods.

To use sophistic techniques of ’learning:’ memorise arguments,

cram before tests, and take ’short cuts’ is futile because those

’study methods’ fail to work.

e.g.: it is harder to fall into the ’the long memory & short on

understanding trap’ in a class organised under the aegis of the

Moore method or a modified Moore method.

The Moore method is an educational experience that hones an

internal locus of control.

Gaining more from & with the Moore method

∗ Instructor must be aware of students’ abilities and potential.

∗ The pace increases most every semester as students acclimate

to the method.

∗ Be prepared to lead a discussion if there are no presentations

on a given day.

∗ Students come to office at all hours to chat about material

wanting to present ideas, ask about their creations of new claims,

Some students ’complain’ class is too short.3

3A huge difference with other classes where there are the cell phone,laptop, movie watching zombies led by unenthusiastic drones.

Gaining more from & with the Moore method

∗ Instructor must be aware of students’ abilities and potential.

∗ The pace increases most every semester as students acclimate

to the method.

∗ Be prepared to lead a discussion if there are no presentations

on a given day.

∗ Students come to office at all hours to chat about material

wanting to present ideas, ask about their creations of new claims,

Some students ’complain’ class is too short.3

3A huge difference with other classes where there are the cell phone,laptop, movie watching zombies led by unenthusiastic drones.

Gaining more with the Moore method(Instructor)

The principle of, ’that student is taught best who is told the least,’

makes for very interesting classes.

You have to be confident in your abilities, talent, and perspicacity

or else any variation on the Moore method could be disastrous.

You will make mistakes so just as we expect from students own

up to them, minimise making mistakes, and learn from them.

Much of the encouragement of further study in math4 is

actualised because the students have done original (to them)

Our mistakes help us learn how to teach better (as well as

demonstrate our humanity).

Harumph

4Or any number of careers, vocations, etc.M. Padraig M. M. McLoughlin (KUP) Gaining More From a ’Modern’ Moore Method

Harumph

Faculty who employ traditional methods seem to suffer from

boredom (same - old - same - old). I opine such does not afflict

Moore method instructors (at all or as much).

Fantastic satisfaction in observing authentic intellectual growth.

We get to learn new things about familiar topics.

We create new ways to encourage students’ intellectual growth.

Many ideas naturally percolate from members of the class and that

many ideas can be provoked by the instructor by asking a sequence

of questions.

The end result is many wonderful, new, interesting, etc. ideas arise

from individuals in the class. The ideas oft are not of what one would

first (second, third, . . . ) think.

The instructor must be extremely well versed in the subject and

constantly vigilant; we can’t be on ’auto pilot.’

A pilot to infinity and beyond.

Summary

There is a heavy burden placed upon the student & instructor.5

Constructivist colleagues might not support its use.

Traditionalist colleagues might not support its use.

Administrators might not support its use.

Progress can be slow (achingly so at times).

Some students may whine.

5However, when done well many non-Moore method faculty (and somestudents) think the instructor has less work to do than a lecturer.

Summary

But, always try to remember the Chinese proverb R. L. Moore quoted.

That proverb provides a summation of the justification of Moore

methods.

It states:

“I see, I forget;

I hear, I remember;

I do, I understand!See, hear, forget?

Summary

methods.

It states:

“I see, I forget;

I hear, I remember;

Summary

methods.

It states:

“I see, I forget;

I hear, I remember;

Summary

MMM helps us find the ’good’ students rather than ’weed out’ the

mediocre.

However, . . .

‘...My job is to make great students greater – not make mediocre

students less mediocre.’ Dean Hardscrabble in “Monsters University.”

The Moore Method: A Celebration ofLearning

‘From failure you learn; from success, not so much.’

Aunt Billie in “Meet the Robinsons.”

The Moore Method: Celebrate Learning

“You must be imaginative, strong-hearted. You must try things that

may not work, and you must not let anyone define your limits

because of where you come from. Your only limit is your soul. What I

say is true - anyone can cook... but only the fearless can be great.”

Chef Auguste Gusteau in “Ratatoulli”

“In the past, I have made no secret of my disdain for Chef Gusteau’s

famous motto, ‘Anyone can cook.’ But I realize, only now do I truly

understand what he meant. Not everyone can become a great artist;

but a great artist can come from anywhere...”

Anton Ego in “Ratatoulli”

Pull-yourself-together! "What will you do?" Is this a question? You

will show him you remember that he is Mr. Incredible, and you will

remind him who *you* are. Well, you know where he is. Go, confront

the problem. Fight! Win!

Edna Mode in “The Incredibles”

References (Abridged)

∗ Chalice, Donald R., "‘How to Teach a Class by the Modified Moore Method.”American Mathematical Monthly, 102, no. 4 (1995): 317 - 321.∗ Cohen, David W., “A Modified Moore Method for Teaching UndergraduateMathematics.” American Mathematical Monthly 89, no. 7 (1982): 473 - 474, 487 - 490.∗ Coppin, Charles; Mahavier, Ted; May, Lee; and, Parker, Edgar. The Moore Method,MAA Notes #75 Washington, DC: Mathematical Association of America, 2009.∗ Fitzpatrick, Benjamin, Jr., “The Teaching Methods of R. L. Moore.” HigherMathematics 1 (1985): 41 - 45.∗ Foster, James A., Barnett, Michael, & Van Houten, Kare, “(In)formal methods:Teaching Program Derivation via the Moore Method.” Computer Science Education,6, no. 1 (1995): 67 - 91.∗ Halmos, Paul R., Moise, Edwin E. and Piranian, George, “The Problem of Learningto Teach.” American Mathematical Monthly 82, no. 5 (1975) 466 - 476.∗ Jones, F. B. “The Moore Method.” American Mathematical Monthly 84, no. 4 (1977):273 - 278.

∗ Moise, Edwin E. “Activity and Motivation in Mathematics.” American Mathematical

Monthly 72, no. 4 (1965): 407 - 412.

GainingMore From a’Modern’ Moore Method

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