keystone method

04/19/23 Keystone Group-Daley College 1

Keystone MethodKeystone MethodA Synergistic Model for Teaching and Learning

by

Prof. Vali Siadat

Prof. Deloris Holman

Prof. Cyrill Oseledets

Prof. Euguenia Peterson

Prof. Sonia Ramirez


Have you ever noticed how training

in calculation helps make

a slow mind quicker?

Plato, The Republic


Remedial Mathematics Education

is a major problem at

U.S. colleges and universities.

The Keystone Method was designed to address the needs

of these students.


Keystone Method Hypothesis:

•Unsuccessful students do not lack the intelligence or the desire to succeed.

•Rather, they are held back by behavior patterns, which inhibit learning.


Specifically, the Keystone Method recognizes:

1) Students’ short attention spans;

2) Inadequate attention to assigned homework;

3) Short time horizons;

4) Failure to learn from errors;

5) Passivity in class, hoping to pass unnoticed;

6) Poor attendance patterns;

7) Low self-esteem;

8) Ignoring teachers’ statements.


1) To address students’ short attention spans:

•At each class meeting, the instructor gives a time-pressured quiz that requires the students’ full concentration.

•At the beginning of each term, the quizzes are short, no more than 10 minutes.

•Quizzes are gradually lengthened as students’ attention spans increase.

•The quizzes are all cumulative.


2) To address students’ inadequate attention to assigned homework:

•The daily quizzes are a reflection of assigned homework.

•Students who regularly complete homework assignments should receive good grades on the quizzes.


3) To address students’ short time horizons:

•Students are examined every class period.


Research has shown that frequent testing has important educational

benefits for the learner:

•It encourages regular study habits and discourages cramming.

•It mitigates test anxiety.

•Students favor frequent testing over longer tests that carry exorbitant weight.

•It motivates students to constantly review the earlier topics and concepts and helps with consolidation of their learning.


4) To address students’ failure to learn from their mistakes:

•Students are provided with immediate feedback.

•Similar questions are repeated in subsequent quizzes until students achieve mastery in the topic.


5) To address students’ passivity:

•Students engage in peer tutoring and cooperative group learning.

•Group learning techniques are employed when the standard deviation of test scores exceed 25%.


6) To address students’ poor attendance:

•The instructor issues administrative drops for more than three absences, to be reversed only upon the student meeting certain conditions.


7) To address students’ low self-esteem, the instructor gives the students:

•Well-defined tasks,

•The tools to carry out those tasks,

•Prompt feedback for their attempts,

•Repeated success when they achieve mastery.


8) To address students’ ignoring teachers’ statements:

•The professor gives the students repeated evidence that his/her instructions produces success.


Gains in Arithmetic Percentile Rank 1998-2000

0.00

5.00

10.00

15.00

20.00

Math 110 Math 112 Math 140

Ga

ins

in P

erc

en

tile

Ra

nk

Project

Control

Results of the Keystone Study


Students in Keystone classes improve in their ability to

focus their attention on a task, even if that task is

not a mathematical one.


Mean Final Exam Scores 1998-2000

0.00%

20.00%

40.00%

60.00%

80.00%


Me

an

Fin

al E

xa

m S

co

res

Project

Control



Pass Rates on Final Exam 1998-2000

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%


Pa

ss

Ra

tes

Project

Control



Retention Rates 1998-2000

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%


Ret

entio

n R

ates

Project

Control



Math 112 Fall 2001

0.00%

20.00%

40.00%

60.00%

80.00%

Mea

n S

core

s


Math 112 Spring 2002

0%

20%

40%

60%

80%

Me

an

Sc

ore

s

Math 110 Spring 2002

0.0%

20.0%

40.0%

60.0%

80.0%

Mea

n S

core

s



41% of students entering Keystone classes went on to take and pass a college credit math class in a future term.

23% of students entering Control classes went on to take and pass a college credit math class in a future term.

79% of students entering Keystone classes went on to take and pass a take any class in the subsequent term.

63% of students entering Control classes went on to take and pass a take any class in the subsequent term.


Math-110 Student Performance on External Summative Assessment

Instrument (COMPASS Test)

2003-2005

Group N

COMPASS Test,passing score = 29 Normalized

GainRaw Score on Pre-Test

Raw Score on Post-Test

Test/Keystone Weekly

65 20.0 32.7 1.41

Test/Keystone Biweekly

58 19.9 36.4 1.81

Control 138 20.3 28.0 0.88


Math-110 Student Performance on Internal Summative Examinations(Departmental: midterm and final)

Measured by Mean

2003-2005

0%

10%

20%

30%

40%

50%

60%

70%

80%

Test/KeystoneWeekly

Test/KeystoneBiweekly

Control/TrainedInstructor

Control/Non-Trained Instructor

Midterm Exam Final Exam



2003-2005 Measured by Passing Rate (70% or higher)

0%

10%

20%

30%

40%

50%

60%

Test Gr. I Test Gr. II Control Gr. III Control Gr. IV




Measured by Retention Rate 2003-2005

0%10%

20%30%

40%50%60%

70%80%

90%100%

Test Gr. I Test Gr. II Control Gr. III Control Gr. IV



Correlation Between

Internal and External Summative Exams 2003-2005

Keystone Weekly

30

40

50

60

70

80

90

50 100 150 200

COMPASS, % (out of 29)

Fin

al, % Series1

Linear (Series1)

Keystone Bi-Weekly

20

40

60

80

100

120

50 100 150 200


Fin

al,

% Series1

Linear (Series1)

Control Group

10

30

50

70

90

110

0 50 100 150 200 250


Fin

al,

% Series1

Linear (Series1)


56%

70%

50%

69%

56%

66%

57%

66%

0%

10%

20%

30%

40%

50%

60%

70%

80%

T. Sp05 K. Sp05 T. Fall04 K. Fall04 T. Sp04 K. Sp04 T. Fall03 K. Fall03

T. Sp05

K. Sp05

T. Fall04

K. Fall04

T. Sp04

K. Sp04

T. Fall03

K. Fall03

Math-112 Student Performance on Departmental Final Exam

Measured by Mean

2003-2005


28%

33%

29% 28%

35%

18%

26%

31%28% 27%

59%56% 56% 55%

53%51%

63%

51%

59%

53%

0%

10%

20%

30%

40%

50%

60%

70%

K. Fall2003

T. Fall2003

K. Spring2004

T. Spring2004

K. Fall2004

T. Fall2004

K. Spring2005

T. Spring2005

K. Total T. Total

Math-112 Student PerformanceMeasured by Passing and Retention Rate

2003-2005


71% 71%

64%62%

65%

45%

0%

10%

20%

30%

40%

50%

60%

70%

80%


Keystone

Traditional

Math-112 Student PerformanceMeasured by Success Rate

2003-2005


Conclusion:

The formative assessment in the form of frequent cumulative multiple-choice quizzes with immediate, constructive feedback reveals the levels of conceptual understanding in a timely manner and improves student academic performance on the summative assessment instruments.

Increased frequency of formative assessment provides better results on the summative assessment.

The results achieved on valid and reliable internal (departmentally designed) summative assessments are an accurate predictor of the scores on external examination (COMPASS Test).


The Keystone Method is the essential piece in an arch: the stone that holds all others in place.

Conclusion:


Recommendation:

The Keystone method should continue to be studied, along with other effective methods, to foster student learning in all developmental mathematics classes.


What is next?

Powerful computer technologies will simplify the practical use of Keystone and provide:

A. Computerized grading of assignments;B. Automatic item analysis;C. Real-time grading and feedback;D. Automatic assessment of learning

outcomes.


What we hope for?

Synergetic combination of the Keystone Method with powerful software technology will further improve students performance.

Computerized Keystone Method will create a possibility for an effective coordination of multiple section classes.

Simplicity and power of this approach will result in wide use of the Keystone Method.


The End

keystone method

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