The Design of Learning
Environments
Presented by
Patty Copeland
Changes in Educational Goals
Math Through the Decades
Teaching Math in 1950: A logger sells a
truckload of lumber for $100. His cost of
production is 4/5 of the price.
What is his profit?
Math Through the Decades
Teaching Math in 1960: A logger sells a
truckload of lumber for $100. His cost of
production is 4/5 of the price, or $80.
What is his profit?
Math Through the Decades
Teaching Math in 1970: A logger exchanges a
set, "L", of lumber for a set, "M", of money.
The cardinality of set "M" is 100. Each
element is worth one dollar.
Make 100 dots representing the elements of
the set "M."
The set "C", the cost of production contains
20 fewer points than set "M."
Represent the set "C" as a subset of set "M"
and answer the following question:
What is the cardinality of the
set "P" of profits?
Math Through the Decades
Teaching Math in 1980: A logger sells a
truckload of lumber for $100. His cost of
production is $80 and his profit is $20.
Your assignment:
Underline the number 20.
Math Through the Decades
Teaching Math in 1990: By cutting down
beautiful forest trees, the Logger makes $20.
What do you think of this way of making a
living? Topic for class participation after
answering the question: How did the forest
birds and squirrels feel as the logger cut
down the trees?
There are no wrong answers.
Math Through the Decades
Teaching Math in 2000: A logger sells a
truckload of lumber for $100. His cost of
production is $120.
How does an Enron Accountant determine
that his profit margin is $275?
Math Through the Decades
Teaching Math in 2010: El hachero vende
un camion carga por $100.
La cuesta de production es . . . .
Changes in Educational Goals

1800s


Instruction in writing focused on the
mechanics---oral messages to written
messages.
Writing instruction aimed at giving children
the capacity to closely imitate very simple
text forms.
Changes in Educational Goals

1930s


Primary students were expected to express
themselves in writing.
Analysis and interpretation of what is read
became an expectation of all school
children.
Literacy: Then and Now


Colonist were literate
enough if they could
sign their name, or even
an “X”…
Immigrants arrived in
large numbers and
schools gave them
“recitation literacy”
Literacy: Then and Now


WWI—Army redefined
reading....“extraction
literacy”…who, what,
when, where, or how.
Now—full or “higher
literacy”…inferences,
questions, or ideas
Literacy: Then and Now
“The idea of a classroom where young women,
poor and minority students, and learning
disabled students all read (not recite) and write
about (not copy) Shakespeare or Steinbeck is a
radical and hopeful departure from the longrunning conception of literacy as serviceable
skills for the many and generative, reflective
reading and writing for the few” (Wolf, 1988).
Eighth Grade Test - 1895



Name and define the fundamental Rules of
Arithmetic.
A wagon box is 2 feet deep, 10 feet long,
and 3 feet wide. How many bushels of
wheat will it hold?
If a load of wheat weighs 3942 lbs., what is
it worth at 50 cents/bushel, deducting 1050
lbs. for tare?
Eighth Grade Test - 1895




What is the cost of 40 boards 12 inches wide and
16 feet long at $20 per meter?
Find bank discount on $300 for 90 days (no grace)
at 10 percent.
What is the cost of a square farm at $15 per acre,
the distance which is 640 rods?
Write a Bank Check, a Promissory Note, and a
Receipt.
Eighth Grade Test - 1895



District No. 33 has a valuation of $35,000. What is
the necessary levy to carry on a school seven
months at $50 per month, and have $104 for
incidentals?
Find cost of 6720 lbs. of coal at $6.00 per ton.
Find the interest of $512.60 for 8 months and 18
days at 7 percent.
Mass Production Vs. Providing Mass
Education
in Factories
Structure efficient
“Scientific” organization of classrooms
factories
 Children
Raw materials
 Teachers
Technical workers
 Assembly line process
Assembly line process to
to graduation
end product
 Administrators &
Efficiency experts/superiors researchers.
Measurement of product  Standardized Test
cost and progress
 Central District
Management
Authorities








Society today…

Envisions graduates of school systems
who:



Identify and solve problems
Make contributions to society through their
lifetime
Display the qualities of “adaptive expertise”
Why Are We Doing This?
Curriculum/Instruction/Assessment
Curriculum: What
(TEKS/TAKS, district,
campus, teacher)
Quality
Student
Performance
Instruction: How
(lesson attributes,
designs, strategies)
Assessment: To what extent
(TEKS/TAKS, district, teacher)
Assessing Student Progress
Addressing the Varied Needs and
Characteristics of All Learners
Alignment of Learning Objectives
Thinking at High Cognitive Levels and Making Connections
Perspectives on Learning
Environments
Community
Learner
Centered
Knowledge
Centered
Assessment
Centered
Learner-Centered
Environments



Knowledge, skills, attitudes, and beliefs
that learners bring
Culturally responsive, appropriate,
compatible, and relevant
Diagnostic teaching
Learner-Centered
Environments



Students use their current knowledge to
construct new knowledge.
What they know and believe at the
moment affects how they interpret new
information.
Sometimes learners’ current knowledge
supports new learning, sometimes it
hampers learning.
Learner-Centered
Environments
Previous
Knowledge
& Experiences
Academic
Tasks
Building Background



Listen to the passage
Write a description or
draw a picture of the
main character
Compare your vision of
the character to the
visions of others
Martin…
Building Background

What is meant by activating prior
knowledge?
What is meant by building background?

Do they differ instructionally?

Building Background

Activate Prior
Knowledge:





Discuss
Brainstorm
KWL
Think-Pair-Share
Show and Tell

Building
(Knowledge)
Background




Realia
Demonstrate
Model
Pictures
Frayer Model
Definition
Picture
(in your own words)
(that will be relevant to you)
Word
Example
(from your life experiences)
Non-example
(from your life experiences)
Function that is not
constant and is not a
line.
ax2 + bx + c = 0
y = x2
Quadratic
Function

Building Background
The inverse of
the positive
side of the
quadratic
parent
function.
Square
Root
Function
Word Wall
A
A
A
A
R
R
R
R
E
E
E
E
A
A
A
A
Sim
i
lar
Building Background
Knowledge-Centered
Environments


The ability to think and solve problems
requires well-organized knowledge that
is accessible in appropriate contexts.
Overlaps with Learner-centered


Begins with concern for students’ initial
preconceptions about the subject matter.
Concerns about what is developmentally
appropriate at various ages.
Knowledge-Centered
Environments

Highlights the importance of
thinking about designs for curricula


Learning with understanding
vs.
promoting the acquisition of
disconnected sets of facts and skills?
Assessment-Centered
Environments
Assessment-Centered
Environments



Formative Assessments
Feedback
Theoretical Frameworks
Formats for Assessing
Understanding
Assessment
Lower level reproduction,
procedures, concepts,
definitions
Assessment
Middle level connections and
integration for problem
solving
Assessment
Higher level mathematization,
mathematical thinking,
generalization, insight
Consider the following:




A rectangular prism is 2cm x 4cm by 6cm. One
dimension is enlarged by a scale factor of 3. What is
the volume of the enlarged figure?
A rectangular prism is 2.7cm x 0.45cm by 609.01cm.
One dimension is enlarged by a scale factor of 3.5.
What is the volume of the enlarged figure?
When a figure is dilated by a scale factor k to form a
similar figure, the ratio of the areas of the two figures
is ___ : ___ .
A certain rectangular prism can be painted with n
liters of paint. The factory enlarged it by a scale
factor of 3 to make a similar prism. How much paint
do they need to paint the larger box?
Assessment Items - Where?
Assessment Items - Where?




A rectangular prism is 2cm x 4cm by
6cm. One dimension is enlarged by a
scale factor of 3. What is the volume of
the enlarged figure?
A rectangular prism is 2.7cm x 0.45cm
by 609.01cm. One dimension is enlarged
by a scale factor of 3.5. What is the
volume of the enlarged figure?
When a figure is dilated by a scale factor
k to form a similar figure, the ratio of the
areas of the two figures is ___ : ___
A certain rectangular prism can be
painted with n liters of paint. The
factory enlarged it by a scale factor of 3
to make a similar prism. How much
paint do they need to paint the larger
box?
Content-process space of
Science Assessments
Science Content Knowledge
Rich
Science
Process
Skills
Open
Constrained
Lean
Organized
Cognitive
Activity
Structure of Knowledge
Fragmental
Meaningful
Problem
Surface Features and Underlying
Representation shallow
principles and
understanding
relevant concepts
Strategy Use
Undirected trial-and- Efficient,
error problem solving informative, and
goal oriented
Self-Monitoring Minimal and sporadic Ongoing and
flexible
Explanation
Single statement of
fact of description of
superficial factors
Principled and
coherent
Community-Centered
Environments

Classroom and School Communities



Value learning
High standards
These norms increase opportunities to:



Interact
Receive feedback
learn
Community-Centered
Environments

Connections to the Broader Community




Homes
Community centers,
After-school programs
businesses
Comparison of time spent in
school, home and community, and sleep.
33%
53%
14%
Home and Community
School
Sleep
Television

Watching Different Kinds
of Programs



Educational
Purely entertaining
Effects on Beliefs and
Attitudes


Personal perception
Perceptions of others
The Importance of Alignment




What is taught.
How it is taught.
How it is assessed.
Without this alignment, it is difficult to
know what is learned!!
Conclusion

Student-centered

Knowledge-centered

Assessment-centered

Community-centered


There needs to be
alignment among
the four
perspectives of
learning
environments.
They all have the
potential to
overlap and
mutually
influence each
other.
Thank you!
pcopeland@esc11.net