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 long-running 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 Mass Production in Production in FactoriesFactories

“Scientific” organization of factories

Raw materials Technical workers Assembly line process to

end product Efficiency experts/superiors Measurement of product

cost and progress Management

Structure efficient classrooms

Children Teachers Assembly line process

to graduation Administrators &

researchers. Standardized Test Central District

Authorities

Providing Providing Mass Mass EducationEducationVsVs

..

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?

QualityStudent

Performance

Curriculum: What(TEKS/TAKS, district, campus, teacher)

Instruction: How(lesson attributes, designs, strategies)

Assessment: To what extent(TEKS/TAKS, district, teacher)

Curriculum/Instruction/Assessment

Thinking at High Cognitive Levels and Making Connections

Assessing Student Progress

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Learner Centered

AssessmentCentered

KnowledgeCentered

CommunityCommunity

Perspectives on Learning Environments

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 Academic

Knowledge Tasks& Experiences

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

Word

Picture(that will be relevant to you)

Example(from your life experiences)

Non-example(from your life experiences)

Definition(in your own words)

Frayer Model

Quadratic Function

Function that is not constant and is not a line.

ax2 + bx + c = 0

y = x2

Building Background

Square Root

Function

The inverse of the positive side of the quadratic parent function.

Word Wall

Building Background

A R E A

A R E A

A R E A

A R E A

Sim i lar

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

AssessmentLower level - Lower level - reproduction, reproduction, procedures, concepts, procedures, concepts, definitionsdefinitions

Assessment Middle level - Middle level - connections and connections and integration for problem integration for problem solvingsolving

Assessment Higher level - Higher level - mathematization, mathematization, mathematical thinking, mathematical thinking, generalization, insightgeneralization, 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

Rich

Open

Constrained

Lean

Science Content Knowledge

Science Process Skills

Organized Organized Cognitive Cognitive ActivityActivity

Structure of KnowledgeStructure of Knowledge

Fragmental Meaningful

Problem Representation

Surface Features and shallow understanding

Underlying principles and relevant concepts

Strategy Use Undirected trial-and-error problem solving

Efficient, 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.

53%

14%

33%

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 what is learned!!learned!!

ConclusionConclusion

Student-centeredStudent-centered

Knowledge-centeredKnowledge-centered

Assessment-Assessment-centeredcentered

Community-centeredCommunity-centered

There needs to There needs to be alignment be alignment among the four among the four perspectives of perspectives of learning learning environments.environments.

They all have the They all have the potential to potential to overlap and overlap and mutually mutually influence each influence each other.other.

Thank you!

pcopeland@esc11.net