Math in Context:

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Math in Context

• Percents in the Marketplace

Mims, Sriram, Wilkerson LS425 Introduction to
Design Reiser, Kuhn
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Audience

• Our audience consists of adults who want to
  improve basic mathematical skills in order to
  help them function better in a market society.
• We want to help people develop practical skills
  for our currency-driven society.

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Audience

• Our audience members are interested in developing
  skills for estimating
• Sales prices
• Taxes
• Tips
• Salary raises
• Credit cards
• Car loans

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Audience

• The setting for project will include market-math
  courses offered by community colleges.
• The ideal demographic for our design will include
  both urban and suburban men and women who
  voluntarily enroll.

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Needs Analysis

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

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Contextual, Market Math Need

• Consumers Basic Math Everyday
• But General Skills Lacking
• Numerous studies show this
• (Details to come)

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

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Traditional School Contexts

• School setting

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

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Traditional School Contexts

• School setting

Real World

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

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Traditional School Contexts
If 12.3 million dollars is 75 of the budget,
then how much is the full budget? First solve the
problem by drawing a picture. Explain how the
picture helps you solve the problem. Then solve
the problem numerically. (Beckmann, 2003)

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

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Traditional School Contexts
If 12.3 million dollars is 75 of the budget,
then how much is the full budget? First solve the
problem by drawing a picture. Explain how the
picture helps you solve the problem. Then solve
the problem numerically. (Beckmann, 2003)

• Out of context

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

Mims, Sriram, Wilkerson
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Traditional School Contexts
If 12.3 million dollars is 75 of the budget,
then how much is the full budget? First solve the
problem by drawing a picture. Explain how the
picture helps you solve the problem. Then solve
the problem numerically. (Beckmann, 2003)

• Out of context
• Process instead of Concepts

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

Mims, Sriram, Wilkerson
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Traditional School Contexts
If 12.3 million dollars is 75 of the budget,
then how much is the full budget? First solve the
problem by drawing a picture. Explain how the
picture helps you solve the problem. Then solve
the problem numerically. (Beckmann, 2003)

• Out of context
• Process instead of Concepts
• Unrealistic scenarios

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

Mims, Sriram, Wilkerson
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Traditional School Contexts
What's wrong with this?

• Dead knowledge (unusable, inert)
• Smart students vs. Stupid students
• Math Anxiety

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

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Traditional School Contexts

• School setting

Real World

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

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Traditional School Contexts

• School setting

Real World

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

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Needs Analysis

• Why concentrate on Percents?
• Frequently Appear in Marketplace and Personal
  Finance
• Variety of Contexts
• Particularly Misunderstood

• Contextual, Market Math Need
• Traditional School Contexts
• Percents
• Specific Difficulties with Percents

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Needs Analysis

• Why do adults need to know percents?
• knowledge of percents is required for effective
  understanding of and performance in numerous
  real-world situations, such as managing personal
  finances dealing with work-related tasks,
  and comprehension of messages in the media
• - National Center for Adult Literacy

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Adult Understanding of Percents

• Do adults really not understand percents?
• 50 cannot solve everyday problems
• Fewer than 4 can solve most difficult problems
• 57 of adults could estimate 25 of 80 in a
  shopping context

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Adult Understanding of Percents

• Specific problem areas
• Number sense regarding percents
• Inability to compute percents

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Number Sense

• 100 as a whole
• Percent as dependant on a starting value
• Unable to generalize

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Inability to Compute Percents

• Time-consuming and frustrating computation
• Avoidance/withdrawal
• Trust calculators, computers, salespeople

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Summary of Needs

• Transfer Adults need to be able to apply learned
  concepts to the real world
• Number Sense Adults need to understand what is
  meant by percent
• Computation Adults need a simple way to
  determine values

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Alignment Table
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Learning Objectives
Wiggins McTighe

• Big Idea
• Estimation and number sense regarding percents

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Estimation

• effective functioning does not necessarily
  require people to have strong computational
  skills, but rather a general, perhaps intuitive,
  understanding of the percent system, as well as
  number sense and mental math skills
• -National Center for Adult Literacy

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Learning Objectives
Wiggins McTighe

• Essential Questions
• What general concepts should I know to quickly
  and accurately estimate percents?
• How can I use what I already know regarding
  percents to make informed financial decisions?

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Learning Objectives

• Implement a general strategy for estimating
  percents in financial contexts. 
• Check the feasibility of an estimated price.  
• Differentiate between valid offers  and
  manipulative financial tactics regarding
  percents. 
• Produce realistic and cost-effective budgets or
  plans for different financial contexts.  

Anderson Krathwohl
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Alignment Table
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Alignment Table
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Alignment Table
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Alignment Table
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Alignment Table
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Instructional Design

• Learning for Use (Edelson, 2001)

Authentic, real world tasks
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Instructional Design

• Learning for Use (Edelson, 2001)

Authentic, real world tasks

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Instructional Design

• Learning for Use (Edelson, 2001)

Authentic, real world tasks

Support with Feedback
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Instructional Design

• Learning for Use (Edelson, 2001)

Authentic, real world tasks

Support with Feedback
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Instructional Design

• Learning for Use (Edelson, 2001)

Authentic, real world tasks

Support with Feedback
Appropriate Environment for Learning
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General Task Plan

• Introductory Task
• Motivate Experience Demand
• Lesson Development
• Construct Students construct understandings and
  receive instruction
• Assessment
• Refine Apply knowledge and Reflect

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Sample Task Shopping
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Sample Task Shopping

• Introductory Task
• Design a game room
• Within a given budget
• Using Catalogs, Ads, Internet, etc.

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Sample Task Shopping

• Lesson Development
• Discuss estimation strategies
• Compare prices
• Create chart of misconceptions and best practices

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Sample Task Shopping

• Assessment
• Project selection
• Reasonable budget
• List of items to purchase (several deals for each
  item)
• Use Strategies discussed
• Present or Discuss

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Alignment Table
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Alignment Table
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Alignment Table
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Alignment Table
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Alignment Table
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Questions?