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Algebra Mastery Through Relevant Applications. Opening Remarks. The Rigor/Relevance Framework. K N O W L E D G E. T A X O N O M Y. 6 5 4 3 2 1. Ev aluation. C Assimilation. D Adaptation. Synthesis. Analysis. Application. A Acquisition. B Application. - PowerPoint PPT Presentation
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Algebra Mastery Through Relevant Applications
Algebra Mastery Through Relevant Applications
Opening Remarks
2
The Rigor/Relevance Framework
AAcquisition
BApplication
CAssimilation
DAdaptation
KNOWLEDGE
TAXONOMY
6
5
4
3
2
1
Evaluation
Synthesis
Analysis
Application
Understanding
Awareness
APPLICATION MODEL
1 2 3 4 5Knowledge Apply in
discipline
Apply acrossdisciplines
Apply toreal worldpredictable situations
Apply to real-worldunpredictable situations
International Center for Leadership in Education
Defining Rigor
Level PerformanceLevel 1 - Knowledge Label the x and y axis
Level 2 - Comprehension Graph ordered pairs
Level 3 - Application Graph a scatter diagram from data
Level 4 - Analysis Find the slope of a line
Level 5 - Synthesis Generate an equation for a given set of data
Level 6 - Evaluation Write a scenario for a given graph of a function
Math Teachers Beware!
Evaluate.
Let x = 2 and y = -3
3xy-12y2
Although the word evaluate is located at a level 6 on the knowledge taxonomy, this question does not require students to think at a high level. This question is a traditional “plug and chug” exercise.
Another Caution for Math Teachers
Content Knowledge
When teaching concepts and skills to students for the first time, it is important to remember that what is easy for the teacher is challenging to the student
Algebra RelevanceLevel Performance
Level 1 – Knowledge in One Discipline
Solve a one-step equation
Level 2 – Application in One Discipline
Find the slope of a linear equation
Level 3 – Interdisciplinary Application
Derive the formula distance = rate x time
Level 4 – Real-world Predictable Situations
Calculate the reaction time of drivers for different speeds
Level 5 – Real-world Unpredictable Situations
Create formulas to predict changes in stock market values
The Rigor/Relevance Framework
Quadrant AAcquisition
Quadrant BApplication
Quadrant CAssimilation
Quadrant DAdaptation
KNOWLEDGE
TAXONOMY
6
5
4
3
2
1
Evaluation
Synthesis
Analysis
Application
UnderstandingAwareness
APPLICATION MODEL
1 2 3 4 5Knowledge Apply in
discipline
Apply acrossdisciplines
Apply toreal worldpredictable situations
Apply to real-worldunpredictable situations
Distinguish rational and irrational numbers.
The Rigor/Relevance Framework
Quadrant AAcquisition
Quadrant BApplication
Quadrant CAssimilation
Quadrant DAdaptation
KNOWLEDGE
TAXONOMY
6
5
4
3
2
1
Evaluation
Synthesis
Analysis
Application
UnderstandingAwareness
APPLICATION MODEL
1 2 3 4 5Knowledge Apply in
discipline
Apply acrossdisciplines
Apply toreal worldpredictable situations
Apply to real-worldunpredictable situations
Calculate medical dosages for different weight animals
The Rigor/Relevance Framework
Quadrant AAcquisition
Quadrant BApplication
Quadrant CAssimilation
Quadrant DAdaptation
KNOWLEDGE
TAXONOMY
6
5
4
3
2
1
Evaluation
Synthesis
Analysis
Application
Understanding
Awareness
APPLICATION MODEL
1 2 3 4 5Knowledge Apply in
discipline
Apply acrossdisciplines
Apply toreal worldpredictable situations
Apply to real-worldunpredictable situations
Solve quadratic equations and linear inequalities
The Rigor/Relevance Framework
Quadrant AAcquisition
Quadrant BApplication
Quadrant CAssimilation
Quadrant DAdaptation
KNOWLEDGE
TAXONOMY
6
5
4
3
2
1
Evaluation
Synthesis
Analysis
Application
UnderstandingAwareness
APPLICATION MODEL
1 2 3 4 5Knowledge Apply in
discipline
Apply acrossdisciplines
Apply toreal worldpredictable situations
Apply to real-worldunpredictable situations
Create formulas to predict changes in stock market values
The Rigor/Relevance Framework
KNOWLEDGE
TAXONOMY
6
5
4
3
2
1
Evaluation
Synthesis
Analysis
Application
UnderstandingAwareness
APPLICATION MODEL
1 2 3 4 5Knowledge Apply in
discipline
Apply acrossdisciplines
Apply toreal worldpredictable situations
Apply to real-worldunpredictable situations
•Solve linear equations•Factor numbers using rules of divisibility
C
A
D
B•Collect data from the speedometer of your automobile and calculate your average speed•Determine the exit pocket of a pool ball when hit
•Solve quadratic equations•Factor polynomials
•Determine how much harder you need to hit an uphill putt•Design a set of golf clubs customized for launch and ball flight options
Why Quadrants B and D?
Whether working with combinations and permutations or angles and speed, algebra is the language of mathematics.
Students need algebra and they need to be good at it,
In a recent report from the Raytheon Company it was reported that 84% of middle school students would rather clean their rooms, take out the garbage, or go to the dentist than do their math homework.
Traditional, lecture-based classrooms are no longer adequate to prepare students for a highly technological society.
Learners in the 21st century need to be captured through interactive experiences.
16
The Rigor/Relevance Framework
AAcquisition
BApplication
CAssimilation
DAdaptation
KNOWLEDGE
TAXONOMY
6
5
4
3
2
1
Evaluation
Synthesis
Analysis
Application
Understanding
Awareness
APPLICATION MODEL
1 2 3 4 5Knowledge Apply in
discipline
Apply acrossdisciplines
Apply toreal worldpredictable situations
Apply to real-worldunpredictable situations
International Center for Leadership in Education
Recommended Resource
Algebra Mastery Through Relevant Applications in Grades 6-10. International Center for Leadership In Education, www.LeaderEd.com $295.00.