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.