Dep

th

Level of ComplexityAdapted from ILT to ILD, Moving Texas Forward 2002

Facts Topics Concepts Generalization Principle

Synthesis

Evaluation

Analysis

Application

Comprehension

Knowledge

Blooms’ Taxonomy

and Erickson’s Structure of Knowledge

Theory

TABS

TEAMS

TAAS/TAKS

STAAR/EOC

The Conceptu

al Age

Dep

th

Level of ComplexityAdapted from ILT to ILD, Moving Texas Forward 2002

Facts Topics Concepts Generalization Principle

Synthesis

Evaluation

Analysis

Application

Comprehension

Knowledge

Blooms’ Taxonomy

and Erickson’s Structure of Knowledge

Theory

Content

Process

(Skills

)Context

(Tra

nsferred w

ithin or a

cross D

isciplines)

Big Ideas

(Tra

nsferable)

(Knowledge)

Facts Topics

Comprehension

Knowledge

Content

(Knowledge)

Mathematics

• Introduce ordered pairs on the coordinate grid• Students practice plotting points and labeling• Introduce transformations – including reflections,

rotations and translations • Student quiz utilizing a multiple choice format.

Transformations are identified in diagrams

and named using both conversational and

mathematical terms. Students are

assessed by matching transformations

and diagrams.

Dep

th

Facts Topics

Synthesis

Evaluation

Analysis

Application

Comprehension

Knowledge

Content

Process

(Skills

)

(Knowledge)

Mathematics

• So, we add depth by asking students to use higher level cognitive skills.

• Students are asked to evaluate the results of transformations

Skills are taught in isolation.

Transformations are modeled using

manipulatives, with and without grids.

Connections are rarely made between the

coordinate grid, transformations, similarity,

and congruence.

Dep

th

Level of ComplexityAdapted from ILT to ILD, Moving Texas Forward 2002

Facts Topics Concepts Generalization Principle

Synthesis

Evaluation

Analysis

Application

Comprehension

Knowledge

Theory

Content

Process

(Skills

)

Big Ideas

(Tra

nsferable)

(Knowledge)

• So, we add complexity by asking students to predict and analyze specific translations on a coordinate grid.

• Students have hands on experiences utilizing the coordinate grid to produce transformations and combinations of transformations.

• Students can now make the connection between the coordinate grid and the various transformations.

• Students hypothesize congruency and test their hypotheses to make conjectures.

Mathematics

Dep

th

Level of ComplexityAdapted from ILT to ILD, Moving Texas Forward 2002

Facts Topics Concepts Generalization Principle

Synthesis

Evaluation

Analysis

Application

Comprehension

Knowledge

Theory

Content

Process

(Skills

)

Big Ideas

(Tra

nsferable)

(Knowledge)

However, while our students have knowledge, skills, and understanding of transferable

concepts and generalizations . . .

they have never been asked to transfer these concepts and understandings within the

discipline of mathematics, or across academic disciplines.

Mathematics

Dep

th

Level of ComplexityAdapted from ILT to ILD, Moving Texas Forward 2002

Facts Topics Concepts Generalization Principle

Synthesis

Evaluation

Analysis

Application

Comprehension

Knowledge

Theory

Content

Process

(Skills

)Context

(Tra

nsferred w

ithin or a

cross D

isciplines)

Big Ideas

(Tra

nsferable)

(Knowledge)

So we ask our students to apply these ideas in a new context. Students are asked to design a quilt square utilizing a specific number of colors and transformations.

Students will describe their process in designing their quilt square using applicable vocabulary,.

Mathematics

So why do students need to know the connections between transformations and a coordinate grid?

THE GENERALIZATION: Spatial visualization is essential when . . .

• planning and designing transportation routes

• designing plans for a home or office building

• making purchases for furniture in a new restaurant or school

• creating animations

Mathematics : Deepening the Curriculum

• Teachers will utilize a 3-step method to ensure that students have opportunities to transfer knowledge in a real life context.

• Formative and summative assessments will be written to coincide with the scope and sequence and appropriate level of cognition.

• STAAR information will be shared to give background for our work.

In secondary math…

• The Math Workshop model will extend into middle school with America’s Choice throughout the year. Rich tasks have been identified within the curriculum to increase student engagement and participation in discourse.

• Increased opportunities for lesson study and formative assessment creation among the high schools will be supported in after-school meetings and teleconferences.