The 21st Century Context for Learning Mathematics

1. The 21st Century Context for Learning Mathematics From Transferable to Transferred

2. Blooms’ Taxonomy and Erickson’s Structure of Knowledge Evaluation Synthesis Depth TAAS/TAKS STAAR/EOC The Conceptual Age Analysis Application Comprehension TABS TEAMS Knowledge Facts Topics Concepts Generalization Principle Theory Level of Complexity Adapted from ILT to ILD, Moving Texas Forward 2002

3. Blooms’ Taxonomy and Erickson’s Structure of Knowledge Evaluation Depth Context (Transferred within or across Disciplines) Synthesis Process (Skills) Analysis Application Comprehension Big Ideas (Transferable) Content (Knowledge) Knowledge Facts Topics Concepts Generalization Principle Theory Level of Complexity Adapted from ILT to ILD, Moving Texas Forward 2002

4. 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. Comprehension Content (Knowledge) Knowledge Facts Topics

5. Mathematics Evaluation • So, we add depth by asking students to use higher level cognitive skills. • Students are asked to evaluate the results of transformations Depth Synthesis Process (Skills) Analysis Application 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. Comprehension Content (Knowledge) Knowledge Facts Topics

6. Mathematics • 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. Evaluation Depth Synthesis Process (Skills) Analysis Application Comprehension Big Ideas (Transferable) Content (Knowledge) Knowledge Facts Topics Concepts Generalization Principle Theory Level of Complexity Adapted from ILT to ILD, Moving Texas Forward 2002

7. Mathematics 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. Evaluation Depth Synthesis Process (Skills) Analysis Application Comprehension Big Ideas (Transferable) Content (Knowledge) Knowledge Facts Topics Concepts Generalization Principle Theory Level of Complexity Adapted from ILT to ILD, Moving Texas Forward 2002

8. Mathematics 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. Evaluation Depth Context (Transferred within or across Disciplines) Synthesis Process (Skills) Analysis Students will describe their process in designing their quilt square using applicable vocabulary,. Application Comprehension Big Ideas (Transferable) Content (Knowledge) Knowledge Facts Topics Concepts Generalization Principle Theory Level of Complexity Adapted from ILT to ILD, Moving Texas Forward 2002

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

10. 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

11. 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.

12. 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.

13. The 21st Century Context for Learning Mathematics From Transferable to Transferred