1. Introduction 1.How do you use technology now? 2.What helps? 3.What hinders? Definition of Technology Computers Software Internet Digital cameras and camcorders Robotics Audio-visual (movies, podcasts, etc.) Voice recorders – iPod with recorder AlphaSmart word processor Social Networking… Other....

2. What Technology Has to Offer Authentic challenging tasks Active learning - students benefit from exposure to real world problems, scientific modeling, feedback from peers and experts and global communities. http://www.cofc.edu/bellsandwhistles/research/retentionmodel.html Beyond Bells and Whistles: Affecting Student Learning Through Technology

3. What Technology IS … Constructivist, higher level thinking, communication, creation of original work, and problem solving in non- routine ways and authentic ways Technology as a means of providing support, opportunity and meaning.

4. Learning and Retention Rates Beyond Bells and Whistles: Affecting Student Learning Through Technology http://www.cofc.edu/bellsandwhistles/research/retentionmodel.html

5. ISTE – NETS Standards International Society for Technology in Education National Education Technology Standards −Students −Teachers −Administrators Most states have adopted, adapted or referenced in their own state standards ISTE is in the process of updating their standards

6. NCTM Content Standards Numbers and Operations Algebra Geometry Measurement Data Analysis and Probability www.nctm.org

7. NCTM Process Standards Problem Solving Reasoning and Proof Communications Connections Representations www.nctm.org

8. Where Do I Start? 1.What content, topic, or lesson should I start with? 2.What technology may help students to better understand? 3.Where can technology enhance the content, process or products in my classroom? 4.What technology can assist in meeting student readiness, interests, or learning styles? Who will assist me? Who will support me? What more do I need to know to get started? −Resources −Information −Access

9. Changing the Process... Math concepts −Virtual manipulativesVirtual manipulatives

10. Integrating Technology How Do I Do That?

11. Technology can be used as a tool to differentiate Content, Process, Product, and Environment Technology can be used in key components of differentiation: readiness, interest, learning styles Product Environment Standards Process Readiness Content Learning Styles Interest

12. Content, Process, Product... Content −Everyone is learning the same concept, but using different levels of complexity, depth or sophistication Process −Everyone is learning the same concept, but using different methods to learn it Product −Everyone is using different ways of showing what they know.

13. Where’s the Content?

14. Steps to Designing Tiered Lessons 1.Identify the grade level and subject for which you will write the lesson. 2.Identify the standard (national, state, district, etc.) that you are targeting. 3.Identify the key concept and generalization. 4.Be sure students have the background necessary to be successful in the lesson. Provide needed scaffolding. 5.Determine in which area you will tier. −Content, process, product 6.determine the type of tiering you will do: Readiness, interest, learning profile 7.based on your choices above, determine how many tiers you will need and develop the lesson. −Differentiation means doing something different--qualitatively different −Secondly, be sure each tier is doing moderately challenging, respectful work. We don’t want one group doing blackline practice sheets and another doing Japanese cooking! 8.develop the assessment component to the lesson. −formative, summative, or a combination of both. For more information on tiering, please contact the Center for Gifted Studies and Talent Development at 1-800-842-4251.

15. Technology Integration ideas for teachers Technology Integration for Teachers −resources for reading and doing A Different Place Tammy’s Technology Tips 4Teachers Education World – Technology in the Classroom

16. Bloom’s Digital Taxonomy

17. Mathematics Mathematical Interactive Tools The Math Forum @ Drexel University A Creative Encounter of the Numerical Kind Language Arts Carol Hurst’s Children’s Literature Thinkmap Visual Thesaurus

18. The Business of Schools The Business of Schools Is to produce work that engages students, that is so compelling that students persist when they experience difficulties, and that is so challenging that students have a sense of accomplishment, of satisfaction—indeed, of delight—when they successfully accomplish the tasks assigned. Inventing Better Schools * Schlechty

19. Pedagogical Content Knowledge Teaching requires a structured knowledge network of specific subject matter facts, skills, and concepts that are intimately connected. (Schulman 1986, p. 9)

20. Mathematics Knowledge for Teaching (MKT) In the context of teaching math, PCK requires: (1)a conceptual understanding of the core knowledge; (2)fluency in carrying out procedures; (3)strategic competencies in planning effective instruction; (4)adaptive reasoning in justifying and explaining one’s instructional practices; and (5)a productive disposition towards mathematics, teaching, learning, and the improvement of practices. (Hill & Ball 2004, NRC 2001)

21. Technological Pedagogical Content Knowledge (TPCK) Effective teaching with technology requires “understanding the mutually reinforcing relationships between all three elements taken together to develop appropriate, context specific strategies and representations”. (Mishra & Koehler 2006, p. 27).

22. Research Questions 1.What are the perceived benefits relating to the development of participants’ technology, pedagogy, and content knowledge through designing digital learning objects for mathematics? 2.How does the Math Through Computers class depict the nature of preservice teachers’ Technological Pedagogical Content Knowledge for teaching mathematics? 3.In which ways do the specific components of the digital learning objects reflect preservice teachers’ Mathematics Knowledge for Teaching?