1. Mara AlagicCambridge July 20021 What Change Is Technology Bringing to Conceptual Understandings of Mathematical Ideas? Mara Alagic Wichita State University Wichita USA

2. Mara Alagic Cambridge July 20022 Paradigm Shift Teaching/learning of mathematics is influenced by –standards-based teaching (NCTM, 2000) –current findings about the nature of human learning (NRC, 2000) –development of the IC technologies, e.g. Pythagorean Theorem:

3. Mara Alagic Cambridge July 20023 Pythagorean Theorem n What does it say? n Pythagorean triples? n How does that make sense to you? n Proof anyone? n Demonstration? (Water-Demo, Behold)Water-Demo Behold

4. Mara Alagic Cambridge July 20024 Learners’ Meaning Making n Tool - knowledge construction n Information vehicles - exploring n Context - doing, representing and simulating n Social medium - conversation n An intellectual partner - reflecting

5. Mara Alagic Cambridge July 20025 Mathematics Teaching and Technology n Technology Principle: –"Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning" (NCTM, 2000) n Technology in context

6. Mara Alagic Cambridge July 20026 Teaching for Conceptual Understanding n Understanding as flexible performance (Perkins, 1993) n Computational versus calculational orientation (Thompson, Philipp, Thompson, & Boyd, 1994)

7. Mara Alagic Cambridge July 20027 Representations n Representing knowledge n Problem-based representations n Representation standard – both process and product n Things before words, concrete before abstract. (Pestalozzi,1803)

8. Mara Alagic Cambridge July 20028

9. Mara Alagic Cambridge July 20029 Conceptual Understanding via Multiple Representations n Perception-based representations n Multiple representations n External and internal representations n Problem-based representations n Translations among representations

10. Mara Alagic Cambridge July 200210 MENTAL MODELS/ INTERNAL REPRESENTATIONS EXTERNAL REPRESENTATIONS & TRANSLATIONS

11. Mara Alagic Cambridge July 200211 Impact of Technology on Student Learning...... depends on how the technology is used and therefore implies the need for different instructional processes and better preparation of teachers (Jonassen, Peck, & Wilson, 1999)

12. Mara Alagic Cambridge July 200212 Technology-based Environment: Cognitive tools n Dynamic geometry n Spreadsheets n Concept maps n Programming n Web Quests Computer algebra systems

13. Mara Alagic Cambridge July 200213 Question 1 How are technology-based representations of mathematical concepts different from standard representations? Explain in details an example appropriate for the level you are teaching (or will be teaching).

14. Mara Alagic Cambridge July 200214 Question 2 What do you think is the influence of technology-based representations on YOUR conceptual understanding of specific mathematical ideas and on the development of your pedagogical content knowledge?

15. Mara Alagic Cambridge July 200215 Question 3 What criteria are you as a teacher going to use to balance between technology- based and "other" representations?

16. Mara Alagic Cambridge July 200216 Question 4 How can technology help in differentiating instruction for individualized learning? Be specific.

17. Mara Alagic Cambridge July 200217 IF TIME,... "... the defining characteristic of knowledge workers is that they are themselves changed by the information they process" Kidd (1994, p. 186)

18. Mara Alagic Cambridge July 200218 IF TIME,... n http://education.wichita.edu/alagic/su mmer2002/752r/752r_first_page.htm http://education.wichita.edu/alagic/su mmer2002/752r/752r_first_page.htm n Promoting Appropriate Uses of Technology in Mathematics Teacher Preparation ( http://www.citejournal.org/vol1/iss1/c urrentissues/mathematics/article1.htm) http://www.citejournal.org/vol1/iss1/c urrentissues/mathematics/article1.htm