1. Understanding velocity in one dimension David Trowbridge & Lillian McDermott University of Washington, Seattle

2. Success Factors in Science Interpreting reality Hypothesizing and deductive reasoning Ability to discriminate between different but related concepts ( Distance vs Velocity)

3. Criterion to assess the understanding of velocity Being ABLE (or not!!!!!) to interpret SIMPLE MOTIONS of real objects

4. Assessment Methods Piagetian motion tasks – presented no challenge Students Interviews: More quantitative version of interviews – revealed difficulties Speed Comparison tasks – revealed confusion between distance and velocity Written questions – confirmed the confusion between distance and velocity

5. More quantitative students interviews Uniform motion Problem: A train is traveling with a uniform velocity of 45 cm in 1.5 sec. How FAR!!!! did the train travel in 2.5 s ? Students’ typical answer: 45 cm for 1 ½ s … 22 cm for ¾ s (right??) I need one more sec... 11cm as I quartered it again… 45 + 22 + 11 = 78 cm WRONG Answer!!!!!

6. PROBLEM DETECTED by the more quantitative version of interviews Looking @ speeds as distances covered by time and having 2 different sets of numbers One for distances Another for times

7. Tasks that accompanied students’ interviews Speed Comparison Task 1 (see graphs) Speed Comparison Task 2 (see graphs)

8. PROBLEM DETECTED (Speed comparison interviews) Students associate same position with same velocity Students associate being ahead as having more speed Problems in accepting the concept of instantaneous velocity

9. Success (%) Prior/Post to Instruction: In-service elementary teachers 41 / ???? Academically disadvantaged students 53/90 General Physics students (SPS) 59/73 Calculus Physics students 68/92

10. Instructional Strategies for Success Regular dialogue with students addressed the difference between Position @ Velocity Daily work helped to clarify the distinction Labs designed to address conceptual difficulties Assessments also referred to this issue

11. Notes Acquisition of physical concepts strongly depend on the building of satisfactory connections between new concepts and students’ experiences. (Reformulation of students’ schemata) Technical words used by students often did not always correspond to an understanding of how they relate to reality. The precise use of vocabulary is a consequence of a better understanding of physical concepts. GRADING In a Physics Course does not necessarily correspond to the level of conceptual understanding achieved by students!!!!!