## Figures index

#### Loo Kang Wee, Tze Kwang Leong

American Journal of Educational Research. 2015, 3(2), 197-207 doi:10.12691/education-3-2-13
• Figure 1. LEFT to RIGHT a) Cart push on level slope slowing down at constant negative acceleration) b) Cart on slope speeding up at constant acceleration and c) Bouncing ball, complex accelerating motion divided into phases
• Figure 2. Students directed video analysis inquiring on the inelastic collision of 2 marbles on a track. Teal trail is the right moving marble and the Red trail is the right moving marble. Model A and B were added on later by the authors for teacher professional network learning purposes
• Figure 3. A dynamics lesson using Tracker again to illustrate frictional forces bridging from kinematics topics allows students to build understanding based on what they have already experience themselves in kinematics topics with the now more familiar Tracker horizontal displacement x vs time t, horizontal velocity vx vs t and horizontal acceleration ax vs t graphs
• Figure 4. Tracker DataTool showing a Fit Line of vx = -0.2456*t+0.7022
• Figure 5. Tracker Dynamics Model Builder interface showing mass m = 0.2 kg and force model fx = if (t<0.2,3.2*m,-0.246*m)
• Figure 6. Atwood Machine video showing 3 different mass, m carts, pulled by the same weight F (RIGHT) and their respectively accelerations ax
• Figure 7. N=273 whole cohort of students and N =30 for high-performing and mathematically-inclined class’ pre- and post- perception survey on a Likert scale from 1 (strongly disagree) to 6 (strongly agree), middle is 3.5 point. Note the mean and standard deviation are added for ease of interpreting the self reporting perception survey
• Figure 8. Sample screen shots of the students report on the complex roller blading motion broken into simpler 4 phases of motion as determined by the student, mentored by the teachers
• Figure 9. roller-blading (http://weelookang.blogspot.sg/2014/05/tracker-koaytzemin-student-video-roller.html) down an inclined slope video analysis by student with a model added by the teachers to guide-mentor the students where initial velocity, vx = -0.3991, vy = 0.7494, forces in x’ and y’ parallel and perpendicular to the slope directions are defined as Fx’ = g*sin(5.7*pi/180)-k*vx where pi =π = 3.14159, gravitational acceleration, g = 9.81, air drag coefficient k= 0.708 and lastly Fy’ = 0
• Figure 10. Carom stiker motion includes position A at t=0.9 s, striker disk (red) struck by finger, position B at t=1.0 s, striker disk strikes object disk A, position C at time = 1.3 s, striker disk hits the side of the board, position D at time= 1.5 s, striker disk strikes object disk B (magenta) and Position E at time= 3.8 s. Striker disk comes to rest
• Figure 11. The carom stiker disc motion (red) of motion A-B-C-D is modeled in Tracker model A (green) allowed for deeper mathematical and computational thinking. model A included position A-B-C-D modeled with the following variables contact force with (blue) disk at centre of carom board, Fx1 = -200, Fy1 = -20, contact force with upper wall of carom board Fx2 = -40, Fy2 = -520. Initial values are, time of model t = 0.042, horizontal x position, x = 0.0276, vertical y position y = 0.0252, horizontal velocity vx = 1.103, vertical velocity vy =1.3218. The dynamics model is fx = if(t<0.167,0,if(t<0.171,Fx1,if(t<0.458,0,if(t<0.462,Fx2,0)))) and fy = if(t<0.167,0,if(t<0.171,Fy1,if(t<0.458,0,if(t<0.462,Fy2,0))))
• Figure 12. On the left is the experimental setup and the close-up of the Car A and Car B with the balloon deflated. On the right is the data analysis of the motion of Car A moving to the right as it is propeled by the releasing of air from the inflated balloon
• Figure 13. Model A is a constant accelerating model (blue) that does not match the real motion of the balloon propeled car A. Model B is a data analysis evidence based model of dynamic force in the x direction fx = (-1.853E-1*t^2+2.551E-1*t+3.494E-1)*m where mass of Car A is found by the students to be m = 0.125 kg. Notice how Model A does not fit the real motion whereas the Model B is clearly a better model to describe the real motion of car A
• Figure 14. Officially in Tracker as Shared Library http://iwant2study.org/lookangejss/indexTRZdl.php