In a Montessori preschool classroom, students work independently on tasks that absorb their attention in part because the apparatus are carefully designed to make mistakes directly observable and limit exploration to one aspect or dimension. Control of error inheres in the apparatus itself, so that teacher intervention can be minimal.1 Inspired by this example, I created a robotic kinematics apparatus that also shapes the inquiry experience. Students program the robot by drawing kinematic graphs on a computer and then observe its motion. Exploration is at once limited to constant velocity and constant acceleration motion, yet open to complex multi-segment examples difficult to achieve in the lab in other ways. The robot precisely and reliably produces the motion described by the students' graphs, so that the apparatus itself provides immediate visual feedback about whether their understanding is correct as they are free to explore within the hard-coded limits. In particular, the kinematic robot enables hands-on study of multi-segment constant velocity situations, which lays a far stronger foundation for the study of accelerated motion. When correction is anonymous—just between one group of lab partners and their robot—students using the kinematic robot tend to flow right back to work because they view the correction as an integral part of the inquiry learning process. By contrast, when correction occurs by the teacher and/or in public (e.g., returning a graded assignment or pointing out student misconceptions during class), students all too often treat the event as the endpoint to inquiry. Furthermore, quantitative evidence shows a large gain from pre-test to post-test scores using the Test of Understanding Graphs in Kinematics (TUG-K).

1.
A. S.
Lillard
,
Montessori: The Science Behind the Genius
(
Oxford University Press
,
2007
), pp.
174
175
.
2.
R. J.
Beichner
, “
Testing student interpretation of kinematics graphs
,”
Am. J. Phys.
62
,
750
(Aug.
1994
).
3.
D. E.
Trowbridge
and
L. C.
McDermott
, “
Investigation of student understanding of the concept of velocity in one dimension
,”
Am. J. Phys.
48
,
1020
(Dec.
1980
).
4.
D. E.
Trowbridge
and
L. C.
McDermott
, “
Investigation of student understanding of the concept of acceleration in one dimension
,”
Am. J. Phys.
49
,
242
(March
1981
).
5.
L. C.
McDermott
,
M. L.
Rosenquist
, and
E. H.
van Zee
, “
Student difficulties in connecting graphs and physics: Examples from kinematics
,”
Am. J. Phys.
55
,
503
(June
1987
).
6.
S.
Guidugli
,
C. Fernandez
Gauna
, and
J.
Benegas
, “
Graphical representations of kinematical concepts: A comparison of teaching strategies
,”
Phys. Teach.
43
,
334
(Sept.
2005
).
7.
R.
Hake
, “
Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics
,”
Am. J. Phys.
66
,
64
(Jan.
1998
).
8.
M.
Wells
,
D.
Hestenes
, and
G.
Swackhamer
, “
A modeling method for high school physics instruction
,”
Am. J. Phys.
63
,
606
(July
1995
).
9.
M.
Rosenquist
and
L.
McDermott
, “
A conceptual approach to teaching kinematics
,”
Am. J. Phys.
55
,
407
(May
1987
).
10.
R. K.
Thornton
and
D. R.
Sokoloff
, “
Learning motion concepts using real-time microcomputer-based laboratory tools
,”
Am. J. Phys.
58
,
858
(Sept.
1990
).
11.
R. J.
Beichner
, “
The impact of video motion analysis on kinematics graph interpretation skills
,”
Am. J. Phys.
64
,
1272
(Oct.
1996
).
12.
For example, The Ultimate Graphing Challenge, http://www.theuniverseandmore.com/; the Phet Moving Man simulation, http://phet.colorado.edu/en/simulation/moving-man; and the Graphs and Tracks Model by Wolfgang Christian and Mario Belloni, http://www.compadre.org/osp/items/detail.cfm?ID=12023.
13.
J.
Laverty
and
G.
Kortemeyer
, “
Function plot response: A scalable system for teaching kinematics graphs
,”
Am. J. Phys.
80
,
724
(Aug.
2012
).
14.
R.
Mitnik
,
M.
Recabarren
,
M.
Nussbaum
, and
A.
Soto
, “
Collaborative robotic instruction: A graph teaching experience
,”
Comp. Educ.
53
,
330
342
(
2009
).
15.
Currently available for $129.99 from Parallax, Inc., http://www.parallax.com/product/28136.
16.
The Scribbler, as most educational robots, comes preloaded with software designed to help students learn robotics, develop problem-solving and programming skills, and apply a little physics, by programming the robot to perform autonomous tasks such as follow a maze, avoid obstacles, or trace a geometrical figure. For these purposes, it does not require a mathematically precise motor driver. As long as the robot completes the desired task in a reasonable (or fastest possible) time, it does not matter whether the velocity or acceleration are constant. However, my goal was to use a robot as a physics apparatus rather than to teach robotics with physics applications. In the development process, I ruled out more than a dozen other possibilities, including building my own robot from parts, because the hardware lacked the desired precision, or the microprocessor and its available programming languages were not up to the task.
17.
VPython version 6 is available from http://www.vpython.org and comes with the wxPython module. These were convenient for creating the graphical user interface because I was already familiar with them from other physics education applications. c.f. R. Chabay and B. Sherwood,
Matter and Interactions
(
Wiley
,
2010
).
18.
My blog at http://aphysicsmicrocosm.wordpress.com/ describes the lessons in more detail. A school site license for the software is currently available for $100 by contacting me by email at [email protected], and will soon be available through an online storefront connected to the blog. It installs all components with a single standard windows installer. You may also contact me for a version that runs on Mac computers, although it is not fully featured and requires some minimal programming experience to install, as I have not yet packaged it in a professional installer.
19.
The curriculum materials are available for download from the American Modeing Teachers Association at http://modelinginstruction.org/teachers/resources/, and for AMTA members is also available in the resource section of the members area at https://www.eweblife.com/prm/AMTA.
20.
When they subsequently encounter difficulty, it is usually sufficient to suggest students draw a one-segment approximation to the position-versus-time graph (and note whether its slope is positive or negative) followed by a two-segment approximation (and note whether the magnitude of the slope is increasing or decreasing). Since they've already seen a lengthier limiting process, most students are then able to draw or interpret the curved position-versus-time graph.
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