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A very influential paper on improving math
outcomes was published in 2008. The authors refused to divulge their data
claiming that agreements with the schools and Family Educational
Rights and Privacy Act (FERPA) rules prevented it.
- It turns out that this is not true.
- The claimed legal foundations do
not say what these authors said they do,though this is a widespread
misconception among education researchers.
When we found the identities of the schools by other means, serious
problems with the conclusions of the
article were quickly revealed.
- The 2008 paper was far from unique in this
respect.
- There are many papers that have had huge influences on K-12
mathematics curricula, and could not be independently verified because the
authors refused to reveal their data.
In this article we describe how we were
able to find the missing data for the 2008 paper. We discuss the
huge difficulties they revealed,
and point out the legal constraints that should
make it very difficult for authors of such papers to legally
withhold their data in the future.
By Wayne Bishop (with R. J. Milgram)
An error filled complaint was recently posted on the Stanford web-site of
Professor of Mathematics Education Jo Boaler,
[B1]. It begins
"Honest academic debate lies at the core of good
scholarship. But what happens when, under the guise of academic freedom,
people distort the truth in order to promote their position and
discredit someone's evidence? I have suffered serious
intellectual persecution for a number of years and decided it is now
time to reveal the details."
The irony of this claim of violation of honest academic debate - absolutely
essential to academia - is overwhelming. Herein are addressed
some of the more obvious points.
Abstract:
Jo Boaler, an Associate Professor at the Stanford School of Education
has just published an already well known study of three high schools that she called
Hillside, Greendale, and Railside. This study makes extremely strong claims for
discovery style instruction in mathematics, and consequently has the potential to
affect instruction and curriculum throughout the country.
As is the case with much education research of this nature, Prof. Boaler has
refused to divulge the identities of the schools to qualified researchers.
Consequently, it would normally be impossible to independently check her
work. However, in this case, the names of the schools were determined and
a close examination of the actual outcomes in these schools shows that
Prof. Boaler's claims are grossly exaggerated and do not translate into
success for her treatment students. We give the details in the following
article.
Click on More Education Box for More Education Papers
Abstract
In this paper we develop a systematic topological approach to
motion planning for a planar 2-R manipulator with point
obstacles. By considering components in the free space for the
second joint as the first joint varies, we build a two-dimensional array
representing the cells of the free space and an asociated graph
representing the boundaries of those cells.
Using this graph,
we derive a closed formula for the number of components of the
free space. At the same time we solve the motion existence
problem, namely, when are two arbitrary configurations in the
same component? If so, we develop two explicit algoritms for
constructing the path - a
middle path method and a linear interpolation method.
These
algorithms give complete solutions to the path planning problem.
Extensive examples are worked out which verify the correctness
and efficiency of the resulting program. Then we briefly discuss
how these methods generalize to a 3-R planar manipulator.
Abstract
In this note we analyze the topology of the spaces of configurations
in the euclidian space Rn of all linearly immersed polygonal circles with
either fixed lengths for the sides or one side allowed to vary. Specifically,
this means that the allowed maps
of a k-gon [ l1, l1, ..., lk] where the l_i are
the lengths of the successive sides, are specified by an ordered k-tuple
of points in Rn, P1, P1, ...,
Pk with d(Pi, Pi+1) = li,
0 < i < k and d(Pk, P1) = lk.
The most useful cases are
when n = 2 or 3, but there is no added complexity in doing the
general case. In all dimensions, we show that the configuration
spaces are
manifolds built out of unions of specific products
(Sn-1)H×R(n-1)(k-2 -H), over (specific) common
sub-manifolds of the same form or the boundaries of such manifolds.
Once the topology is specified, it is
indicated how to apply these results
to motion planning problems in R2.
In [M1] we studied the moduli space of serial revolute mechanisms in
R3. A particularly important subspace ℵ℘(n)
of n-link mechanisms that have at least one planar configuration,
(a configuration that lies entirely in a single plane R2 ⊂ R3),
was a major focus. ℵ℘(n) contains most of the
serial revolute mechanisms, including protein chains, that come up
in applications, and the set of critical points for the end-point
map of any configuration in ℵ℘f(n) was determined
in [M1].
Abstract: We start by giving a rigorous definition of serial mechanisms
with offset revolute joints. We give a number of examples, and introduce
the main problem of determining their workspaces and the inverse map. We
then determine the workspaces for all serial mechanisms with offset revolute
joints that are simple deformations of the backbones of proteins. This
work is in preparation for later work on the inverse map for protein
backbones.
Abstract: The problem of planning a collision-free
motions of a planar 3R-manipulator among point obstacles is
studied using techniques from topology and homology. By
completely characterizing the set of singular configurations (the
points in configuration space corresponding to an intersection of
the chain with itself or a point obstacle), the complementary
space, the free space, is also completely characterized. This
characterization dictates an exact, complete, motion planning
algorithm that builds on the authors' algorithm developed for
2R-manipulators. Results obtained with a preliminary
version of the algorithm are given.
Abstract: We study the path planning problem, without obstacles, for
closed kinematic chains with n links connected by spherical joints in space or
revolute joints in the plane. The configuration space of such systems is a real
algebraic variety whose structure is fully determined using techniques from
algebraic geometry and differential topology. This structure is then exploited
to design a complete path planning algorithm that produces a sequence of
compliant moves, each of which monotonically increases the number of links in
their goal configurations. The average running time of this algorithm is
proportional to n3. While less efficient than Lenhart's and Whiteside's O(n)
algorithm, our algorithm produces paths that are considerably smoother. More
importantly, our analysis serves as a demonstration for how to apply advanced
mathematical techniques to path planning problems. Theoretically, our results
can be extended to produce collision-free paths; paths avoiding both
link-obstacle and link-link collisions. An approach to such an extension is
sketched in §4.5, but the details are beyond the scope of this
paper. Practically, link-obstacle collision avoidance will impact the
complexity of our algorithm, forcing us to allow only small numbers of
obstacles with "nice" geometry, such as spheres. Link-link collision avoidance
appears to be considerably more complex. Despite these concerns, the
global structural information obtained in this paper is fundamental to
closed kinematic chains with spherical joints and can easily be
incorporated into probabilistic planning algorithms that plan
collision-free motions.
Abstract
This paper studies the structure of the inverse kinematics (IK) map of a
fragment of protein backbone with 6 torsional degrees of freedom. The
images (critical sets) of the singularities of the orientation and position
maps are computed for a slightly idealized kinematic model. They yield
a decomposition of SO(3) and R3 into open regions where the number
of IK solutions is constant. A proof of the existence of at least one
16-solution cell in R3×SO(3) is given and one such case is shown.
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