Creative Education
2012. Vol.3, No.4, 513-519
Published Online August 2012 in SciRes (
Copyright © 2012 SciRe s . 513
Teach Ourselves: Technology to Support Problem Posing in
the STEM Classroom
Carole R. Beal, Paul R. Cohen
School of Information: Science, Technolo g y and Arts, The Unive rsity of Arizona, Tucson, USA
Received May 18th, 2012; revised June 20th, 2012; accepted July 3rd, 2012
The theory of problem posing in mathematics education suggests that there are motivational and cognitive
benefits for students from creating their own problems, yet such activities are not typically integrated into
the traditional classroom. A field study was conducted to learn if middle school students (N = 224) could
successfully create math and science problems using a web-based content-authoring and sharing system,
and if the activity could be successfully integrated into classroom instruction. Over the twelve-week ac-
tivity, students created their own math and science problems, and solved problems authored by their peers.
Results showed that students were able to create problems successfully, but that problem solving domi-
nated problem posing activities. The process of reviewing and approving students’ work was also chal-
lenging for teachers. Both students and teachers reported strongly positive responses to the activity.
Keywords: Mathematics Education; Technology-Based Instruction; Middle School Students
There is an urgent need to improve educational outcomes in
math and science, and to encourage more K12 students to fol-
low a steady trajectory towards math and science careers. The
nation is facing a significant shortage of workers with skills in
science, technology, engineering, and mathematics (STEM).
Unfortunately, math and science achievement for middle and
high school students in the United States remains discourag-
ingly low (National Center for Education Statistics, 2011). In
international comparisons, US students score in the average
range overall, and much less well than students from other na-
tions that are comparable in terms of economic development
(Gonzales, Williams, Jocely n, Roey, Kastberg, & Brenwald, 2008;
Organization for Economic Cooperation and Development
[OECD], 2010). The United States also appears to have a lower
proportion of students who achieve scores in the very top levels,
relative to other nations (OECD, 2010).
A related problem is that although the national need for a
new generation of engaged, accomplished STEM learners is
great, relatively few students appear to be interested in these
field s. In sp it e of ma ny investments in STEM mentoring, public
service campaigns and other programs, participation remains
low. On average, American students are not very interested in
math and science, compared to students in other nations (Sjo-
berg & Schreiner, 2007). Many hold the perception that STEM
fields are difficult and dull (Davis et al., 2006). Students’ be-
liefs about the demands of STEM par ticipation are not curren tly
balanced by an awareness of the potential rewards of creative
intellectual engagement, and the excitement of discovery that
deeply engages STEM practitioners.
The low achievement and lack of interest in STEM by stu-
dents is especially striking when considered in relation to recent
changes in social and entertainment venues, which have in-
creasingly involved direct user creativity and active participa-
tion. Over the last decade, new technologies have led to an
explosion of user-created content posted, shared and viewed on
the Internet, including text, images, videos and even home-
authored games. The shift towards user-contributed content has
been termed “Web 2.0”. Web 2.0 technologies could lead to
significant changes to the existing model of education, in which
students would move from passive consumers of educational
resources that have been developed by others to creators of rich,
innovative and authentic STEM content that can be used to
develop and demonstrate their understanding, and to be shared
with others. More specifically, digital technologies now offer
students the opportunity to define their own questions, search
online repositories of digital resources and find information to
spark questions and find solutions, create instructional materials
in digital form, and then share their content with other learners
as well as their instructors. Unfortunately, although user-con-
tributed content has proliferated dramatically in students’ social
and entertainment worlds, very little activity involving user
content-creation has moved into the classroom. Classrooms
typically still follow a traditional model of instruction in which
students spend most of their time solving problems created by
others, including textbook publishers and teachers. Even when
students do create instructional materials such as presentations,
reports or papers, the only consumer is likely to be the teacher.
The idea of integrating more user-created content activities
into the classroom receives support from a theoretical frame-
work originating in the field of mathematics education: the
practice of problem posing. In problem posing, students gener-
ate new math problems and questions from available informa-
tion, or seek out new information about a topic of interest and
use the information to discover new numerical relations (Brown
& Walter, 1990; Cai, 1998; Cai & Huang, 2002; Knuth, 2002;
Mathematics Project, N.D.; Polya, 1962). Problem posing is
thus distinct from the much more common practice of requiring
students to solve problems that have been prepared by teachers
or that are presented in textbooks. Examples of specific prob-
lem posing strategies and activities that are mentioned in the
literature include (but are not limited to) creating an analogous
problem on a different topic or with different content, thinking
about how a problem connects with personal experience, think-
ing about how problem information that can be varied and con-
sidering what would happen if information was negated or re-
versed (“what if not?”), explaining how a problem should be
solved, changing a problem so that a different solution is re-
quired, or finding an alternative way to solve the same problem,
and applying mathematical operations to information gleaned
from real-world contexts.
Problem posing is argued to provide students with the op-
portunity to reflect on what is known and not known, to restate
a problem in a new equivalent form or to vary problems in new
ways, and to engage in explanation, all cognitive activities that
should deepen students’ understanding of the material (Arroyo
& Woolf, 2003; Bonotto, 2010; Contreras, 2003; Chi, 2009;
Cotic & Zuljan, 2009; English, 1997; Hausmann & Van Lehn,
2007; Hirashima, Yokoyama, Okamoto & Takeuchi, 2007;
Martinez-Cruz & Contreras, 2002; Mestre, 2002; Roscoe & Chi,
2007; Roy & Chi, 2005; Silver & Cai, 1996; Silver, Kilpatrick,
& Schlesinger, 1995; Xia, Lu, & Wang, 2008).
In addition to the hypothesized cognitive benefits, problem
posing has also been suggested to increase student motivation,
whereas solving problems defined by others day after day often
leads to student boredom (Contreras, 2003; English, 1997;
Knuth, 2002; Miller, 2006; Whitin, 2004). Teachers have re-
ported anecdotally that the activity of problem posing leads to
class engagement and higher interest in math, especially among
students who are not generally enthusiastic about math (Miller,
2006; Simic-Mullter, Turner, & Varley, 2009; Wilson, Fernan-
dez, & Hadaway, 2006; Verzoni, 1997). Problem posing has
also been suggested to reduce math anxiety because students
who define their own problems become more confident and feel
a greater sense of “ownership” about the topic (Miller, 2006).
Noted mathematics educator Lyn English reported, “… prob-
lem-posing can encourage children to take greater responsibil-
ity for their learning and dissipate common fears and anxieties
about mathematics learning” (1997: p. 173).
Although problem posing has considerable promise as an
innovative instructional activity, several researchers have re-
ported that it can be difficult for teachers to implement in the
classroom. For one thing, it is more work to review a set of
distinct problems created by different students, compared to
grading 26 identical worksheets or problem sets. In addition,
problem posing activities require good classroom management
skills, because students may be at quite different places in the
process of creating their materials. Finally, options for students
to share their work with peers and see what other students are
creating are relatively limited with traditional paper-based ac-
To address these implementation challenges, we developed
Teach Ourselves (TO), a web-based application that supports
student creation of instructional materials, along with tools for
sharing their content with others. The TO application is driven
by an economy in which students earn points both for creating
materials and for solving problems created by their peers, mak-
ing the activity game-like. Although the literature on problem
posing has focused primarily on mathematics learning, there is
no theoretical reason why the same principles of engagement
would not apply to problem posing in other domains. Thus, the
Teach Ourselves application includes multiple domains: math,
and life, earth, physical, space and applied science. Specific
features are described next:
Features of the Teach Ourselves Application
When the student logs in, he or she can decide to solve a
math or science problem that is already available in the system,
or to create a new one. Students who want to solve can view a
list of the problems that have been created by others, along with
their current points value. The list can be filtered by domain, or
by the points associated with the problems. If the student con-
tracts to solve a problem and does so successfully within three
attempts, he or she earns the contracted points value. Each in-
correct attempt elicits a brief feedback hint, and the problem
solver can also view a multimedia help file created by the
problem author. If the student does not enter the correct answer,
he or she can try the problem again (although the points value
may have fluctuated by the next try). Teach Ourselves includes
Web 2.0 features such as the ability for students to +1 (“like”) a
problem, make a comment, or flag it as inappropriate or incor-
rect in some way. To includes leaderboards that show users in
terms of overall points, points by domain, class, school and
other groupings, as well as individual progress summaries that
can be viewed by the student on his or her profile page.
Students can also earn points by creating their own problems;
in fact, in the TO economy, the points values for creating are
significantly higher to provide an incentive for students to cre-
ate content. The student contracts to create a problem at the
current value for that domain. The student works with a tem-
plate that includes areas for typing in a problem, adding a
graphic, entering two pieces of feedback that would be shown if
the future problem solver enters incorrect answers, and upload-
ing a help item (Birch & Beal, 2008). Help items can be pic-
tures, slide shows (created with PowerPoint), anim ations, screen-
cast or cell phone videos, or other media. The function of the
help item is to provide an explanation or worked example that
can guide the user to the solution without providing the answer.
Students are required to include source information and attribu-
tions for images or other media in corresponding areas of the
template. Students can preview their problem and save it to
work on another time, or they can submit it to their teacher for
review and approval.
When teachers log in, they can see a list of problems submit-
ted by their students that are waiting to be reviewed. Teachers
are provided with an integrated rubric to guide the process of
checking that each problem includes accurate content and ap-
propriate content, that the answer is correct along with any
associated units that need to be specified, and that the attribu-
tions for any source materials are listed. If the teacher approves
the problem, the student can publish it to the open market so
that it is available for other students to solve, and earns the
contracted number of points. Teachers can also return the prob-
lem to the author with comments and suggestions for revision.
Sample student-authored problems are available in the “try
this!” area of
We conducted a field study to learn if students would be able
to create instructional materials, including problems and help
items, andwhat the impact of the activity would be on student
engagement and interest. An additional study goal was to learn
if the activity could be implemented successfully by teachers.
Copyright © 2012 SciRe s .
Data were obtained from 224 middle school students (120
girls, 94 boys, and 10 students whose gender was not identi-
fied). Mean age of the participants was 13.8 years. Written
parent consent was obtained for the participants. Students
worked with TO as part of their math or science class instruc-
tion approximately once a week for twelve weeks. The activity
was directed by teachers (N = 9) who were recruited via an-
nouncements sent to list-services reaching math and science
teachers throughout the state. One group included two classes
of students (N = 58) with one teacher. Teachers received small
stipends in recognition of the out-of-class time involved in the
project, such as the professional development training and
completion of online surveys.
Teachers participated in one two-hour online training session
in which they were introduced to the theoretical framework and
the features of the Teach Ourselves web application, including
management of student accounts, and the rubric for the review
and approval of students’ work. Teachers then scheduled TO
days for the equivalent of one class period per week. The Teach
Ourselves application was seeded with 182 problems that had
been created by students in a small pilot study conducted in the
previous year.
The activity ran for approximately twelve weeks in each
classroom. Students’ activity within the Teach Ourselves web
application was automatically logged, including the points
earned from solving and creating problems, and social behav-
iors such as making comments, complimenting via the +1
mechanism, or flagging problems for a perceived issue. At the
conclusion of the activity, students were asked to complete an
online survey about their experience with the application, and
what other features they would like to see included. Teachers
also completed an exit survey about their perceptions of the
activity, and other features they would like to see.
Problem Solving
The mean number of problems solved by each student is
shown in Table 1 by domain. As may be seen in the table, the
most popular category was Space Science, followed by Math.
As indicated by the relatively high standard deviations, there
was a considerable range, from seven students who solved only
one problem to one student who solved 785 problems over the
course of the activity.
Problem Creating
Students produced a total of 961 new problems that were ap-
proved by their teachers and thus became available in TO for
other students to solve. The mean number of problems ap-
proved and published by each student is shown in Table 1. The
range was from 0 (N = 32 students) to 9 problems published (N
= 1 student). A key step in creating a problem involves the
creation of a help item that the solver can access for assistance
with the problem. An examination of the help files revealed that
76% involved a simple image file, 20% involved the creation of
Table 1.
Mean number of problems solved and created by domain.
Solved Created
Life Science 16.0 (22.1 )a 0.6 (1.2)
Earth Science 10.6 (14.5 ) 0.3 (0.7)
Physical Science 9.7 (16.2) 0.7 (1.2)
Space Science 36.2 (42.1) 0.7 (1.4)
Applied Science 11.7 (15.9 ) 0.3 (0.9)
Mathematics 21.9 (38.3) 1.7 (2.1)
Total 106.1 4.3
aStandard deviation s are shown in parentheses.
a PDF (usually from a PowerPoint slide show) and only 4%
involved an animation or video file.
In addition to the successfully approved and published prob-
lems, students had an average of 0.42 problems sitting in the
review queue waiting for teacher approval, and another 1.5
problems that had been submitted for review at least once but
then returned by the teacher for revision. Thus, overall, students
created about 6 problems (roughly 4 published, 1.5 in progress
and 0.5 waiting for approval).
Some students (N = 32, 14.3% of the total sample) did not
produce any published problems. Most of them (85%) were in
the group supervised by the teacher who had two classes of
participants. Although these students did not successfully pub-
lish any problems, they had submitted an average of 2.8 prob-
lems that had been returned for additional work, and at the end
of the study, they had an average of 1.4 problems that had been
submitted but remained in the review state. Thus, these students
did participate in the creation process although they were not
able to complete the cycle of obtaining approval. Their teacher
reported that she was not able to keep up with the review and
approval of her students’ work. As noted below, this teacher
also had the highest average number of submission attempts per
problem, typically approving a problem only after its third try.
Balance of Solving and Creating
There was considerable variation across the nine groups in
terms of the total points earned per student, and whether the
points were earned from solving versus creating problems.
Results by group are shown in Table 2. The pattern suggests
that even though creating problems earned more points per
problem, students who put more of their overall effort into
problem solving tended to accumulate more points.
Use of Social Media Fe at ures
When solving other students’ problems, students could com-
pliment (“+1”) a problem, and they also had the option to criti-
cize (“flag”) a problem. Students complimented 6% of the
problems they solved, and flagged 17% of them. The reasons
that problems were flagged included complaints that the in-
tended answer was flawed in some way (43% of flags, e.g., “I
put in Khronos but it said it was incorrect” when the expected
answer was “Chronos”), the help item was not helpful (25%,
e.g., “the help item isn’t helpful at all!!!”), the attribution was
wrong or not specific enough (9%, e.g., “Google is not an
Copyright © 2012 SciRe s . 515
Table 2.
Points earned by solving and creating problems by gr oup.
Group N Mean points per stude n t Solving Creating
Cougars 15 7372 74% 26%
Cobras 20 7108 82% 17%
Axolotls 22 6400 72% 27%
Condors 17 3749 65% 34%
Jaguars 26 3176 54% 45%
Eagles 32 2516 62% 37%
Mustangs 58 2188 89% 11%
Owls 10 1682 38% 61%
Hawks 24 1394 35% 64%
attribution its a search engine”), the problem contained a spell-
ing or grammatical error (4%) or another issue (16%, e.g., “to
The frequency with which problems were flagged varied
across the groups, suggesting that were may have been differ-
ences in the quality control imposed by teachers during the
review process. Table 3 shows the mean number of times a
problem was submitted for review before its final approval,
along with the mean number of flags per problem, presented for
each of the nine groups. As may be seen in the table, when
teachers approved problems after fewer than two submissions,
problems were more likely to be subsequently flagged as
flawed than problems from groups where teachers were not as
quick to approve problems.
Student Survey
The exit survey was completed by 180 students (80%). Stu-
dents were asked to review seven key components of Teach
Ourselves and indicate how important each component had
been. Results are shown in Table 4. Sample comments in-
cluded, “I like how it focuses on points and badges.” “I like that
you get ponts that motivaits me”. “I enjoyed extremely the
leader board I think it iskinda fun”. “I trying to git in first rank-
ing”. “I love Teach Ourselves. I like the thrill of getting points
and getting on the leader board.”
In response to the survey item about what additional features
students would like to see added to TO, the most popular were
“prizes and rewards” (75%), “an avatar” (66%), “option to
unpublish my work so I can edit it” (49%), and “more help with
making help items” (36%). (Students could choose more than
one feature so percentages do not sum to 100%). Examples of
comments include, “use points for avatar customization and
cool prizes,” “getting a prize for the most points,” “something
to reward your work, more points.”
Students were asked to indicate how much they felt that they
had learned from different activities in TO. Results are shown
in Table 5. Interestingly, students gave the lowest rankings to
making the help items for their problems, even though the
theoretical framework outlining the cognitive benefits of prob-
lem posing would suggest this should be the most beneficial
part of the process.
Another survey item asked if students would use TO outside
of school: 46% selected the option “Yes, I would use it on my
Table 3.
Mean number of problem s ubmissions and flags by group.
Group Submits Flags
Hawks 1.28 0.91
Axolotls 1.40 3.54
Cougars 1.76 2.53
Cobras 1.91 2.24
Condors 2.05 2.58
Owls 2.40 0.40
Eagles 2.48 0.60
Jaguars 2.50 0.77
Mustangs 3.21 0.15
Table 4.
Student responses regarding impor ta nce of TO components.
Important Sort of
Important Not
“Approved” comments 75% 22% 3%
Getting poi nts 72% 24% 5%
“Denied” comments 69% 23% 8%
Checking Le aderboard 49% 33% 18%
Discussing 49% 33% 17%
Flagging 46% 35% 18%
Giving +1s 39% 43% 18%
Table 5.
Percent of student respondents indicating amount learned from TO
A lot Some Very little
Solving problems 58% 36% 6%
Creating pr o blems 53% 40% 7%
Creating he lp it ems 29% 48% 22%
own,” 20% selected “Yes, I would use it with my friends,” and
34% selected, “No, I would never do it outside of school.” Thus,
over half indicated that they would consider using TO on their
own time. Sample comments included, “It’s fun. I do it after
school on my own, unlike ALEKS.” “IT’S SUPER FUN AND
HELPS ME LEARN!!!! “I like creating problems and solving
problems has become something I do everyday.” “It was fun
making my own problems.” “I think its coo l that w e get to create
problems that we want to do.” “I think that solving other people
problems, and other student's problems is really cool, because I
get to see what they have learned.” “It’s an easy way to learn
new cool things.” “I like the fact that all the problems are made
by other students and often they are very interes ti ng.”
Spontaneous Activity Ou t of Scho ol
An unexpected result was that a routine review of the log
Copyright © 2012 SciRe s .
files showed that students were using TO during out of school
hours, even though they were not required or expected to do so.
The greatest periods of activity occurred during school hours,
as expected. However, there was also a fair amount of activity
in the after-school hours (e.g., 4 pm through 10 pm). A review
of the discussion log files during this time period revealed
interchanges suggesting that students were motivated by the
goal of achieving extra points: “Guess what! Were in the top 10
on the lader board! It said Canyon Ridge ” “I’m in 25th place
of everybody I’m excited. How many points you got?” “I been
on a couple of hours but I have to get off you better not pass me
while I’m off”. “Yay I’m finally ahead of Lily!”
Teacher Exit Survey
Teachers also had a generally positive reaction to the activity.
Every one asked if they could continue to use Teach Ourselves
in the next school year. Responses to the exit survey are shown
in Table 6. On the survey, teachers we re also asked to describe
one thing they liked about the activity and one thing that they
felt needed to be improved. Positive comments included the
following: “It helped the students be more analytical about their
work.” “They had to decide the best way to express their ques-
tion and the appropriate format for the answer.” “It got the stu-
dents really thinking about the information and how to ask a
robust question about it instead of just telling someone the in-
formation.” “I enjoyed seeing the creative problems that were
Other comments by teachers included, “I’m amazed at how
creative and well- written some of my stud ents’ ques tions are.” “I
really think this is helping my students with their higher-order
thinking.” “Their excitement about the program was evident—
they LOVED having Teach Ourselves days.” “I witnessed my
students take pride on their work and become more confident
and sure of themselves.”
Teachers’ comments about what needed to be improved fo-
cused mostly on technical issues and features: “My students
experienced many problems with the application. They often
received error messages or the application was very slow. They
found this to be frustrating.” “Maybe a way to email students
from within the program in case they are not logging into TO,
you can still send a message to them about their problem.” “A
better way to express mathematical expressions using fractions,
exponents, and other math symbols.” “The help item input.”
“Have a way to block more than one account being made with
the same name and/or email.” In addition, two teachers com-
mented on the need to ensure that all published problems
Table 6.
Teacher responses on exit survey.
Do you think… No M aybeYes
Your students enjoyed TO? 0 0 100%
TO helped them learn math & science? 0 33 67
TO improved their higher-order thinking? 0 11 89
TO fits your instructional approach? 0 11 89
TO helped you assess thei r knowledge? 22 11 67
TO helped them learn digital citizenship? 11 22 67
were of high quality: “One thing that really needs to be im-
proved is controlling the quality of the problems being ap-
proved by mentors.” “The only thing is probably the criteria for
every approved problem.”
One goal of the study was to learn if students could success-
fully create math and science problems within the application.
The answer was a tentative “yes,” in that students did create an
average of four problems that successfully made it through the
entire creation cycle, with another 1 - 2 problems in the produc-
tion pipeline. However, the relative balance was clearly towards
solving problems that had been created by others rather than
authoring new content, even though the points value was de-
signed to be higher for creation than for solving. In some re-
spects this result may not be surprising given that the activity of
creating new content was unfamiliar to students. Creating con-
tent also involved multiple steps, including obtaining the ap-
proval to publish from the teacher, which took two attempts on
average. The overall pattern was also consistent with recent
observations, that even within the Web 2.0 community, most
users browse the available content rather than contribute to it
themselves. One observer noted the “1% rule,” meaning that
out of 100 people who are online, only one will actually con-
tribute content (Arthur, 2006). In addition, our analysis indi-
cated that students who accumulated the most points did so by
mostly solving, and that overall scores were lower when stu-
dents allocated more time to creating. One strategy may be to
increase the value associated with creating content relative to
solving more dramatically than was the case in this study, to
provide a stronger incentive for students to allocate more of
their time to the problem posing activity.
A second goal of the study was to learn if the activity would
engage students’ interest, as suggested by the problem posing
theoretical framework. The reaction was generally positive,
indicated by students’ responses on the end-of-activity survey,
their comments recorded in the logs of the online discussions,
and the spontaneous activity within the application during out-
of-school hours. Students reported that they liked earning
points for their work, even though there was nothing that stu-
dents could actually do with their points within the application.
The competitive component also seemed to be highly engaging,
perhaps because there were multiple opportunities to earn a
spot on one of the leaderboards. Teachers also reported that
they thought their students enjoyed the activity. One sent us a
note that a student had written in class: “I like how it makes
learning fun and I am d oing it on my own time. I think the idea of
it is genius!”
A third goal was to learn if the activity could be successfully
integrated into classroom instruction. Again, the answer ap-
peared to be a tentative “yes” in the sense that students and
teachers were able to use the application successfully. In fact,
students produced 961 math and science problems that are now
available to be solved by others. However, one lesson learned
was that the activity was demanding for teachers, even with the
integrated rubric and checklist to assist with the review process.
One teacher with a double class was not able to keep up with
managing her students’ work, resulting in a backlog of stu-
dent-created problems that remained in the queue in various
states of completion at the end of the study. Also, it became
clear that teachers play a critical role in quality control of stu-
Copyright © 2012 SciRe s . 517
dents’ work, and that the approval standards were not entirely
consistent from teacher to teacher. The teacher who could not
keep up was also the teacher whose standards were so high that
each approved problem was on its third submission. However,
the problems that she eventually did approve were rarely
flagged as flawed by other students. In contrast, teachers who
required fewer rounds of revision were more likely to have their
students’ problems flagged as flawed by others. One solution
might be to allow students to conduct initial reviews of peers’
work, perhaps by requiring approval by several peers before the
problem is submitted to the teacher for final approval and pub-
One finding of interest was that although the problem posing
theoretical framework emphasizes that the student should
deepen his or her own understanding through the activity, stu-
dents themselves reported that they learned most from solving
other students’ problems. However, conclusions are limited
because students did not necessarily solve and create problems
in the same domains. Thus, a student might have found it easier
to write problems about a topic that was well-known, but then
chosen to solve problems in a less familiar domain. Additional
research in which students are assigned to solve and create in a
specific domain might help to resolve this issue.
The greatest limitation of the study was that there was no as-
sessment of student learning. Teachers reported that they
thought students had learned, and that the activity had improved
their critical thinking skills. However, it is quite possible that
students were highly engaged with solving and creating but that
the activity did not necessarily deepen their knowledge of the
domain-specific material. One student commented on the sur-
vey, “I have learned a lot from solving problems but I usually
don't learn as much when creating my own problem because I
already know what my question is about.” Additional research
will be required to investigate this issue.
We would like to thank Jane Strohm, Tom Hicks and Wil-
liam Mitchell for their outstanding work on the project, and the
student and teacher participants for their enthusiastic support.
The research presented here was supported by the CS-STEM
program in the United States Defense Advanced Research Pro-
jects Agency. The views expressed here do not necessarily
represent those of the funding agency.
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