Understanding students’ hierarchical thinking: a view from continuity, differentiability and integrability

See article at: https://academic.oup.com/teamat/article/37/1/1/2975824

Understanding students’ hierarchical thinking: a view from continuity, differentiability and integrability

Eyup Sevimli

Teaching Mathematics and its Applications: An International Journal of the IMA, Volume 37, Issue 1, 5 March 2018, Pages 1–16, https://doi.org/10.1093/teamat/hrw028

26 February 2017

Article history


This report examines how students link continuity, differentiability and integrability concepts in their mind maps within the context of hierarchical thinking. A survey research design was used to obtain a large group of participants from three different mathematics departments in Turkey. While primary data acquired with the help of the concept map were analysed using descriptive statistics, secondary data acquired by way of interviews were analysed according to their content. The findings revealed that a great majority of the participants built wrong hierarchies between these concepts. The results also show that the students’ epistemological beliefs, or their sequential learning and instrumental understanding instead of relational understanding, hinder building correct hierarchies, and some suggestions show lecturers how to effectively use concept maps and counterexamples.

See article at: https://academic.oup.com/teamat/article/37/1/1/2975824


New NSF awards will bring together cross-disciplinary science communities to develop foundations of data science

Article from https://www.nsf.gov/news/news_summ.jsp?cntn_id=242888

News Release 17-079

New NSF awards will bring together cross-disciplinary science communities to develop foundations of data science

TRIPODS awards are NSF’s first major investment toward Harnessing the Data Revolution, one of ’10 Big Ideas for Future NSF Investments’

August 24, 2017

The National Science Foundation (NSF) today announced $17.7 million in funding for 12 Transdisciplinary Research in Principles of Data Science (TRIPODS) projects, which will bring together the statistics, mathematics and theoretical computer science communities to develop the foundations of data science. Conducted at 14 institutions in 11 states, these projects will promote long-term research and training activities in data science that transcend disciplinary boundaries.

“Data is accelerating the pace of scientific discovery and innovation,” said Jim Kurose, NSF assistant director for Computer and Information Science and Engineering (CISE). “These new TRIPODS projects will help build the theoretical foundations of data science that will enable continued data-driven discovery and breakthroughs across all fields of science and engineering.”

Technological advances and unprecedented access to computing infrastructure have resulted in an explosion of data from different sources. The availability of these data — their volume and variety, and the speed at which they are collected — is transforming research in all fields of science and engineering. Through Harnessing the Data Revolution, one of the “10 Big Ideas for Future NSF Investments,” the foundation seeks to support fundamental research in data-driven science and engineering; shape a cohesive, federated, national-scale approach to research data infrastructure; and develop a 21st century data-capable workforce.

The TRIPODS awards will enable data-driven discovery through major investments in state-of-the-art mathematical and statistical tools, better data mining and machine learning approaches, enhanced visualization capabilities and more. These awards will build upon NSF’s long history of investments in foundational research, contributing key advances to the emerging data science discipline, and supporting researchers to develop innovative educational pathways to train the next generation of data scientists.

“TRIPODS will accelerate the development of modern foundations of data science through a truly transdisciplinary collaboration between mathematicians, statisticians and theoretical computer scientists, while also creating opportunity for fundamental development to occur in finding solutions to important data science challenges in the domain sciences,” said Jim Ulvestad, NSF acting assistant director for Mathematical and Physical Sciences (MPS).

TRIPODS is a partnership between NSF’s CISE and MPS directorates. NSF’s Established Program to Stimulate Competitive Research (EPSCoR) also co-funded one of the projects.

A portfolio supporting another of NSF’s Big Ideas, Growing Convergent Research, contributed $1.1 million to the new TRIPODS awards, co-funding three of them. Convergence is the integration of knowledge, techniques and expertise from multiple fields to address scientific and societal challenges. To build an ecosystem that truly supports convergent science, NSF seeks to strategically invest in research projects and programs that are motivated by intellectual opportunities and important societal problems. The goal is that everyone, not just scientists and engineers, will benefit from the convergence of the physical sciences, biological sciences, computing, engineering and the social and behavioral sciences.

The TRIPODS Phase I awards announced today will support the development of small collaborative institutes. A future TRIPODS Phase II is planned to support a smaller number of larger institutes. Phase II will select awardees through a second competitive proposal process from among the Phase I institutes, as well as any new collaborative partners Phase I awardees bring on board.

The award titles, principal investigators and institutions for the TRIPODS Phase I projects are listed below:


Worm Uploaded to a Computer and Trained to Balance a Pole

The article is from https://www.tuwien.ac.at/en/news/news_detail/article/125597/

Worm Uploaded to a Computer and Trained to Balance a Pole

Is it a computer program or a living being? At TU Wien (Vienna), the boundaries become blurred. The neural system of a nematode was translated into computer code – and then the virtual worm was taught amazing tricks.

Die analoge, natürliche Version: C.elegans

It is not much to look at: the nematode C. elegans is about one millimetre in length and is a very simple organism. But for science, it is extremely interesting. C. elegans is the only living being whose neural system has been analysed completely. It can be drawn as a circuit diagram or reproduced by computer software, so that the neural activity of the worm is simulated by a computer program.

Such an artificial C. elegans has now been trained at TU Wien (Vienna) to perform a remarkable trick: The computer worm has learned to balance a pole at the tip of its tail.

The Worm’s Reflexive behaviour as Computer Code
C. elegans has to get by with only 300 neurons. But they are enough to make sure that the worm can find its way, eat bacteria and react to certain external stimuli. It can, for example, react to a touch on its body. A reflexive response is triggered and the worm squirms away.

This behaviour can be perfectly explained: it is determined by the worm’s nerve cells and the strength of the connections between them. When this simple reflex-network is recreated on a computer, then the simulated worm reacts in exactly the same way to a virtual stimulation – not because anybody programmed it to do so, but because this kind of behaviour is hard-wired in its neural network.

“This reflexive response of such a neural circuit, is very similar to the reaction of a control agent balancing a pole”, says Ramin Hasani (Institute of Computer Engineering, TU Wien). This is a typical control problem which can be solved quite well by standard controllers: a pole is fixed on its lower end on a moving object, and it is supposed to stay in a vertical position. Whenever it starts tilting, the lower end has to move slightly to keep the pole from tipping over. Much like the worm has to change its direction whenever it is stimulated by a touch, the pole must be moved whenever it tilts.

Mathias Lechner, Radu Grosu and Ramin Hasani wanted to find out, whether the neural system of C. elegans, uploaded to a computer, could solve this problem – without adding any nerve cells, just by tuning the strength of the synaptic connections. This basic idea (tuning the connections between nerve cells) is also the characteristic feature of any natural learning process.

A Program without a Programmer
“With the help of reinforcement learning, a method also known as ‘learning based on experiment and reward’, the artificial reflex network was trained and optimized on the computer”, Mathias Lechner explains. And indeed, the team succeeded in teaching the virtual nerve system to balance a pole. “The result is a controller, which can solve a standard technology problem – stabilizing a pole, balanced on its tip. But no human being has written even one line of code for this controller, it just emerged by training a biological nerve system”, says Radu Grosu.

The team is going to explore the capabilities of such control-circuits further. The project raises the question, whether there is a fundamental difference between living nerve systems and computer code. Is machine learning and the activity of our brain the same on a fundamental level? At least we can be pretty sure that the simple nematode C. elegans does not care whether it lives as a worm in the ground or as a virtual worm on a computer hard drive.

Original publication

Picture downloadContakt:Dott.mag. Ramin HasaniInstitute of Computer EngineeringTU WienTreitlstraße 3, ViennaT: +43-1-58801-18228ramin.hasani@tuwien.ac.at

Some of the Surprising Reasons Why Students Drop Out of School

See full article at: http://neatoday.org/2017/12/19/why-students-drop-out-of-school/

It is sad to hear that “Math, in particular, seemed to be the academic trip wire where they stumbled on and never recovered from” and that “Algebra was often the culprit”.

Students and Social IssuesDropouts

December 19, 2017 • 10:20AM
322 4

Some of the Surprising Reasons Why Students Drop Out of School

By Cindy Long

why students drop out of school“Why We Drop Out”: Understanding and Disrupting Student Pathways to Leaving School by Deborah L. Feldman, ‎ Antony T. Smith,‎ and Barbara L. Waxman, recounts the compelling stories of kids who explain in their own words why they decided to leave school.

NEA Today spoke with Feldman to talk about what she learned from her interviews with the more than 50 young people who dropped out of high school.

What surprised you most about your findings in your interviews with the students?

Deborah Feldman: What really surprised us was that the overwhelming majority of the youth we interviewed really liked elementary school. Another surprise was how many were willing to blame themselves and how much they deeply regretted their actions that led to dropping out. Finally, what surprised me personally was the lack of interventions. We never know the full story, only the kids’ perspective, but very few recalled having any official interventions for truancy, or interventions from parents or the school.

They seemed to be forgotten by the schools or consciously ignored. We don’t know, but we suspect that in some districts, if a kid isn’t doing well and is a problem, it’s easier to let them slip away. Around the country, districts are cash-strapped and don’t have the resources to follow up on kids with numerous absences.

What was a common reason for dropping out?

DF: There were very distinct patterns we see with kids starting to pull away usually in middle school. The through line in many of their stories was some kind of academic challenge that undermined their faith in themselves as learners, that then led to helplessness and hopelessness about their ability to be a student, which was their primary job in life. Math, in particular, seemed to be the academic trip wire where they stumbled on and never recovered from. Algebra was often the culprit. They developed an “I’m no good at math” sensibility and when they started believing they weren’t able to succeed, they started skipping.

See the rest of the article at: http://neatoday.org/2017/12/19/why-students-drop-out-of-school/

An Insider’s Take on Assessment: It May Be Worse Than You Thought

See full article at: https://www.chronicle.com/article/An-Insider-s-Take-on/242235/

An Insider’s Take on Assessment: It May Be Worse Than You Thought

By Erik Gilbert January 12, 2018

Katherine Streeter for The Chronicle

No doubt many of you will spend part of the month of January looking over assessment material from the fall semester. Equipped with some pre- and post-tests, a couple of artifacts, a rubric, a curriculum map, and, perhaps, a little bourbon, you will study your data carefully, make a few quick inferences and then identify a minor problem that you can address by making equally minor changes to your course or program.

However, you may find that upon close examination the data don’t seem to be saying anything at all to you. You may even be tempted to just make something up. If you do go that route, it’s probably because you have concluded that assessment data do not tell you anything useful about your program, so there is no harm in fudging your analysis of the data.

If that was you, don’t worry. It turns out that the assessment program your college imposed on you was probably never going to improve anything. A new article by an assessment insider explains why this is so and suggests that assessors have known for sometime now that assessment does not work.

The article, in Intersection, the journal of the Association for the Assessment of Learning in Higher Education is by David Eubanks, assistant vice president for assessment and institutional effectiveness at Furman University and a board member of the association. In it Eubanks details the methodological flaws that are inherent to assessment and argues that because of the broad scale on which assessment is done, few of the methods employed by social-science research are used.

Read the rest of the article at: https://www.chronicle.com/article/An-Insider-s-Take-on/242235/

Topological Data Analysis

See Full Article at Wikipedia: https://en.wikipedia.org/wiki/Topological_data_analysis

In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools.

The initial motivation is to study the shape of data. TDA has combined algebraic topology and other tools from pure mathematics to allow mathematically rigorous study of “shape”. The main tool is persistent homology, an adaptation of homology to point cloud data. Persistent homology has been applied to many types of data across many fields. Moreover, its mathematical foundation is also of theoretical importance. The unique features of TDA make it a promising bridge between topology and geometry.

See Full Article at Wikipedia: https://en.wikipedia.org/wiki/Topological_data_analysis

Laura Kipnis Says She Faced Another Title IX Investigation, This Time for Her Book

See full article at http://www.chronicle.com/blogs/ticker/laura-kipnis-says-she-faced-another-title-ix-investigation-this-time-for-her-book/

September 20, 2017 by Andy Thomason

Laura Kipnis Says She Faced Another Title IX Investigation, This Time for Her Book

Laura Kipnis, the Northwestern University professor whose Chronicle article titled “Sexual Paranoia Strikes Academe” sparked a chain of events that led to a Title IX investigation of her, faced another inquiry, The New Yorker reports. That one was prompted by the publication of her book Unwanted Advances: Sexual Paranoia Comes to Campus, she said.

In her initial essay in The Chronicle, Ms. Kipnis argued that a culture of protection rather than empowerment around sexual issues on campuses was wrongheaded. The response to that essay included the filing of a Title IX complaint against Ms. Kipnis, alleging, in part, that the essay had had a chilling effect on complaints, and an investigation was opened. She chronicled the proceedings in another Chronicle essay, “My Title IX Inquisition,” and was cleared of wrongdoing.

But over the summer, The New Yorker reports, Ms. Kipnis faced another university investigation, prompted by the publication of her new book. The allegations, according to the magazine, were similar to those of the first complaint. In a statement to the university, Ms. Kipnis wrote that “these complaints seem like an attempt to bend the campus judicial system to punish someone whose work involves questioning the campus judicial system, just as bringing Title IX complaints over my first Chronicle essay attempted to do two years ago.”

She was cleared of violating university policy, the magazine says. Northwestern did not respond immediately to The New Yorker’s request for comment.