This post is a summary and reflection on the webinar “Data Science Education in Traditional Contexts”. The webinar was hosted on Aug 28th by the South Big Data Innovation Hub as part of their *Keeping Data Science Broad: Bridging the Data Divide *series. You can watch the entire webinar here. The webinar consisted of 5 speakers and a discussion section. I’ve provided a short summary of each panelist’s presentation and the questions discussed at the end. The speakers, in order were:

- Paul Anderson, College of Charleston
- Mary Rudis, Great Bay Community College
- Karl Schmitt, Valparaiso University
- Pei Xu, Auburn University
- Herman “Gene” Ray, Kennesaw State University

The first speaker was Paul Anderson, Program Director for Data Science at the College of Charleston. His portion of the presentation runs from 0:01:50-0:13:45, and expands on three challenges he has experienced, (1) being an unknown entity, (2) recruiting, and (3) designing an effective capstone. His first point, being an unknown entity, impacts a broad range of activities related to implementing and running a data science program. It can cause a challenge when trying to convince administrators to support the program or new initiatives (such as external collaborations). It means that other disciplines may not be interested in developing joint course work (or approving your curricular changes). His second point discussed what he’s learned from several years of working on recruitment. His first observation here ties to his first overall point: If your colleagues don’t know what data science is, how are most high school students to know (or even your students)?. This has led him to have limited success with direct recruitment from high schools. Instead, he’s focused on retooling the program’s *Introduction to Data Science Course *to be a microcosm of his entire program, both in terms of process and rigor. He’s also worked to make his program friendly to students switching majors or double majoring by having limited prerequisites. His final portion discussed the various forms of capstone experiences Charleston has experimented with. Starting from an initially 1-to-1 student-faculty project pair, moving into more group-based with a general faculty mentorship model. If you are considering including a capstone experience (and you should!) it’s probably worth listening to this portion. However, not all colleges or universities will have sufficient students/faculty to move into their final model.

The second speaker was Mary Rudis, Associate Professor of Mathematics at Great Bay Community College. Her portion runs 0:14:25-0:19:19 and 0:20:46-0:29:08. A significant portion of her presentation outlines the large enrollment and performance gap of non-white and first generation college students. Dr. Rudis saw building both an Associate Degree in Analytics, and a Certificate in Data – Practical Data Science as the best way to combat these gaps. In researching the state of jobs/education she found that community college students were struggling to compete for the limited internships and entry-level job opportunities available in data science, compared to 4-yr college students (like local M.I.T. students). Most companies in terms of hires were looking for Master’s level education, or significant work experience in the field. To help her students succeed, she built an articulation program with UNH-Manchester so that upon final graduation, students originally enrolled at GBCC would be full-qualified for the current job market.

The third speaker was Karl Schmitt, Assistant Professor of Mathematics and Statistics, Affiliate Professor of Computing and Information Sciences, and the Director of Data Sciences at Valparaiso University. His presentation runs from 0:30:30 – 0:45:20. The core of the presentation expanded on Dr. Anderson’s first point about data science being an unknown entity. He sought to provide ideas about how to differentiate programs from other similar programs, both at the college/university level, but also make the programs different when looking outside his own institution. Valparaiso has 6 data-focused programs:

- B.S. in Data Science
- B.A./B.S. in Statistics
- Minor in Applied Statistics
- B.A. in Business Analytics
- Masters of Science in Analytics and Modeling
- Graduate Certificate in Applied Econometrics and Data Science Foundations Using SAS

His talk described how the programs can be differentiated in terms of the data user/professional that the program trains, and also in terms of course content and focus. He also talked about how Valpo is differentiating its program from other schools with a focus on Data Science for Social Good. This has been achieved in part by seeking industry partners from the government and non-profit sectors, rather than traditional industrial partners.

The fourth speaker was Pei Xu, Assistant Professor of Business Analytics, Auburn University. Her portion of the presentation runs from 0:46:05 – 0:57:55 and describers Auburn’s undergraduate Business Analytics Degree. Auburn’s curriculum is designed around the data science process of **Problem Formulation -> Data Prep -> Modeling -> Analysis -> Presentation**. Each of the core classes covers 1-2 stages of this process, with the specialized degree courses typically beginning in a student’s sophomore year. Their program also actively engages many businesses to visit and provide information sessions. Dr. Xu detailed 4 challenges she’s faced related to their program. First, she has found it hard to recruit qualified faculty for teaching courses, which she’s overcome by progressively hiring over the last few years. She has also found many students to be turned away by the high quantitative and computational nature of the program. This has been addressed by building a stronger emphasis on project-based learning and more interpretation than innovative process development. Third, she discussed how many of the core courses in their program have significant overlap between courses. For example, many courses in different areas all need to discuss data cleaning/preparation. Auburn’s faculty has spent significant curriculum development time discussing and planning exactly what content is duplicated and where. Finally, deciding between the various analytics tools for both the general curriculum and specific classes has proved challenging (you can see an extended discussion by me of Python/R and others in here).

The fifth speaker was Herman “Gene” Ray, Associate Professor of Statistics and Director for the Center for Statistics and Analytics Research, Kennesaw State University. His presentation is from 0:58:36 – 1:07:35 and focuses on KSU’s *Applied Statistics Minor*. KSU’s program strongly focuses on domain areas, with most courses having a high-level of applications included and types of experiential learning opportunities. Additionally, almost all their courses use SAS in addition to introducing their students to a full range of data science software/tools. The first experiential learning model KSU uses is an integration of corporate data-sets and guided tasks from business. The second model is a ‘sponsored research class’ with teams of undergraduates led by a graduate student on corporation provided problems or data. Gene provided extended examples about an epidemiology company and about Southron Power Company. The key benefits KSU has seen are that students receive real world exposure, practice interacting with companies, potentially even receiving awards, internships, and jobs. The largest challenge to this experiential learning model is that is requires a significant amount of time, first to develop the relationships with companies, managing corporate expectations, and finally in the actual execution of projects for both faculty and students.

The additional discussion begins at 1:08:32. Rather than summarize all the responses (which were fairly short), I’m simply going to list the questions, in-order as they were answered and encourage interested readers to listen to that portion of the webinar or stay tuned for follow-up posts here.

- What can High Schools do to prepare students for data science?
- What sort of mix do programs have between teaching analysis vs. presentation skills?
- Is it feasible for community colleges to only have an
*Introduction to Data Science*course? - How have prerequisites or program design affected diversity in data science?
- How is ethics being taught in each program? (and a side conversation about assessment)

Keeping Data Science Broad: Data Science Education in Traditional Contexts | Aug 31, 2017 | Virtual

This webinar will highlight data science undergraduate programs that have been implemented at teaching institutions, community colleges, universities, minority-serving institutions, and more. The goal is to provide case studies about data science degrees and curricula being developed by primarily undergraduate serving institutions. Such institutions are crucial connectors in the establishment of a robust data science pipeline and workforce but they can have different constraints than large research-focused institutions when developing data science education programming.

More details about the webinar will be posted soon on the South Hub website: http://www.southbdhub.org/datadivideworkshop.html

]]>This is a challenging question, made even more difficult if LA actually is a mathematics program’s introduction to proofs for majors. Generally speaking, the disciplines that use mathematics as a tool don’t particularly value this proof-based approach. Additionally, traditional proof-based mathematics are almost inherently non-computational, in the sense that very few proofs of traditionally taught concepts require the use of a computer, or complex computations not possible by hand. This leads educators to spend significant portions of a course teaching things like row-operations which are then executed by hand. This leads to a (potentially) deep disconnect between many of the concepts and skills learned and the actual application of LA to solve problems.

Recognizing this disconnect, I’ve long wanted to develop a “Computational Linear Algebra” course, that potentially builds on a traditional LA course. A course that takes all the basic linear algebra but moves it into the computational realm, highlighting key applications and algorithms. I haven’t had that chance, but this week I got forwarded a blog post from a colleague that got me revved up again about this idea. Jeremy Howard and Rachel Thomas of fast.ai have just released a new course that exemplifies this idea.

The course takes a non-traditional (for math) approach to learning, focusing on a “try it first” mentality. This sort of idea has a lot of support from within CS as an alternative way to teaching introductory programming. So, while it might seem a bit unusual for a math course, in the crossover world between mathematics and computer science (where the topic lives) it makes a ton of sense. Rachel does a great job of motivating and explaining their approach in this other blog-post from fast.ai.

I have not had the time yet to dive into their materials, but will report back again when I do. Or, feel free to contact me if you try their materials in a course (good or bad!)

]]>Before considering each language, I want to frame the discussion by (re)stating a program level student learning objective (SLO). In my first post about SLO’s objective 2 states: “**Students will be able to implement solutions to mathematical and analytical questions in language(s) and tools appropriate for computer-based solutions, and do so with awareness of performance and design considerations**“. Based on this objective, I’ll state three specific objectives for selecting a programming language:

- A language which can implement (complete) solutions to data science questions
- A language which allows good programming practices in terms of design
- A language which allows implementation of solutions which can be improved/aware of performance issues

As a programming language that originated in academia, particularly within the statistics community, R seems like a very natural choice in terms of teaching data science. Much of the syntax, function naming and even thoughts about how to construct a data pipeline/workflow comes naturally from a statistical analysis perspective. This makes it very easy to convert knowledge of statistical processes into code an analysis within R. The easy conversion between notation and code becomes even more valuable when trying to work with advanced/obscure statistical techniques. With R’s origination in academic statistics, there is a much broader range of packages for uncommon techniques than in most other languages. This suggests a strong candidate for the first requirement when working in statistical domains.

Other software/packages that make R appealing to teach with are RStudio, Jupyter Notebooks and R Markdown. RStudio provides a clean, user-friendly interface for R that makes interacting with plots and data easy. It even aids the transition from spreadsheet software (like Excel) by providing a similar, GUI-driven interaction with (simple) data-frames. With Jupyter Notebooks’ recent addition of an R kernel option, it is also easy to transition from mathematics focused software like Maple and Mathematica. See this DataCamp blog-post for more information on using Jupyter Notebooks (or similar software) with R. Notebooks also facilitate teaching good practices such as code-blocks and code annotation. Finally, R Markdown provides a (reasonably) simple way to convert executable code directly into final reports/outputs. That functionality further supports the teaching of (some) good programming and design practices.

Python was originally developed to be an easy to learn programming language (see Wikipedia’s history on Python). This means the whole language’s syntax and styling is easier to learn from scratch than most other languages (notably R). The basic Python data structure of lists naturally works like mathematical sets while dictionaries closely match logical constructions for unstructured data. Together with the use of indentation to indicate control flow, it is natural to when doing any introduction to the language, how to make Python code (human) readable. These traits speak directly to teaching/achieving our second language-related objective, “allows good programming practices/design”.

For teaching, Python starts with many of the same advantages as R. There is a long standing Python kernel for Jupyter Notebooks and several markdown packages available for turning code directly into html-styled reports. What makes Python noticeably different from R is that it is a general purpose programming language. In terms of teaching, this opens up some interesting options related to the first and third goals above. In terms of developing solutions to data science problems, Python easily allows a very broad range of both input and output. Specifically, it has high quality packages designed to deal with streaming data and better techniques for unstructured or big data. Also, because Python is regularly used to develop full programs and deployed software solutions, the methods available to study and improve performance are already well developed.

There are way, way more Python users than R users (and probably will be for the foreseeable future) simply because Python is a general purpose programming language. However, we are more concerned with users within the data science communities. That focus however doesn’t make the answer to our question any more clear. 2016 Data from O’Reilly’s Data Science Salary Survey places R (57%) slightly ahead of Python (54%) which matches KDnugget’s rankings of R being slightly ahead in 2016. However, the 2017 KDNugget survey results now places Python slightly ahead. Burtch Works’ 2017 survey data however still has R significantly ahead, and in-fact still gives a very large market share to SAS which didn’t even make KDnugget’s list. But Burtch also notes that Python has been gaining shares each year. Remember when considering these results however, that these are all self-reported and self-selecting surveys! It is hard to tell if these changes are actual changes in use, or just a changing definition/reach of who’s responding to the surveys. For example, when Burtch Works breaks down their results at least one sub-group rarely used SAS and, similar to O’Reilly and KDnugget, had Python ahead. More and more people are identifying with doing data science each year, but many of them have been doing similar things for a long time.

There is obviously value in either programming language, but from my perspective there is a really strong winner in Python. From a curriculum/planning perspective, since Python is a general-purpose language it is entirely feasible to have standard, introductory programming courses from a computer science department taught in Python. This reduces (potentially wasteful) duplication of similar courses (does every discipline *really* need its own intro programming?). It also lets computer scientists take advantage of years of educational research into how to better teach programming! Not to mention that Python was intentionally designed to be easier to learn programming in.

Add to this that data science students don’t really experience any major *disadvantages* from having Python as the primary curricular language but do gain several benefits. Key benefits include longer-term skill viability and increased versatility in job options, etc. This versatility even plays out when considering including advanced CS courses in a data science curriculum. Most data science curriculums are already going to struggle to incorporate all the necessary foundational skills in a reasonable length undergraduate (or graduate) program. So why add programming courses beyond those already needed to meet typical CS prerequisites?

Finally, looking at the trends in language/tool use in data science just adds more validation to this idea. As companies move to working with unstructured or streaming data, Python becomes even more natural. All the surveys report increasing use of Python, without any signs of slowing down that increase. It is important for academic programs to not just react, but even anticipate trends and needs in the job market and industry.

While I didn’t go into lots of details on the pro’s and con’s of R or Python (and didn’t even talk about SAS/SPSS) I have collected a few links that you might find valuable to read in making your own decision.

R vs. Python for Data Science: Summary of Modern Advances — EliteDataScience Dec 2016 — Does a nice job of highlighting the new things that make the languages pretty equal.

Python & R vs. SPSS & SAS — The Analytics Lab – 2017 — This is nice because it also puts into perspective how SPSS and SAS play into the landscape as well as provides additional historic perspectives

Python vs. R: The battle for data scientist mind share — InfoWorld, 2017 — a fairly balanced perspective on the value of both

R vs. Python for Data Science — KDNuggets 2015 — A bit dated, but still provides some good comparisons.

]]>ACM and IEEE jointly released Curriculum Guidelines for Undergraduate Programs in Computer Science in 2013 (CS2013). The most valuable component of CS2013 for me is the specification of ‘Knowledge Areas’ that are obviously related to Data Science, and being able to see the professional community’s consensus on central learning objectives in these areas. Some clearly important/relevant areas are:

- Computational Science
- Discrete Structures
- Graphics and Visualization
- Information Management
- Parallel and Distributed Computing

Other areas such as *Algorithms and Complexity*, *Information Assurance and Security*, or *Programming Languages* probably include specific learning objectives that are relevant to data science, but may not be needed in their entirety. Additionally, CS2013 allows you to to examine the suggested course hours expected to be devoted to these topics. From an industry perspective, this can provide valuable insight into whether a data scientist or computer scientist might be more knowledgeable about a particular subject. This differentiation in knowledge is important as data science strives to define itself independently of its founding disciplines. If you are interested in throwing your net a bit wider, ACM also has guides for other programs like Computer Engineering and Information Technology (coming in 2017) on their guidelines site.

The MAA’s 2015 Committee on the Undergraduate Programs (CUPM) in Mathematics Curriculum Guide to Majors in the Mathematical Sciences — CUPM Guide for short — can serve in largely the same way the CS2013 guide does, but from a mathematical/statistical approach. With more detailed reports on Applied Mathematics, Computational Science, Operations Research, and other areas of mathematics that data science often operates in, the CUPM Guide makes it possible to understand what exactly (from a mathematician’s or computational mathematician’s perspective) are the most relevant areas of mathematics to understand for success. This guide can also serve to help clarify exactly what sorts of mathematics courses a data science curriculum should require, by explaining where in the course structure specific topics like sets, relations, and functions, or other ideas get covered. In addition to their extensive undergraduate guide the MAA also provides a lot of interesting materials related to masters/Ph.D preparation, etc. These might be particular interesting as you consider what sorts of students to recruit or include in a master’s program.

Finally, the ASA has perhaps the most relevant and diverse, but in many ways least detailed, set of curriculum guides. The set of undergraduate guidelines and reports include how to assess instruction, program guidelines for statistical sciences, and even the Park 2016 Data Science guidelines (which I have commented on in other posts). They also have two sets of graduate guidelines from 2009 and 2012 for statistics masters/Ph.D. programs. What the ASA guidelines provide are much bigger, sweeping statements about the sorts of skills and knowledge that a statistics major should have. It includes side notes that give more details such as encouraged programming languages and even file formats. In many ways, I think the majority of the ASA guidelines could just replace “Statistics Major” with “Data Science Major” and remain nearly as applicable. The biggest difference might be in the level/depth required in “Statistical Methods and Theory” (less) and “Data Manipulation and Computation” (more). In a sense, this is at the heart of many statistician’s argument that “Data Science” isn’t really its own field. In practice though, I think the final implementation and mindset behinds a statistics major and a data science major will be very different, and certainly heavily influenced by the ‘host’ department.

That covers the breadth of the major professional societies’ curricular recommendations. I wasn’t able to find any (official) guidelines for a “business analytics” major from a professional society (see my resource page for a few unofficial documents), so if you know of one, please let me know.

]]>If you are looking to find wholesale curriculums, including course materials, there are a few options available to start the creative juices flowing. The first, and probably most academic, is the European Data Science Academy (EDSA). The EDSA is grant funded with a large number of academic (university) and research institute partners from across Europe. The thing I like best about this work is that they started with a demand analysis study of the skills needed and current jobs in data science across the EU. Furthermore, from the start the project built in a feedback and revision cycle to improve and enhance the topics, delivery, etc. To understand their vision, see the image below.

This idea of continual improvement was more than just a grant seeking ploy as shown by their list of releases, revisions, and project deliverables. While the current site still lists four learning modules as unreleased, they are expected July 2017.

Overall, their curriculum structure (I haven’t evaluated their deeper content) has a fairly high emphasis on computational topics, with less statistics/mathematical underpinnings. You can experience their curriculum directly (it’s free/open access) through their online course portal. What might be far more valuable though is their actual grant’s deliverables. These deliverables include details on the overall design principles in their structure with learning objectives, individual courses with their own learning objectives, descriptions of lesson topics/content and more. Using their outlines and ideas to guide your own construction of a curriculum is both reasonable and a great way to make sure you aren’t missing any major, important topic, however, this should be done with proper attribution and license checking (of course).

The other two places to look for curricular inspiration are also in the ‘open source’ category, but not funded by grants or (traditional) academic institutions. The Open Source Data Science Masters was constructed by Clare Corthell, who has gone on to found his own data science consulting firm and other initiatives. While not every link on the site is actually to a free resource (there’s several books to buy etc), it does a pretty nice job of highlighting the topics that will need to be covered (if possible), and provides lots of places to start pulling course materials from (or getting inspiration/ideas for content). The primary curriculum is python focused, however he also has a collection of R resources.

Corthell isn’t the only one though with an “open source” or “free” data science (masters) degree. Another collection of relatively similar material was collected by David Venturi, who’s now a content developer at Udacity (writing data science curriculum of course). For those designing curriculums, both Corthell and Venturi provide excellent resources and places to frame your learning. However if you hit this page trying to get into data science, read this Quora post that I think accurately highlights the challenges of learning from/with these open source programs.

Another similar alternative, that I’d peg closer to an undergraduate degree, is the Open Source Society University‘s data science curriculum. Their curriculum assumes a lot less pre-knowledge in mathematics and statistics, providing links for Calculus, Intro Statistics, etc. This content is probably more in-line with the recommendations for curriculum from the Park’s paper (see my Curriculum Resources page). What I particularly like about this (from a learning perspective) is that it actually details the amount of work per week required to learn from each course. You’ll see a large repetition of topics, but the OSS-Univ’s curriculum has a lot less advanced material, with only a few courses in big data, wrangling, etc.

At the end of the day, if you are looking to implement an undergraduate or graduate degree in data science, your university is going to have to offer duplicates of a significant subset of classes from these curriculums. While emulation might be the highest form of praise, we’ll each need our own, unique take on these courses while striving for sufficient similarity to have a semi-standardized knowledge base for practitioners. Good luck!

]]>

Learn2Mine (L2M) is the first site I used in conjunction with my Data Mining course, and more recently my Introduction to Data Science course. Learn2Mine is a free, open source platform developed at the College of Charleston (CoC). While I have only really made use of the contents already there and CoC’s hosted site, you can contribute, or host your own version by getting the source directly from github. Dr. Anderson is fairly responsive about keeping the site running and grading.

The positive features for L2M (beyond being totally free/open source) are that it includes a mix of both introductory programming assignments and several more advanced machine learning/data mining lessons. It even has several search algorithm lessons (which I tend not to use). All of the lessons include auto-graded response boxes which also provide limited feedback of the errors generated when comparing submitted work to answers. There is also an interface for instructors to create their own ‘courses’ which consist of a series of the lessons on L2M. This allows the instructor to see student progress through lessons and download a grade-book in spreadsheet format.

Downsides for L2M are in-line with what you pay for (or invest in time-wise). Even though there is feedback when students get answers wrong, this often just consists of the identification of mismatched output lines (so pretty sparse). Students often get very frustrated trying to figure out what they are missing. This is exacerbated by the fact that often the instructions are unclear or insufficient to allow students to simply do the lessons. Also, as might be expected from a locally built/maintained project, there are a lot of “polish” features missing, such as being able to reorder assignments in a course, or associate a name with an account. Students have an account associated with the email they login with so it can sometimes be challenging to connect records with students. Overall, I’ve been considering phasing L2M out of my normal assignment structure, though the possibility of hosting my own local version and implementing different, more explained lessons has also been tempting.

The prime contender to replace L2M for me has been DataCamp. I’ve know about DataCamp for a while now but had the first chance to actually use it and make assignments from it this spring when I was looking for data visualization lessons (see visualization resources post). I’ve gone through a few lessons myself and found DataCamp to basically be exactly what I’d want/envision online course-work to be. Most courses consist of short videos (a best practice) followed by several guided coding exercises. DataCamp is not (sort of) free, which turns out to be a pro and a con.

If it’s not free, why is DataCamp going to replace L2M for me? Great question. Because, for academic purposes, Datacamp IS free. If you are an instructor for an academic institution teaching a course with 10+ students in, you can request free, premium access for students enrolled in your course(s). That access is limited (they give you 6 months), but hey, it’s free. What else makes DataCamp a nicer replacement? First the coding exercises are scaffolded, that is, early exercises have more prewritten code while later exercises require you to remember and use what you’ve already learned. In addition, the coding exercises have reasonably helpful error messages and help often allowing you to more accurately debug code. They’ve also got built in hints/help available, so a student can’t get permanently stuck. Using those however decreases the “exp” they gain, so you can still track how success a student has been without help. The other major advantage is that DataCamp has a SIGNIFICANTLY larger set of lessons/courses available to pull from.

There is no free lunch in data/computer science though. DataCamp does have a few downsides. Perhaps the biggest is the granularity available in assignments. You have three choices, “collect xp”, “complete chapter”, or “complete course”. Given that a chapter is really the smallest cohesive learning unit on DataCamp, this makes a lot of sense educationally. However, that also means it’s not exactly an alternative for giving individual lab/homework assignments. Instead, it would serve best as a resource/major assignment related to learning how to program in python/r, or a bigger topic.

Finally, I want to mention Gradescope. Gradescope isn’t data science educational site. Instead it’s a jack-of-all trades which can help ease the burden of assignments and grading. If DataCamp took L2M and removed granularity/options, Gradescope (in this context) goes the other direction. Lots of faculty use it for all kinds of courses, from computer science or mathematics to writing. Given its purpose, Gradescope doesn’t have any specific assignments (maybe that was obvious). Instead, it can serve as an autograder or collection site for your assignments. I’ve included it here for those that might already have assignments (or who get them from others) but still want a speedy, simple way to get feedback to students.

I’d be remiss if I didn’t point out that there are some alternatives to DataCamp, depending on your goals. If all you need students to do is learn to program (not necessarily in a data-centric style) try Codecademy or explore Code.org. I also know there is an alternative to Gradescope (but I couldn’t track down the name/site if someone knows, please email me or leave a comment). What I recall is that the alternative is NOT free, but does provide better support and scaling. You might also consider what options are available or integratable with your learning management system (DataCamp IS…but maybe not by you..).

Hopefully you found this post informative, if you’ve got other suggestions of websites with assignments (particularly data-science related) please let me know or leave a comment.

]]>

So why bring this up on a educational blog? I think its important to embed the idea of reproducible work deep inside our teaching and assignment practices. While the idea of repeating a specific analysis once the data has changed isn’t really novel, it becomes far more relevant when we begin talking about filtering or cleaning the input data. Just think about searching for outliers in a data-set. First, we might plot a histogram of values/categories, then we go back, remove the data points that we want ignored, and replot the histogram. BAM! The we have a perfect opportunity to teach the value of reproducible work! We used exactly the same visualization technique (a histogram), on practically the same data (with outliers and without outliers).

Where does the reproduction of the work fit in though? Python and R both have histogram functions, so this is definitely a toy example (but the whole idea of functions can serve to emphasize the idea of reproducible/reusable work). Instead, I think this is where the instructor has an opportunity. This idea of cleaning outliers could easily be demonstrated in the command line window of R or an interactive Python shell. And then you’ve lost your teaching moment. Instead, if this is embedded in an R script or Python/R Notebook you can reuse the code, retrace whatever removal process you used, etc. In the courses I’ve taught, I’ve seen student after student complete these sorts of tasks in the command-line window, especially when told to do so as part of an active, in-class demo. But they never move the code into a script so when they are left to their own devices they flounder and have to go look for help.

I titled this post “Version Control and Reproducible Research” … you might be wondering what version control has to do with this topic. The ideas described above are great if you are the sole purveyor of your code/project. But if you have your students working in teams, or are trying to collaborate yourself, this might not be exactly ideal. But it’s getting pretty close! Here’s the last nugget you need to make this work… version control. Or in this case, I’m specifically talking about using GitHub. The short version of what could be an entire separate post (I’ll probably try to do one eventually) is that git (and the cloud repository github) is the tool that software developers designed to facilitate collaborative software development without the desire to kill each other from broken code. It stores versions of code (or really any file) that can be jointly contributed to without breaking each other’s work. For now, I’ll point you to a few resources on this..

First, a bit more from an industry blog on workflows to promote reproduction using github — Stripe’s Notebooks and Github Post

Second, for using Git/GitHub with R — Jenny Bryan, Prof. University of British Columbia — Note that this is a really long, complete webpage/workshop resource!

Third, a template/package for Python to help structure your reproducible git-hub work — Cookiecutter Data Science — (heck, this could be an entire lesson itself in how to manage a project– more on that later)

Fourth, a template/package for R to help structure your reproducible git-hub/R work — ProjectTemplate

]]>

The original blog introduction, with a bit of why the blog exists and what it seeks to cover is here.

]]>An ACM organized workshop in 2015 included participants from ACM, ASA, IEEE-CS, AMS and more. That workshop’s report does not explicitly state any math requirements, but does make clear the need for sufficient supporting statistics courses. The clearest recommendations come from a group of faculty at the Park City Mathematical Institute in the summer of 2016. Their report gives suggestions on how to make a data science degree from existing courses and ideas for new integrated courses (this is the real gold in the report). If constructing a curriculum from existing courses, the group recommends three mathematics courses: Calculus 1, 2, and Linear Algebra. Last, a series of round-table discussions is currently underway by the National Academy of Science to discuss Data Science Post-Secondary Education. While all three NAS round tables are interesting, only the first is relevant to this discussion. At that meeting, there was a presentation on the underlying mathematics of data science. Their list of mathematics supporting data science included linear algebra, numerical analysis and graph theory.

In summary, all three groups clearly support the need for linear algebra to be a part of any data science curriculum. I doubt you’ll find many objections to this idea since linear algebra forms the mathematical foundation for manipulating data contained in tables or arrays as rows/columns. If nothing else, simply learning the notation is vitally important for anyone wanting to extend algorithms for data science. All three also clearly support at least two traditional statistics courses, up through regression analysis. A little less clearly, I would argue that all three support the requirement of a Calc 1 course. The NAS round-table discussed needing numerical analysis, which is traditionally based on calculus concepts. The ACM workshop supported disciplinary knowledge and just about all science disciplines require at least one semester of calculus.

Alright, on to the differences. The PCMI group included Calculus 2 in their “minimum” courses needed for data science. In my opinion, the suggestion that Calc-2 be included in the bare minimum courses for data science is indicative of the dominance of mathematicians (many applied) and statisticians in the group (there were a FEW computer scientists). While I think overall they are quite good, I think the inclusion of Calc 2 over discrete mathematics (as well as the odd location of data mining) clearly reflect this make-up. The presentation on mathematics (from two mathematicians) at the first NAS however included graph theory as one of the three main supporting mathematical areas. So, perhaps the question from these two groups is: “Calculus 2 or Discrete Mathematics?”

Here’s an alternative way to build an answer to this question. Instead of just focusing on the topics covered, what about the requirements for the other supporting disciplines that make up data science? Computer Science is pretty easy. Almost all programs require Calculus 1 and discrete mathematics, and the ACM 2013 guidelines include a list of core topics (set theory, graph theory and logic) that are traditionally covered in either a discrete mathematics course, or a combination of several mathematics courses. They also articulate very clearly that for some areas of computer science (like visualization or data science) linear algebra and statistics will be required. We can contrast this with typical mathematics requirements for statistics curriculum. For many statistics programs, a minimum of Calc 2 is required to support advanced probability courses (with a preference for multivariable calculus). The ASA 2014 guidelines specify that statistics majors should have both differentiation and integration (typically covered by Calc 1 and 2), and linear algebra.

Development from supporting disciplines can leave us just as confused as to what to require. I think there is an answer, but it requires taking off the mathematician glasses, and thinking about jobs, applications, and where a student might be headed. First, a good portion of researchers and practitioners doing data science use graphs and networks, often doing mining on those graphs for information. Turns out graphs (the node/edge type, not the line/bar plot type) are also a great way to visualize a lot of information. Another key skill when doing data science is the ability to partition data. That is, to think of data as either meeting, or not meeting specific criteria. This is encompassed in set theory in mathematics, and is sometimes partially covered as part of logic. Together these topics provide two new ways of thinking about data that aren’t included in other mathematics courses. The need for this sort of knowledge, and a basic introduction to proofs is why discrete mathematics courses came into existence, to allow CS majors to get these topics without taking another 3 or 4 mathematics courses. To me, this is a far stronger case for including discrete mathematics than the (possible) need of Calculus 2 for advanced statistics courses. If you are requiring 4 math courses, by all means, include Calculus 2 next. Or, if a student is particularly interested in understanding the theoretical underpinnings of data science (by taking more statistics courses) then they should take Calc 2. But if we are really thinking about an undergraduate degree as a stand-alone, prepared to enter the work force degree, Calc 2 does not seem to add a lot of direct value to the student’s degree.

]]>