Archives For math ed

On July 27, 2013, I created a petition on Change.org to get math.ED – Mathematics Education added as a category on the arXiv. You can find the petition here. At present, there is no dedicated category on the arXiv for math ed. In addition, there is no culture of math ed folks utilizing pre-print servers like the arXiv. I’d like to change both of these facts. If you want to know how all this got started, check out this post.

As of August 1, there was just shy of 200 signatures. My initial goal was 50. The support has been quite impressive. Most of the signatures are from the United States, but there are others from around the world. As far as I can tell, support is coming from people with interests in math ed, physics ed, STEM ed, ed tech, math, stats, operations research, secondary education, and more. I even recognized at least one philosopher. Thankfully, it seems we have the support of a few prominent math ed researchers (e.g., Alan Schoenfeld), which I think is crucial for this to really work.

I’ve also had about a half dozen people contact me to say that they would be willing to serve as a moderator for a math ed category on the arXiv. This is one of the things the arXiv told me that we would need to move forward. The list of people I have is probably more than sufficient.

As exciting as all this has been, it hasn’t all been rainbows and unicorns. Without going into detail, I had one person post a response to a comment I left on a discussion board announcing the petition that essentially told me that mathematics education is worthless and that there is nothing worth placing on the arXiv. If you are interested, I’m sure you can find the discussion. I maintained control and didn’t respond.

Also, I used Change.org on someone else’s recommendation and so far it has seemed to work well. However, I received an email from someone that signed the petition that was upset that Change.org sent them follow-up emails. I sincerely apologize if anyone else was annoyed or offended. According to Change.org:

Every so often you can expect to hear from Change.org about campaigns we think you’ll be excited to join. If you’d prefer not to receive these emails, you can unsubscribe by clicking the link at the bottom of any message you receive from us.

I realize it is a hassle, but it appears that you can opt out of any future correspondence with Change.org.

There was also an interesting discussion on Twitter that Republic of Math (@republicofmath) and I (@danaernst) had. You can read more about that conversation here.

In addition, there have been a few people here and there that aren’t supportive for one reason or another of the endeavor to utilize the arXiv for math ed. I’m okay with that. Heck, maybe this is a bad idea and if someone has arguments about moving forward, I want to hear them. I’m not so dead set on this happening that I won’t listen to reason. In general, I’m in favor of sharing knowledge in ways that are open and easily accessible. This is my motivating principle.

OK, so where do we go from here? There have been a couple of developments with the folks at the arXix, which started with a comment that Greg Kuperberg left on my original blog post. Greg is the chair of the math advisory committee for the arXiv, which is the committee that would approve a new math category. According to Greg:

What I can tell you at this stage is that the “petition” that I would like to see is enough postings to math.HO to justify a separate math education category. Creating a separate category first just in the hope that it will attract interest hasn’t usually worked well in the past.

Another possibility is to change the name of the math.HO category to better reflect its purpose. That’s a more welcome option than multiplying the list of categories.

I would rather negotiate a change to the name of a category in private. However, I can say that the name “History and Overview” has never been all that great of a fit for the topics listed with it, so a name change of some kind could make sense. Of course those topics don’t just include math education, but also closely or loosely related topics such history of mathematics and recreational mathematics.

In any case, “a rose by any other name would smell as sweet”. Getting more math education submissions to the current math.HO is partly a separate matter. I’m certainly all for more encouragement of that. Again, we can discuss techniques in private.

Getting a moderator for math.HO is also a good idea; once again, we can discuss.

I’ve since followed up with Greg privately and it seems that the most likely scenario is a name change to the math.HO – History and Overview, which lists math education as one of the possible topics. A name change seems reasonable to me. However, in order to move forward, the arXiv would like to see math ed submissions to the math.HO category. Again, this seems reasonable. In addition, there is currently no moderator for the math.HO category, so we would still need to move forward with the list of folks I gathered.

At this point, what we need is for people to start uploading their math ed related manuscripts to the math.HO category on the arXiv. I think this will require some guidance, as well as a discussion about copyright and such. I think I’ll save that for a future post.

Thoughts and comments welcome.

During Susan Ruff’s talk in the IBL Best Practices Session that Angie Hodge, Stan Yoshinobu, and I organized at MathFest, she made reference to an article by Kirschner, Sweller, and Clark. The paper is titled “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching” (PDF) [1]. As a practitioner and serious proponent of inquiry-based learning (IBL), I am extremely interested in what this article has to say. Here is the abstract:

Evidence for the superiority of guided instruction is explained in the context of our knowledge of human cognitive architecture, expert–novice differences, and cognitive load. Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process. The advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide “internal” guidance. Recent developments in instructional research and instructional design models that support guidance during instruction are briefly described.

I intend to read the whole article, but haven’t read much more than the abstract. Here are few thoughts before I dive in.

When discussing the advantages of an IBL approach with people, I’ll often cite academic work that supports the claim that it is beneficial for students. For example, see the work of Sandra Laursen et al. located here. However, to be honest, despite my interest in seeing data that validates my own opinions, the reality is that I don’t do IBL because the research told me to. I do it because I’ve seen it work! My students tell me it works. Alright, to be fair, my students told me that my lecturing worked, too. But the types of comments I get now from my IBL students make it clear to me that something really good is happening. For example, read this. IBL may not work for everyone in all situations and I’m okay with that. If it stops working for me, I’ll try something different.

The first thought I had when I saw the title and abstract was, “what does ‘minimal guidance’ mean?” I certainly provide a lot less direct guidance in my IBL classes than I do than when I lectured, but is it “minimal”? I do my best to provide scaffolded guidance to my students and to set up a support network in a safe learning environment. This is crucial in my opinion. I’ll have to digest the whole paper to see what their take is.

It appears that there are several reflections and discussions of this paper online already. For example, go here, here, and here. In addition, Kirschner, Sweller, and Clark have written a response to criticism that they have received in their “Why Minimally Guided Teaching Techniques Do Not Work: A Reply to Commentaries” (PDF) [2]. I’ll try to read this paper, as well.

Bibliography

[1] P. A. Kirschner, J. Sweller, and R. E. Clark, “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching,” Educational Psychologist, vol. 41, no. 2, pp. 75–86, 2006.

[2] J. Sweller, P. A. Kirschner, and R. E. Clark, “Why Minimally Guided Teaching Techniques Do Not Work: A Reply to Commentaries,” Educational Psychologist, vol. 42, no. 2, pp. 115–121, Apr. 2007.

On July 27, 2013, I created a petition on Change.org to get math.ED – Mathematics Education added as a category on the arXiv. You can find the petition here. At present, there is no dedicated category on the arXiv for math ed and I’d like to change this. If you want to know how all this got started, check out this post.

The last time I checked, we were just shy of 200 signatures on the petition. My initial goal was 50. The support has been quite impressive. Most of the signatures are from the United States, but there are others from around the world. As far as I can tell, support is coming from people with interests in math ed, physics ed, STEM ed, ed tech, math, stats, operations research, secondary education, and more. I even recognized at least one philosopher. Thankfully, it seems we have the support of a few prominent math ed researchers (e.g., Alan Schoenfeld), which I think is crucial for this to really work.

There have been a few developments with the folks over at the arXiv and I’ll share the current state of affairs in another post. In the meantime, I thought you might enjoy a conversation that happened on Twitter between myself (@danaernst) and Republic of Math (@republicofmath). Matt Boelkins (@MattBoelkins) chimes in at the end, too. The conversation wasn’t linear, but I’ve done my best to list the tweets in an order that makes sense.

I’ve recently finished coauthoring two different math education papers. Both papers have been submitted for publication. Neither paper is likely to change the world, but I still want to openly share what we have. Like most mathematicians, I’ve posted my pure mathematics research articles on the arXiv. In case you don’t already know, the arXiv was started in 1991 as an electronic archive and distribution server for research articles. Covered areas include physics, mathematics, computer science, nonlinear sciences, quantitative biology, and statistics. Readers can retrieve papers off the arXiv via their web interface and authors can submit articles (and resubmit if they make changes). It is standard practice for mathematicians to post their articles on the arXiv prior to submitting them for publication. In fact, some articles only appear on the arXiv. When I want to find a particular article, I first look for it on the arXiv. In short, the arXiv is awesome.

However, when I went to go look for a mathematics education category, I was surprised to see it was not among the list of mathematics categories. The math.HO – History and Overview category lists mathematics education as one of the possible topics, but it doesn’t appear to be commonly used for this purpose. In contrast, there is an active physics education category.

After exploring this a little further, it doesn’t appear that there is a culture among math ed folks to use pre-print servers like the arXiv. I think this is unfortunate and I’d like to help change this. If there is going to be cultural shift, I believe that there should be a dedicated place for math ed papers. Authors need to know where to submit papers and readers need to know where to look. A category called History and Overview doesn’t cut it in my view. A precedent has been set by the physics education crew and we should follow in their footsteps. I’d also like to point out that Mathematics Education is listed as one of the American Mathematical Society’s subject classification codes, namely number 97.

I have two proposals:

  1. The category math.ED – Mathematics Education be added to the arXiv.
  2. Math ed people start posting to the arXiv (when copyright allows it).

A couple days ago, I contacted the arXiv about the first item and here is their response:

The creation of a new subject class requires considerable support from the community that will use it. We do not want to create subject classes that will be useless because of under use.

More precisely, we require a commitment from a significant group of researchers to submit papers using the proposed subject class. This should include promises to submit a number of initial papers to get the subject class going (a solution to the chicken-and-egg problem).

If this issue is important to you then you must first start by canvassing support from your community. If you receive overwhelming support, and have a significant number of researchers who have agreed to use arXiv, please feel free to contact us again with more specific information.

I then followed up and asked for clarification about what “overwhelming support” and “significant number of researchers” means, to which they replied:

Overwhelming support would include quite a number (more than, say 50) prominent researchers who agree that such as category should be added, and who would agree to make use of it.

Okay, that sounds like a lot of people to try to get on board, but I say, let’s go for it. One obvious question: what’s the best way to gather interest and then record this interest to the arXiv? Would a petition be sufficient?

In the arXiv’s first response to me, they also said:

We also need a volunteer to moderate the class by reviewing daily submissions and flagging inappropriate submissions. This moderator should also review a significant number of already archived papers, looking for submissions that can be cross-listed to the new subject class and contact authors encouraging them to do so.

I don’t think I am the appropriate person for this and I’m not really willing to take it on anyway. Any volunteers?

Update, July 27, 2013: There is now a petition on Change.org. If you are in favor of the arXiv including math.ED – Mathematics Education as a category, please sign the petition. If you would also utilize this category by uploading articles related to mathematics education, please leave a comment (on the petition) indicating that this is the case. You can find the petition here.

Update, July 28, 2013: We’ve exceeded 100 signatures on the petition to get math.ED – Mathematics Education added to the arXiv. The next step is to round up 2–3 volunteers to help moderate category submissions. I don’t think this requires a tremendous amount of work. I’d like to have a list of potential moderators before I contact the arXiv again. Any takers? After all is said and done, there is no guarantee that the mathematics subject board at the arXiv will approve our request. However, they asked for support from at least 50 people and we have 100. Fingers crossed.