Dec 282017
 

On to the qualitative analysis. (For the quantitative, see previous post)

In the #mtbos, we talk of ourselves as a ‘community.’ We talk of the community of TMC, and a community of mathematics educators. The problem, then, is that there is not a clear definition of the ‘community.’ Anyone who says they are a member of the community IS a member. Literally the only requirement for membership is that the person claims membership.

In the literature of communities, one of the main authors is Wenger (1998) Communities of practice: Learning, meaning and identity. Connected to this book is the theory of learning called situated learning (Lave & Wenger, 1991). The theory of learning is a social theory, which fits well with the practices of TMC, however there is a critical difference, in my opinion. In situated learning, the learners move from incompetence to competence in a linear, unidirectional method. The goals and methods of learning all fit into this ideal of moving the learners from incompetence to competence.

Although the social elements of Wenger’s theory of learning are relevant, the theory doesn’t connect with the ideals or practices of TMC in a strong manner. Another theory of learning does fit better, however. This theory is Engeström’s theory of expansive learning (2017). This theory does not require everyone move from incompetence to competence. Rather, it focuses on the idea that the process of learning expands the realm of knowledge as learners learn. The theory of expansive learning also has roots in Vygotsky’s Activity Theory. Instead of only looking at individuals, tools, and objects of activity, Engeström expanded activity theory to include communities, rules, and a division of labor.

image
Engeström’s diagram of Cultural-Historical Activity Theory (CHAT)

In this model of the theory, there are four sub triangles that can be explored, however to fully understand a community of expansive learning, the entire triangle must be utilized. The one element of the triangle that is difficult to pin down is the objects, because individuals and the community can work on different objects simultaneously. Each individual or groups of individuals in the community can interpret what their objects of focus are independently. (sounds like morning sessions to me!)

For there to be a community, there must be rules of the community, and those rules must be taught somehow. That is the lower left triangle, because ‘must be taught’ is shorthand to must be taught ‘to people.’ The individuals in the community matter!

As I thought about why CHAT and expansive learning is a better theory to use to understand the workings of TMC, I made this diagram based off of Engeström’s.

image
CHAT applied to TMC

This is a qualitative analysis, so I will analyze all 6110 unique tweets that occurred at TMC over the 41 days I collected data and see how the fit into this schema. To do this analysis I will be using MaxQDA. I imported all of the tweets into the software as a survey, so I have some information as quantitative (for example the names of who tweeted so I can quickly see the frequent tweeters and the hashtags used other than #TMC17) but the most important data is the text of the tweets. I will have to read each and every tweet, and tag the tweet with one of the tags in the diagram.

But the tweets were not the only qualitative data generated from the conference. Since its inception, TMC has archived blog posts from the conference, and this year was no different. Therefore, I also collected all of the text and images from the blog posts (there were over 110) archived on TMathC.com for the 2017 conference. Each of those blog posts is now saved in a separate word docx file, and will be imported to MaxQDA as well.

Finally, in order to reach some understanding of the ‘Historical’ part of CHAT, I also collected the 2012 blog posts. Well, let me be clear. I did not collect them. I paid a small amount to a programmer on Upwork.com who created a script which did the web scraping for both the 2012 and 2017 conference. That saved me hours of work on the data collection phase.

I have done none of the analysis yet. I have a proposal meeting in late January, early February, and then I can start analyzing. I just know how much data I have at the moment. It is a lot.

So far, I have explained the quantitative, and the qualitative, but not the mixing part. That is the next post.

Dec 212017
 

I have been buried this semester with work, teaching two full sections of an education theory class, doing observations of our preservice teachers, and also writing my proposal for my dissertation.

dissertation via

Lets say the first two items in that list got far more priority during the first half of the semester, and I had to kick it into gear the last half. But, I did kick it into gear, took a ‘mental health day’ for the first time in my life, and accomplished a working introduction and literature review for my proposal. In the list above, I have experienced all 6 steps. What is missing to the list is step 7; “Repeat”. You print the introduction, then start the lit review while you wait for feedback on the intro, then print the lit review, and revise, resubmit, and revise again. And again. It is worth the work, but wow. I know now why so few people finish nationwide. Next up, is my methods section.

And, I need to work through some details, so I thought I would post them here. I am not sure anyone will be interested in the lit review, but there may be some small interest by one or two people. I am going to over explain things, because it will help me shape the academic writing I need to do over the next two weeks.

The big idea, is that I am going to do a mixed method analysis of a particular math conference, founded by teachers, created organically from the ground up to create a different type of professional development experience; TMC17.*

Why mixed methods, and what type of mixed method analysis?

The quantitative analysis is going to be Social Network Analysis (SNA) of the tweets which occurred over the week prior, the 4 days of, and the month after TMC17. I used NodeXL to collect the public tweets each day of the 41 days. NodeXL downloads the entire network of tweets, so for a tweet from someone to 3 other people, that creates 4 lines of text in the spreadsheet. It also downloads whether it is a retweet, a reply, or something else. It is very powerful software, which is very inexpensive if you are a student ($29 per year). The software calculates radial measures of centrality, betweenness, density, and other calculated statistics on the data set. These calculations and the resulting graphs will allow influencers, central individuals, and other patterns of tweeting to be discovered.

One type of SNA graph can look like:

Capturevia

Each dot is a node, person, or vertex, and the line between people is a tie, connection, link, dyad, or relationship. The language depends on the book you use to guide the analysis. I need to pick which terms I want to use, and why. Nodes which are larger have a larger influence, the distance between the nodes is a measure of betweenness, and the distance from the center is radial measure of distance. There is a lot of info packed into these graphs. The number of rows in the TMC excel file is over 17,000!** There is a LOT of information to unpack.

I am looking for patterns in the information. Are there groups of individuals who are on the inside? Are those people first time attendees? Experienced attendees? Leaders of morning sessions? Keynote speakers? Etc. A really rough draft of a question for this data set is; “What are the tweeting behaviors of the participants of TMC17?” Or: “What are the online practices of the attendees of TMC17?” I am not sure which way to go yet.

This analysis is sufficient for a dissertation, I think. There is a lot of data here to unpack, to analyze, and to show the online behaviors of the participants. However, this is only the start. I am going to use this data to divide the actual tweet contents into groups for comparisons.

That is the qualitative part of the mixed method design.

That is another post, entirely!

Thanks for reading this far, and please leave any questions in the comments or on Twitter.

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*If you are saying, “wait a minute, how can you have data from TMC17, and yet not have written the full proposal yet?” It is because I wrote a mini version, a pre-proposal, which justified to my committee enough to allow me to collect data prior to the full proposal to be written. I have not been allowed to look at any data until the proposal is accepted by my committee. This will allow me to graduate May 2018 instead of 2019.

**A very important point to make clear is that these are only the PUBLIC tweets, that used the hashtag #TMC17. If a conversation was held that never used the hashtag, it never came up in the search. If a person’s twitter feed was private, it was ignored by the search. Only public, hashtagged tweets were allowed into the data set by the search.

Oct 292015
 

I am in year two of my PhD program, and am enjoying the process, learning, and exploration so far. Yes, I am only a little over half way with the coursework, but that is a great place. I was thinking, however, about what advice I would give to someone just starting his / her PhD. What books/resources would I recommend?

I came the realization that I would not recommend any books of content at this point, but two books on process. The first book is one that I have used heavily and it has saved me hours (literally, not figuratively) on formatting APA papers. The book is, “Doing your dissertation with Microsoft Word.

disserationword

Why do I recommend this book to anyone starting a PhD? Because it walks you through step by step on how to create a template in Word that will contain every single element of APA formatting. Have a Header 1? Write the text and click the style for Header 1. It is that easy. It took me several hours and much tweaking to get it finally right, but when I go to write a paper now, I load the template, and BOOM! I am ready to write. I have all the APA formatting done in Styles, I have a page (that I delete before printing) that has definitions of the Styles, and all settings are done. All I worry about is text. This book has saved me so much time over the last three semesters.

The next book I would recommend is “Stylish academic writing” by Helen Sword.

academicwriting

This is a quantitative and qualitative (a mixed methods design) study of good and very bad academic writing made me take a hard look at my own writing, but also not fall into the trap of jargon and technical writing. Write with style, write with intent, and write so other people will want to read your writing.

Finally, I offer one piece of software to use: Zotero.

zotero

You can use Mendeley, or Endnote, or any one of the other packages, but use a citation manager ASAP in your studies. I started using Zotero right away, and it has made such a difference in the ease of writing, the ease of citations, and the management of my PDF’s and notes. Best of all, installing and using Zotero is free (unless you use the online storage option and exceed 300 megs of storage. More on that below.)

You can have folders and subfolders for your citations and PDF’s, and a citation can be in many folders at once, or in no folder. It can be tagged, categorized, searched, and using the Word add-in inserted into the inline and bibliographic citation with one click.

zotero2 (click to see full size)

The PDF’s are attached, notes are kept together with the citation (and the notes are searchable as well) and it takes one click to add most citations to the database.

This little piece of software has saved me hours as well. It is not perfect, you have to double check to make sure the Sentence case vs. Title case was done correctly. You have to double check to make sure the PDF was downloaded (sometimes it doesn’t download and you need to save and drag and drop it to be included.)

I ended up paying for the the 2 gig option. This was $20 for 1 year. 6 gigs is $60 and unlimited storage is $120. To give you some idea, I had 330ish citations in my database, probably 300 of them with PDF’s attached when I ran out of room on the free account. I end up hoarding the PDF’s and the citations, so if you are not a digital hoarder, you could probably go longer before needing to pay.

These three items have made being a PhD student enjoyable, fun, and much less work than the first or second time I was a grad student. I don’t stress over citations, I just double check them. I don’t stress over formatting, because I know the Styles I created are correct to the APA version I need.

I DO stress over writing. But isn’t that what I am supposed to stress over?

Sep 172014
 

brickwall

One thing I am really working on in AP Stats is the amount of notes, the lack of notes, and the engagement of my learners. AP Stats is one of those courses where the amount of vocab to assimilate is so huge, that it cannot all be done by activities. I have found that a mixture of activities and notes, and assignments and cycling back again helps tremendously.

I have the one slide from my notes today above. The literal, not figurative, brick wall between the two ideas of mean & standard deviation and median & IQR was very well communicated this year. The learners told me they understood. The formative checks I did supported that.

I still am not confident. Too many learners mess up this idea every year for me to take the face value word on it. I will be giving some questions over the next couple of days to make sure.

The re-writing of my slides to be word minimal, picture heavy, and discussion focused has changed how the class goes when I am doing notes, at least. I am happy with that aspect, and the learners I have asked directly about the notes have told me they are very useful and not boring.

That is something at least!

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PhD spillover

As an aside, the class on non-parametric statistics has taught me one thing that has impacted my AP Class. The structure I used last year as far as how I teach the content is right on the money.

2014-09-16 16.08.00

In the PhD level class, we look at every problem first from the perspective of “is it categorical or quantitative” and then “how many variables”. So far, we have limited the decision to just categorical, non-normal problems (hence the non-parametric! label of the course.)

For Inference section, the course will be divided up into a. quantitative 1 sample, a1. confidence interval, a2 hypothesis testing; b. quantitative 2 sample b1. confidence interval, b2. hypothesis testing, etc. I think this structure leads better to the advanced level stats if they take a next class.

It is also the exact opposite of what our textbook does. Oh well. I didn’t use the textbook structure for 2nd semester anyway for the last 3 years. This just reinforces that decision as a good one.

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Finally, some lesson ideas I am working on.

2014-09-16 16.09.51 2014-09-16 16.09.01

That’s right. Funky dice!

On the left we have odd shaped, non-standard dice. Awesome. Are they fair? Not sure. On the right we have, yes, for reals, 5 sided, 7 sided and up dice. No joke. I once argued that a 5 sided fair die could not exist. Is it fair? Not sure. I am writing some lessons for expected value to take advantage of both of these.

I also received word from Robert at http://thedicelab.com/ that my order of weighted dice is coming soon.

Heh heh heh. That’s right. Real, honest to goodness (well, dishonest to goodness) weighted dice.

Expected value here we come! More later on this idea.

Sep 082014
 

One of my classes is “Qualitative Research in Education” taught by Dr. Diane Barone. She is a pretty amazing professor so far, and I am really looking forward to the actually doing the research project in this class.

Which brings me to the idea I had for the research. Dan Meyer, in his Keynote at TMC14 was asking “Who is the #MTBoS? Dan was doing a quantitative study on the #MTBoS, and I think he created more questions than he answered.

One advantage to qualitative research over quantitative research is it is more focused on the Who and the Why questions. In tonight’s class we had to present our potential questions, and mine was accepted with no revisions or modifications.

“How are K-12 math teachers using Twitter in their Personal Learning Networks?”

This is just a pilot study, I am not going to go through the IRB to get approval for publication. I think there is absolutely some worthwhile research that can be published, but not in this first class.

I have found research about Library Information Specialists and their use of Twitter, I have found research about technology specialists and their use of Twitter, but nothing about classroom teachers, let alone math teachers.

What do you think? Are you interested in the answer too?

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