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I am doing the qualitative analysis of the TMC17 data right now, and there are so many words! OMG, my eyes were swimming in my head, so I took a quick break and did some additional quant analysis. I wondered (based on a book I was reading about Twitter analysis) what times the participants were tweeting?

So, a little spreadsheet magic with NodeXL, and I had the following graph.

What do you notice? What do you wonder?

The first thing I noticed is that y’all need to go to bed. Seriously.

12 am 332
1 am 318
2 am 309
3 am 257
4 am 98
5 am 66
6 am 37

Seriously, at 2 am, there were 309 tweets with the hashtag #TMC17? And you can’t tell me that this was after the conference.

There are not zero tweets in that long stretch, but there are not enough to add up to 309! 

Being an early bird, I have heard of the late nights attendees spent staying up doing math, playing math games, and engaging in math activities (nothing else could be going on ) but I never imagined it would be this many!

What I also noticed is the fact that the graph is two humped. That tells me something. It says that more people were engaging in social activity on Twitter than in session activity.

That is surprising to me. I did not think it would be that unbalanced. I may need to add some elements to my qualitative analysis to take this into account somehow. This is …. surprising!

I love it. I love this process.

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What about the different clusters? The entire data set was 1348 nodes, but the software clustered them together based on the communication patterns. If you go back to the first post on this, you can see the different clusters shown. So, what do the individual clusters look like, and behave like?

Cluster 1 has a small, tight group of participants in the middle with a cloud of mostly remote participants (RP) on the outside. There are a few blue lines radiating outward, which show attending participants (AP) tweeting with other APs. The red lines show one of three possible communication patterns, either AP to RP, RP to AP, or RP to RP. [I am not sure how to show all 4 on a graph. I tried, it looks so busy as to be almost unreadable.]

The thickness of the line is proportional to the quantity of tweets between the nodes, so not every node is a one and done communication. In fact, it would be wrong to assume that a single line indicates a single tweet, for at least two reasons. First, the software has a stepwise function for determining thickness of the line. This keeps the graph from being a solid blob of color. Second, it is common practice in tweeting to NOT include the hashtag in any replies. This means that that any graphs or counts from the dataset should be understood as an undercount and underestimating the behavior. This cannot be stressed often enough.

What was said in this cluster? What were the word pairs? Who was most mentioned?

Top Hashtags CountTop WordsCountTop Word Pairs Count

I was honestly puzzled by the “1” that was the 142nd top word, until I connected it with the “one” and the “1tmcthing”. Maybe the use of “1” as a standalone word had to do with 1TMCThing? I won’t know until I do the qualitative analysis, but that is a question I have already.

Already, the idea of equity is coming through strongly, with TMCEquity, Grace Chen showing up in all three columns. IN addition, other sessions also showed up, with TalkLessAM and ClotheslineMath. Gratitude is a surprise word, with “thanks” having a strong showing, along with “love”. The context of those words being used is unknown as of yet, but the fact they are there indicates something positive.

The people who were most replied to or mentioned in Cluster 1 were:

Top Replied ToCountTop MentionedCount

Comparing this list with the list above, it is clear that “pushsend” had a lot of traction, even if the participants didn’t connect it with CarlOlitwitter every time. In fact, it is clear from the counts that it is much more common to name someone than to reply to someone using the hashtag (see my bolded comment above). Also, that Grace Chen was mentioned 310 times, which is almost 3 times as much as the next closest person is telling. It suggests that “thanks” and “love” show up in the word count above because the three Keynote speakers also show up in the mentioned column, Grace Chen (graceachen), Graham Fletcher (gfletchy), and Carl Oliver (carlolitwitter).

It appears this cluster is composed of individuals who were having conversations about the keynotes and sessions, typically. Compare this with Cluster 2.

Top HashtagsCountTop WordsCountTop Word PairsCount

Just looking at the counts, there is something different with the cluster. Looking at the top word pairs, in cluster 1 there was a small range compared with the range of counts in cluster 2. The counts of word pairs in cluster 2 was also higher, across the board. The smallest of the top 10 was 31, whereas the third largest in cluster 1 was 32. This may indicate there was more unanimity in the cluster. More people saying the same thing.

Top Replied-ToCountTop MentionedCount

There was also a lot of math talk in this cluster, with Desmos and IllustrateMath being among the top mentioned. Grace is mentioned, but the other two keynotes are not. Jenise Sexton is is mentioned, and she had one of the top 10 links for the entire data set. This indicates that equity is playing a role in the cluster, which connects with the TMCEquity hashtag being in the top 10 as well. The surprise is the hashtag TMCJealousyCamp being used 20 times. That requires further analysis as to why that was used in cluster 2.

I am still exploring how to compare clusters with this quantitative data. If you have any suggestions, please let me know. If you have any questions, please ask!

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In my last post I went through some of the graphs that NodeXL created of my data set. There are additional quantitative elements which need to be discussed.

For example, who are the most ‘influential’ people in the data set? There are several ways to indicate influence, and one way is ‘betweenness centrality.’ This measure calculates the shortest (weighted) path between every pair of nodes in a connected graph. So, for my data set of 1319 unique nodes, it calculates the shortest path between each of those nodes. The node with the largest number of shortest paths, ends up with the largest value of betweenness centrality. A node with only 1 connection would have a value of 1.

So who are the most influential nodes of the data set? In order they are:


It is interesting how much larger Julie Ruelbach’s betweenness centrality value is compared to everyone else. Annie Fetter has a solid middle number in between Julie’s and the rest of the bunch. If these were placed on a numberline, we would have a cluster of values for 10 – 8, a gap to Annie, and then another larger gap to Julie. What creates that huge value for Julie? She is in the center of group 1, and she pulled many people to her in tweeting and retweeting. She also had a very large number of self-tweets as well. Self-tweets are a ‘circle’ dyad, where no one replies, retweets, or likes her tweet, and includes no other person in her tweet. Julie had both the largest number of connections AND a large number of self-tweets.

NodeXL also gives the top 10 elements of the entire data set, and each of the top 10 clusters. In the data set, the top two shared links were the google form for archive submission (#1 at 44 times) and the single page with reminder links for the conference (#2 at 35 times). That is unsurprising. Numbers 3 and 4 are more interesting. Jenise Sexton’s blog post on “Being Black at TMC was shared 33 times, while Annie Perkin’s blog post on “The Mathematicians Project: Mathematicians Are Not Just White Dudes” was shared 27 times. This shows a strong element of equity attention by the community. The 5th most shared website (23 times) was CreativeCommons.org, which is surprising to me. Perhaps one of the morning sessions had a great discussion about creative commons licences?

Finally, the last 5 sites were both the first and last 20 minutes of Grace Chen’s keynote on equity (22 and 16 times respectively) [links not included on purpose], Julie Ruelbach’s post (21 times) on using Desmos for assessment, how-old.net (19 times) and a google document entitled “Learning about Contemplate then Calculate“.

What can be learned from this list of top 10? There was strong interest in equity. Of this top 10 list, four of them are directly tied to an equity discussion. Three of the top 10 are connected to sessions and mathematics, and the last three are connected to conference management somehow.

Notice he difference between the Top URL’s and top domains, however.


Twitter.com comes from sharing someone else’s tweet, and tweets were shared a lot. Five of the top 10 are blogging platforms, with three of them individual’s blogs, and pbworks.com is where the conference stores documents from the sessions. No one session sessions shared a pbworks link enough for the link to be in the top 10, but in total the sessions shared links enough to make it to the top 10 domains. Desmos is, well, just awesome. Still, only 24 times was a Desmos link shared with the hashtag TMC17.

When the top 10 hashtags are listed, the similar connections as above are seen.


Ignoring the top two as pro-forma hashtags, Carl Oliver’s “PushSend” was the top hashtag used at the conference. In fact, there is essentially one use for every single attendee. Similarly with TMCEquity and Descon. ITeachMath makes a showing during the time that TMC17 was occuring as well. That Descon was the day before the conference, with a smaller group of people shows its strength in the discussion. The Sketchnote hashtag showing up at number six is interesting, because if word pairs are examined, the top word pair has to do with sketchnotes.


In fact, the top two word pairs are connected with Jill Gough’s sharing of the sketch notes created during conference sessions. In addition, the pairs “relationships, kids,” “kids,think,” “numbers,mfannie,” “think,math,” and “math,relationships” show a that a good deal of the conversations on Twitter had to do with math content and how to bring math learning to kids.

This is the entire data set, however. The different clusters may show differences in discussions (which hopefully they do, otherwise what is the point of different clusters?) That is another post, however.

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First, some context. This is going to be rough. I am trying to wrap my brain around what is important, what is not, and how to frame the important to tell the story. First off, here are the three research questions I am addressing:

RQ1: What are the network behaviors of participants in TMathC in 2017?  RQ2: What is the human activity of conference participation of TMathC in 2017?
RQ3: How are the network behaviors and professional development activity of the participants interrelated in TMathC in 2017?

This blog post is a first attempt at answering the first question only. The second question is a qualitative question that will be answered by actually reading each of the tweets and blog posts from TMC17. The third question will be answered by putting the results of the first and second together.

The software I am using to do this analysis is NodeXL. NodeXL is created by the Social Media Research Foundation (https://www.smrfoundation.org/nodexl/) and is available in both free and pro versions. I am using the pro version to do the analysis you will find in this and later posts.

To collect the data for this analysis, I every day from 4 days before TMC17 through the end of August, I downloaded the Twitter activity using a search on the hashtag #TMC17. This only collected public tweets that contained the hashtag. That means that followup tweets between people may not be collected unless they used the hashtag in their replies. This is typically not frequent behavior, so all of the analysis below should be understood as underestimating the actual patterns of communication. I bolded this statement, because it cannot be stressed enough.

First off, is the pattern of communication different from a “typical” math teacher conference (whatever that may be?) The easy answer is yes. Working from the public list of TMC attendees (https://twitter.com/TmathC/lists/tmc17) the number of attendees was 189. The data set I downloaded and compiled has 1348 unique accounts in it. Comparing the two lists, 169 of the 189 listed show up among the 1348. This means that 89.4% of the participants at the conference had some kind of Twitter activity. That is a huge percentage of attendees in the attending participants (AP) in the data set. A little arithmetic shows the number of remote participants is 1159. This means the ratio of AP to RP is 0.1458, or 14.6%.

These 1348 nodes (they are not all people, some are accounts like NCTM) created the following network map.

The G1-G25 reference the Clusters the software segments the nodes into based upon their patterns of communication. So, for example, the G1 cluster has a tight group of nodes in the center, with a radiating pattern of nodes around it. The small central cluster communicated with each other frequently, and the radiating nodes had less communication. The words are the top words used by the nodes within each cluster. I set the software to ignore the TMC17, MTBoS, and ITeachMath hashtags. Otherwise they showed up in every cluster.

This graph tells me that there is a great deal of communication between the different clusters. In fact, almost every single cluster has strong communication ties with cluster 1, 2, 3, and 4. Cluster 8 has none, but given that TMCJealousyCamp shows up in that cluster it makes sense.

But which of these nodes are AP, and which are RP? When that question is asked, I realized there are actually four different communication patterns which must be explored.
AP to AP; AP to RP; RP to AP, and RP to RP.

It is very difficult to see all four one map. The tightness of the communication patterns means that the colors overlap, and wash each other out. What if, I only look for RP to RP communication in the data, and I hide all other communication? Is it reasonable to think that remote participants talk to each other about TMC17?

Surprisingly, the answer is YES! In fact, in some clusters (notice I changed the default “G1” notation to “C1” to align with the vocabulary I am using) there is a tremendous amount of RP to RP communication. In addition, each of the clusters has RP to RP communication. C9 has strong grouping of communication, which aligns with the fact that is a cluster of GlobalMathDepartment communications. I also limited this graph to only the top 10 clusters, and added the count of the number of unique nodes into the labels. This helps give further context to the graph (I hope).

Do the RPs engage with the APs?

Again, yes. The RPs engage with not just other RPs, but in large amount with the APs. This graph shows RP to RP and RP to AP directed activity. The graph shows that the RPs engage with the APs more than with RPs, which is to be expected. But do the APs engage with the RPs?

Adding in the AP to RP directed activity creates more edges where there already existed edges, resulting in more lines between the participants, and a darker red. The RP AP communication definitely worked both ways. When the AP to AP communication is added back in the result is:

This graph shows in blue the AP to AP communication along with any RP communication in red. At this point, it is clear that TMC17 was not just a conference for the people in attendance, but it was a conference for a much larger number of people who were participating remotely. The numbers also show this:

Total number of APAP dyads: 7592
Total number of APRP dyads: 1620
Total number of RPRP dyads: 1559
Total number of RPAP dyads: 2778
APAP/(all others) = 7592/5957 = 1.274

A dyad is a two part communication pattern. For example if I were to tweet (not a real tweet, mind you):

Hey @TMathC, you should check out the blog post on the initial analysis of TMC17! @cheesemonkeySF, @druinok, @lmhenry, you should too!

This tweet creates the following four dyads:

gwaddellnvhs to TMathC

gwaddellnvhs to cheesemonkeysf

gwaddellnvhs to druinok

gwaddellnvhs to lmhenry

Should one of those individuals reply, it would create an additional four dyads. This is how the directionality of the tweets is maintained, and how I managed to show the directionality in the graphs above. It also means that while the largest number of dyads is between AP and AP, the ratio of APAP dyads to any dyad which contained an RP is 1.3. This Remote Conference Participation Ratio (I think I just created a new metric) is interesting. A ratio of 1 would mean that there is equal participation between attending and remote attendees. It isn’t a ‘clean’ ratio, because AP shows up in RPAP and APRP categories, but it does suggest a level of RP participation.

That is enough for today. Hopefully this gives the mtbos and iteachmath community something to challenge and think about.

Please, give me feedback. If there are questions here I have not addressed, ask. I welcome the pushback and opportunity to answer your questions. After all, that will just make my dissertation better.

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It is crazy, but I have not blogged once during this semester. My last post was a forward looking statement on class closures that I wanted to do. The good news is, I did it. Every single day, I had an alarm set, and I did the class closure. You can find my form here: http://bit.ly/Knowing2018.

I had an alarm set to go off 5 minutes before class ended, every single day. When the alarm went off, the learners in my Knowing and Learning class knew there were 5 minutes left, and they reached for their devices. It worked so well.

The learners were honest with the questions as well. I had some learners say, “Agree” to the fact that they were not challenged in class. They told me why. I had an agree with “treated kindly by my peers” one day when a learner was sarcastic and mean.

The real payoff was in the “Answer the question on the board.” I had a day by day reflection on what the class learning was for them. I will do this again, definitely. I encourage others to as well. It worked.

I have some other things to say about things I tried this semester. I created an asset/ deficit thinking exercise that I want to share. It was a good semester, but crazy busy. I was in a writing rut, and was not making progress on my dissertation, and the entire thought of writing anything outside of that scared me to death.

Good news is, I passed the proposal by the end of the semester, and am furiously doing my data analysis. I will have much, much more to say about this, because I am going to use my blog as a rough draft writer. Stay tuned!

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The semester starts tomorrow for me, and I am working hard at addressing some of my shortcomings. One weakness I have always had was the closure to my lessons. 

I could never really figure out how to close the lesson. No, scratch that. I knew how, I never really could REMEMBER to do a good closure! With that in mind, I have done a couple of things this semester to help me.

  1. I have set a repeating alarm on my cellphone. It goes off 5 minutes before class ends. I have selected kind of a soothing, interesting music to sound, as well as vibrate. This is my reminder to stop, and DO the closure.
  2. To make the closure process easy, efficient, and solid, so that I WILL do it every day, I have spent some time this summer collecting ideas for solid closures. That link will take you to a google doc where you will see many of the ideas and questions I have collected.  [Please feel free to add more!]  One thing that is going to make it easier, is my use of google forms to do the collection. (thank you Mari Venturino!) I think her form is amazing, and I have adapted it for my own use. This takes my 50 minute class down to 45, but I think it will be worth it. 
  3. I really like the 6 questions she has embedded in the middle of her form. 
Mari’s class feedback

I have challenged my apprentice teacher to ask question 2. I think he will be surprised by the answer. I really wonder why we don’t ask that question every single day, every single class! I think we are afraid of the answers. 

So, my first goal this semester. Every single class, an exit ticket of some form. Non-negotiable. I must close the class by modeling exit tickets, and USE that information in the next class planning. 

I am excited to begin the new semester! It is going to be a rough one. 5 different classes to teach, AND writing a dissertation. No big deal. I got this!

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