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.

Sep 062015
 

In my Feedly this morning popped up the article by Larry Ferlazzo called, “Disappointing NY Times Article On Teachers & ‘A Sharing Economy’.” Okay, let me be more blunt. I am not disappointed in the NYT, I am frustrated and a little ticked off. It stems from this article in the NYT: A Sharing Economy where Teachers Win by Natasha Singer.

Read the article. I call foul AND shenanigans. How much did TeachersPayTeachers pay for this fluff piece that was nothing more than an advertisement for teachers selling out other teachers.

youblewit

Maybe it is because I am active and love the #MTBoS (that is the MathTwitterBlogo’Sphere, if you are not familiar with it.) I embrace the sharing, the collaboration and the freely giving of resources that the math teachers do on Twitter, their blogs and the internet in general.

The article should have been titled, “A sharing economy where teachers win, but collaboration dies.” Sure, some teacher just made $1000 by selling her lesson plans to a 1000 different teachers for a buck. She won, but collaboration died. Is she seeking feedback from people who have used her lessons? Is she improving them by discussing and talking about how others have used them? Probably not. It is in a store, and people are buying it. There is no reason or need to improve it.

Meanwhile, in the #MTBoS, teachers are making, sharing, improving and resharing lessons all the time. They are coming together to make better lessons. And then, they talk about these lessons, which spawn more, better lessons. This is a collaborative community where ALL teachers win, and more importantly, our learners win. And our learners continue to win. Over and over again.

Seriously, look at the amount of resources freely created and given away.

First up, websites created by teachers collaborating:

  • Let’s start with the MTBoS Directory. No one claims this is an exhaustive list. It requires teachers to add their names to it, but there are currently 344 teachers in the list, all with an online presence, and all sharing things.
  • Nixthetricks.com – created by Tina Cardone and teachers all over the #MTBoS who contributed tricks. You can download the most excellent book for free.
  • Fawn Nguyen’s Visual Patterns and Math Talks. Both are excellent sites. I have used the Visual Patterns site frequently in my high school classroom, and am working on learning more about Math Talks and implementing them in the college classroom where I am now.
  • Would you Rather Math is a site I used regularly in my teaching as well. Great questions, created by and curated by John Stevens.
  • Michael Pershan’s Math Mistakes. See an interesting math mistake? Submit it to this site and have a discussion on the thinking the learner made while making the mistake. We can learn more from mistakes than we can from correct work.
  • Dan Meyer’s Google spreadsheet of 3 Acts lessons. More on this to come. I am working on an idea taking shape out of my current position as a Master Teacher with a UTeach model school.
  • Mary Bourassa’s Which One Doesn’t Belong. So Mary saw Christopher Danielson’s great shapes idea, and realized that there was some amazing math thinking that could be done. BOOM, another collaborative website created.
  • Open Middle Dan Meyer introduced the idea, Nanette Johnson, Robert Kaplinsky and Bryan Anderson ran with and created the platform.
  • Desmos Activity Bank A site created by Jed Butler out of the need to share Desmos files, first showed at TMC15 at Harvey Mudd College.
  • MTBoS Activity Bank created by John Stevens (second time his name is on the list) to collect and curate some of the awesome materials created. Anyone can submit their own, and searching is easy.
  • The MTBoS Blog Search also created by John Stevens (I don’t think he sleeps). This site allows you search the blogs of a long list of math teachers for lessons, content, whatever you are looking for.
  • Robert Kaplinsky has a Problem Based Search Engine, to find those specialized lessons that are, you guessed it, problem based!
  • The Welcome to the MathTwitterBlogoSphere website has a further collection of collaborative efforts that includes some of the above but is even larger.

But that isn’t even all of it. There are teachers who are collecting curriculum, links or materials and sharing it all back out; lock, stock and barrel. These teachers have “Virtual Filing Cabinets” full of lessons that have been tried and tested, re-written and shared back out. Some call their pages VFC’s, some are just curated sites of materials.

And then there are great organizations giving away curriculum:

  • Illustrative Mathematics, free ever-more-complete curriculum that is CCSS aligned and incredibly high quality.
  • Shells Center/Mathematics Assessment Project, good as lessons, problems or assessments. I forget about this site until I am desperate, and then kick myself because it is just so good and thorough.
  • Mathalicious has free lessons and paid lessons. I have used them in class. They are worth paying for!
  • Igor Kokcharov has an international effort in APlusClick. Lots of great problems and lessons.

And this list is FAR from complete. It is what I pulled together in 15 minutes of thought. And this list does not even begin to talk about the 180 blogs

So, NY Times and Natasha Singer. You blew it. You didn’t show teachers winning, you showed teachers selling out. If you want to see winning teachers, click on any link above and read their sites.

The above are all winning teachers. TeachersPayTeachers is an example of teachers losing out on this kind of collaboration.

Nov 092013
 

Peg had a very busy Friday at NCTM Las Vegas, giving 3 different presentations in 1 day. The first was for newbies to the NCTM conference, the second was the resource presentation I already posted about, and then there was this presentation entitled: Pedagogical Judgment & Instructional Choices for Building Mathematics Classrooms.

I thought this presentation was the best one of the two I attended, mainly because it allowed the audience to get inside of her head and see what she thinks about. Short answer, she thinks about helping kids succeed. A lot.

That also means she is not thinking about BS like micromanaging homework, parents, etc. She thinks about how to support learners, how to know what they know, and how to demonstrate what they know.

This is going to turn into another “link fest” post because she cited some resources that I need to link to as I go. With good reason. She also could have used another 4 or 5 hours instead of the 1 she had. I would love to sit down with her and spend some time one on one just talking and learning from her.

Point 1: Management of Homework.

She started with a simple question, “Why are you assigning the homework?”

Are you assigning it for practice? Why? Are you assigning it as pre-learning? Why? Are you assigning it for some other reason? Why?

Are you THINKING about the homework you assign? Do you care more about the homework then your learners do? If so, you really need to stop and think about what you are doing.

This conversation immediately put me in the “Rethinking Homework” by Cathy Vatterott discussion that has occurred in my school and department. Other people mentioned Alfie Kohn’s “Rethinking Homework” article and discussion. I am embarrassed to admit I had not read that article, but I have rectified that deficiency.

Here are some quotes / statements on homework by Peg that I captured because they really struck home:

Distributed Practice not focused practice & one topic practice.  Focused practice does not show the long term results in research. [I would love to see and read the research, I am a research junkie.]

Assigning something the learners have never seen before is a way to get them to persevere.

Instead of reviewing, have the learners write the test questions. You will be surprised at how difficult they make the questions.

Turn homework into a way to take possession of their own learning. 1. Teach someone else how to do it. 2. Exeter type presentations

Teach parents to Ask, Don’t Tell. Teach the parents to ask questions instead of trying to help do the math and tell the learners answers.

Point 2: Putting work on your walls

Are you putting the perfect work on your walls? If so, think about what message that says to the rest of the class who are not there yet. If you only celebrate the perfect work, you are devaluing the work of the F, D and C learners. Their work is not important, so it does not count. Is that really the message you want to send?

Public displays of work should create an “Institutional Memory for the reminders of what happened in class.” That is a very different use of displays of work than most teachers do.

Point 3: Assessment

How do the learners inform what you do in the classroom?

At this point, Peg was running out of time and she listed off some resources that are impactful on this discussion.

Dylan Wiliam and Paul Black wrote an important article entitled, “Inside the Black Box”. (another source is http://weaeducation.typepad.co.uk/files/blackbox-1.pdf). Peg strongly recommends reading the thinking about the impacts of the article. A follow up article that should be read as well I think. “Working Inside the Black Box”

Peg also recommended Dylan Wiliam’s “Embedded Formative Assessment”. This is a book I have not read (shocking) and I know is very well regarded in the #MTBoS community.

And then Peg slipped in some gems on assessment, grades and feedback that where pure gold. Seriously, pure 24 caret gold. These are things she has done in her classroom to encourage learners to take ownership of their learning.

Give the homework back to a group, with comments only, no grades, and the comments written for the group on a separate page. The learners have to then go through everyone’s homework and correctly matchup the comments to the correct problem on each person’s homework.

On EVERY CHAPTER Test, Peg required (as in not optional) a correction and reflection. The grade was such, that if a perfect test taker failed to turned the reflection (because there was nothing to correct) they ended up with a 89% on the test.

Yes, that is correct. The reflection & correction was worth 10% of the test grade, and not doing it took you down an entire letter grade.

Again, no grades on the actual test handed back, only comments. They can look online for the grade or speak to you one on one if they want to know the score.

These are ideas I will be implementing.

Finally, somewhere along in the conversation, Peg plugged the PCMI, the Park City Math Institute as one of the absolutely best Professional Development she has ever done.

http://pcmi.ias.edu/ I may have to look into it in a serious way. Especially since it is on my end of the country.

Feb 042013
 

Homework, to give, nor not? How much to give? How much is too much? What purpose does it serve? What is the purpose in assigning it?

I will be honest, I don’t have answers to these questions, but I do have some research, some documents downloaded that may help you shape your own answers to these questions.

by John Dunlosky, et al.

Let’s start off with some super new research (Jan 2013) that identifies 5 very useful study skills that make up homework and 5 that do not help. While this is related to homework it is not about homework. I feel we as teachers need to think about why we are assigning homework, and to make it completely useful we should follow some best practices. I read about this article online, and then followed the links to find the free download from the Association for Psychological Science. Thank you for providing the research for free! This article could shape the homework assignments given to make them more useful to the learner; and one hint, practice testing was found to be very useful!

by Joseph Murphy, et. al.

Okay, this article is a bit dated, but when I was researching homework for a paper, I didn’t find much that wasn’t shrill and emotional. It is relevant, because I think some teachers haven’t changed much of their homework planning from 1987 when this study was done. Again, I really think about why I am assigning this or that as homework, there are different uses for homework, and what use am I using.

?
by Etta Kralovec, John Buell and David Skinner

This short little 9 page section out of an older edition of a book entitled Taking Sides: Clashing views on educational issues by James Wm. Noll gives a pro and a con to the question. It is short, and gives both sides of the debate. In math, I think we have to give some homework. I am firmly on the Yes side of the question, but it does come down to the purpose of it.

by Nevada’s Northwestern Regional Professional Development Program for Educators

Okay, I have said “purpose” several times in this post, because that is something that resonated with me closely when I went through the training our RPDP did for our math department a couple of years ago. It was based around Cathy Vatterott’s book “Rethinking Homework” that I found to be very useful in shaping my own ideas. The Whole Homework guide above is a 138 page document created by our school district to give blackline masters, thinking guides, and tools to our teachers to help us think about homework in a more constructive manner. All in all, I recommend both the Guide and the Rethinking Homework book.

As always, I hope something here is useful to someone.

Jan 282013
 

Last week I posted research and articles on vocabulary in math, this week I have a topic of reading and writing in math class, including some mathematical poetry. Sounds interesting, right?

by James Henle

This paper offers six different versions of mathematical poems, both traditional and modern. I really liked the fact that it offers Pascal’s Triangle as a modern mathematical poem. A very different way to look at it.

by Patrick Bahls

While the author uses examples from Calculus in this paper, the justifications, descriptions, and everything else about the concepts are applicable to any math classroom. Very well thought out and very thorough treatment of why we should use some poetry in our writing assignments in math class.

by Vicki Urquhart and McREL (an organization)

This 24 page document goes through the research on using writing in math class and then gives strategies and methods to incorporate more writing in the math curriculum. There are some good ideas here, although most of the content is geared towards elementary school concepts.

Finally, some websites that have content related to this topic.

Pat’s blog, (which I love because of the ongoing “this day in math” series) had a posting on Math, Shakespeare and some good ol’ Limericks. Great article, expecially when combined with the poetry articles above.

A college professor, Derek Bruff, had a great posting on How to read a math textbook. This is a skill that is too often not taught, just assumed. Although we all know reading a math textbook is radically different than reading other textbooks.

An entire website dedicated to Writing in Math Classes by Dr. Annalisa Crannell has lots of good resources for the math teacher. Again, it is geared to Calculus, but there is enough there to figure out how to use it in other classes at the high school level as well.

That is all for today. Hopefully, as always, it will help someone.

Jan 202013
 

I think like most teachers, I read a lot. When I say I read a lot, I mean a freakin’ lot, and I save articles that I think will have an impact on my teaching either now or later. This means I have an folder with a couple of hundred research reports and articles. Over the weekend the question was posted on Twitter whether or not anyone has anything to share on vocabulary in math class.

I has some articles and emailed them to the couple of people who requested, but it made me think that a terrific #Made4Math series would be to post some of the articles. It will be doubly good because it will force me to re-read the articles.

So today, I start with vocabulary in mathematics.

by Kathryn Sullivan

This article is short, and it gives a good introduction to many of the “little” words that we use in math class often that really does create problems for many learners. What surprised me was that it wasn’t words like add, subtract, etc. It is words like “the,” “each,” “how,” etc.

by Suzanne Irujo

This article is short (6 pages) and breaks down the different parts of English that are used in math class. It definitely makes you think about the difference between Academic and Informal uses of language. In math, it is almost entirely Academic use, which causes problems for the learner (especially the ELL learner.)

by Dr. Madeline Kovarik

This 20 page research paper gives some great insights into how important the use of and development of vocabulary is in the math classroom, and then it gives some curriculum insights into how to achieve good vocabulary learning. I need to study this paper some more, because I have only recently found this paper, but on first reading it seems a valuable addition.

is by the AISD Elementary Mathematics Department.

It is an elementary level research paper, but that is okay because it has some great insights into learning vocab and bridging the Academic vs non-academic language usage. It included black line masters, ideas for helping ELL and below level learners. It is completely of use to the secondary level teacher as well.

In addition, I found a book online and downloaded it. It is a good book on the issue, but there is no way I will post the pdf file. It is still copyrighted and would be a HUGE violation.

The book is “Teaching and Learning Vocabulary: Bringing Research to Practice” by Elfrieda H. Hiebert and Michael L. Kamil. I have found some great ideas in the book, but it is a little long and very dense reading. Here is a short review of the book to see if it is something you would like to purchase.

I hope this helps someone.