But, they are the 800 lb gorilla of PBL. There are not a lot of resources for teaching mathematics through PBL. Heck, we can’t even agree what PBL means in math. I have seen the acronym used for Project Based Learning (this is how BIE uses it). I have seen it used for Problem Based Learning. I am helping teach a class for preservice teachers this semester called PBI, which is short for Project Based Instruction.

Way too many acronyms here. So in the interest of keeping things straight and organized, I will consistently use the following acronyms:

PBL: Project Based Learning

prBL: Problem Based Learning

PBI: Project Based Instruction

prBI: Problem Based Instruction

I think each of these has merit, and a use.

That is the goal of this post. To tease out the differences, and justify the need for both.

First off. I am not going to focus on the difference between Learning and Instruction. I don’t think it is that important. The difference is the difference between whether we are talking about the teachers (Instruction) or the Learners (um, learning :)).

So the issue is the difference between Project and Problem. Where does that fall? What does it mean for the classroom?

Projects, according to BIE has 8 pieces.

- Key knowledge, understanding, and success skills
- Challenging problem or question
- Sustained inquiry
- Authenticity
- Learner voice and choice
- Reflection
- Critique and revision
- Public product

An amazing new book by NCTM called Rigor, Relevance, and Relationships: Making Mathematics Come Alive with Project Based Learning mirrors these elements.

But, there needs to be some explanation. When they say “Sustained Inquiry” in the third element, and “Learner Voice and Choice” in the 5th, they are not talking a free for all. If we put the inquiry into the context Trevor MacKenzie uses in his inquiry books (see the image below).

No, we are not talking about Free Inquiry when doing either PBL or prBL. We ARE talking about Guided Inquiry. This was never made explicit at PBLWorld, but they hinted at it strongly. In fact, it must be. The whole point of a teacher coming up with a guiding question (second point), and making sure that standards are being hit (first point) means we cannot be doing Free Inquiry.

And the standards to be addressed are not just the CCSSM or CCSSELA standards. The standards are also the 21st Century Practices standards. Some districts are requiring teachers to show how they are incorporating these standards into your teaching. When doing PBL, it is simple. They are put into the project right from the start, and clearly practiced at the end in step 8: Public Product.

Problem Based Teaching or prBL is very similar. If you want to read an expert on the topic, Carmel Schettino has a wonderful series of posts on the NCTM’s Blog. There are 4:

- Aspects of Problem Based Teaching
- Aspects of Problem Based Teaching – The need for community
- Aspects of Problem Based Teaching – Assessment
- Aspects of Problem Based Teaching – Student Conversations

Carmel also runs a conference in the summer of prBL, called the PBL Math Summit, and she has many resources available on her blog.

If you examine what she writes, she has essentially the following steps:

- Key knowledge, understanding, and success skills
- Challenging problem or question
- Sustained inquiry
- Authenticity
- Learner voice and choice
- Reflection
- Critique and revision

I think Carmel may actually merge a couple of these. I think it is silly to have step 3 “Sustained Inquiry” separate from “Learner Voice and Choice” but that is a Buck Institute thing. I left it, because Carmel talks about inquiry and learner choice as well. (Carmel can correct me if I am mistaken in that, I don’t want to put incorrect words in her mouth.)

The big differences are the public product, and the nature of the ‘guiding question’. The guiding question (step 2) for PBL should be open ended and allow for a great variety of learner choice. That isn’t to say that prBL questions can’t, but types of Open Middle questions or even closed ended, but interesting questions avaiable to prBL would be excluded in PBL.

The biggest difference is the Public Product. In prBL, there is not a demand for a public product as a concluding phase to the prBL. This means that many more prBLs can be done in the course of a school year than a PBL. It also means that prBLs can be done as practice elements for a full PBL. Imagine doing a couple of interesting prBLs and then opening up the question more on the next one and turning it into a PBL.

There are other people who work on the topic of PBL. John Spencer is an author of materials on PBL. I definitely get the feeling he is very ELA based. He writes in that link how he failed at a math PBL, but writes at length about how to incorporate ELA standards into his classroom.

If you are looking for math, specifically, there are people to follow and engage with.

Carmel Schettino for starters. If you are interested in expanding your horizons on this, follow her. Talk to her. She is amazing. Her publications include the following:

Schettino, C. (2003).

Transition to a Problem-Solving Curriculum. Mathematics Teacher, 96(8), 534-537.Schettino, C. (2011).

Teaching Geometry through Problem-Based Learning. Mathematics Teacher, 105(5), 346-351.Schettino, C. c. (2016).

A Framework for Problem-Based Learning: Teaching Mathematics with a Relational Problem-Based Pedagogy. Interdisciplinary Journal Of Problem-Based Learning, 10(2), 42-67.

Another person is Tia Vandermeer. She works in Canada, and does PBL in mathematics.

Also, follow the hashtag #PBLChat. Many, many teachers using PBL in their classroom (and some of them are doing prBL too!)

Get the book mentioned above. It is FABULOUS! If you want the link again, here it is: Rigor, Relevance, and Relationships: Making Mathematics Come Alive with Project Based Learning. Buy it. I promise the full retail of $36 is a much, much greater value than the $1100 of PBLWorld.

]]>Instead, I want to draw your attention to this image. You can click to embiggen it.

Source: https://arxiv.org/pdf/1806.03163.pdf

The beauty of the proof is immediate and powerful. No mathematics beyond the image is necessary to understand the idea, but it helps. The 1 page paper also has the following math to support the proof.

That is it. The author gives only those two lines. Which really, are three lines, because the author abuses the equal sign notation in line 1. I spent some time deconstructing this, and came up with the following, more easily followed, version of the proof.

Brilliant. It is just beautiful in its presentation. Such an amazingly approachable proof. But notice that red square. There is some magic going on in that square.

Could this proof be done with a function f(x)=-x? Or how about f(x)=(x=pi)^2? The visual element appears to yield the same information.

The area of the rectangle is greater than the area under the curve. But does this yield the same proof? I worked it out, and I ended up with some cool math, but nothing which approached e^pi or pi^e. Visually good, mathematically on the wrong track.

So what is going on in the red box in the hand drawn proof above? What is so different?

The difference is that in the original paper, the author recognizes that out of infinite number of functions that are decreasing from the interval { e, pi } the one function that will yield the area under the curve as log(x) + constant is f(x)=1/x. Recognizing that and realizing that one must work in base e, and from there we can create the necessary exponential.

That is very creative.

Amazingly creative.

I have been enamored with this problem ever since Taylor Belcher posted it. It is obvious at one level, and so not obvious at other levels. The graph and areas are obvious, but it is not clear how that translates to the idea that pi^e < e^pi. That leap, that jump from any decreasing function, to a specific decreasing function which creates the necessary area is the creative leap that can be difficult.

I see that with the college learners as the move from the calc series to the proofs based courses like groups, fields, and rings. The approach to the proofs classes must be different because instead of procedures, the learners must push creativity into their work. They must think of the options they have for an approach and pick and choose with intentionality.

The balancing of the goal with the multiple paths which can approach the goal, and choosing made me think of Bob Ross and his painting show on PBS. “I need a happy tree here, so I will use this brush and …” He talked about what outcome you wanted, and decisions that had to be made along the way. He spoke of the joy of selecting color, making mistakes, fixing mistakes, and not becoming trapped in decision, but pushing forward to obtain the outcome you wanted.

That is the beauty and joy of math. The art that can be found in math.

I really need to stop procrastinating, but I found so much joy in this proof that I wanted to share it.

]]>Here it is in it’s entirety:

Engaging the Mathematics Community; Miscellaneous Assignment 2: 10 points

The goal of this assignment is to encourage you to engage with the existing larger mathematics education community. You must do one Global Math Department video presentation and one Twitter Chat.

To get full credit, you must provide a transcript of your interactions (copy and paste) to verify the Twitter chat. For the Global Math Department, if you participate in a live chat, copy and paste the transcript. If you watch a video of a past presentation, reflect on the material. For the reflections, you should answer the following questions at a minimum. What did you learn from the activity? Who was the person or persons who had the largest interaction with you? Describe them based on your interaction. What is the value, in your opinion, of the activity? How would you use this in classroom practice?

Global Math Department:http://globalmathdepartment.org/ These weekly video chats occur weekly on Tuesday evenings, 6:00 pm Pacific time. They are an hour long, on a variety of topics relevant to mathematics K-12 educators. For example, recent presentations have been on the topics of ‘Improving student discourse through debate in the math classroom’ or ‘Interactive notebooks: Tapping into left & right brain thinking.’ Go to the link and hit the big blue “Conference Info” button for more information. All videos are archived at the end of the session.

Twitter Chats:https://twitter.com or even better, https://tweetdeck.twitter.com Twitter chats are hashtags used to collect people who have a similar interest. There are ‘live’ chats at certain times (usually an hour, sometimes 30 minutes) and there are ‘slow chats’ where individuals post a question using the hashtag and others reply when they can. Every hashtag is used throughout the week in the ‘slow chat’ model even if there is a ‘live chat’ time. When engaging in a chat of either type, always introduce yourself, and use the hashtags in every tweet.

- #alg1chat: “slow chat” style, no set time or evening
- #alg2chat: “slow chat” style, no set time or evening
- #geomchat: “slow chat” style, no set time or evening
- #msmathchat: Monday evenings, 6:00 pm Pacific time
- #mathchat: “slow chat” style, no set time or evening
- #statschat: “slow chat” style, no set time or evening
- #teachNVchat: Thursday evenings at 7:30pm Pacific time
- #swdmathchat every other Thurs 6pm Pacific
- #elemmathchat every week, 6pm Pacific
- #makeitreal every Wednesday, 6:30 pm Pacific
These last two hashtags are not chats, but are general hashtags used to include the larger community of mathematics teachers. Make it a practice to include both of these tags in each tweet. #mtbos #iteachmath

My college students laughed at me. They said, “I don’t use Twitter, it is just for celebrities and stupid politics.”

Ha! I had the last laugh.

Three brave souls said, “Okay, Waddell, I will try it.” I retweeted their first post (because they had zero followers), and the Math Community stepped up! Within 1 minute, all three had responses. And then more responses. And they had a discussion. And within 5 minutes they were so excited that other math teachers were actually sharing and talking with them.

They were so loud, that within 5 minutes, three additional PSTs joined Twitter and tweeted. The same thing happened. One PST said, “I can’t wait to be out in the classroom, get stuck, and realize I have a whole community of people to help me out. This is awesome.”

I was proud. I am proud.

This is a heartfelt Thank You! Thank you to all who helped my learners see there is a larger community of math teachers who want to help. Thank you to all those that didn’t help last night, but help others every day, once a week, once a month, or whenever they can. Thank you to all the teachers who are lurking, and thinking they are gaining something from reading others posts. Thank you to all those who will be joining the community in the future.

We all grow when we learn from others.

Thank you.

(edited to add additional chats, 1 July)

]]>I made something! I haven’t been very ‘makey’ lately. Focusing a lot on teaching college students, observing college students in the classroom, and then observing more. But, we got a new classroom on campus at the beginning of the semester, and we needed decorations. I looked all over for some good, high quality posters of the Standards for Mathematical Practice, as well as the Mathematical Teaching Practices (from the Principles to Actions) but couldn’t find anything .

Seriously, nothing. I looked on publishers sites and couldn’t find any good looking posters that matched.

So, I made my own. Much thanks to Meg Craig who helped me get out of my own head and improve the design. I used the golden ratio in the design elements a couple of different ways. Below I attached files that are standard sized (good for printing on regular paper) and a high resolution version for poster printing. I am having them printed 2ft wide by 3ft tall to hang in the classroom.

I got permission from Trevor Makenzie for his “types of inquiry” graphic. I think it adds something to the poster to have that additional information, especially since it relates strongly to MTP 4 and 5. The other images are public domain, no attribution necessary, or taken by me personally. The diagram of the types of representation is Figure 9 out of the Principles to Actions, and the book is cited at the bottom.

As I was making the two, however, I realized that I needed a third. My learners were asking for questions to ask and how to develop better questioning strategies. I had just read Cathery Yeh’s book and she listed a whole series of questioning strategies. So, I made third poster.

Not all of these are Cathery’s. I modified them, deleted some that wouldn’t work well for the secondary school arena, and added some from Steven Leinwand’s presentation at the Breakfast and Math we held in Reno a couple of weeks ago.

All in all, I think they turned out well, they represent what we are trying to do well, and they will be something that can be printed off and given to future math teachers as they graduate.

Let me know what you think!

Math Posters for classroom (standard sized for viewing or printing on 8.5×11 paper)

Math Posters for classroom – high resolution (larger file size for printing poster sized)

Update: Half Tau Day 2018

Here are pics of them in the classroom.

Right wall (facing students) Left wall

]]>One take away (and I had more than one) was from Samuel Otten, (twitter: @ottensam) host of the MathEd Podcast and Zandra de Araujo, both are assistant professors of math education at the University of Missouri. The team gave a fabulous presentation on why we need to nudge teachers, and not expect radical transformation of teachers. They are right on the money, in my opinion. Radical transformation is hard, but incremental steps are easy. Think about changing my diet. If I say, “tomorrow I will become a vegan” that will take huge amounts of energy and effort. However, if I say, “tomorrow I will start eating an apple every day” that is easy, and a great first step. Day 2 I swap out regular milk for soy milk, day 3 I swap out breakfast, etc. Small, incremental steps are easy to adopt and lead to the same results.

Think about Steven Leinwand’s 10% rule. No teacher should be expected to change more than 10% of their practices in a year. However, every teacher should be expected to change 10% of their practices in a year! Small, incremental changes.

During their presentation, they put up this image.

Don’t get hung up on the percentiles or quality of instruction axis. There is no scientific basis for this graph, just a gut check, a collective grasp of what do we think is the distribution of teachers at each level of quality. But, we believe there is a distribution of teachers who are at the low end of quality of instruction, and some at the high end, and some in the middle.

And we have been talking about radical change in the quality of instruction since 1989 when NCTM published the Curriculum and Evaluation Standards. That is 30 years of conversation about changing math instruction.

30 years.

At that point, we really have to admit, that the real leaders of mathematics education are those teachers who are on the low end of the Quality of Instruction scale, whether they are 25% or 75% of the teacher population.

That group has been driving and leading the discussion on Quality of Instruction for 30 years.

We don’t discuss the gains we have made in changing mathematics instruction, we constantly talk about and research the lack of gains. They are the real leaders.

That is really sad!

They also showed what happens when we stop talking about radical change, which only moves the right side of the graph higher, and does little to move the left.

Moving the left side of the curve requires nudging teachers. Introducing small changes, that build over time. If we really want to change the shape of the curve, we need to stop expecting radical change, which only a small number of teachers adopt. We need to gently add to the skills and abilities of all teachers.

This was a powerful presentation. I only cherry picked 2 slides out of the entire thing. He gave a much stronger argument, using a variety of approaches.

Thank you Samuel and Zandra!

]]>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.

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.

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.

]]>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:

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.

——————————-

*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.

]]>Reason number 1:

I don’t know what to say about this other than express my complete and utter revulsion at the ideas expressed by this new graphing calculator app called Graphlock. From the video on the site, “Want to save thousands of dollars on calculators while also helping to reducing distractions in the classroom?” That is the first sentence of the video.

Their solution? Charge students $4.99 a YEAR for a graphing calculator app that also locks down the phone so that learners can only do math. That’s right. Don’t trust the learners, don’t create better, more engaging lessons. Don’t actually do something that is better, just lock down devices so learners can’t use them for anything else.

And it gets better. The “don’t trust learners” statement? It is literally true. The video says that if a learner tries to do something else on their phone, it alerts the teacher so the learner can be punished for being bored and distracted during the boring lesson.

Reason number 2:

According to the article in Inc magazine, the “Real Problem” of math education is that,

There is an even bigger problem underneath the seemingly big problem of the rising cost of school supplies and it’s kind of shocking: when students can’t afford the supplies they need to finish their schooling, oftentimes, they give up or drop out. Mallory pointed out that she watched this happen repeatedly while in college at Central Arizona to become a professor of mathematics. Students in her Algebra class would realize they needed this graphing calculator that costs around $100, couldn’t afford it, and would give up.

That’s right. The real problem of math education is it is too expensive to learn math.

What?

No challenge of the assumption of the college to require learner to purchase a TI calculator. No, goodness sake, we can’t challenge that. We can’t show the college she taught at all the wonderful, free math learning software like Wolfram Alpha, Google (have you tried typing an equation into Google’s search bar?), or Desmos.

Nope, the requirement is inviolate. And besides, those other things that definitely help learning? They also allow the learner to do other things besides math.

How does this create punishment?

The assumption throughout the articles is that when learning math, the teacher is the absolute authority, and must be listened too at all times. The teacher knows all, and must be in full control of every aspect of the learners thought, actions, and technology. If the learner does something contrary to the teacher’s instructions, the learner must be corrected.

Math class, becomes a class of punishment and …. not sure about the reward. Certainly punishment. Some teachers will reward, but this software absolutely entrenches the observation state and punishment in the class.

It is the Panopticon on steroids, except instead of the observation state being built into the building, it is built right into the learners’ devices. Besides, from the award she won, it isn’t about math education at all. It is about winning seed money for a business. The **Real Problem** is companies making education more expensive through the corporatization of education.

This horrible software feeds into the reasons for the US failing behind in mathematics. Math class is one of memorization and regurgitation, not thinking, creativity, or joy.

Just so that I don’t leave this post angry and hostile, I will leave this here. “Math for Human Flourishing.” This article from Quanta Magazine about a talk given by Francis Su restores my soul a little bit.

As an aside:

Here is a college professor named Mallory Dyer. She is the creator and inventor of the calculator.

Yes, she has a name. You wouldn’t know it by the headlines about the software. Here are the two that came up in my reader and made .

Coolidge woman develops app to make studying math affordable (Casa Grande News, a local newspaper)

and

How one woman is making math affordable (Inc magazine, a national business magazine)

They wouldn’t even name her in the headline? No mention of her academic credential. She is just “a woman.” How about, “Professor at Coolidge develops app to make studying math more affordable.” Those 7 extra characters going to kill them? Or “How one professor is making math more affordable.” This isn’t an issue with software (more on that below) but the way this professional was treated. Stop the sexism, already.

]]>I am stunned by how many I have. Clearly, this topic is one that mathematics professionals are discussing and writing about. Communicating this to educators who are not aware of the breadth and depth of the conversation is why I am posting these.

Mathematics organizations’ official positions

- NCTM position statement on Access and Equity April 2014
- NCTM position statement on Closing the Opportunity Gap February 2012
- NCTM position statement on High Expectations July 2016
- NCTM post on Response to Charlottesville (n.d. listed) but published August 2017
- NCSM and TODOS: Mathematics for All, position statement on Math through the lens of social justice (PDF) Not dated, but published 2016
- AMTE (Association of Mathematics Teacher Educators) position statement on Equity in Mathematics Teacher Education November 2015
- The MAA (Mathematics Association of America) has 3 standing committees for the topic of underrepresented groups in mathematics
- The AMS (American Mathematical Society) has multiple program for underrepresented groups in mathematics

Blog posts from other mathematics organizations

- The AMS post on Discussing Justice on the first day of class (17 August 2017)
- The AMS has a blog dedicated to underrepresented groups in mathematics: inclusion/exclusion
- The Math Ed Matters blog of the AMS has a post on Equity in Mathematics with more links. 29 February 2016

Journals whose content is focused on Equity and / or Justice, or important articles

- TODOS: Mathematics for All, Teaching for Excellence and Equity in Mathematics (TEEM) Journal
- Journal for Urban Mathematics Education (JUME)
- Journal of Mathematics and Culture (sponsored by North American Study Group on Ethnomathematics, NASGEm)
- The Journal of Humanistic Mathematics (current)
- The Humanistic Mathematics Network Journal (HMNJ, 1987-2004) See #9, which is the new journal.
- Marta Civil. (2006). Working towards equity in mathematics education (PDF article)
- Lawrence Lesser. (2007). Critical Values and Transforming Data: Teaching Statistics with Social Justice. (PDF article)

Sites or Organizations focused on Math Equity

- Benjamin Banneker Association, Inc (BBA)
- Women and Mathematics Education
- The Math Forum’s resources on Equity
- The Mathematics Assessment Project (MAP via MARS) TRU framework
- Math and Social Justice: A Collaborative MTBoS Site : This could be a very important site for these issues. How can we build it up?
- Twitter search for #TMCEquity hashtag

Non-Mathematics, but other education organizations

- The NCTE (National Council of Teachers of English) posted, There Is No Apolitical Classroom: Resources for Teaching in These Times. This page has a thorough collection of resources which can be used across curriculums. 15 August 2017.

When I think if equity, I think along the direction CMC does:

The other day, I heard another definition that I had not encountered. The (paraphrased) quote was, “It is important that we think of equity in our classrooms, so that a B in one section with one teacher means the same thing if that student transfers to a different class in the same school or different school. We have to think of equity in our classrooms.”

The word ‘equity’ was specifically mentioned twice. The teacher meant to use the word.

I have a trouble reconciling this meaning of equity with the meanings outlined in the graphic above, unless we push it into “achievement.” But the text for ‘achievement’ doesn’t easily allow for this definition. The text is “What are some of my beliefs, expectations, behaviors and practices, and tools that ensure mathematics proficiency for every student?” Maybe, but it is not obvious where consistency in grading practices across teachers is an equity issue. It appears to me it may be more of an equality issue, not equity.

Clearly, equity is a term that needs to be given some additional context so we are speaking to the same topic.

My huge takeaway? Listen more and listen for understanding, not responding. I learn more that way.

]]>