Showing posts with label Equity. Show all posts
Showing posts with label Equity. Show all posts

Thursday, December 19, 2019

Anti-Racist

Listening to Ibram X Kendi read his book, How to Be an Anti-Racist, and these are some notes along the way.

The introduction starts out with his humble admission of a speech he shared for a Martin Luther King Jr Day competition/celebration which he now views as racist. This leads into his focusing on the word racist, and how it has become viewed as an attack or a slur instead of a descriptor. Anything that blames a whole group for its problems is or can be racist. The struggle is to both be fully human and to treat others as fully human.

Which I love as basically the central problem of human existence. In a recent Zadie Smith interview, she responded to a question:
"You recently wrote about Toni Morrison that the thwarting of human potential was her great theme. What is yours? My own feeling is that it’s about the failure to be human. Everybody’s born and everybody exists. But to be fully human takes a little bit of effort. I think my novels are about the challenge of actually being human and not avoiding the responsibility of being human, which is very heavy. There’s a responsibility of the single person, the responsibility of the married person and of the person with children, the person without, of the dog lover — each tiny path has its kind of demands upon you, which are incredibly hard to fulfill."
Whew.

Dr. Kendi points out that racist acts or statements are often followed with denial. When we say we're not racist, we're joining in denial and warping the meaning of the term as a descriptor. The distinction is not between racist and not racist, but between racist and anti-racist. Not racist, Dr Kendi points out, is a denial, and racists are the first to deny. So denials are no way to distinguish. Denial is akin to colorblindness, and antiracists aren't ignoring important characteristics of people that have affected their lives. They are seeing the effects and working to counteract racist thought and action. 

Each chapter covers a different specific kind of racism and antiracism. Starts with definitions, tells stories, often personal, sometimes historical, and supports with science and statistics. Then he illustrates the definitions with examples of what a racist and antiracist do or say. It's a robust structure that really supports the book's aim, which is really just the title.

Group vs individuals is a major theme of the book. Racism is the historical most harmful way of grouping individuals that we have manufactured. Dr. Kendi makes clear that every time we think or use 'because they are <fill in race>' we are being racist. To be anti-racist is to break those narratives, to treat people as individuals, to work against the consequences that racism has caused. One of the major shifts in this way of thinking is that black people can be racist if they are engaged in this kind of thinking and action. His motivating example is his own anti-black racism, and he shares anti-white racism from his story as well. Including himself in this analysis is humility and truth speaking in action, and it is powerful. 


In most of the diversity and inclusion learning I have had up until this point, the focus has been on the inequities produced by individual and systemic oppression of non-white (even as that definition has shifted) people. In this view, the minority groups can not be racist because they have no authority or power to oppress. Bias has come to be the identifier for individual racial preference, explicit or implicit.  Dr. Kendi's vision is more powerful to me because it addresses the cause of the oppression and fights against the core of what went wrong as racism was constructed.

Recently, a friend and colleague asked me for resources for anti-racist math education resources and I couldn't really think of any. I made a Google Doc to gather the resources I do now about: http://bit.ly/antiracistmath Please feel free to add or comment. We do have people in the math ed community working toward this and I know I don't know the half of it.

As Dr. Kendi discusses education, he is particularly concerned with the "racial achievement gap". The whole concept is, necessarily, in his framework, a racist idea. To be antiracist is to believe that individuals face greater challenge in schools and each learner is capable of achievement. Here is a blogpost where he details the enraging history of the idea and the tests which maintain it today.

I've taken long enough to write this that Mindshift has a post today about these ideas applied to education.

This book was specifically helpful to me this semester. One of my classes was driving me a little crazy. Pre-service teachers who were not engaged, who didn't listen to instructions, who didn't seem to care even when it involved working with kids. But this book made me realize I was treating them monolithically. I was not treating them as individuals, I was not seeing and encouraging the work of those who were engaged, and I was lowering expectations. I am a spoiled college teacher with low numbers of classes and small class sizes and I was struggling with this most fundamental of my responsibilities. This realization helped me have a better attitude, helped me individualize my thinking towards the learners. 

I love the synergy between this view of antiracism and call to action. It feels of a piece with the call to rehumanize mathematics from Rochelle Gutierrez from Sam Shah's and Hema Khodai's Humanizing Mathematics Conference

Thursday, August 2, 2018

ꓕWCƖ8

My favorite professional meet of the year has come and gone. Here's what I'm still thinking about... divided into everything else and the equity session, Take a Knee, led by Marian Dingle and Wendy Menard.

Necessary proviso: there is so much good at a TMC.  The signal to noise ratio is unimaginable compared to any other meeting/conference I've been to. I'm not trying to represent everything, and I'm skipping good stuff. This is literally what I'm still thinking about.

Everything Else

Desmos preconference: this was all about computation layer for me. Despite Michael Felton's great introduction last year I did nothing with it. Sigh. Now I feel like maybe I could, if I get some time to just process. There's a help forum, an improved Scavenger Hunt (which are the learning activities) and some documentation. Look at Chase's and Madison's Estimation Stations for what is possible. (Or watch their My Favorite on it)Plus Eli's description that computation layer is really about connecting pipes to send data. Connect a source to a sink. Christopher led a design session that covered their principles for building an activity and showed it in action in the activity Marcellus the Giant. That was also the first peek of Snapshot, an amazing new teacher tool. Turn any of the Desmos tools on or off at teacher.desmos.com/labs.

Marian's keynote. Quiet, intense and personal. This is directly a challenge to the community of math teachers. Are we on the side of equity? Are we doing what we can? Do we even see the problems, issues and concerns in front of us. Please watch.

Amie Albrecht teaches a problem solving course where she is doing so much fabulous pedagogy. The course has explicit goals of learning to problem solve, and to be able to share that verbally/presented or in writing. Feedback before grading, reiteration with wider and wider audiences... just beautiful. Folder of resources. Some things I'm still thinking about for our teacher education classes and for the redeeming mathematics class. Part of it, the Back of Mathematics, she shared as a My Favorite.

I caught Robert Berry's keynote at Desmos and his afternoon session on day 1 on the NCTM's Catalyzing Change book. Honestly, because I am terrible at reading programs ahead of time, I was just surprised he stayed! He really participated and was great about connections between the MTBoS and NCTM. One of the cool things in Catalyzing Change is that the NCTM is against tracking of students and of teachers. Are the most effective teachers teaching all the students? I do think it is a huge mistake for NCTM to paywall their essential high school content in this book. The 1999 Standards and Principles were so formative for me, and so hard to get into teachers hands. One lesson I'd love for NCTM to get from the teacher twitter community is that shared resources increases buy-in and participation. Teachers are naturally community-minded, and if you make them welcome and support them they will join. (Opinion.)

Julie's keynote. I was in two minds here. One, appreciative audience in need of the message, and two, person speaking the next day having to follow Marian and this. Wurg. The impostor syndrome message was timely. And if an old man who speaks regularly and has taught for 30+ years feels that way... sigh. But also, as a teacher educator, her message about being a teacher leader was perfect. It's not about doing everything, it's about finding what you love, doing that, and sharing. It reminded me of Dave Coffey's favorite Teaching Gap quotation:

The star teachers of the twenty-first century will be teachers who work every day to improve teaching—not only their own but that of the whole profession. -Stiegler & Hiebert
Sasha Fradkin presented on impossible problems. I love the idea of learners doing the work of mathematicians, and showing something can not happen is just as important as finding out what can. But how rarely do we ask them to do that? I'm still tossing over in my head what the difference might be between doing a general investigation, and specifically asking for outcomes that can't happen. Sasha is the author of Funville Adventures, which session I missed, but be sure to check it out.

Brian Bushart is still developing numberless problems with the teachers and learners of Red Rock.  It's really impressive to me, that they are making some great improvements to something that was already fabulous. But he realized that some teachers were using the structure in a deficit mindset. And thinking about Rochelle Gutierrez's ideas about mathematics identity, they reframed the problems with a story telling lens. Just amazing. (His slides.)

Some My Favorites: (all the TMC18 vids from Glenn Waddell)



Take a Knee
I spend a lot of time thinking about this, and trying to educate myself. I try to use the understanding I build as an inclusion advocate at the university, and in my teacher education classes, as well as some local work in the community. Despite all the time I spend reading about this, I am constantly humbled by how much more there is to learn and work to do on my own thinking. Last year's TMC session by Grace Chen, Brette Garner, and Sammie Marshall revolved around connections between equity and the Standards for Mathematical Practice. Personal work included developing a checklist to get past our internalized schema, and 'equity eyes' -training ourselves to see. (All three are/were Lani Horn's grad students. Never wrote it up for the blog, bad blogger.) It revolved around developing equity eyes.  This year I got to see Calvin Terrell who sometimes refers to this work as decolonizing. Then a 5 week workshop at work was titled Decolonizing White Consciousness, which seemed timely. That featured work of Robin DiAngelo (watch this on white privilege), adrienne maree brown (read Emergent Strategy), and a variety of readings and videos around the idea of identity.

So the morning sessions for me came down to Take a Knee or Islamic Art, and I couldn't not join Wendy and Marian. (Session resources. Twitter - #tmcequity) Both were a part of the TMC17 equity session and Wendy & José Luis Vilson's Racially Relevant Pedagogy session at TMC16 is the single most affecting hour workshop I've ever been to.

Day 1 started with us introducing ourselves with our identities. This feels very odd if you're part of a group or groups that gets to take this for granted. Straight, more white than not, male... naming has power and self-naming invites vulnerability. The day closed with an activity for trying to suss out how central all these identities are to you. It was gently brutal. In between, we tried to figure out what take a knee even meant in the context of our work in math education. A theme that continued over the three days started here: equity for our students and what did that mean, and using our lessons as a way to be relevant and real with our learners. Both are a part of the larger discussion of how teaching is political.

Day 2 revolved around standards and methodologies. Teaching Tolerance's Common Beliefs help us understand how what teachers bring to the classroom influences what we teach, and the Standards for Social Justice are as good a framework as I've seen for how we should aspire to teach. Rochelle Gutierrez's article on Creative Insubordination (in here from TODOS) provided a lot to talk about. And we had an awesome poster session on that.























It's insubordination because we are consciously trying to work against the status quo.

Day 3 was preparing to go back into our worlds. We began with powerful identity statements again. "Because of my race I can..." Says something about a group of people that can share such things. We then worked in small groups on what we can do, short, medium and long range.  My group was thinking about math lessons that reflect and think about the diversity of our schools, communities and country.

For me:

  • Short: diversify follows on Twitter. I got some great suggestions in responses to this tweet, and from the hashtag #disrupttexts.
  • Medium: incorporate SJ standards into teacher training.
  • Long: transform colleagues. Makes me woogly just to say it.
Further reading: Kent Haines - Pedagogy and Equity, Dylan Kane - Disrupt Math, Michael Pershan (not even there!) - Power Works by Isolating.

Next Year
Still thinking about this. I've been lucky enough to go 5 years in a row - is it time to make space for someone else? Selfishly, it is amazing to participate. But there won't be space if all the same people always go. I'm also conscious of not being a classroom teacher, and the thought of taking that spot is chilling. Maybe the TMC Midwest will happen? And absolutely no judgment on anyone else who is a repeat attender - I am only trying to process this for myself. 









Sunday, May 29, 2016

All the Way

Missed another #MTBoS30 post yesterday, but it was in the service of a day chock full from 6 am to midnight, so no regrets. Time with one of the bravest people I've ever met, my son doing well on his first dan (permanent blackbelt) tae kwon do test, church, dinner with family...

With a free Sunday morning, we (as a family, even) finally got to watch the Lyndon Johnson biographical movie All the Way.

It's amazing.

I'm 51 (with considerable less grace and style than this 51 year old) and this was my birth year. I don't remember it, then, but this was the backdrop of my first memories. Kennedy and King being shot, Nixon, Vietnam and Watergate was what I knew about politics and government. It was amazing to watch this movie, with its decidedly modern viewpoint. It took decades for me to move beyond childish black and white images of these people and my black and white judgment of their actions. The filmmakers are good at filming what was actually said then in a way that makes connections to today possible.

Looking back, it's so easy to identify the right side of history. To see bigotry and name it when we are free of it (we think!). My spouse is excellent at challenging us (okay, me) to see what is inequitable now.

One of the things I enjoyed most was seeing Robert Moses portrayed as a young man, working for the Student Nonviolent Coordinating Committee. That fits seemlessly into his work as a math educator. The Algebra Project, interviews (on a Selma anniversary, NPR), or his book Radical Equation. He is one of my dearest heroes.

In All the Way, Dr. Moses is portrayed as too radical to effect change. To be so convicted to principle that he can not compromise for some gains. Dr. Moses makes direct connection between the idea of civil rights and the empowerment of mathematics education. It's so complicated, it could be easy to walk away, and understandable when people do. Education cannot solve poverty, but it's such a necessary part of any solution.

Are we not able to affect change because we need an LBJ? Someone with the conviction that can see a path to equitable education and is enough of an asshole to get it done? I think we are accountable both for holding and proclaiming the principles and doing the problem solving to get to a better place. But I am on one side of it, and often in danger of fighting the LBJs who are probably on our side.

I am humbled by how generally useless academics are in society.

One of the reasons that the Math-Twitter-Blog-o-Sphere (almost as ridiculous sounding as "snick") is so encouraging to me. We are self-organizing and devoted to the education of kids independent of what the government or publishers or pundits say. Now I'd love to see the NCTM play the role of the NAACP in pursuing systemic change, too, but I'll take what I can get. And this band of teachers, working one or six classes of students at a time is getting a lot. God bless you all in your work.

We will overcome.

PS. In the Selma anniversary interview, Dr. Moses is asked what he'd like to hear President Obama say in his address. Re responds: "I'd like to hear him speak about education. We can do all we want about voting and everything else, but if we don't provide an education for every child in this country that's what they need for the 21st century then we will just be sending them to the criminal justice system. We do not have in this country an education system that is dedicated to educating every child, so I'd like to hear him speak out about that." Me, too.

Wednesday, May 18, 2016

Brown vs Board of Education

62 damn years. And still the New York Times can print this:

Why this does not fill everyone with rage, I cannot understand.

This does not include Title I, which was designed to make supplemental education for lower income students possible. Over and over statistics show that we are falling short. The best predictor for success in school is zip code.

Is this just unfixable? If it is, is it because of financial inequality? History of white privilege? Racism, current, prior, explicit, implicit?

Man, I'm bumming myself out.

I'm part of the problem. I work at a university that struggles to increase diversity, despite being within 30 miles of 3 very diverse cities. My kids go to a 95%+ white high school, because we had a chance to live close to the water and couldn't resist.

From where will hope come?

I know education helps, but expecting education to fix inequality while being broken is foolhardy and unfair.


Empowerment is the only way out. And math has to be part of it.

Sorry to be a downer. Recommendations from me include:

Sunday, May 29, 2011

Who Are the New Teachers? The Long Story

At our university, content educators are mostly in their respective content departments, which is why we have a dozen or so math educators in our math department.  In our secondary teacher prep, we have three courses that are our "Math Ed" courses: Math 229, which is HS content focused, Math 329 - which is MS content focused, and Ed 331 - which is our content seminar for teacher assisting, when the novice teachers are in schools for the mornings and teaching at least a unit.  We are in negotiations to see them during student teaching, which will be excellent.

This is another guest post from a student assistant: Brock Walsh.  He paused school for a bit, but then came back with a very clear motivation about wanting to be a teacher.  Dave Coffey already posted a bit from him, where he used the NCTM process standards as an outside resources.

In his teacher assistant portfolio, he reused a bit from his 229 class, and I thought it was a neat opportunity to follow a student from early on until later in their teacher education. As an add on, I also included his piece from this past semester on the Conditions of Learning, which Dave recently posted in the Learning Museum.

Equity - Insights from the Past

(The following is a paper that was written for MTH 229, in which I had looked into the principle of equity as I related it to my experience of a nine week observation.)

Articles: Excellence in the high school classroom is something that teachers strive for. Sometimes conducting a learning filled classroom can be easy, but other times a teacher might not fully see and take advantage of teachable moments for all students. Being aware of and preparing for these teachable opportunities for all students to learn at a higher cognitive level is vital and defined under the Equity Principle of the high school principles and standards.

The article “Focusing on students’ Mathematical Thinking” by M. Lynn Breyfogle and Beth A. Herbel-Eisenmann focuses on trying to understand the thought processes of a student’s reasoning instead of relying on a student’s answer. Reasoning occurs when a student has time to think and then explain their thoughts. The time that is given after a question and before an answer is known as “wait time” and within this time, a student’s cognitive thoughts will increase. In the article, the authors emphasize an important detail. They quote from their findings, “Although most teachers are aware of the importance of waiting after they have asked a question, the importance of waiting after a student responds has received less emphasis (Rowe 1986). This all relates to students maximizing their learning by having the time given to them so they can process ideas for themselves.

The article goes further to say that when a student has given a correct answer, we as teachers should question them as to how they arrived at that. Students will often learn the most from themselves or when another student explains their reasoning. Asking for justification is a great way to evaluate not only a student, but the class as a whole when they respond and get involved in the discussion. Putting both “wait time” and “justification” together strongly represents the idea of equity and its importance in class.

The article “Unveiling Student Understanding: The Role of Questioning in Instruction” by Azita Manouchehri and Douglas A. Lapp relates to the Equity Principle directly by emphasizing the point that we as teachers need to ask the right questions for optimizing a lesson. Our questions need to facilitate learning and with the right questions being asked we can pull out conceptual reasoning from the entire class.
Magoo0311 @ Flickr

Personal: The only class in high school that ever truly challenged my reasoning was AP Calculus. Not because it was a hard class, but because the teacher invested so much into our learning and asked questions that forced us to explain ourselves. The mathematics classes that I have taken in college act the same way. The professors ask questions that require my justification. Sometimes I don’t fully know how to justify my answer and that can be blamed on the fact that I never had to do it through grade school. The in-class illustrations from the articles represent teachers asking questions that facilitate class, but do not emphasize reasoning like the classes that I have taken in college.

One specific instance of equity that I can remember my AP Calculus teacher applying was related to group work. The class was split into groups of fours and had to present on asymptotic behavior. Each person in the group had to focus on one specific aspect to present to the class and the groups had to hold each other accountable for their work. I can remember that there was a ton of questioning that occurred which felt like a debate. Within that debate, a lot of reasoning was taking place and uncertainties were being explained! The class as a whole was involved, and that is something special when an entire class is participating in discussion. In general, any time a teacher is at the front of a classroom instructing or going through a worksheet, and maybe only asking questions that a few students answer is a case of poor equity and should be avoided.

Observation: I conducted my observation at a well funded school with nice facilities. I observed a teacher and her freshmen/sophomore Geometry class during sixth period on Tuesdays and Thursdays. The class was primarily of white ethnicity, but there was one black boy and girl, and a hispanic girl. There were 15 females and 12 males in the class. The three learning objectives that I observed were review on algebraic properties, theorems about angles, and the last day was devoted to preparing for an upcoming test.

The questions posed in class were probably 50/50 for being open or closed. I noticed that when a question was presented in open form, there would generally be justification with the response. I compared notes with Susie K. from class to find a comparison between in class questioning. She told me that from her observation at Jenison High School, students were asked open questions about half the time in an algebra class but in the geometry class there were generally more open-ended questions. This makes sense to me as it seems fit that the higher level class should be challenged by the questions they get asked. A teacher should expect that as a student’s cognitive level grows; then they should also be able to reason more in depth. The wait time in the class I observed was generally around 3-4 seconds. This is reasonably good, but like the article proposed, there was really no wait time after a student responded. A good way that the teacher made sure each student in the class would have time before a response was by saying, “Everyone think about the problem by yourselves and then compare with a neighbor.” This way, students have time to learn by themselves and from their peers.

Further identifying the questions asked in class, about 22 percent of them required justification. I consider this to be a relatively adequate amount for a Geometry class, but would be something I would like to see get higher in preparation for more advanced math classes. A good example of an open-ended question that required justification was, “What justification do we get for AB+BC=AC?” I realize this seems obvious but sometimes that is exactly what is needed. She also asked, “If both L1+L2=180 and L2+L3=180, then shouldn’t they equal each other? Explain how you know this.” This question set-up made the students think about the properties and theorems that apply to these statements. These types of questions force students to think about possibilities. When called to answer, then the student can explain their best reasoning for an answer. Justifying yourself will sometimes correlate directly with equity if an explanation is clear and insightful so that the whole class learns from the response to the question. All of this stems from the question though, if a good open-ended question was not asked to begin with, then the opportunity for and learning in general has been lost. A good open-ended question posed in class was, “When I say adjacent angles, can you picture that in your mind?” Another one was, “How do you prove something true? What does it take to accomplish this?”

Interview: I conducted my interview questions by simply asking a few questions after each class to get a general sense of what she expects form her students. About instruction and questions Cristina said, “When I generally ask questions, I expect the students to think before giving a response. I’ll ask for understanding from the entire class and if nobody has a question then we move on. I expect students to ask if they don’t know. For communicating, specifically in Geometry, I expect students to use the correct language and correct theorems/properties. It’s important for students to have this foundation.” For the workload she said, “Homework happens every night, and each student is expected to complete their work or at least give a good attempt towards answering the question. Of course, I want all of my students to do well. It is really up to the student to provide the effort, and I am here to help each individual student as much as possible.”

Outside Resource - Conditions of Learning

One Laptop Per Child @ Flickr
This is my opportunity to share my understanding for the “outside resources” portion of my portfolio. During the exit interview, I was asked to explain my reasoning for using the Process Standards from NCTM, and Cambourne’s Conditions of Learning. Somewhat confused by this inquiry, I responded that I included them because they are both a framework that I feel needs to be implemented in the classroom everyday. These are both a resource that I want to keep a focus on when I teach because when using them, I feel my learners will effectively learn more. I was told that these were not the usual types of resources that are used, but upon my explanation, John and Dave understood my intentions of having them included and commended me for seeing these outside resources as a means for having a framework that benefits me in the classroom. Including them in this portfolio is a way for me to have a constant reminder of them.

Monday, August 16, 2010

Making Magic

"One learns by doing," Zia said. "This is not school, Sadie.  You cannot learn magic by sitting at a desk and taking notes.  You can only learn magic by doing magic."
From The Red Pyramid, by Rick Riordan.  Now that my kids are old enough to read real books, I find myself mostly reading what they recommend.  Which is a lot of YA fiction.  I love that this genre has appeared in time for them.  Rick Riordan is the author of Percy Jackson, and this is the first book in a new (somewhat similar) Egyptian-themed series.  It's a fun read.  (But I miss JK Rowling.)

But how about that quote?  Doesn't it apply to everything?  What can you learn by taking notes?

I want a powerful metaphor to start my classes this year that gets this across.  At least gives students a chance to understand that they have been robbed.  Misinformed.  Abused.  Neglected?

A recurring theme - at least since Dickens, and certainly post-Potter - is the child with a suboptimal life discovering that they have an amazing destiny.  I think that appeals to us because it is, in fact, true.  Without getting all religious here, I really believe that there's something each of us can do that no one else could do as well, or as opportunely, or where we could do it. One of the reasons I love teaching math is that, if learned, it opens doors, creates possibilities, and enables new choices.

Another recurring theme is that we find ourselves with new powers.  Magic, demi-god stuff, athletic ability, spider-sense... but sadly it's often the result of genetics (Kal-El, Percy and Harry) or an accident (Spider-Man, Daredevil, ... Captain Underpants?) and less often the result of study. (Batman.  It's always Batman.)  Another thing I love about teaching math is that when students learn something they can literally do something that they couldn't do before.  Even if it's something insignificant, like solve any quadratic equation that anyone could ever dream up.  One of the reasons I love Potter is that being a wizard doesn't solve Harry's problems, it's the start of a whole new world of even-harder problems. 

So I'm thinking that one of my fundamental teaching problems is how to communicate these ideas to my students.  It's all muddled up with the growth mindset stuff, and deeply connected to the Equity Principle.  What is a metaphor that will connect?  What is the narrative?  What experiences have they had with which I can connect?  What experience can I provide from which they can draw?  In a teacher education class, I think we can motivate through their profession - I've had some luck with that.  Sometimes it works connecting with other learning.  Athletes considering their sport.  But in a pure content class, when the students are convinced they know what it means to learn or do math and they are just, almost totally, wrong?

My biggest successes so far have come with trying to convince the students that my real goals are to teach problem-solving and/or learning how to learn, and we're just using the math as a context for it.  With these other subjects, they're willing to think it might be different.  "I've never had a problem-solving class before.  Must be what they're like."

This reminds me of the Robert Duke video that's making the rounds.  He talks about how students only pay attention to what's assessed.  And, somewhat more subtly, teachers only attend to what's assessed.  And chances are, you are not assessing what you really want students to learn from you.  He goes on to share a model of Whitehead that boils down to get your students doing the magic to learn magic.  (His example is playing the drums, but...)



This is the Gene Krupa magic.


Didn't learn that in a lecture.


What is your model of math?  Do you share it with your students?  How?

I would love to hear about it, by email, by comment, by your blogpost... but please, share!