Welcome to the first week of Liberation Math. Over the next 13 weeks, we are going to explore mathematical identities, the way that those identities are constructed, and how mathematics and math education interact with our culture. During this course, we will be collectively unpacking our ideas about the doing and learning of mathematics, and talking back to those ideas and imagine other possibilities. My goal is to create a community of people that develops a critical consciousness about mathematical identity and the place of mathematics both in our lives and in the world, which will allow us to move from reacting to structures outside of ourselves to being empowered actors who create our own identities. Participants will also work on mathematical problems that grow out of contexts that we identify as interesting, as well as mathematical problems that are abstracted (as is much of school mathematics), and that work will inform our developing and shifting perspectives on mathematical identity and the place of mathematics in our world. Anyone is welcome to participate, so feel free to read, comment, question, or argue!

You can start by reading some short pieces critical of math education. These are interesting to read together since the solutions proposed are so divergent:

- How Much Math Do We Really Need? (opinion piece from Washington Post, 10/2010)
- Is Algebra Necessary? (opinion piece from New York Times, 07/2012)
- Algebra and Activism: Removing the Shackles of Low Expectations (article in Educational Leadership, 10/2001 about Bob Moses and the Algebra Project)

This class is really a research collective — we’re researching ourselves and our memories in order to understand mathematical identity and culture, using a research method known as memory-work. Everyone is invited to write a mathematical memory and post it via this form or through a post on a blog or other venue (just provide a link in the comments, or post link to twitter with hashtag #liberationmath). The important thing is to write the memory under a pseudonym (to create some distance), to be as detailed as possible (don’t leave out anything, even what seems unimportant, and to write one memory, not a string of events or biography. We’re looking for the raw memory, rather than how you interpreting it (for more information about this, see the Haug reference below). We’ll be collectively identifying similarities and differences, themes, what seems to be missing, and what our writing says about who we are. That conversation will begin next Monday. To read more about the memory work method, check out the following three articles. The first talks about mathematics specifically, the second is by Frigga Haug, the woman who developed the method, and the third is a paper by a research collective of adult learners that used the method in a class.

- Ingleton, C., & O’Regan, K. (2002). Recounting Mathematical Experiences: Emotions in Mathematics Learning. Literacy & Numeracy Studies, 11(2), 95–107. This piece is specifically about looking at
- Haug, F. (1999). Memory-work as a Method of Social Science Research: A Detailed Rendering of Memory-Work Method.
- Lapadat, J. C., Black, N. E., Clark, P. G., Gremm, R. M., Karanja, L. W., Mieke, M., & Quinlan, L. (2010). Life Challenge Memory Work: Using Collaborative Autobiography to Understand Ourselves. International Journal of Qualitative Methods, 9(1), 77–104.

What do you think about math and it’s place in our culture? What kinds of memories (good or bad) do you have of mathematics? Leave a comment below! Anyone who is going to be posting about Liberation Math, please leave a link to your blog and/or twitter account below — I’ll be compiling the links on the sidebar.

(Lesley Students who are enrolled in the course, make sure you cover all of the assignments in the course outline under Week 1 — it’s a big week, so I recommend starting early!)

Related articles

- From Math Shame to Math Liberation (liberationmath.org)
- Mathematics Liberation and MOOCs (liberationmath.org)
- Shame and Mathematics Presentation at Joint Math Meetings (liberationmath.org)

Why I hated math, or should I say math class. Two things stand out for me “show your work” and “negative numbers’. As a kid I could do math in my head, doing basic mathematics without using a calculator or pencil (when I do laps I still do fractions in my head). Every test, there were marks off for not showing my work. If I answered a question on the board I had to show my work. Well sometimes I couldn’t do that because my brain “knew” the answer. Now when I do math it is painful because I write down all my work. What used to be instantaneous is now a process. Negative numbers for me was also math voodoo. As I grew older, high school math was hit or miss for me. A good teacher who explained things to me in a way I understood, would result in an A. For those that didn’t a C. Sometimes I wondered if it was because I was a girl and the math teachers (mostly male) worked harder with the boys.

In university I left chemistry (which I really loved) because I would have to take university mathematics to proceed to 2nd year inorganic chemistry. (I had an A in first year organic and inorganic chemistry)

So really math and my math avoidance changed what I ended up pursuing for a career as an adult.

Thanks for the comment, Karen. I think a lot of people are in your shoes, having turned aside from dreams because of math. The article “Is Algebra Really Necessary?” argues this exact point, that algebra is unnecessarily keeping people from success. OTOH, Bob Moses (see the third article above) would say we should push for more algebra to get more people through those gates. So do we tear the gates down, help people climb them, or something else entirely.

I really think your point about showing work is interesting — I know that the curriculums used in my area are all about showing work, often showing multiple methods. I can get that we want students to be able to communicate their thinking, but can we do that without making it drudgery?

Angela, when did we decide, as educators, that we had to show work in math? My grandfather was an accountant and brilliant with figures but he did them in his head. That is how I did math when I was young. Having to show it actually made me have to rethink my answer, leading me to doubt my accuracy, which lead to me “showing my work” and making more mistakes. Math was intuitive, almost instinctive prior to that point. Now it is something I fumble over, except when I am swimming laps and almost in a trance.

Why is intuition in learning a bad thing?

OK, so actually you are blowing my mind a little. As a math educator who started in teaching in the current constructivist reform wave, I’ve always thought that showing work is the most important thing — more important than the answer. For you clearly that wasn’t helpful. This is really why I think we need to pull people who aren’t mathematicians and math educators into conversation about math, because those of use that do this all the time get too wrapped up in our own worldview and what we already “know” to be true. I really have to think about why I ask students to show work in light of what you are saying. I think I worry that if they don’t, then they don’t really understand — it’s a bit paternalistic I guess (that is, that I know what you know better than you know it yourself). You’ve given me a ton to think about, so thank you!!

Angela, I too, was trained in the constructivist milieu, but when I think of teaching math to children I think of my students using blocks, fingers etc. to learn how to count and do early numeration in order to facilitate arranging knowledge in their head. I was taught multiplication through a song about multiplying rabbits two by two (very effective.) But once it is in there, doesn’t it, like most learning, become intuitive? We always remember how to tie our shoe because of motor memory, so if we’ve created a motor memory (or song memory) through the physical teaching of math, doesn’t that link remain? Especially if we exercise it everyday? At some point, if we approach a subject in the wrong way, I think we can break the ” old link” in the brain, by creating the new “show your work” path. And do the two conflict? In my case, yes. I am intuitive by nature and am used to my brain making what appears to be sudden connections but I am in fact just allowing it free rein to make associations that lead to “aha’ moments.

A few thoughts here.

First, maybe there is some difference here between elementary and secondary (or college, as I teach). Elementary grades should be constructing meaning using manipulatives, and getting the math “into their bones.” Typically problems in class are one or two steps. But I know TERC investigations, the school district my kids are in and that I volunteer in has students show work for these, draw out subtraction problems, and show multiple methods. I’m not sure I buy it as useful, unless the student is struggling, if that happens the work can perhaps be a way to see what the student is actually doing. I think you may be write about the potential for harm in cutting off students intuition by forcing shown work, when that really isn’t how the student is actually doing the problem. It’s not authentic work if the student has to write it down in a different way than they did it.

High school and college students are often doing problems that may be more complex, long, and difficult. In that case, they may need record keeping for themselves. College students certainly may need to have records with explanations so that they can go back to unfinished problems and pick up where they left off.

But honestly most of the way that I use showing work is for my own benefit. Sometimes I don’t trust a student is really doing what I want without the work (which brings up a whole host of questions to me). Sometimes they problems are just complex enough that most students won’t complete them 100% correctly, so if I don’t have work I don’t know what they DO understand.

So I think my question is, how do we support student intuition and still help them to develop record-keeping and communication skills that will serve them well as problems get more complex. And if we are having them “show work” to help develop those kind of skills can we make sure that it is authentic, not made up after the real work is done to satisfy requirements? Any thoughts about that?

Hi Angela,

I’ve been thinking about what you’ve written all weekend and I’ve decided to share the story of my eldest son, my math genius. Now I say that because he WISCed at 19 in math and his lowest was 13 in English at 11 years old (he was in French Immersion in school). This was the child who came home one night and asked me what the sine/cosine function on his graphing calculator did before he went to bed (his teacher wouldn’t tell him because he wasn’t supposed to learn it until Grade 11) and in the morning told me not to bother finding the answer because he’d figured it out during the night. He went and talked to his math teacher about how he thought sine and cosine worked and he had reasoned out the function correctly and how to apply it. He could figure out complex math problems but always made mistakes because as he said, “I can’t add two plus two together successfully half the time.” Luckily he had a math teacher who understood him and wasn’t too fixed on the numeration but on the reasoning.

This changed when we moved in Grade 11. He ended up with a math teacher who was fixed on numeration rather than the reasoning behind complex equations. My son’s love of math within a school setting disappeared. He did not take math in university but English. Now, he is thinking of going to graduate school for literary theory, but works for a company that when they found out his skill in math, had him check for fraud and help with the audit. He has created a predictor program for certain stocks for fun that he makes money on every quarter.

Irony of ironies, one of my other sons who was gifted in English ended up being turned off the subject and is now a chemical engineer.

Sadly Angela, you and I both know that this story is very common.

So I think a fundamental question that needs to be asked is “What are we looking for?” in our math students. Is it accuracy in numeration or the ability to apply reasoning? Does it have to be both? It reminds me of an episode in “Big Bang Theory,” where Sheldon has sent a math proof to Stephen Hawking and Stephen Hawking finds a mistake. Sheldon is humiliated but he is still a genius. Are mistakes not permitted in math? I can’t tell you how many times I’ve found grammatical mistakes in textbooks. Surely there must be an equal number of math errors.

When we look at teaching math we are, in a sense, trying to develop two skills within math once the basic math foundations are in place. The ability to edit numerically (see your mistakes) and to be able to reason mathematically (knowledge, logic and intuition). This is predicated on the foundation being strong (but we both know sometimes it isn’t.) In English, I have had many students who have a wonderful writing style, a true “voice”, but their grammatical skills are terrible. I have always counselled them to keep writing and find themselves a good editor. Not every student can see their mistakes, which is why we have groups share papers to help proof at all grade levels. So why can you not have math conversations and math proofing shared between students? If sharing is how we build knowledge and understanding this would help support student math learning and math intuition.

This is why I found that math video so powerful because he is talking about the math conversation I wish we could have in schools rather than the “gotcha” mentality we seem to have developed.

Blog link:

http://kelseyhooperliberationmath.wordpress.com/

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