Friday, March 24, 2017

mathemagical thinking & NPM challenge

www.fromvictoryroad.com 
The world is such a different place these days...

No, I'm not going rail against the state of our democracy or the demise of our Earth (again), but I am going to take on a polarization of positions that is just not serving us any longer.

It's that divisive notion that in this world there are word people and there are math people and that they are fundamentally different.



I shouldn't have been quite so slow to get here, since both my offspring are walking talking reminders that you can have a natural knack for both spelling and calculus, for both algebra and narrative.  But I was raised (through absolutely no ill intent on the part of my parents) to understand that I was a word person, a poet, and that I would not be good at math.  When they took me out of kindergarten because I could already read and put me in first grade, I cried on Mrs. Walker's lap because I knew I was "smart," but there was something about subtraction that, try as I might, I just couldn't get.

Now, developmentally speaking, that was true.  I was not ready at 6 to travel easily backwards on the number line, and I WAS a person who needed concrete models that were not offered to me.  The whole 100 chart did not lie open before me in my mind's eye, the way it does for some of those kids whom I would have called, as recently as last year, math brains. I couldn't get it--YET.

So I struggled through, taking no fewer than 4 years to memorize the multiplication table because it was only that for me--memorization of unanchored phrases, not representations of numerical relationships. I learned the logarithms of borrowing and carrying without understanding what they achieved as a computational efficiency.  (When I finally encountered Base Ten blocks at the age of 22 in a Math for Teachers course, it was a moment of Great Enlightenment!) No one ever said to me, "Heidi, math is a language, and you're good at languages.  Off you go."

And then last year, aged 52 and teaching 2nd grade for the first time, I realized that I had never really understood the function of the equal sign.  Seriously.  I had been teaching my kindergarteners about number "sentences" which are special "because you can read them left to right AND right to left," because I myself had never come to my own solid understanding of what "balancing an equation" really means, an equality on either side of a fulcrum.  Now I'm finally getting that the grammar of math may be different than the grammar of English (or German or French or Spanish, all of which I get), but it's still a system, with--as my math major daughter will attest--a lot less need of fuzzy uncertain interpretation than English!

Imagine learning all this anew in the middle of middle age!  Now I'll just let you watch this video that in ONE WEEK transformed all of my students' attitudes about who is and who isn't, who can and who can't be, strong mathematicians.  It came to me through colleagues who are studying this "duh-obvious" yet only recently explored idea of growth mindset, a concept which I knew but had not really applied to myself until I began to think about me and math.  It's long but it's worth it.



Now you may be asking, "What has all this to do with POETRY?"  Last summer I started planning a collection of math poems for young readers, but its concept was very different even eight months ago than it is now.  Now I'm positively excited to explore some of my own math development through poetry, and I'd like to ask for your help with a National Poetry Month challenge for myself.

I'm going to try to draft a math poem each day in April, and while some of the poems will be specifically about number and operations, I also want to write about experiences of math learning.  Will you help me gear up by leaving your math thoughts, questions, anecdotes and confusions in the comments?  I'd love to have a trough full of math fodder to dig into as I embark on my project.

I leave you with a poem I wrote when my mathematician daughter turned 8, and with thanks for sharing your mathemagical moments if you choose to!
                                                                   (c) Heidi Mordhorst 2007

According to my calculations, Catherine is our host today over at Reading to the Core.  Off you go, in search of the only solution to the problem of dichotomy...you know it's POETRY.

24 comments:

  1. The pressure for a meaningful comment! Nail-biting over here. I'm afraid I've always been literate in numbers, able to shift groups in my head like taking 16 and 12 and shifting it into 10 plus 10 equals 20. 6 and 2 equals 8, making 28, stand on my head, tie my shoe, multiply, divide, add facts and divide out the excess, leaving the total, so obvious to me that the hard part was slowing down enough to "Show My Work" the death knell of the mathematically nimble. But it's so obvious, just a shifting of a piece to fit it in a jigsaw. I like to write Fibs, they are a fun use of math. Do you plan to write only about math, being a math student and numbers? Or will you be writing to illustrate the larger math mysteries, like geometry and fungibility? Sounds like a fun project.

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    1. Brenda, that is almost exactly like what my 14yo son described the other day about how his processes, and for him also "Show Your Work" the worst words in the language. In about 3rd grade he said to his teacher, "Why should I have to show you my work? In my head I'm doing it exactly the way you taught me!"

      Yes, the working title is *Your Days Are Numbered: Poems You Can Count On* and I'll be addressing the cultural meanings and associations of numbers also. You rose to the challenge!

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  2. Eight really IS great. Super poem, Heidi! Ben was shocked that I did better on the analytical reasoning section of the GREs (back when that was such a thing) than he did, what with him being an EE major and me being an English major. As you say, though, our abilities aren't in wee boxes. I'm excited about your project!

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  3. Ha! I am having a problem with your poem... I am so sorry but my CLIGS (Can't Let It Go Syndrome) is kicking in and I can't for the life of my make out why you would have the stanzas going in the order you have them? As a visual I'd start where the three is (assuming you wanted to avoid going through the middle twice), then up to two, over to one and continue to four... I'm constantly trying to write an eight following the stanzas and I can't!
    So, is that a topic that you can use?

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    1. Now that I look at it, Donna, I can't "figure" out why I did it that way either! It's not even how I write my own 8's. Time to rework...

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  4. Hi Heidi
    Simultaneous equations, to me, always made the same sense as baking a cake. I can adapt the ingredients, as long as I keep everything in proportion. If I overdo any one element, I am sunk.

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  5. I have no math experiences to offer, but wanted to say that: 1. yes, 8 is great (as an age, and as your series of poems, and maybe you were drawing a left-handed 8 when you placed them?) and 2. I'm looking forward to reading your math poems.

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  6. Oooh...math stuff. Not the place for me, but I did love the poem, Heidi. Words, I get!

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  7. Fascinating post and your poem about 8 is great. =)

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  8. Love this.A pet peeve as a teacher was when the kid would say,"I stink at math".Or parents would say, I was never good at math so it is hard for him, he got that from me.Boom!Potential stifled from the start based on false notions of math or whatever and human potential.For years I never understood math, but my great memory allowed great grades.I learned to see it when I had to teach it.My education in the early 50s was rote.But I got it eventually.Too late to truly get higher math-anyhow-a story: my gr.5 student,Tony,back in the days before spec ed, poor Tony only had me for support. You kept up or you failed. I didn't want him to fail. A great athlete, a fine person. Quiet, friendly. Corraled my then available grad-student hubby to help. They worked on comparing fractions. The like denominators were not hard, right? Then my hubby said which is bigger 1/2 or 2/4, Tony pointed to 1/2, then 2/4. They drew a picture. My husband waited. Finally an "aha" moment for Tony. He sort of smacked himself on the head, smiled and said "it's a tie!". This was an "aha" moment for me,too. Make it real..Tony was recess kickball king...he knew about tie scores. Anyhow-sidenote- I had to read John Holt's book in college: How Children Fail. Excellent....set me on my course to always think about how kids learn. Another was Sideways Arithemetic From Sideways School by Sachar. I would use it in gr 5 (this story from the 90s) and the "strong"students who memorized to get top grades, did not want the challenge to have to think.Others saw it as a puzzle, could use a trial and error strategy and would stick with it. Another thing that always bothered me was how kids would get a math test back, look at the score and shove it in their desk to be forgotten. I then created a great system that kids, parents and I loved. They had to C&A for every error on all work.And never erase the original answer so I could see what they had. It meant "correct and analyze". Had a chart of all potential types of errors: goofed, misread something, sign error(didn't notice the sign),rushing,understanding, forgot, didn't do, fact error, copied wrong. Then I would show how an 82% could easily have been a 95 or even 97. I also gave a "PRETEST For the post-test. Our book came with a free response and multiple choice version. Similar question per item. Always made them show work. Here's the key: you did not have to take post test if you scored 85 or higher.But,the higher score would count. No penalty for trying again. This simple incentive changed kids. With a couple of days between tests I could re-teach as needed. Kids always tried again and grades went up. 2 years after I retired we got a truly knowlegeable math coordinator. He brought us the "Investigations" program, had excellent PD in the summer which he presented and I attended. Finally, an approach that gets kids to think. He also made the point that teaching the tricks to kids would not allow them to mentally understand the conceot, that multiple thinking strategies are viable and acceptable. Not one size fits all! And once the pre-teen brain"sees" math then it can move to automaticity. Last one, in gr.5 my 4th yr.in the classroom, I had a girl, Sally, who had just moved to town. She believed math was hard. I helped her.For teacher apprection day she wrote a card I still have. It said something like,"for you I'd do 100 math sheets to thank you for being my teacher." She grew up to be a teacher and was the computer teacher in her elementary school! She always laughs when she tells me that.YET.A powerful and important word.I recommend Peter Johnston's Opening Minds.Looking forward to your math poetry. By the way I was a whiz at algebra and intermediate algebra in high school. I could do those trains in 2 directions and when they'd meet.No more, though. Kids need math brains and word brains. And whole, giving hearts.And you probably thought I only loved poetry.Janet Clare F.

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  9. I had a similar midlife experience with finally deeply developing a solid number sense. Our district briefly adopted the Investigations math program, and it changed my life. I love math. I love the inherent growth mindsetedness of it. When we start something completely foreign (except nothing ever is in math...it's all connected), my students will struggle and struggle. Within a week, they will have taken control of the "new" concept and be in awe as they think back on where they started.

    What a FABULOUS (and marketable) project! I can't wait to follow along!

    (Oh. Just thought of a favorite/worst math memory that keeps me on my toes differentiating for the top end of my class: in sixth grade, I remember sitting in the back of math class, so bored that I yawned until my eyes watered.)

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  10. You are more evolved than I on the math front. I was enlightened when I learned the connection between fractions and percentages. My husband taught me maybe 2 or 3 years ago. You are brave to write math poetry. Don't forget about Zeno and Fib poems. We recently wrote fractal poems in my class. (Check my blog.) There is pi-ku. I'm sure there are many more. I look forward to watching this journey through April with math.

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  11. Fantastic post and project, Heidi. My brother, who is quite evolved literarily, went off to Vanderbilt at 16 to double-major in math and electrical engineering. When I was a high school junior, he was home on break and I asked for his help with logarithms or something in my trig/analyt homework. Wasn't long before he stood up, frustrated, and announced (leaving the room), "I can't bring myself down to such an elementary level." ;0) His social skills have drastically improved since then; my math skills have not.

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  12. What a grand project. I like all the poems, but especially the infinity ones where the 8 lies down. I am a visual person and love that image. I'm not sure how you can work this in, but I've found when teaching math that drawing (visualizing) the problems helped some understand a concept, how that "balance" worked, etc. I've been doing mental math problems while in the car with my 2nd grade granddaughter. Mostly addition, but some subtraction. She breaks apart the numbers when adding (like 153 + 209) and can do it quickly. She says it's like putting each part on a shelf, then going back to get them. I taught pre-Algebra & many problems can be "drawn". Best to you Heidi, sounds like lots of fun!

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  13. I can so relate to your story. I was an early and avid reader, but numbers just didn't do anything for me. I can remember sitting on the school bus, trying to memorize addition and subtraction and multiplication and division facts. I could memorize, but they didn't make sense until I took my math methods class to earn my teaching license. Because I struggled with math facts, I hated math and thought I was no good at it. Then in high school, the math department asked me to be on the freshman algebra team. I promptly turned it down until the head of the department called my mom to intervene. They bribed me to take part by promising I could eat at my favorite restaurant the day of the competition. I scored high enough to go to the next level of competition, and remained on the school math team all the way through calculus, but I still hated math. My college calculus professor begged me to major in math until I finally had to ask another professor to get her to lay off. I may have seemed good at math, but I hated it and didn't think I was good at it. Who knows what could have been if someone had taught me the grammar of math when I was younger? My daughter, though, is one of those who is fluent with both numbers and words. She is a strong writer and reader, and has a calculus brain (as well as organic chemistry, which she describes as fun--just patterns). I think your math poetry project is amazing!

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  14. I'm reading Jo Boaler's Mathematical Mindsets to support my venture into teaching math next year. I'm scared but she gives me hope that I'll develop my math brain and help others develop. I know I did not develop as a mathematician in elementary school. I did not see the creative aspects of it. The pedagogy of teaching math and the idea of it being a creative visual way to see the world has me excited. I'm looking forward to your NPM work and more math.

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  15. I somehow missed the concept of what came after the decimal point and that it meant tenths. Thankfully I was still in high school when a teacher realized that I didn't understand, and somehow explained it again to me in a way I got. OH! Now it made sense. I also had a really hard time with multiplication tables. I remember having to stay in at recess when I was - no kidding - six, because I had to practice them. So many things are about readiness! Your 8 poem is fantastic, and I bet your daughter loved it!

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  16. Heidi that was a cool video, wish some of my math teachers long ago had seen it. Fortunately, I keep on working on problems even when I can't get them. Math was definitely a difficult area for me in school. The one year in high school I actually did do well, was when I was in a class that moved more slowly, and then I was understanding everything. I think we need to look more at the students and what kind of learners they are. Literature, history, social sciences, and the arts I always sailed through, but I squeaked through math and science. Although when I had to take science in college I did much better, maybe it was the age and my brain had grown some. I liked your "8" poem and also the art on the top. I'm eager to see where your poems will take you . . . Thanks for all here.

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  17. Heidi, I could weep. I struggled and struggled with math....to the point that I to this day say "I'm math dyslexic". I needed to learn math as a language...I do happen to be good at THOSE! What a beautiful forward you've written to your collection. How soon can I pre-order?
    xo and have a great week....April is coming!

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  18. This sounds like a wonderful project. I look forward to reading though the month.

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  20. I remember having the same aha moment in my math teaching methods course. Teaching third grade for ten years helped develop my math understanding even more, although advanced fractions still trip me up. Your project sounds terrific, and I love your "Figuring 8" poem. I think others have hit on something when they talk about drawing or visualizing a problem. Looking forward to reading more of your math poems!

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  21. What a cool poem and project idea. I had a bad third grade math experience with an unkind teacher that did color the subject for me. I wish someone had taught me about growth mindset as a child...and poems and books like this one will help children see and understand that "YET" - even when something is difficult. One thing I think is neat is the way that a fraction has a decimal equivalent, kinda like we have nicknames. And do love infinity and the way that something can go on forever, like pi. Our Gg memorized it out to 100 places when she was in grade school, and that blew me away. And geometry - so much beauty and art there. This will be a magnificent project, and I am grateful we'll get to see it here first. x

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  22. I'd be interested in early childhood foundations for math that people don't think of as math. We think of counting and equations, but not things like patterning, sorting, grouping, subitizing. What looks like play (setting out small stones in a line with a pattern, building with blocks, sorting groups of objects into equal piles...) is actually the foundation for more complicated math later on. I've realized with my own students (play-based K) that some of them need to be explicitly told when they are "doing math" to build confidence.

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