Yes, New York Times, Algebra is Necessary. August 2, 2012

Andrew Hacker, being all-important at some podium somewhere. Taken from his blog.

The New York Times recently published an article written by Andrew Hacker entitled “Is Algebra Necessary?“.  This article comes at an interesting time: during the 2012 London Olympics where Michael Phelps, today the most decorated Olympian of all time, placed fourth in a [preliminary, but still] race just days before.  Did he give up just because the going was tough?  No he didn’t!  He swam a crappy race and dealt with it by coming back and becoming the best Olympian to ever walk Planet Earth.  So, Andrew Hacker, should the US give up in Math just because the going is tough right now?  Oh, “yes” you say?  You’re no Olympian.--It is my firm belief that anyone can learn Math and even love it.  It is upon this notion that I base my career.  If baffles me that Andrew Hacker - a PhD and professor – has reaped all of the benefits of a good education yet has the audacity to stand on his podium and announce to his students, and all who read the New York Times (shame on you too, NYT), that we should all just give up on our Math. 

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For some, this idea is an awesome one and they are no doubt behind Hack[er] 100%.  And I guess that’s fine, as long as they don’t go announcing their positions to kids who are still trying to graduate.  As of 2012, they still have to pass Math. 

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For many years as a Math teacher, I have been faced with the question “When am I ever going to use this?”.  My position on this has recently changed.  For years I have responded that “it is the thinking process that you will use.  You use this same thinking process in figuring out crimes, building cases in the courtroom, figuring out how things work.”  This is legit and true (thanks, Dad).  But after a lot of thinking on this question, as it is a serious one, it dawned on me that I don’t have to make up some far-stretching response (sorry, Dad), that the answer has been right in front of my face all along.

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Math describes Nature.  It’s not that it “describes Nature (la-di-da)”; Math actually describes Nature. 

broccoli, magnified. It’s a spiral. Spirals = Math.

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Math describes the Universe.  Don’t you watch the Big Bang Theory?

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Hokusai knew it.

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Lastly, and probably most importantly, is Hacker’s ASSertion that students drop out of school because of Math.  Really?  I invite him to teach for 1 YEAR in any inner-city public school where the dropout rate is >50% and to see if Math is really all the kids have on their plates.  A lot of kids are not proficient readers, either.  Do you suggest they give that up, to?

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The author can be reached at shanadonohue@gmail.com.

Is Common Core meeting its Goal? May 21, 2012

Is the original goal of Common Core being lost in the upper grades?

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One major difference between the U.S. and so-called ”A+ Countries” is, while we focus on breadth, they focus on depth.  While there is a natural progression throughout a student’s school years from one math topic to another in these high-achieving countries, in the U.S. we seem to have a “throw at the wall and see what sticks” mentality.  For example, in grade 8 we cover 32 unique mathematical topics.  In high-achieving countries this number is just 18. 

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The new Common Core curriculum aims to bring our focus back to depth in the lower grades but seems to miss this mark once the abstract maths are reached.  While it is true that more topics have been cut out than added in most grade levels, topics traditionally covered in Algebra 2 (and some may say pre-Calculus and above) – piecewise functions, limits, logarithms, areas under curves, Algebraic proofs, and rational function graphing to name a few – are now part of Algebra 1.  Does adding so many advanced topics to the Gateway of Higher Math (ok, I’m biased) do what Common Core initially set out to do? 

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Below is a comparison of the math topics taught each year in A+ countries (first chart) and those covered in the U.S. (second chart) each year (compiled by Professor W.H. Schmidt).  These comparison charts were created before, and as a support for, Math reform in the U.S.  Still, to meet the new upper-grade Common Core Standards, school districts are turning to hybrid-type courses: “Algebra/Geometry/Stats Year 1″, etc. (Yes, that’s ONE year’s course) to meet all of the new high school requirements.  While the Common Core sets out for mastery at the Elementary level, did it really mean to hybridize high school math?  If depth is more important that breadth, what are we doing?

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Math manipulatives lead to student failure May 19, 2011

During a 4th grade substituting assignment, the teacher left a set of word problems for the kids to do.  A bunch of these word problems involved division, and the students were directed to use their counting blocks.  As I walked around the room, I saw kids doing just about everything a kid will do with giant leggo-type blocks.  There were guns, there were swords, there were towers.  Some kids were using the blocks to work the word problems, but many of the students who wanted to use them for good were having trouble.  My role morphed from teaching math to teaching the kids how to use the counting blocks.  One word problem called for dividing 125 by a variety of numbers.  There is a large margin of error while counting 125 of anything, and with a string of problems that all rely on a 100% accurate count, it felt to me that the kids’ time could have been better spent.  When do manipulatives cross the line from helpful to hurtful?

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A great article titled Teacher Learning and Mathematical Manipulatives: A Collective Case Study About Teacher Use in Elementary and Middle School Mathematics Lessons  by Laurel Puchner, Ann Taylor, Barbara O’Donnell and Kathleen Fick, outlines one of the many problems that can arise while using manipulatives in math.  This article is a worthwhile read, especially for those teachers wondering why manipulatives don’t seem to work as well as advertised. 

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contact blog author Shana Donohue: shanadonohue@gmail.com

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My Harvard Math for Teaching Thesis: Complete! And ready to share… March 20, 2011

After many many years of jumping through many many hoops, I am finally graduating with my MA in Mathematics for Teaching in May.  My thesis, Negative Number Misconceptions in High School: An Intervention Using the ZeroSum Ruler is right now at the printers being printed and bound.  I don’t know about you, but that instantaneous feeling of relief after taking a final exam or passing in a final paper stopped hitting me sometime in college.  So now, I’m just feeling a bit burnt out.  OK, completely burnt out.  But I’m sure it will hit me soon since it kind of needs to; I need to now get in a post-Bach program to get my Initial teaching license.  I like to do things backwards.

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So here it is for download!  For all to read!  Or maybe to just glance.  In my study, the ZeroSum ruler proved effective in reducing eleventh grade error on integer addition and subtraction problems (especially with negative integers).  If I wasn’t so burnt out, I’d want to test it with younger kids.  Imagine how our world would be if my eleventh graders actually mastered integers when they learned them in, and only in, 7th grade.  But that’s in my thesis.]

 

Public school? Supersize my class! January 25, 2011

There are two upsides of a larger class: more diversity among students and the drive to succeed (and/or not act out in front of peers).  I found that when I was teaching if too many students were out on a day, the kids who were in school felt it should be a “free day”.  Kids weren’t there to bounce ideas off each other or to push each other. 

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So does class size matter?  It definitely does.  Even when I had less students in class and the ones who were there were less motivated to do work, I was better able to connect to the students who were there.  There were less kids to reach.  And isn’t that what good teaching is half about?

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Read the article The Class Size Debate on Huffington Post.

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The recession-proof Exam: When will it pop? December 19, 2010

 

The article by Todd Farley “Standardized Testing: The New Wild West” pretty much sums up why high-stakes testing has such a stronghold.  It’s a recession proof industry!  I knew that millions went into it, but I didn’t know the full extent of greed that’s going into it.  Farley himself admits to capitalizing. 

 

But like all bubbles, this one will pop.  Hopefully.  Then maybe our kids can go back to learning again.

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In somewhat related news, here’s a great chart of just how many math topics we throw at our kids each year as opposed to A+ countries where students excel in math…
http://zerosumruler.wordpress.com/2010/12/06/us-vs-a-countries-breadth-vs-depth-in-math-which-is-better/

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US vs A+ Countries: Breadth vs Depth in Math. Which is better? December 6, 2010

(Click chart to enlarge)

Schmidt, William H., Wang, Hsing Chi., McKnight, Curtis C., J Curriculum Studies, 2005, volume 37, number 5, pages 525–559

 

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