# ZeroSum Ruler (home)

## Blogging on math education and other related things

### Grade 10 Math MCAS Review – A Prezi!April 27, 2013

You can get to the Grade 10 Math MCAS review Prezi here or by clicking the above screenshot.

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It’s about that time again. No wait, it is that time again: Grade 10 Math MCAS. Forget about grades 11 and 12 as these grades are meaningless. The new Grade 12 is Grade 10. The new SAT is MCAS.

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I write this with both a migraine and with my tongue in cheek. As a Special Education 10th grade Geometry teacher, I have very mixed feelings about this dreaded test. As a teacher who never had to take MCAS, I think that my students will come out perfectly fine without proving their 10th grade knowledge on some expensive test. I did. All [most] of my friends did. As a person who has taken a boat load of tests and who has become very aware of the unique sense of accomplishment that comes from passing the seemingly-impossible, I want to give my students every tool to show this test who is boss. There is no better feeling than whipping a test’s ass. I want my students to experience this feeling.

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I learned an important lesson from an unlikely source at UMass: Kids in Mr. Chandler’s inorganic Chemistry class who had internet and could access Chandler’s old exams would do better than me. Why? Because his tests were partially-recycled. Above is a screenshot of a Prezi I made from 2012′s Grade 10 Math MCAS multiple choice questions.  Every kid gets 4 colored index cards with either “A”, “B”, “C”, “D” written on it. My “A” is red, but that part doesn’t matter so much. As we click through the slides, kids do their work on scrap paper then hold up the colored card that corresponds to their answer choice. This does two things: makes the kids feel that they’re playing a game and lets me see the class-wide weaknesses to focus on during explicit cramming. In addition to practicing the concepts exemplified in these multiple-choice questions, we’ve been doing the open response questions in class, being sure to review Statistics. MCAS creators love mean, median, mode, range, box-and-whiskers, stem-and-leaf, line plots. “When will I ever use a box-and-whiskers thing in real Life?” Never kids, just possibly on May 13th.

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The best of luck to your students!

### 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 failureMay 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?

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

### 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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