Expert witness, 8th grade edition

This "Op Doc," a verbatim re-enactment of a legal transcript, is both obnoxious and hilarious.

Obnoxious because the filmmaker elected to give the smart person a Northern accent, the dumb person a Southern accent.

Hilarious because the expert witness, who was paid $940 for his services, actually cannot do middle-school math.



Verbatim: Expert Witness

The “expert witness” in this case would not answer questions without his “formula sheets,” which were computer models used to reconstruct accidents. When asked to back up his work with basic calculations, he deflected, repeatedly derailing the proceedings. The lawyer’s questioning became increasingly specific, until the conflict revolved around two short words with very different meanings: “won’t” versus “can’t.”

The deposition is a warning for experts who rely heavily on technology. When it comes to expertise, knowing how to plug numbers into software is not a substitute for understanding the subject matter.

Teachers take risks when they decide to teach middle-school math

The headline in the WSJ article says “Denver Teachers Object to Changes In Pay-for-Performance Plan”

Yawn

But what really caught my eye when reading this story was this sentence:

But the biggest rewards will go to early- and midcareer teachers -- and to those
willing to take risks by working in impoverished schools or taking jobs few
others want, such as teaching middle-school math.

No one who reads KTM regularly is surprised to find that teaching middle-school math is considered a job desired by few teachers. It must be darn hard to teach students who’ve emerged from elementary school not having mastered such things as fluency with multiplication tables, long division or fractions. These are considered by many mathematicians to be critical stepping stones on the way to higher-level mathematics. Instead, middle school math teachers might typically find students who have mastered things like math journaling, sorting colored manipulatives as a way to demonstrate they understand the “concept” of multiplication and pizza-slice fraction analysis.

Middle school math – where the math sh*t hits the fan.

PS – Actually, the entire article is worth reading.

The Denver teachers may decide to strike while the Democratic Convention is in town.

That could create some awkward moments. The Democrats don't want to anger
teachers unions, which are key allies. Nor do they want Denver's plan to fall
apart.

Merit pay did make a difference.

Before the plan took effect, she said, "we almost never sat down with our
principals to say, 'Where are our students now, where do they need to be and how
do we get them there?' This really has changed the culture in our schools."

for parents of new middle schoolers--

The single most useful piece of advice I've ever read as a parent of a middle school child:

Andromeda on organization and the middle school child.

Also, 3 years ago a lot of us wrote posts and comments about books and products that had helped our kids deal with middle school.

(fyi: the old site is broken. Can't be edited. That's why the links are slowly deteriorating with no one to fix them...I have no idea what to do about it other than get rich enough to hire someone to copy all the source code and then take the whole thing down.)


posts on middle school & organization:

• mom gets wake-up call at end of school year
  
• accordion files for middle school students
• Donna Goldberg on students' sense of time
• Donna Goldberg's web site
  
• the 3 simple building blocks of success (How to Double Your Child's Grades in School)
• an approach to reading that really works (part one) (How to Double...)
  
• an approach to reading that really works (part two) (How to Double...)
  

my two favorite middle school books:

• The Organized Student by Donna Goldberg
  
• How to Double Your Child's Grades in School by Eugene Schwartz
  

if you decide to go the expanding file route...

The Globe-Weis Fabric Poly Expanding File is amazingly sturdy.

Karen Chenoweth on the Loveless report

The really bad news is in eighth-grade reading, where the top performers stayed absolutely steady and the bottom performers dropped a net of three points.

This is where we need to be sounding the alarm, because this is further evidence that we really haven’t figured out:

1) middle school [I'll say]

2) how to help those kids who have mastered the mechanics of reading to understand material that is more sophisticated than the relatively simple fourth-grade reading selections. If there is an argument that schools don’t have a broad enough or rich enough curriculum, the evidence lies in the eighth-grade reading results. Once basic decoding skills are mastered, reading comprehension is heavily dependent on vocabulary and background knowledge, which are taught in science, social studies, and the arts. It is a longstanding problem that too many middle schools don’t bother teaching much of any of those subjects, and one that we as a nation need to tackle.

Good News (and some Bad): A Report Card on U.S. Education

Was it the NY Times that called middle school the black hole of public education?

I don't remember.

Natl Math Panel: increase algebra in 8th grade

All school districts should ensure that all prepared students have access to an authentic algebra course—and should prepare more students than at present to enroll in such a course by Grade 8. The word authentic is used here as a descriptor of a course that addresses algebra consistently with the Major Topics of School Algebra (Table 1, page 16). Students must be prepared with the mathematical prerequisites for this course according to the Critical Foundations of Algebra (page 17) and the Benchmarks for the Critical Foundations (Table 2, page 20).

FINAL REPORT
p. xviii

Table 1: Major Topics of School Algebra

Symbols and Expressions

• Polynomial expressions
• Rational expressions
• Arithmetic and finite geometric series
  

Linear Equations

• Real numbers as points on the number line
• Linear equations and their graphs
• Solving problems with linear equations
• Linear inequalities and their graphs
• Graphing and solving systems of simultaneous linear equations
• Quadratic Equations
• Factors and factoring of quadratic polynomials with integer coefficients
• Completing the square in quadratic expressions
• Quadratic formula and factoring of general quadratic polynomials
• Using the quadratic formula to solve equations
  

Functions

• Linear functions
• Quadratic functions—word problems involving quadratic functions
• Graphs of quadratic functions and completing the square
• Polynomial functions (including graphs of basic functions)
• Simple nonlinear functions (e.g., square and cube root functions; absolute value;
• Rational functions; step functions)
• Rational exponents, radical expressions, and exponential functions
• Logarithmic functions
• Trigonometric functions
• Fitting simple mathematical models to data
  

Algebra of Polynomials

• Roots and factorization of polynomials
• Complex numbers and operations
• Fundamental theorem of algebra
• Binomial coefficients (and Pascal’s Triangle)
• Mathematical induction and the binomial theorem
• Combinatorics and Finite Probability
• Combinations and permutations, as applications of the binomial theorem and Pascal’s Triangle

Recommendation: Proficiency with whole numbers, fractions, and particular aspects of geometry and measurement should be understood as the Critical Foundations of Algebra. Emphasis on these essential concepts and skills must be provided at the elementary and middle grade levels.

Recommendation: The coherence and sequential nature of mathematics dictate the foundational skills that are necessary for the learning of algebra. The most important foundational skill not presently developed appears to be proficiency with fractions (including decimals, percents, and negative fractions). The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in algebra can be expected.

Table 2: Benchmarks for the Critical Foundations

Fluency With Whole Numbers

1) By the end of Grade 3, students should be proficient with the addition and subtraction of whole numbers.

2) By the end of Grade 5, students should be proficient with multiplication and division of whole numbers.

Fluency With Fractions

1) By the end of Grade 4, students should be able to identify and represent fractions and decimals, and compare them on a number line or with other common representations of fractions and decimals.

2) By the end of Grade 5, students should be proficient with comparing fractions and decimals and common percents, and with the addition and subtraction of fractions and decimals.

3) By the end of Grade 6, students should be proficient with multiplication and division of fractions and decimals.

4) By the end of Grade 6, students should be proficient with all operations involving positive and negative integers.

5) By the end of Grade 7, students should be proficient with all operations involving positive and negative fractions.

6) By the end of Grade 7, students should be able to solve problems involving percent, ratio, and rate and extend this work to proportionality.

Geometry and Measurement

1) By the end of Grade 5, students should be able to solve problems involving perimeter and area of triangles and all quadrilaterals having at least one pair of parallel sides (i.e., trapezoids).

2) By the end of Grade 6, students should be able to analyze the properties of two-dimensional shapes and solve problems involving perimeter and area, and analyze the properties of threedimensional shapes and solve problems involving surface area and volume.

3) By the end of Grade 7, students should be familiar with the relationship between similar triangles and the concept of the slope of a line.

Source:
FINAL REPORT, 2008.

Andromeda on organization & the middle school kid

Organizing notebooks:

1) I teach middle school, and it's just scary how much of success at this level is linked to organizational abilities and work habits, not intelligence. I've got crazy-smart kids who do terribly because they do the homework and can't find it, or (more likely) never did the homework because they don't have some consistent way of writing it down, or couldn't do it correctly because they didn't have the notes, or, or, or...All organization. I don't believe in notebook grades, but that does put me in a bit of a bind...

2) Joan Sedita's book on study skills is the bible. I don't remember if it touches directly on organization, but it does a great job identifying and breaking down study skills things that students may be having trouble with, and its general approach is illuminating.

3) As a basic template for organizing notebooks, you can seldom go wrong with this:
Get a three-ring binder with as much looseleaf paper as will fit. (Notebooks where you tear out paper are the devil; paper, once torn out, cannot be put back in any helpful way.) If at all possible, get one which doesn't have folders in the front or back, because then all the paper will end up *in* the folders, getting dogeared and disorganized.

Make four sections: notes; homework; tests and quizzes; handouts. Or maybe five: blank paper.

Everything in those sections is to be chronological. It doesn't matter if the most recent is first or last, as long as it's consistent. This gives you an easy organizing principle: whatever you are working on should be placed directly after the last page with writing on it (or as the very first page of the section, depending on whether you prefer chronological or reverse). Actually, having all the blank paper segregated in a blank paper section will probably benefit the very disorganized (who tend to have random quantities of blank paper interrupting stuff).

Also:

HAVE A HOLE PUNCH which lives in the binder. (You can get little thin three-ring punches which have holes so they can live in three-ring binders.) If the teacher gives you anything unpunched (which I think is unacceptable but no one made me god), hole-punch it immediately so you can put it in the appropriate section.

The virtue of the notes/homework/tests and quizzes/handout layout is that pretty much every paper you will ever get in class goes in one of those, and it's generally obvious which. There are a couple of odd cases like syllabi, but they are rare.

As long as we're on the topic of notebooks, rereading your notes within a day of taking them is also a great habit to be in -- it's spooky how much that aids retention (and especially the retention gained/time spent ratio).


THANK YOU, Andromeda!!!!!!!

(And tell us more!!)

Newsflash – Middle-schoolers hate math homework

For Catherine, and all the other afterschoolers out there:

A national Raytheon survey found that 84 percent of middle school students would rather clean their rooms, eat vegetables, take out the garbage and to go to the dentist than do their math homework.

From Discovering the magic of math

fractions speak louder than nerds

brand new blog!

from a middle school math teacher!

This is exciting.

Believe it or not, I have thoughts of going back to school, majoring in math (after I finish high school math, that is) and teaching math to middle school kids.

This is one of the craziest impulses I've had in my life, no doubt, so we'll see.

As much as I'm not a fan of credentialism, in this case it's saving my life, since the years it would take to acquire the relevant credentials are the only thing standing between me and the abyss.

otoh, now that I'm becoming seriously interested in the teaching of composition.... I'm equipped for that, though not credentialed.

That's another thing. I guess I'd have to get an English literature degree to teach ELA, right? But I don't want an English literature degree!

Maybe I should be rooting for the writing-across-the-curriculum folks, after all.

Anyway..... one way or another I'm probably headed back to the classroom in some way. I come from a long line of teachers on both sides of the family. My grandpa was superintendent of schools in my hometown; my mom's mom taught English 'til middle age when her eyes started to bother her (too much paper grading) so she went back to school, took calculus, and switched to math; my sister was an elementary school teacher; my other sister taught high school (she subs now); I began life teaching college ..... plus I spend every day thinking & writing about teaching not to mention attempting to teach my son and me.....

(And let us not forget the fact that I taught Jimmy^* to tie his shoes. Now that is a credential.)

Looking forward to Ms. Longhorn's blog.


^* for newbies: Jimmy has autism

Jay Matthews on good middle schools

Over the last few months, we have asked readers to tell us about the best middle schools they have encountered. Having heard so many horror stories, it was a surprise to read e-mails and letters from more than 500 parents, students, educators and community members pointing out great teachers and wise principals making real progress with children at that itchy age. [ed.: I'm surprised] The results are the following snapshots, in alphabetical order, of 30 area middle schools that are doing things right.

We have provided some basic information on each school, including how long each principal has been at the school and the most telling and universal measure of a middle school's level of challenge: what percentage of eighth-graders complete Algebra I.

source:
Unstuck in the Middle
Jay Matthews
WAPO
Sunday, April 15, 2007; Page W12

I count at least 5 affluent middle schools in the bunch. There may be more, but I don't feel like looking them all up on School Matters.


Here are the 5:

Capitol Hill Day School
D.C., 225 students, pre-kindergarten to 8; principal Catherine Peterson (22 years); tuition $20,590; 62 percent white, 38 percent other; 100 percent completed algebra.

Rachel Carson Middle School
Herndon, Fairfax County, 1,149 students, grades 7 and 8; principal August "Augie" Fratalli (four years); 6 percent low income, 59 percent white, 6 percent black, 4 percent Hispanic, 28 percent Asian; 64 percent completed algebra.

Cooper Middle School
McLean, Fairfax County, 931 students, grades 7 and 8; principal Arlene Randall (10 years); 1 percent low income, 76 percent white, 1 percent black, 4 percent Hispanic, 14 percent Asian; 59 percent completed algebra.

Kilmer Middle School
Vienna, Fairfax County, 1,070 students, grades 7 to 8; principal Deborah Hernandez (two years); 12 percent low income, 59 percent white, 4 percent black, 10 percent Hispanic, 21 percent Asian; 54 percent completed algebra.

Piccowaxen Middle School
Newburg, Charles County, 492 students, grades 6 to 8; principal Kenneth Schroeck (1 year); 14.2 percent low income, 81 percent white, 16 percent black, 2 percent Hispanic, 0.4 percent Asian; 44 percent completed algebra.



compare and contrast

Irvington Middle School: approximately 30% complete algebra

$21,000 per pupil spending

Japanese math textbooks

Instructivist links to a video of a presentation on constructivist math by David Klein and James Milgram hosted by Where's the Math.

I haven't seen it yet, but apparently Klein mentions a translated Japanese middle school curriculum he likes.

Instructivist thinks Klein is referring to these books:

[14] Mathematics 2: Japanese Grade 11 - Kunihiko Kodaira, Editor - AMS, 1997, 262 pp., Softcover, ISBN-10: 0-8218-0582-7, ISBN-13: 978-0-8218-0582-4, List: US$32, All AMS Members: US$26, MAWRLD/9

[15] Basic Analysis: Japanese Grade 11 - Kunihiko Kodaira, Editor - AMS, 1996, 184 pp., Softcover, ISBN-10: 0-8218-0580-0, ISBN-13: 978-0-8218-0580-0, List: US$26, All AMS Members: US$21, MAWRLD/11

[16] Algebra and Geometry: Japanese Grade 11 - Kunihiko Kodaira, Editor - AMS, 1996, 174 pp., Softcover, ISBN-10: 0-8218-0581-9, ISBN-13: 978-0-8218-0581-7, List: US$26, All AMS Members: US$21, MAWRLD/10

[17] Mathematics 1: Japanese Grade 10 - Kunihiko Kodaira, Editor - AMS, 1996, 247 pp., Softcover, ISBN-10: 0-8218-0583-5, ISBN-13: 978-0-8218-0583-1, List: US$32, All AMS Members: US$26, MAWRLD/8

I have in my own files this list, which may be the same as Instructivist's books:

Resource Materials available from the UCSMP Director's Office

• Soviet Studies in Mathematics Education, vols. 7-8
• Japanese Grade 7 Mathematics
• Japanese Grade 8 Mathematics
• Japanese Grade 9 Mathematics
• Russian Grade 1 Mathematics
• Russian Grade 2 Mathematics
• Russian Grade 3 Mathematics
• Developments in School Mathematics Education around the World, vols. 1-3

About UCSMP's Translation Series

Translations of Japanese Elementary textbooks are sold here: Global Resources. (Klein didn't mention these, I gather. I have no idea whether he's seen them.)

You can look at sample pages here

Myrtle (hi, Myrtle!) found this link: Japan: A Different Model of Mathematics Education (pdf file)

I still can't do these middle school entrance problems. At least, not the first one. Not in two minutes.

sigh

UPDATE: Yes, I can.

In fact, I may even be able to do this problem in 2 minutes.

Saxon Math to the rescue.