ACTION ALERT! Join us tomorrow to demand access to information on IMPACT On Tuesday, June 30 at 9 am join fellow DCPS educators, parents and other WTU allies at the Wilson Building to oppose cutting off access to information about the DCPS teacher evaluation system, IMPACT. Tomorrow morning the City Council will vote on legislation that would cut off access to IMPACT information, which your union, researchers and others need to judge the fairness and effectiveness of the evaluation system, and to determine whether D.C. Public Schools’ policies are really helping our children succeed. The Washington Teachers’ Union (WTU) has always stood for transparent decision-making and open government. The union and others have urged the mayor and council members to remove from the Mayor’s Budget Support Act the provision that would prevent the union, educators and others from having access to IMPACT data, and to hold hearings on the provision. This is an urgent matter!
Be at the Wilson Building (14th St. and Pennsylvania Ave. NW) on Tuesday morning at 9 and let the DC City Council know that you strongly oppose keeping important IMPACT evaluation data secret.
Send us an email at dialogue@wtulocal6.net and let us know you’ll be joining us! |
Demonstrate at the Wilson Building Tomorrow at 9 AM to Allow the Washington Teachers’ Union Access to Important Teacher Data
- DC
- education
- Educational DEforms
- history
- mathematics
- measurement
- NAEP
- public schools
- Standardized Testing
Tags: data, DC, DC-CAS, DCPS
“Math for America” teachers meet with some members Congress and apparently give them some sound advice
During the First National Math Festival here in DC (which I missed), back in April, some Math for America – DC* teachers I know were invited to speak with some Congressmen and Senators. According to the press release I was recently given, my colleagues appear to have given the elected reps** sound advice that may or may not be heeded.
{** including Nancy Pelosi, Harry Reid, Chuck Shumer, Al Franken, Lamar Alexander, Patty Murray, Steny Hoyer, among others}
I quote from the press release, in green and my own comments in black:
“House and Senate leaders, field experts, and MfA DC teachers spent the first hour and a half engaging in dialogue on how the ESEA reauthorization would affect the classroom. Joe Herbert spoke to the adverse effects standardized tests had had on his school and his classroom. David Tansey, a[n] MfA DC Master Teacher, offered criteria that such tests should meet in order to provide instructional value to the teacher and the student.”
{notice the clear implication, which Tansey has spelled out to me in detail on several occasions, that the standardized tests that he and his school are required to administer many, many times a year are of absolutely no use to teachers in figuring out how to help their students learn more stuff, better.}
“Joe Herbert wrote, ‘I spoke of the harmful effects of standardized testing on K-12 education, and of the complete lack of statistical basis for evaluating teachers based on their students’ test scores.'”
While Max Mikulec, one of the other teachers, was initially somewhat awestruck by listening to amusing anecdotes from Senator Al Franken, he …
“…went on to say, ‘As I reflected on the day, my initial reaction of pride and hope turned into a feeling of skepticism and apprehension. You cannot imagine how great I would feel if the nation spent billions more dollars developing math education and math teachers. However, I do not see this happening in an effective way. There are endless debates over what standards should be taught in our schools and what the kids should be tested on. Amid all of the debates, the ones who are losing here are the nation’s kids. In their most formative years, a time where they struggle to find any consistency in their own lives, they are being let down by an educational system that will change several times before they graduate high school. Ev en though all of these powerful and important people say that they support math education and that [they] see math teaching as a real profession, I will not believe them until something is actually done to show their support.'”
In addition, Joe Herbert wrote me the following:
“Another point I made is just how much money gets wasted on these tests. I don’t remember the exact number now, but I looked up how much is spent annually on testing before I went to the event (I remember the number was in the billions), and I made the point that we could increase spending on education by that much money without raising taxes a penny if we got rid of the annual testing mandate in NCLB.
======================================================
*Note: MfA and MfA-DC are as far from the TFA idea as it is possible to be. Unlike ‘Teach for Awhile”, MFA actually gives its members a FULL YEAR of math-content and math-pedagogy classes and student teaching experience, assigns them a mentor, and in return expects them to stay in the city, teaching, in their field for a full five years, and does not pretend to have a one-size-fits-all “no excuses” magic wand that will miraculously reproduce the irreproducible miracle that Michelle Rhree pretended to achieve at Harlem Park Elementary in Baltimore in the early 1990s, magically moving 90% of her students from below the 13th percentile to being over the 90th percentile. Right now, MfA DC teachers are some of the most senior math teachers anywhere in DC, either in the regular public schools or charter schools.
- DC
- education
- history
- mathematics
- public schools
- social policy
- Standardized Testing
- teaching
- Washington
Tags: achievement, congress, data, DC, Math for America, NCLB, testing
A closer look at charter and regular public school enrollments, percentages of students at risk, and percentages of students ‘proficient’
Here is another look at the brand-new data concerning four variables in the District of Columbia schools, about which I wrote a couple of days ago. The difference here is that the dots representing the schools are more-or=less proportional to the size of the student body.
1. Is this a regular public school, or a charter school (blue or red):
2. What fraction of the kids at that school are officially considered to be At Risk? (That’s the scale along the x-axis at the bottom of the page)
3. What is the average percentage of the kids at that school are ‘proficient’ in reading and math on the DC-CAS? (That’s the scale along the y-axis at the left-hand side of the page)
4. How big is the school? (That’s the size of the dot, more or less; the legend is at the bottom left-hand corner of the graph)
Time spent looking carefully at this graph will be well-spent. If you click on it, it will expand.
It will certainly show that charter schools have not revolutionized education for the better in DC: for both types of schools, there remains a very strong, negative correlation between the percentages of kids At Risk and ‘pass’ rates on the DC-CAS.
Note that most schools have between 200 and 500 students and that most of the ones that are smaller are actually charter schools. As I wrote a couple of days ago, the schools with the largest fraction of At-Risk students (say, over 2/3 of the student body) are almost all regular DC public schools.
On the second graph, which is otherwise identical to the first, I’ve labeled some of the larger schools.
Here is the one with names of some of the larger schools, so you can see how individual schools fall on this graph.
(Sorry, I there was not enough room to label every single one, and my non-existent HTML skills won’t allow me to make it so that any of the dots are clickable. If any of my readers know how to do that and would like to offer to make that happen, then please let me know in the comments.)
And here is the entire data table. So you can see where every single school lies on these three dimensions.
(PS: I added a few more names of schools and corrected four other small errors, two pointed out by an alert reader.. 2/22/2015)
- charter schools
- DC
- education
- history
- mathematics
- measurement
- public schools
- social policy
- Standardized Testing
- Washington
Tags: achievement, achievement gap, At Risk, charter schools, correlation, DC-CAS, DCPS, education, enrollment, poverty
Atlantic Magazine Article on What’s Wrong With the New SAT
Interesting article in the Jan. 20 The Atlantic Magazine concerning the problems with the new SAT (which once was called the Scholastic Aptitude Test).
One problem is that the problems are wordy as all get out and are mostly testing the students’ ability to decipher highly abstract text, not their ability to do math. For example, I present two questions that were cited in the article.
First problem, which you may click on to enlarge:
Not having studied the bones of the hand since junior high school, I didn’t recall what the “First Metacarpal Bone” was;I wrongly guessed it was one of those little tiny bones that allow you to bend your wrist. Only when I looked at how long thse bones are ( 4 to 5 cm) and looked it up online did I find that this is the long bone at the base of your thumb, as you see here in red.
Of course, this fact was was not explained anywhere in the text; and if your first language isn’t English then you are going to have a very hard time with this question. I suspect that the reading level of this problem is very, very high.
Having studied and taught some statistics, I know that the slope of the line of best fit for this graph shows how an increase or decrease of 1 cm in the length of that thumb-bone will predict an increase or decrease in the height of those people.
Now, here is a graph of a very similar correlation (hand length and height) from a real study (and for which a line of best fit would be a whole lot more realistic!):
Why does David Coleman feel the need to make everything so obscure? Oh! I remember! He’s never taught students, ever!
Oh, and by the way, this question is considered by Mr Coleman to be “easy”.
As is this one, which I am also taking from the Atlantic article:
I will recommend that you read the Atlantic article, since that author has much more patience than I do to explain all of this stuff. The basic idea is that when you sample more items in a population of things or people, then your margin of error gets smaller, which is highly counterintuitive! So asking more people will give you better results, hence a smaller margin of error. Which is not really taught outside of statistics classes. (Assuming that these students generally read for pretty close to an hour and a half a day and feel like telling the truth, OR that they know that they are supposed to say something near 90 minutes a a day…)
In any case, the readability of this question is pretty high, according to the Fry and Lexile algorithms that I used.
Recall, this is supposed to be an EASY question!
And PS: I defy my readers to solve this question: (p,.111)
An international bank issues its Traveler credit cards worldwide. When a customer makes a purchase using a Traveler card in a currency different from the customer’s home currency, the bank converts the purchase price at the daily foreign exchange rate and then charges a 4% fee on the converted cost. Sara lives in the United States, but is on vacation in India. She used her Traveler card for a purchase that cost 602 rupees (Indian currency). The bank posted a charge of $9.88 to her account that included the 4% fee.
part 1
What foreign exchange rate, in Indian rupees per one U.S. dollar, did the bank use for Sara’s charge? Round your answer to the nearest whole number.
part 2
A bank in India sells a prepaid credit card worth 7,500 rupees. Sara can buy the prepaid card using dollars at the daily exchange rate with no fee, but she will lose any money left unspent on the prepaid card. What is the least number of the 7,500 rupees on the prepaid card Sara must spend for the prepaid card to be cheaper than charging all her purchases on the Traveler card? Round your answer to the nearest whole number of rupees.
How Well are Charter Schools in DC Educating Students Who are Officially At-Risk?
The results may surprise you.
To answer this question, I used some recent data. I just found out that the DC City Council has begun requiring that schools enumerate the number of students who are officially At-Risk. They define this as students who are
“homeless, in the District’s foster care system, qualify for Temporary Assistance for Needy Families (TANF) or the Supplemental Nutrition Assistance Program (SNAP), or high school students that are one year older, or more, than the expected age for the grade in which the students are enrolled.” (That last group is high school students who have been held back at least one time at some point in their school career.)
So, it’s a simple (but tedious) affair for me to plot the percentage of such at risk students, at each of the roughly 200 publicly-funded schools in Washington, DC, versus the average percentage of students who were proficient or advanced in math and reading on the 2014 DC-CAS.
I was rather shocked by the results. Here are my main conclusions:
1. For almost all of the schools, to get a rough idea of the percent of students passing the DC-CAS, simply subtract 90% minus the number of students ‘At-Risk’. The correlation is very, very strong.
2. There are only THREE DC charter schools with 70% or more of their students At-Risk, whereas there are THIRTY-ONE such regular public schools. So much for the idea that the charter schools would do a better job of educating the hardest-to-reach students (the homeless, those on food stamps, those who have already failed one or more grades, etc).
3. The only schools that have more than 90% of their students ‘passing’ the DC-CAS standardized tests remain, to this day, the small handful of schools in relatively-affluent upper Northwest DC with relatively high percentages of white and Asian students..(Unless you include Sharpe Health school, where students who cannot feed or dress themselves or hold a pencil are somehow deemed ‘proficient’ or ‘advanced’ by methods I can only guess at…)
4. As I’ve indicated before, it appears that for the most part, DC’s charter schools are mostly enrolling smaller percentages of At-Risk, high-poverty students but higher fractions of the students in the middle of the wealth/family-cohesion spectrum than the regular DC public schools. There are a few exceptions among the charter schools: BASIS, Yu Ying, Washington Latin and a few others are succeeding in attracting families and students at the high end of the socio-economic and academic scales.
5. It looks like we are now turning into a tripartite school system: one for affluent and well-educated familes (relatively high fractions of whites and Asians; mostly but not all in regular Ward 3 public schools); one for those in the middle (mostly blacks and hispanics, many enrolled in charter schools), and one for those at the seriously low end of the socio-economic spectrum, overwhelmingly African-American, largely At Risk, and mostly in highly-segregated regular public schools.
Very, very sad.
Here is the graph that sums it all up. Click on it to see a larger version.
In blue we have the regular public schools of Washington DC for which I have DC-CAS data for 2014, from grades 3 through 8 and grade 10. In red we have the privately-run but publicly-funded charter schools. Along the horizontal axis, we have the percentage of students who are officially At Risk as defined by the DC CIty Council. Along the vertical axis, we have the average percentage of students who scored ‘proficient’ or ‘advanced’ in math and reading on the DC-CAS at those schools. The green line is the line of best fit as calculated by Excel. Notice that the data points pretty much follow that green line, slanting down and to the right.
To nobody’s surprise, at both the charter and regular public schools, on the whole, the greater the percentage of students at a school who are At Risk, the smaller the percentage of students who ‘pass’ the DC-CAS standardized tests.
The colors do help us see that at the far right-hand end of the graph, there are lots of blue dots and only a small number of red ones. This means that the vast majority of schools with high percentages of At Risk students are regular DC public schools. You could interpret that to mean that parents in more stable families in those neighborhoods are fleeing from what they see as the bad influence of potential classmates who are extremely poor, homeless, have already repeated a grade, and so on, and are flocking to charter schools who have the freedom to expel or ‘counsel out’ such students and to impose a relatively strict behavior code that the DC Council forbids the regular public schools from using. (Their latest initiative is to forbit ALL out-of-school suspensions, no matter what…)
Dots that are above the slanted green line supposedly represent schools that are doing a better job at teaching to the tests than would be predicted by the At-Risk status alone. Dots below the line are doing a worse job than would be predicted. Notice that there are dots of both colors both above and below the line.
=====
I wish to thank the indefatigable Mary Levy for collecting and passing on this data. You can find the original data source at the OSSE website, but I’ve saved the larger table (all 2008-2014 DC-CAS data) on Google Drive at this link. I took the average of the percentage of students ‘passing’ the DC-CAS in math and in reading as the proficiency rate. The note on the at-risk data table reads as follows:
Data Source: SY2013-14 student-level data from OSSE. The list includes DCPS traditional, DCPS citywide specialized, DCPS selective schools, and public charter schools, but excludes any DCPS or public charter adult education or alternative school. The definition of at risk students includes students who are homeless, in the District’s foster care system, qualify for Temporary Assistance for Needy Families (TANF) or the Supplemental Nutrition Assistance Program (SNAP), or high school students that are one year older, or more, than the expected age for the grade in which the students are enrolled. |
- charter schools
- DC
- education
- Educational DEforms
- history
- mathematics
- measurement
- public schools
- social policy
- Standardized Testing
- teaching
- Washington
Tags: achievement, achievement gap, At Risk, correlation, DC-CAS, homeless, overage students, poverty, standardized testing
Exodus of Senior Teachers in NJ, NY, and everywhere, I bet
A recent post on Facebook indicates that what I see happening here in DC is much the same as what’s happening in NY, NJ, and elsewhere. Here is the post:
It’s Worse Here Than In NY! A New Jersey Teacher’s Lament
- DC
- education
- Educational DEforms
- history
- mathematics
- measurement
- public schools
- resistance
- social policy
- Standardized Testing
- teaching
James Tanton on the Math Common Core Standards
James Tanton is an experienced math teacher and educator of other teachers whom I respect a lot. Part of his take on math is that it should relate to the real world and it should be a joyful activity, because math is all around us if we care to look; if we do, it makes our lives better. (My paraphrase of his general ideas, not a literal quote at all; but the way I expressed it, expresses my own personal thoughts on the topic. If you want to see examples of his work, I suggest you look at his site, . Again, I think he does excellent work, and I wish I could be one-fifth as original in my own teaching as he is.
In this video, Tanton gives his take on why the Common Core State Standards in math are actually a very good thing, not a bad thing at all, IF they are implemented correctly.
That “if” is a big one. Let us assume Tanton is right, that the CCSS in math (don’t know about any other subject) was written in a very thoughtful way and will promote these eight general concepts and practices in students towards math:
I’ll retype those for clarity:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning
Those are, in fact, excellent ideals.
And those ‘Mathematical Practice’ goals you see above are, in fact, expressed better there than I recall having seen before in all my years of teaching math.
But — remember that “IF” clause? “If they are implemented correctly?”
As far as I can see, judging by what I see in mathematics classrooms in both charter and public schools in DC, it looks to me as if the worksheets and practice tests were written either by low-paid, low-skilled temps who have almost no experience in teaching math, or else were written by very clever and evil people who want to seriously dumb down the education of urban youth.
And, what’s more, those inequities are being primarily visited upon our poorest kids, especially [but not limited to] those of color.
Let me give examples, judging again by my own personal visits to schools in DC and what math teachers in DC tell me and what students of my acquaintance know tell me and show me (some of whom I have known for years).
What I see is that in the expensive private schools in DC, where there is no test-accountability on the part of the USDoEd, they are continuing to give a pretty good education, sometimes joyful and interesting, sometimes not, mostly depending on the individual math department members and the incoming ability levels and work ethics of the students they teach. Some of the departments use some pretty old textbooks because they prefer them to anything in print at this moment.
At the magnet high schools in DC, there is some pressure from the NCLB and RTTT testing mania, but since nearly all the students are already at or above grade level by any reasonable measurement, they can continue to teach.
However, at the regular, comprehensive high schools and at the middle and elementary school levels, I see that the curriculum is rigidly prescribed and regimented from above, in such a way that NONE of those eight laudable goals can possibly get implemented.
Instead
(1) Unbelievable number of typos and sloppy and incorrect problems (some of which I’ve been documenting on this blog) on centrally-produced tests and worksheets;
(2) Problems that are self-contradictory and involve huge amounts of difficult and confusing text;
(3) Large numbers of multiple-choice test items, which, in my considered professional opinion, can do almost nothing to promote any of those wonderful thought processes; nor do they give useful information to eachers about what the student does or does not understand;
(4) Requiring schools to spend an enormous fraction of their time on testing and test prep, thus preventing them from doing any open-ended investigations into math;
(5) Reliance on electronic on-line worksheets that are at times just as buggy as the worksheets;
(6) Loading teachers with so much time-consumiing but useless busy-work regarding data collection and entry and analysis that they have no time to actually read what the students wrote and drew — and believe it or not, it’s just as important in math as it is in any other class!
(7) Deep understanding is prevented because instead of going at a breakneck speed through umpteen standards a mile wide and an inch deep, it’s now 1.6 kilometers wide but only a couple of millimeters deep! (Get the joke?)
(8) And from what I see over time (30 years in DCPS and 5.5 years retired now), while I thought math instruction in some ways had improved from 1978 to the mid-2000s, it seems to have taken a real turn for the worse since Michelle Rhee and the then-head of the Washington Teachers’ Union, George Parker, along with AFT head Randy Weingarten and the heads of several large foundations (Walton family, an ENRON family, the Broads and one more), along with then-mayor Adrian Fenty and the blessing of Congress and the White House, were able to impose a weird settlement upon teachers which required them to teach to the many, many tests I’ve been complaining about for some time, in exchange for mythical bonuses amd high salaries that almost no teacher will be able to earn because they will be fired or burn out first.
My conclusions:
In mathematical logic, the word “if” is a really big deal.
And it looks to me as if the authorities in DC (both public and charter, with some exceptions as noted above) are NOT implementing the Common Core Standards correctly at all, because everything I see tells me that everything being done in the charter schools and in the public schools that serve poor or working-class kids in DC is in fact thwarting those laudable goals.
Remember what Tanton said, which I granted to him as being valid: If they implement the Math CCS standards correctly, then the results will be excellent.
Logicians say that when you have a sentence of the form “If A. then B”, then it’s only false in the case where the “A” section is true and the “B” section is false. There are three other cases and they all have overall values of “true”. In particular, if the “A” part is false, it doesn’t matter whether B is true or not: the entire “if A then B” statement is true.
I maintain that the “A” part is false. So in one sense, whether the CCSStandards in math are as clearly- and as well-written as many math teachers think, it remains the case that even by their own standards, the idiots running the USDoE and the other billionaire education ‘reformers’ who think they know all the answers, are implementing it in a way as to subvert every single one of the laudable goals that are promoted by the CCSS themselves.
And that’s quite a trick.
It’s kind of like some of the absurdities in 1984 or recent world history: many regimes upholding the universal brotherhood of all working people while imprisoning, torturing, murdering or enslaving millions of said working people. I know it’s not nearly as bad, but this current situation sure is perverse.
So, what do you think? Believe it or not, there is a ‘comments’ button below this text, but it’s really tiny and you have to search for it.
Again, the link to Tanton’s video.
- art
- charter schools
- DC
- education
- Educational DEforms
- history
- mathematics
- Michelle Rhee
- public schools
- social policy
- Standardized Testing
- teaching
- Washington
Tags: CCSS, Common Core, standards
Is it inequity, or poverty, that causes the educational problems we see in the US?
Someone posted this question to me. I think it’s inequity, since poverty is a relative thing. Our ancestors who hunted and gathered 10,000 years ago in the cold or hot and dangerous oceans, rivers, jungles, steppes and meadows of the day, armed only with animal bones, sharpened sticks, rocks and nets they made themselves, mostly didn’t think of themselves as poor. Here in the US we can all see on TV video footage of the most opulent mansions and life-styles the world has ever seen, bar none (not even the Roman or Chinese empires!). If your family only earns a few thousand dollars per year, you are going to live in utter squalor, even though such an income 200 years ago would have seemed amazing.
I’m going to coin a slogan: “It’s the differences, stupid.”
If you see that some kids go to schools where they get to learn horseback riding, soccer, lacrosse, and clay sculpture after school, AND learn foreign languages and have actual physics or biology labs with up-to-date equipment with teachers who are trusted to choose what to learn and experiment with, and your school just gives you multiple-choice worksheets all day in math and reading, with none of that other extracurricular stuff and no classes outside of math, reading, basic science, and ‘social studies’ becomes more worksheets, you will feel like crap. Especially since the never-ending revolving door of teachers who start with high hopes but then are beaten into submission to Test Prep Above All and following idiotic curricula written by folks who never taught is going to condemn you to bad teaching.
Education should be one of a whole raft of methods used by all parts of our government that is used to end poverty. However, our judicial and police systems seem to be bent on promoting poverty for some while promoting rule over the entire universe for others. I could give many examples, such as judges routinely suspending drivers licenses for not paying small fines the person can’t pay. Then they get more tickets for driving on a suspended license, and eventually in jail or many thousands in debt. While the rich are allowed to buy elections, hire lawyers to evade state, local and federal taxes and don’t go to jail for almost any fraud committed. On the rare instances that a billionaire fraudster does go to jail, then it’s at a nice place and when they get out, they then get to set up lucrative ‘foundations’ that prey on the poor. (Think Michael Milken)
One excellent proposal from Ras Baraka, the new Newark mayor, during his campaign is that school house other agencies that help fight the effects of poverty: have free, good dental and optical and medical clinics in evrery single school, as well as free cafeterias on weekends.
Why?
So kids won’t have to miss school if they have toothaches, can’t see, or need a shot or a medical test or a wound bandaged, or psychiatric help for those suffering from acute mental illness attacks – a substantial fraction of the kids in any high-poverty school anywhere in the USA.
Plus, many families and kids actually don’t have food to eat on weekends, snow days, and holidays. Also, if well done, it would let kids know that someone was looking out for them. I thought it sounded like a great idea. I hope he’s managed to put it into effect. Unfortunately, the elected officials of Newark have for over 10 years not been permitted to run their own schools. Instead, Kami Anderson, an administrator appointed by Governor Chris Christie, runs things. She refuses to go to any hearings or meetings in Newark, IIRC.
- art
- education
- Educational DEforms
- Fraud
- history
- mathematics
- public schools
- racism
- science
- social policy
- Standardized Testing
- teaching
David Sirota pointed out that we need a war on poverty, not a war on teachers and schools
Excellent article in Salon by David Sirota that appeared in June. Not sure that I read it at the time; several friends of mine have pointed it out to me recently, so I thought I would return the favor to my readers.
Sirota points out that the strongest socio-economic correlation anywhere in the US is between family income and educational achievement.
I would add that in my town, Washington, DC, that correlation still occurs, yet ALL of the teachers in ALL of the schools are either brand-new (that is, hired by DEformers Rhee and Henderson under mayoral control) or have been rated effective or highly effective. So the low achievement of poor kids in Washington, DC can not be laid at the feet of the imaginary legions of lazy, unionized teachers waiting for retirement!
- charter schools
- DC
- education
- Educational DEforms
- Fraud
- history
- mathematics
- measurement
- Michelle Rhee
- NAEP
- public schools
- racism
- social policy
- Standardized Testing
- teaching
- Washington
Tags: David Sirota, Salon
Bad ‘rigorous’ Common-Core-style geometry problem
Here is a problem put out by Houghton-Mifflin and labeled ‘test prep’ that I came across as a worksheet for a 9th grade Geometry student I’m currently helping here in Washington, DC.
How many things can you find wrong with this question?
If you have a hard time reading the question, it asks, “Why is segment DE the perpendicular bisector of segment FC?” (FC wasn’t drawn by the makers of the worksheet; that was added by the student right before I took the photo with my phone.)
Here is what I find objectionable:
(1) Segment DE is in fact NOT the perpendicular bisector of segment FC. It might be perpendicular, if EB’A’D is a rectangle, which is nowhere given in the problem, but even if the skinny space between the two triangles is a rectangle, DE does not intersect segment FC’ at its midpoint.
(2) We should not be asking students to prove things that are not true.
(3) The first two paragraphs of verbiage* are unnecessary, but if we take them at face value, you could end up with either of these two diagrams instead:
or else the following:
In neither case is it true that DE is even perpendicular to undrawn segment CF, even though I definitely used ‘rigid motions’ to transform triangle ABC into triangle DEF.
(4) In geometry classes, an apostrophe after a capital letter means something: that a point is the result of some sort of transformation performed on the point that lacks the apostrophe. In this problem, points A, B, and C should not be written as A’, B’, and C’.
(5) Here is a much more straightforward problem: You are given the congruences shown in the diagram. Explain why (or “Prove that”) segment HJ is the perpendicular bisector of segment IK.
Maybe this is what Sandra Stotsky was complaining about when she dissented from approving the Common Core math standards, objecting to making transformations (such as rigid motions or dilations) the core of geometry .
*For those of you unfamiliar with the term, a rigid motion means a rotation (turn), a reflection (flip), or a translation (slide) — they normally change the location of a figure without changing its size, area, or angles. And, yeah, I taught geometry to 8th and 9th graders for many years, so I know a little bit of what I’m talking about.