Monday, December 22, 2014

Favorite Comments of '14, cont: Auntie Ann, bj, C_T, Anonymous, forty-two and lgm

On Aiming for Mediocrity:

Auntie Ann said...
Until the standardized tests come along to shatter expectations.

That leads to the second step in the process: dumb down the tests so that you *still* don't know how your kids are doing. Schools don't want accountability.

Hopefully, that will lead to a third step: a brand new testing system which is independent of the teachers and schools. Things like the placement tests for online courses could become very important to parents.
Anonymous said...
I have felt this frustration as well, and, reading through some of your other posts, especially feeling the frustration at the lack of feedback about the high end of performance.

But, in other discussions with those doing the evaluation, one factor that's coming up, is the perceived impossibility of discriminating among the higher performers. Examples include the compression of grades at Harvard, where, in response, teachers will say that it's very difficult to discriminate among the top performers in the class -- one might have excellent ideas, the other be an excellent writer, the other a leader in classroom discussions. They are all "good/great" students but none are superlatives, except for the rare, say, once in a couple of classes or once in a couple of years student, who might excel in all the categories (i.e. the ES criterion).

Another example is a recent analysis showing that grants awarded at NIH in the top 35% can't be distinguished (by percentile within the 35%) based on subsequent publication or citation rates. The analysis is suggestive that expert reviewers cannot effectively differentiate among the top 35% of grants, picking the ones in the top 10%, 20% and so on.

What do we do, if this is indeed the case?

Danthi N1, Wu CO, Shi P, Lauer M. Percentile ranking and citation impact of a large cohort of national heart, lung, and blood institute-funded cardiovascular r01 grants. Circ Res. 2014 Feb 14;114(4):600-6. doi: 10.1161/CIRCRESAHA.114.302656. Epub 2014 Jan 9.

C T said...
This is very painful to read.
First, "proficiency" has lost its meaning if a child can be wrong on 1/4 of an assignment and still be told they are "proficient." Do a quarter of your work wrong at nearly any job, and you're going to lose that job.
Feedback is crucial for children and adults. Can you imagine a workplace where you almost never got feedback from a supervisor? Never knew if you're doing the job well or if your yearly review is going to have unpleasant surprises? How can children be expected to learn if they're never told whether they've actually learned specific things correctly? It's all a mystery to them. When we homeschool in the mornings, I typically give my children feedback within minutes of their having done an assignment. Sure, they're disappointed if they did something wrong, but it's not a big deal because I'm correcting specific things, not labeling them with a negative letter after a year of acting as though their performance is fine.
Anonymous said...
I'm looking forward to having a heart surgeon who thinks getting things 1/4 wrong counts as proficient.

Who needs a left ventricle?
forty-two said...
I admit, I feel sort of uncomfortable at the sentiment that "the goal is to get the highest *grade*" - not to maximize *learning* - that some of the quoted parents seem to have. Who cares if the younger sibling gets a P where the older sibling got an A, if the amount of learning was the same (100% on a grade-level assessment would be both Proficient and an A in my book). I spent my school time doing whatever was needed to get that coveted A and generally not terribly much more. Not a great attitude.

But otoh, the reason I did so was because I had the learning in the bag, and did *more* than I needed to do to learn to get the A. Which isn't a great situation, and I don't know that the students who refuse to do one lick of work more than they need to become proficient aren't choosing the better path (assuming they have areas in their life where they actually have to work to learn things).

I'm guessing they refuse to give out the standards for above expectations partly to avoid grade-grubbing (and/or because the devil's in the details and it's way easier to not bother having to come up with specifics). But it completely ignores dealing with a huge underlying cause of grade-grubbing: where grades are so badly decoupled from learning for some/many kids that if they used learning as their motivation, they'd be doing *less* work, not more. And by not defining what "above the standard" actually looks like, kids have no idea what they should aim for, learning-wise. Without learning goals attached to ES, the *only* reason to aim for it is for the *grade*.

And compressing the range of grades probably makes it even worse. Personally, I rather like grading systems that include tons of above-standard stuff, where proficient at grade level might be 50% - lots of room for separating out the top. Which is the opposite of what they seem to be doing.
lgm said...
My district uses this grading system for ele. It began when full inclusion began. It's a big shock when middle school starts and they are supposed to be earning a 95 or better to qualify for the 7th grade honors/accel program. Or an 85 or better to not be placed in remedial math the following year.

Downfalls: kids that are striving to do well can't as there is nothing in class offered at the advanced, or highest, level. A 100% on every spelling test is still graded as proficient....just like an 85%. NCLB means no above grade level reading the kid who is sitting in the back of the room in 4th (front is reserved for special needs) reading his LOTR while the class is reviewing will be marked as proficient, just like the kid who is mastering Diary of a Wimpy Kid. The kid who could teach the math class, and consistently does his homework as a five minute exercise, looks the same as the kid who needs a resource teacher. need for differentiation, they look the same on paper.
Anonymous said...
The result here, 9 years into this system, is that our 8th grade Algebra numbers are half of what they were when placement and teaching in the elementary was done by instructional need.

Welcome to the soft bigotry of low expectations.

What you will see in the next few years will be the elimination of AP/honors/IB courses. There will be a wave of citizens claiming that remedial double period classes should be offered instead, so that the disadvantaged (who don't attend classes regularly) will succeed. The students who would have taken high level courses will be told to grad early.
Anonymous said...
We just pulled our gifted daughter from a Montgomery County public school for this very reason. Being backed into spending significant amounts on a private school is an extremely unfortunate use of our tax dollars.
Anonymous said...
Proficient means that students have demonstrated mastery of the material so if they have shown that they fully understand the concept, they would be proficient.

The "I" grade is very hard, as there is a wide range at this "score." An "N" would be students who do not understand the concept at all.

This system is VERY frustrating for the teachers especially. We do not get guidance from the County on how to provide ES opportunities for all assessments. How do I provide an ES opportunity for students who are mastering basic addition or subtraction facts???

Some schools are giving ES to students who get 100% while others are only grading something as ES if the students have been able to apply what they have learned to make connections that we have not yet taught in the classroom. Believe me, if you are frustrated as parents, imagine how the teachers feel!

Favorite Comments of '14, cont: Forty-two and Anonymous

On RULER or Roughhousing: what's better for bullying prevention?

forty-two said...
Reminds me of something I read in Switch: How to Change When Change is Hard: that people often commit what the authors call the "Fundamental Attribution Error", and assume that a given problem is a problem with the *people*, instead of looking to see if there's a problem in the *environment*.

I actually value the skills taught through RULER - I think they make for a better life - and I plan to teach them to my dc (and I get some good ideas for how to do it from things like RULER and the like). But I'm not sure they'd do much without an accompanying change in the school environment. And it doesn't surprise me much that changing the school environment itself solves a lot of the school bullying problems - an environment problem instead of a people problem.
Anonymous said...
I wonder if these Yale professors have any idea how brutally the students mock these social/emotional learning lessons -- even when they are delivered by trained social workers. Individual work with individual students on these issues can be helpful; in-class sessions, not so much.

Sunday, December 21, 2014

Favorite Comments of '14, cont: Auntie Ann

On And the silver bullet du jour is...:

Auntie Ann said...
Jay P Greene refers to this as cargo cult solutions.

Finland does well: Finland has lots of recess; therefore, if we have lots of recess, we will do well!

Finns start school when they are 7: Finns do well; therefore, we should start school at 7!

One study showed high schoolers did well with a hands-on project-based science program; therefore, all education should be hands-on and project-based!

Education is a holistic enterprise. Pointing to one fraction of the whole and claiming salvation is never going to work.

Favorite Comments of '14, cont: Lsquared, bj, Auntie Ann, gasstationwithoutpumps, Anonymouse, lgm, and Rich Beveridge

On When final exams should trump “formative” assessments :

Lsquared said...
I'm a big believer in summative assessments (aka tests), but I'd be uncomfortable with giving a grade based only on the final exam. If a student does fabulously well on a final exam, when failing the previous exams and assignments, I'd be likely to suspect cheating rather than studying. I'd like to think that a student could go from not understanding during the bulk of the course to really understanding for the final, but I've never seen it happen. The theory that it's possible to learn all of first semester calculus in the last two weeks (after trying and failing in the previous 10 weeks) seems to be disproven by the evidence of all of the students I've ever taught.

On the other hand, there are a few students who will ace all of the tests while not doing any of the assignments. Those students I'm quite happy to give B's to (B not A because the longest trickiest problems appear only on homework assignments, and not on exams, and I want to encourage distributed practice).
Anonymous said...
I think my take depends on how comprehensive the cumulative exam is. In my higher level math classes, at a tech university, the math exam would not have been cumulative of all the homework, which was more extensive (covered more problems and longer problems and deeper problems) than could be covered in even a long exam. I also believe that this is the case in my child's 7th grade math class -- that *some* of the homework (and by this I mean work done at home) is deeper, more creative, more integrative than the work covered in an exam.

But, I do agree that the practice work (some of the homework, in which the kids are practicing the same skills that are tested in the exam) could reasonably be superseded by the exam. For some students, that would be a bad incentive -- because they might make the assumption that they don't need the practice when they do. But, for others, it would save them from useless tedium.

Anonymous said...
yes, I always ignore the issue of cheating, which is not a reality that arises in my own life or with my children, but it is one that teachers have to consider (for both homework and test work). I do worry about homework being overly loaded in the grade when there is a very realistic fear that it has not been done independently.

Kids can be tricky about getting others to solve problems that they find difficult. Sometimes neither the helper nor the student even knows that's happened, until they try to do the problem alone.

gasstationwithoutpumps said...
As with the others here, putting too much weight on a single exam means having the grade depend on only a fraction of the material—and that the easiest stuff, since there isn't time for the hard stuff.

In my (college senior and grad student) courses, I generally don't use exams, but use multiple week-long assignments that measure what I really want students to be able to do. Anything that can be answered in an hour is too trivial for me to be interested in whether students can do it.
Auntie Ann said...
One of the smartest things a teacher of mine did was to say that every Thursday is quiz day. He said that there might not be a quiz, but that you should always be prepared for one. (Obviously, the students who had him later in the day were at an advantage, because they would know from their peers who had an earlier class whether there would be a quiz or not.) This was a physics class, so systematically climbing to the summit was important. The possibility of a quiz each week meant you had to make some effort to keep on top of the material. I think he understood what a recent study showed, which was that practice tests are an excellent way to learn material. (I think they were, cumulatively, worth about 10% of our grade.)

As for homework grading, I think it's more important for a student to receive feedback and make corrections than to get graded on the first submission. Homework should be where you learn what it is you are doing wrong, so you can make an effort to do it correctly. An iterative system of submission and corrections, where a student might be graded on the last version seems smart to me.

This is perhaps even more important in writing classes, where grammar, spelling, depth of argument, use of phrasing, etc. can all be subject to the red pen and iterative corrections. In writing-oriented classes, there is a big difference between getting an assignment done and doing it well; between going through the motions and writing a concise, cohesive, well-written essay. It is also much easier, when there is often no correct answer, to b.s. your way through and never really learn to write well and come up with a persuasive argument. Every student needs at least one teacher who will stop a student in their tracks, rip their work to shreds, and teach them how it really is done. That take an iterative process of at least a first draft and then a final one.


The biggest problem I've seen with grading in our kids classes is the dreaded rubric, with their cookbook-style assignments. They rely more on following the step-by-step instructions than actually attempting to get kids to understand the material. The ones our kids have gotten also put a maximum limit on effort. If a student reads: paragraph 2 should have 5-6 sentences, you can bet they won't dare do 7 or--heaven forbid--8! even if the material and their observations of it indicate a more in-depth response.
Anonymous said...
I used to tell my students that there were two ways to pass my class and only one to fail it.

A: If they learned all the material, they would pass the class.
B: If they came to class every day, participated, and did all the work, they would pass the class.

If they did neither, they would fail the class.
If they did both, they would get an A.

Depressing how many students still did neither, year in and year out. Remarkable how students who chose Path B never failed the final.
lgm said...
One of the nice thing about the "A on the final = A in the course" is that it allows students who have poor teachers time to get a tutor and make up for the bad teaching. This is valuable in today's middle and high schools that don't bother issuing math texts - which is what the students assigned to dud teachers in the past used to learn the material.
Anonymous said...
Teaching at a community college, I have a lot of students who just aren't good test takers. So, as a result, I keep my exams pretty straightforward and they only count for 40% of the final grade.

I've been giving project work for 10 years now and it has worked pretty well. The projects count for 40% of the final grade and daily quizzes (about 25 quizzes in a ten week quarter) are the other 20%.

My first year, I realized that the math lab tutors were undermining my projects by simply giving out the answers, so I began to ask that students justify and explain each step in their solutions. Then, of course, I had the issue of students copying from each other. I gave them zero on the project, but it didn't make any difference, they kept doing it.

Then I realized - if they don't turn it in, they get a zero, and if they get caught cheating, they get a zero - there was no difference to them. So, I began to give students who cheated on the projects failing grades for the course. My VP fought me hard on this one, but I kept doing it and it worked.

After having one case of plagiarism every term during my first 2 years, I went to having one per year, and then none at all for the last five years.

I gave a presentation last spring on some of these projects that dealt with complex numbers - the presentation is at:

Anyone who's interested can see some of the other projects at:

Many of my students have said that they really learned a lot from doing the projects, which is about the best complement I could hope for. Of course, a small number of students simply don't even try and complain that they shouldn't be expected to write at all in math class, but this is such a small number of students and the benefit I see to the students who do follow through is so great, I've stuck with it.

My inspiration for doing this was the experience I had while working on my master's at UMaine. I saw a few of the projects that were given in their College Algebra course and built on that to make my own projects.

I think that's why graduate education can make people better teachers. It's not so much about the content or curriculum, but the experience and mathematical/educational community that you're a part of, that helps to inform your own understanding of math and math education.

Rich Beveridge

Favorite Comments of 2014, part I: Cranberry

On Mistaking “communication” for language… and shortchanging those with language impairments:

cranberry said...
It gets worse. From the Common Core "Key Points in English Language Arts:"

Just as media and technology are integrated in school and life in the twenty-first century, skills related to media use (both critical analysis and production of media) are integrated throughout the standards.

Yet more time (class time, homework time), deducted from the valuable practice of reading text and writing, well, anything.

So, maybe you can't write an essay about nuclear power, but you can participate in a group of students producing a short video on nuclear power. You can search for images of nuclear plants. Or you can find the music. It's all skills, isn't it?

Saturday, December 20, 2014

Conversations on the Rifle Range, 19: Grant’s Tomb Again, Alice in Wonderland, and the Eternal Question

Barry Garelick, who wrote various letters under the name Huck Finn, published here, is at work writing what will become "Conversations on the Rifle Range". This will be a documentation of his experiences teaching math as a long-term substitute. OILF proudly presents episode number 19:

In all my classes, I required my students to answer warm-up questions at the beginning of class. I used two types of questions:. One was a review-type question to apply what they recently learned. The other required them to some apply their prior knowledge –or what was familiar—in a new or unfamiliar situation. Some may view this as an inquiry-based approach, or an application of the “struggle is good” philosophy that adherents of Common Core seem to say is necessary to develop perseverance in problem solving, as well as the all-important and frequently undefined “grit”. I view a short amount of struggle as appropriate provided that explanation is provided shortly after. That way, even if students do not succeed in solving a problem, most are receptive to explanations that they might otherwise tune out.

In my Algebra 1 class, one of my problems was: “Simplify (√5)2” , which had stumped my 2-year Algebra 1 class at the high school earlier that school year. As was usual, students asked me how to solve it. I advised them to solve (√4)2 to see if that helped. After some thought they realized the answer to the original problem is 5.

"Yes", I said "It's like the question 'Who's buried in Grant's Tomb?' " (I thought I’d try that one out again.) At least this time someone got the joke. Luanne, my star student in my 5th period class shouted "OH! It's Grant!" The class started buzzing about the joke although one boy said he thought it was Fred. In the interest of time, I didn’t pursue his reasoning.

I wanted them to be familiar with the “Grant’s Tomb” example of radicals because the lesson that day was on fractional exponents. We had been covering the rules of exponents, and negative and zero exponents. I wrote 51/2 on the board and asked if anyone knew what that was. They didn’t, though that didn’t stop them from trying to guess. “Stop shouting!” I said. “If you have something to say, raise your hand!” They did, and I got an array of guesses: “Two and a half”, “Ten”, “Grant!”

In proceeding with the lesson, I referred to a poster I had on the wall from Alice in Wonderland in which Alice is talking with the Cheshire Cat. The dialogue is as follows:
“Would you tell me, please, which way I ought to go from here?”  
“That depends a good deal on where you want to get to,” said the Cat.  
“I don’t much care where—” said Alice. “ 
Then it doesn’t matter which way you go,” said the Cat.  
“—so long as I get somewhere,” Alice added as an explanation.  
“Oh, you’re sure to do that,” said the Cat, “if you only walk long enough.”
“In math, sometimes we’re like Alice in the poster on the wall,” I said. “We don’t know where we’re going or where it will lead. So let’s do that with 51/2 and see where it leads. If we have (53)2, then what do we do with the exponents?”

The usual shouting occurred, with a variety of answers and I heard “multiply”. “Right, you multiply them,” I said. “So even though we don’t know what 51/2 is yet, let’s see what happens if we raise it to the second power, like this.” I wrote 〖〖(5〗1/2)]2 on the board. “Now if we follow the rule for raising a power to a power, we get 2 times 1/2 which is 1, so we have 51, otherwise known as 5. Now, switching from Alice in Wonderland to Grant’s Tomb, does this suggest something to you?” More shouting. “Raise your hands, don’t shout!” I shouted. Luanne came through. “You square the square root of five,” she said.

I went on about unit fractional exponents, and one boy picked up on something right away. "So if we have 51/4, if you raise it to the fourth power, will it be 5?"

"Yes!" I said., I felt victorious and invulnerable. In the next few days, we covered fractional exponents in the form am/n). A few more topics came after that, and then there was the chapter test.

Despite their understanding of exponents, both my Algebra 1 class’s performance on the chapter test was not as good as I thought it would be. When I passed back the test, students asked what the class average was, as they always do. It was 79. “Oh, that isn’t good,” said Luanne (who got a score in the high 90’s). “Yeah, we usually get like an 89 class average,” another student said.

The assistant principal was sitting in the back on one of his occasional visits to my class. “It’s bad, isn’t it?” Luanne asked the assistant principal.

“That’s not a bad average—anything above 70 is a fair showing,” he said. But the students they were disappointed, as was I. A few days later, I received an email from the mother of a boy named Brian:

"Hi! Just wanted to let you know I am concerned about my son. He was receiving an A from Mrs. Halloran but now has a C and received a D on the last test. He is continuing with the same amount of effort but is telling me he thinks he understands the material but this is obviously not the case. I am concerned that there is a disconnect at the teaching/comprehension level. Can you please give me some feedback? Thanks!"

As disarming as the “Hi” was at the beginning, I knew she thought it was my fault—the giveaway was that she had copied the principal.

I wrote back that the material this semester is more complex than in the first semester, so that may be contributing to the problem. I also offered to help him after school if he wanted to come. And I copied the principal.

Brian tended to be quite noisy and disrespectful. He was one of a number of students who tried to get a jump on the homework by doing it while I was still giving the lesson. I mentioned none of this to his mother. I never heard back from her. I asked Brian if he wanted help after school. He said he had sports and couldn’t do it.

I didn’t quite know what to do next regarding my teaching approach or whether I needed to do anything. After asking myself the eternal question—“What the hell do I do now?”—I knew there had to be some things to try, taking the Cheshire Cat’s advice that even if I didn’t know where I was going, I was bound to get somewhere. What those things were, I hadn't the slightest idea.

Thursday, December 18, 2014

Math problems of the week: Common Core-inspired algebra problems

From a "High School Algebra Core Curriculum Math Test: Math Common Core Sampler Test" at Math Worksheets Land.

Extra Credit: Is it possible to have mastered algebra without knowing:

a. the meaning of the phrase "solve using elimination" in 12 (as opposed to ...? don't all algebraic strategies for solving systems of equations involve eliminating one of the variables?)
b. what is meant by "the variable that is undefined" in 13 (as opposed to "the variable that is defined"?)
c. what a "discriminant"is
d. what matrices are?

Addendum [with corrections]: The Common Core on Matrices

Included in the Common Core's supplementary material for the high school standards is a topic is a topic that is not covered in many algebra curricula, namely, matrices:

CCSS.Math.Content.HSN.VM.C.6 (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

CCSS.Math.Content.HSN.VM.C.7 (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

CCSS.Math.Content.HSN.VM.C.8 (+) Add, subtract, and multiply matrices of appropriate dimensions.

CCSS.Math.Content.HSN.VM.C.9 (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

CCSS.Math.Content.HSN.VM.C.10 (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

CCSS.Math.Content.HSN.VM.C.11 (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

CCSS.Math.Content.HSN.VM.C.12 (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

While this is only supplementary material, it appears to be inspiring self-proclaimed "Common Core" tests that include problems involving matrices (see above). The latter would appear to be at odds with:

1. The Common Core's claim not to specify particular curricula (since matrices are absent from many algebra curricula).

2. The Common Core's advocacy of a narrower, deeper, focus (especially since the matrices problems one finds in Common-Core inspired material are generally trivial, cookbook style problems of the sort seen in problem 15 above).

Given this, Common Core authors and advocates will want to clarify the Common Core's position on whether or not, and in what ways, matrices should be included in Common Core-based tests.