Math Rant
Fair warning. This is going to be a rant. Those of you who come to this blog for news and information should just do yourselves a favor and not read it.
I've been thinking about this a lot lately, and I've concluded that I need to write rants like this from time to time. I just need to keep them separate from the news - like the newspaper separates the news from the editorials - so the folks who want to read the news aren't offended by having to read an opinion from outside their bubble.
This is going to be a math rant, and they can be among the worst. So, if you want to skip the rants, stop reading now.
When Terry Bergeson was the Superintendent of Public Instruction, she said that the students should not be held accountable for failing the math WASL to graduate because it was not the students, but the adults in the system who had failed. On THAT day they should have all been fired, herself included. They are never held to any kind of accountability yet they have the greatest responsibility. Why does the accountability net catch the small fish and let the big ones go?
The greatest impediment to the kind of reform that our schools really need is not the teachers or their unions. The greatest impediment to the reform we need are the administrators at the school, district, and state level who are responsible for the design and maintenance of the system. Our problems are systemic; it is the system that does not work, not the people in it. Have they never even heard of Deming? Where are they learning management? They are the ones who responsible for the system, they know it doesn't work, yet they refuse to fix it so it will work. That's not only incompetent, it is borderline evil.
I have a report from a teacher about a student in a pre-calculus class who was stumped by simple linear equation. That ain't right, but I don't blame the teachers. I'm sure that the student's high school math teachers are capable people. My daughter has taken Geometry and Advanced Algebra in one of our high schools. I have seen her homework and I know for a guaranteed fact that she would have no trouble with that linear equation. I suspect she would even have recognized it as being in the y=mx+b slope/intercept form. HOWEVER, she learned that from me when she learned algebra at home in the eighth grade.
My daughter has had the great advantage of coming home to a parent with the unusual combination of math skills, math understanding, and the time, interest, and ability to explain things. For any line on a plane, you only need two points to define the line or one point and a direction. One of those points is the y-intercept (when x=0), the other point (or the direction) comes from the rise over the run (the slope). Or, as in the examples from the teacher, one is given as a set of (x,y) coordinates and the other comes from the slope. It should have been easy.
The problem - and I know that I'm preaching to the choir here - is that students working in a spiraling curriculum such as EDM or CMPII, are never allowed to achieve mastery, only familiarity. Familiarity fades so that when they are presented with the material again they do not recognize it. You cannot do higher math if you have not memorized and cannot instantly recognize the familiar patterns - from the simple (the very mention of the number 28 triggers thoughts of 7 and 4, area of a rectangle is l x w) to the slightly less simple (y=mx+b, ax^2+bx=c=0, and volume of a sphere is 4/3 pi r^3). We don't expect them to do anything that is truly complex. You can't drive the path if you don't know the landmarks. Otherwise all the x's look the same. It would be like driving in a city you've only visited once before three years ago for a week. You think you're supposed to turn right at the fast food restaurant but was it a McDonalds or a Burger King and am I even driving the right direction on this street.
The modular workbooks and the inquiry-based pedagogy taught my children a strange lesson about math. They would get a new workbook and for the first two weeks the lessons would be absurdly simple. They were coloring boxes and doing inane busy work without learning anything new. It was frustrating and they hated it. Then, in the third week, they would be expected to make a significant mathematical discovery and the class would suddenly shift from a stroll to leaping an impossible gap. Not surprisingly, they couldn't make the leap. That was also frustrating and hated. These leaps were first made by the finest mathematical minds in history; why do we expect all children to be able to make the same leap? Why should they have to? Bridges have been built since the leaps were first made. My kids couldn't figure it out. My explanations (using the conventional algorithms) were too different from the one they were getting in school. They got in trouble at school if they did it my way (even as they were told that any method that works is a good method "Do it any way you want - NOT THAT WAY!") so they stopped asking me for help. Instead, they figured out that if they could just fake it for a couple weeks the topic would quickly change and they could safely forget all about that part they didn't understand. It would be back to two weeks of the ridiculously simple. That was math for them: two weeks of the boring, inane, childish, and ridiculously simple alternating with two weeks of insanely and impossibly difficult, but none of it mattered because once it was gone you never saw it again. Both phases of the class were frustrating and hateful, so they learned that math is frustrating and they hate it.
One more kvetch on a slightly higher level. People are motivated to do cognitive work by three things: autonomy, mastery, and purpose. Don't make me prove that here, read Drive by Daniel Pink or watch the RS Animation about it. Student achievement is driven primarily by student motivation. Yet there is little focus on motivating students. They are given almost no autonomy (at traditional schools). The higher purpose of education is rarely mentioned. You would think that school would, at least, allow them to pursue mastery. Surely this is what school is all about. Except in math education. Students are rarely allowed to pursue a concept or a process to the point of mastery. In a spiraling curriculum they are not allowed to stay on topic that long. They are not allowed to pursue the idea all the way to the end. And they couldn't do it even if they wanted to because the workbook for that section is taken away from them when the section is complete and they can never refer back to it again. The spiraling curriculum and the modular instructional materials de-contextualizes the subject and makes it un-intelligible. It is oddly perverse that Math, a discipline with perfect unity and interconnectedness, is intentionally de-contextualized. Consequently students are never given a very good reason to learn math and, unless they have someone at home supporting them and motivating them, they are not going to get the necessary motivation at school as a result of the curriculum design - without regard to the individual teacher.
If I'm wrong about any of this, please correct me.
I've been thinking about this a lot lately, and I've concluded that I need to write rants like this from time to time. I just need to keep them separate from the news - like the newspaper separates the news from the editorials - so the folks who want to read the news aren't offended by having to read an opinion from outside their bubble.
This is going to be a math rant, and they can be among the worst. So, if you want to skip the rants, stop reading now.
When Terry Bergeson was the Superintendent of Public Instruction, she said that the students should not be held accountable for failing the math WASL to graduate because it was not the students, but the adults in the system who had failed. On THAT day they should have all been fired, herself included. They are never held to any kind of accountability yet they have the greatest responsibility. Why does the accountability net catch the small fish and let the big ones go?
The greatest impediment to the kind of reform that our schools really need is not the teachers or their unions. The greatest impediment to the reform we need are the administrators at the school, district, and state level who are responsible for the design and maintenance of the system. Our problems are systemic; it is the system that does not work, not the people in it. Have they never even heard of Deming? Where are they learning management? They are the ones who responsible for the system, they know it doesn't work, yet they refuse to fix it so it will work. That's not only incompetent, it is borderline evil.
I have a report from a teacher about a student in a pre-calculus class who was stumped by simple linear equation. That ain't right, but I don't blame the teachers. I'm sure that the student's high school math teachers are capable people. My daughter has taken Geometry and Advanced Algebra in one of our high schools. I have seen her homework and I know for a guaranteed fact that she would have no trouble with that linear equation. I suspect she would even have recognized it as being in the y=mx+b slope/intercept form. HOWEVER, she learned that from me when she learned algebra at home in the eighth grade.
My daughter has had the great advantage of coming home to a parent with the unusual combination of math skills, math understanding, and the time, interest, and ability to explain things. For any line on a plane, you only need two points to define the line or one point and a direction. One of those points is the y-intercept (when x=0), the other point (or the direction) comes from the rise over the run (the slope). Or, as in the examples from the teacher, one is given as a set of (x,y) coordinates and the other comes from the slope. It should have been easy.
The problem - and I know that I'm preaching to the choir here - is that students working in a spiraling curriculum such as EDM or CMPII, are never allowed to achieve mastery, only familiarity. Familiarity fades so that when they are presented with the material again they do not recognize it. You cannot do higher math if you have not memorized and cannot instantly recognize the familiar patterns - from the simple (the very mention of the number 28 triggers thoughts of 7 and 4, area of a rectangle is l x w) to the slightly less simple (y=mx+b, ax^2+bx=c=0, and volume of a sphere is 4/3 pi r^3). We don't expect them to do anything that is truly complex. You can't drive the path if you don't know the landmarks. Otherwise all the x's look the same. It would be like driving in a city you've only visited once before three years ago for a week. You think you're supposed to turn right at the fast food restaurant but was it a McDonalds or a Burger King and am I even driving the right direction on this street.
The modular workbooks and the inquiry-based pedagogy taught my children a strange lesson about math. They would get a new workbook and for the first two weeks the lessons would be absurdly simple. They were coloring boxes and doing inane busy work without learning anything new. It was frustrating and they hated it. Then, in the third week, they would be expected to make a significant mathematical discovery and the class would suddenly shift from a stroll to leaping an impossible gap. Not surprisingly, they couldn't make the leap. That was also frustrating and hated. These leaps were first made by the finest mathematical minds in history; why do we expect all children to be able to make the same leap? Why should they have to? Bridges have been built since the leaps were first made. My kids couldn't figure it out. My explanations (using the conventional algorithms) were too different from the one they were getting in school. They got in trouble at school if they did it my way (even as they were told that any method that works is a good method "Do it any way you want - NOT THAT WAY!") so they stopped asking me for help. Instead, they figured out that if they could just fake it for a couple weeks the topic would quickly change and they could safely forget all about that part they didn't understand. It would be back to two weeks of the ridiculously simple. That was math for them: two weeks of the boring, inane, childish, and ridiculously simple alternating with two weeks of insanely and impossibly difficult, but none of it mattered because once it was gone you never saw it again. Both phases of the class were frustrating and hateful, so they learned that math is frustrating and they hate it.
One more kvetch on a slightly higher level. People are motivated to do cognitive work by three things: autonomy, mastery, and purpose. Don't make me prove that here, read Drive by Daniel Pink or watch the RS Animation about it. Student achievement is driven primarily by student motivation. Yet there is little focus on motivating students. They are given almost no autonomy (at traditional schools). The higher purpose of education is rarely mentioned. You would think that school would, at least, allow them to pursue mastery. Surely this is what school is all about. Except in math education. Students are rarely allowed to pursue a concept or a process to the point of mastery. In a spiraling curriculum they are not allowed to stay on topic that long. They are not allowed to pursue the idea all the way to the end. And they couldn't do it even if they wanted to because the workbook for that section is taken away from them when the section is complete and they can never refer back to it again. The spiraling curriculum and the modular instructional materials de-contextualizes the subject and makes it un-intelligible. It is oddly perverse that Math, a discipline with perfect unity and interconnectedness, is intentionally de-contextualized. Consequently students are never given a very good reason to learn math and, unless they have someone at home supporting them and motivating them, they are not going to get the necessary motivation at school as a result of the curriculum design - without regard to the individual teacher.
If I'm wrong about any of this, please correct me.
Comments
I would also add a similar rant for science and reading/writing instruction K-8. Please give our students more substance and less fluff.
-tired parent
Here are the Community Meeting dates again:
Central: September 17, 6-7:30pm at Mercer Middle School, 1600 S Columbian Way, Seattle, 98108
Southeast: September 18, 6-7:30pm at Rainier Beach High School, 8815 Seward Park S., Seattle, 98118
Northeast: October 1, 6-7:30pm at Bryant Elementary School, 3311 NE 60 St., Seattle, 98115
West Seattle: October 2, 6-7:30pm at Concord International Elementary School, 723 S Concord St., Seattle, 98108
Northwest: October 8, 6-7:30pm at Hamilton International Middle School, 1610 N 41 St., Seattle, 98103
HA Ha ha Charlie! You couldn't possibly be writing about the Seattle Times, right?!
Huh
More than a third of them could not successfully divide 5/6 by 4/5.
More than a third could not successfully rearrange the three-term density equation D = m/v to solve for v (in other words, v = m/D)
Other deficits are apparent, although I haven't tabulated them.
I have my work cut out.
So is this: First Grade Algebra
Math has a language. We need to institutional that language much earlier.
n...
My younger daughters 5th grade teacher told the class at the beginning of the year they wouldn't be doing much math as she was more interested in teaching writing and other means of communication.
I suggest that all teachers should be tested on their own math skills and if they can't do the minimum, then they need to take a refresher course.
Even if they teach French.
Never know when math knowledge will come in handy.
n...
I hope you report those results to the board. The math curriculum needs to be a high priority.
Fortunately, I"m aware of math deficiencies and have my kids tutored. I realize this isn't the case for everyone.
Good intentions (of math reform) are not enough. Results matter.
math ranter
I am not and have never been a "math person." My first real test of math knowledge as an adult came when my son went to 6th grade. I couldn't understand anything, and his "textbooks" were no help -- no examples, no explanations. Did I "discover" how to do the work? Yes, in a sense -- I went to the internet and found some sites that explain the old fashioned way, reviewed how to do it, and taught my son. The next year he went to private school and used older, traditional math textbooks (Holt, I think). Guess what? He didn't need my help all year because if he had home work questions he could figure it out himself using the textbooks.
Unfortunately, that was just a peek at how the year would go for that class as the teacher was out of the classroom caring for her elderly mother, more than she was present that year.
The way I understand it, the reason why the class had rotating substitutes instead of a permanent sub, was because she had not filed for leave of absence and was using her own sick leave as well as donated leave from peers.
The 1st year principal was over her head, and the parents did not learn of the situation until November.
This situation did not stop with my daughters class, but continued for several years, until the mothers death.
Most teachers that I know, put the well being of students first, and if they can't they step back and let someone else do so.
Unfortunately, I saw several cases in the same building where I felt leave/vacation was being grossly abused. If it is important for students to be present in the classroom,shouldn't that hold true for their teachers/principals as well?
An alternative school should not mean that basics are neglected.
The goal for this teachers classroom last year was to raise math scores by 1% according to the schools CSIP.
Sounds like some of the IEP targets I've seen.
-SWWS
For what its worth, my kids have had teachers take extended time off for various reasons. I have no idea if the leave was paid or not, but the sub situation has always been handled much better than the situation described here. Sounds like that particular school was poorly managed.
-SWWS
However, the district should have an obligation to provide students with consistency and appropriate education, or to provide the families with alternatives in the event they are unable to do so.
If education is a profession, that puts the burden on the teacher to act professionally.
- math now, or no $
-SWWS
the REAL failing of the education system? the managers and edu-crats all have big fancy degrees and better than most of us paychecks, and all they can do is blame teachers!
all that data - how much money would be available for tutors if we fired all the math-u-crats who aren't in classrooms helping kids?
(oops! what would those high level "coaches" do who rove around to classrooms, not helping kids, snitching on teachers??)
all that data, all those degrees, all those salaries, all this failure - why don't this non-classroom edu-crats do the right thing, and quit? if they're going to parasites, why don't they go work selling lousy software or managing mercenaries or peddling CDOs to retirement funds -
ParasitesAreParasites
My family has been trying to change it for years, ever since one of my son’s MATH teachers said there were much better textbooks out there. The more research I did, the worse it looked. (Read the Hook, Bishop studies on math curricula conducted in Calif. and the book Betrayed, by Laurie H. Rogers.)
All of the educators with big credentials, from Terry Bergeson to Susan Enfield, promoted this dreadful discovery math. So did members of the past Seattle School Board who defended it against the WA State Board of Education, who argued it was unsound.
Many parents think tutoring alone will solve the problem but it is an insufficient fix for many students. I heard Banda had better math in his district, so he may be the last best hope, if enough parents demand it.
S parent
I agree that we need to hit the community meetings hard. Even at GHS, I know that there are "higher math" teachers )or at least 1) who -- in getting kids ready for PreCalc and Calculus, spend a HUGE amount of time basically "reviewing" all the math many of the kids never learned before they get to that teachers' class. They (correctly) don't blame the kids. But it is a shame they have to do the big fix every year so those kids can take and pass Honors and AP Calc.
Can someone remind me -- didn't we "put off" buying math books last year, for either elementary or middle school, when they came up on the "regular" replacement cycle? If so -- that ought to be ONE piece of the puzzle right there. Buy the books this year, and buy a curriculum that works better. Banda knows how to do this. He just needs to get busy and do it! How many schools now are using "other" programs -- Schmitz Park, Mercer, Muir, -- and I am pretty sure some of the high schools break away, at least after Algebra II, to better materials.
If there is a limit, I don't have a problem.
Unlimited, I do.
When I was a kid, and we had the old style kill and drill, back to basics math, and guess what? Lots and lots of people didn't learn math either. In fact, they learned a whole lot less math than they learn now.
Mercer Middle and Schmitz Park both are schools well known for playing special education kick the can. It's pretty hard to draw conclusions about the effectiveness of your methodologies, when you select your students.
As far as the overall system goes, we've got WAY more kids learning advanced math than we ever did when we were doing "back to basics" math. If we're unhappy with our current results, it's because our expectations are now higher than ever, and cover more people than ever before. If lots of people are now in "remedial" math in college, it's because way more people are actually expecting to go to college. And that's not necessarily a problem.
-parent
First, we are all throwing around a lot of terms "discovery," "spiralling," and "mastery" without using them in a very technical sense. If what you mean by "spiralling" is a curriculum that teaches something to a high level of proficiency, with examples, etc., and then "revisits it" frequently, so that children get frequent refreshing and practice -- then you are describing Saxon Math, which is what North Beach used, and which has a lot of support in the research (it also drives many kids -- especially APP kids -- wild, as it goes TOO slowly). If what you mean is the Discovery version, where most concepts and algorhythms are not taught at all, but are "discovered" in group work, with no direct instruction, no texts to use as resources, nothing to fall back on for kids who fail to grasp the concepts (as there is no master text, and the workbooks are taken away after each unit), and insufficient practice for many kids to develop mastery -- well, THAT is what we have in Seattle! Reread Charlie's description of it. There is no research I know of that supports this method of teaching math -- and MUCH research that has reviewed the ED, CM, and Discovering materials and found them utterly deficient (grades of D and F).
You state "they learned a whole lot less math than they learn now." Reports from college professors would indicate otherwise. While it is true that those who stopped TAKING math may have learned less math, those who were in Algebra II, Trig, Pre-Calc and Calculus classes in my high school in the 70s would NEVER have failed the little math test that Cliff Mass gives his atmospheric sciences kids.
You said: Mercer Middle and Schmitz Park both are schools well known for playing special education kick the can. It's pretty hard to draw conclusions about the effectiveness of your methodologies, when you select your students.
I can't refute your proposition because I don't know the extent to which either school throws SPED kids out, but in most instances, SPED results are separately categorized, and so the comparative numbers are not influenced by SPED numbers (though the overall school numbers might be). In any case, the results are too far out of the norm and, in the case of Mercer, too closely correlated to the change in curriculum to be blamed on SPED discrimination. It just isn't credible to blame the anomaly in test scores on SPED exclusion issues (particularly since many sped kids, like mine, do fine in math if given a decent set of materials and some extra time). It may not be "just" the math book, but it is difficult to believe that the change to clearer, more comprehensible (and more comprehensive), more accessible math materials is not behind much of it.
The point with APP kids is that you do the lessons twice as fast. Some teachers don't understand this (rather simple concept) about AL students.
My APP kid LOVES Saxon math - and as Jan said, it is a spiraling curriculum. Jan described the problem perfectly - as did Charlie. Don't get hung up on the word "spiraling".
Coming in a little late here, but speaking of "getting off your high horse", you might want to look in the mirror. It sounds like you know this teacher personally and have some strong personal bias.
Federal law might not require her to quit her job, but common courtesy would require her to consider the lives of 25-30 kids (and their families) before her own needs. There is not much more damaging to a child's education during the course of the year than a revolving door of teacher-of-the-week. I've seen it up close and it's really hard on everyone. This teacher may have felt like she was sacrificing her own needs for her mother, but in reality she was sacrificing her own needs AND that of 25-30 other families.
What she should have done was to work hard with her administration to arrange a leave of absence so the building could bring in a long-term sub. If the needs were so long-term that couldn't be done, then she really needed to consider another (hopefully temporary) career with flexible hours to take care of her mom. Anyone who sacrifices an entire classroom of innocent children for her own family needs (and for multiple years?!) is being selfish in my book, even if they are doing a very good deed for one person they love very much.
What Jan said.
-dw
Oh, and please pay no attention to research that carves out only specific slices of a problem and attempts to justify an entire strategy. Instead, pay attention to research that analyzes the entire picture and follows up with empirical results.
Spiraling without achieving mastery at any particular level is not just poor planning, but harmful to kids. MANY of us have had kids that are (were) strong at math, but have been turned off because of crappy curricula. From a practical standpoint, something that won't get measured with "brain research" is that spiraling without mastery means every teacher gets to (or is forced to) kick the can down the road. At the end of the day there is no specific teacher or grade level that is responsible for teaching a particular topic from beginning to mastery. There's so much more, but I need to stop before I get into a math rant myself.
Mercer's data speaks for itself. How can you ignore the gains they have achieved by ditching CMP? They have a 75% FRL population and have pass rates rivaling HIMS (19% FRL) and Eckstein (25% FRL).
A comparison of the average MSP pass rates - across 6th, 7th, and 8th grades - vs FRL rates, ranked in order from highest to lowest pass rate (2011-2012):
SCHOOL: Avg MATH pass rate (%FRL)
HIMS: 83.3 (19)
Mercer: 78.4 (75.2)
Eckstein: 77.4 (24.8)
Whitman: 70.9 (30.1)
McClure: 70.7 (32.7)
District: 67.2 (43.2)
Washington: 66.0 (51.7)
Madison: 65.2 (43.4)
Denny: 63.1 (67.1)
Aki: 44.1 (86.5)
math parent
Part of what happened, which Bruner was also critical of, is that spiralling went from a recognition that there are increasingly complex levels of learning building upon prior concepts and that this should be intentional. What spiralling became, which Bruner stated he never intended in his theory about the process of education, is an excuse that "well, they'll get it next time when they see it again". It was a recognition that mastery increases, not an excuse to never master anything to a certain level in the short term.
Bruner wasn't a brain researcher, albeit a fairly decent educational theorist. He cautioned that "drill need not be rote and, alas, emphasis on understanding may lead the student to a certain verbal glibness", so his role as "reformer" in the modern definition is questionable. Most of the math coaches and supers only read the latest research, often based on 2-3 classrooms of data (can we say influenced), instead of return to the full development of the theories.
*frustrated too, but...*
HP
And Saxon works fine with APP kids. I have been single subject homeschooling my son for the last 3years with Saxon. It didn't hinder his understanding. He is now enrolled at Hamilton as a 7th grader in Geometry. Word is correct, it is about proper pacing of any curriculum to fit the needs of the student.
Now is the time to push for a new math adoption. We have a sympathetic board and superintendent. We just have to be build capacity with parents and organize in order to make it a priority. I would love to get a group together, perhaps rent a library space at a school and make this happen. Jan, S Parent, dw, and others I would love to get your contact info and strategize. Our contact info is rickbmail@yahoo.com.
My husband and I were able to get Carla Santorno to consider Singapore Math as a supplement to Everyday Math. Too bad is was used as a ploy to get the approval for Everyday Math. But that is another story...
It's not worth the time/energy protesting to those who won't listen. Time/energy could be spent w/your child or working a few extra hours to afford private school tuition. It's a much better investment.
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