Commentary in Seattle Times
Bruce Ramsey wrote a very good editorial in today's paper about the way math is taught. As a high school math teacher, I see the failure of "fuzzy math" everyday. Students don't learn the basics, so they don't have the foundation to "discover" anything and even if they do "discover" something, they don't know what it means because they don't know the basics or have the fundamentals down. The Seattle School District is working on a district wide math adoption for all the high schools and the last I heard two of the three finals are IMP and Core Plus, both of which are "fuzzy math" curriculums. We will be doing a serious disservice to our students (especially the students below grade level), if IMP or Core Plus becomes the math curriculum for SPS. These programs don't stress the basics enough. In math, you need to know how to walk before you can run. You have to know how to divide fractions before you can work on the equation of a line or factor a polynomial equation.
New-age math doesn't add up
New-age math doesn't add up
Comments
My husband is a UW professor who sees the results of fuzzy math with every beginning computer science class. Beyond the fact that we leaving a generation of students unequipped to do basic math, there are more implications.
As I have noted before, it is more competitive than ever to get into colleges and universities. These institutions are finding many students need remedial math and writing skills. The college/university's goal is to get students out in 4 years. That can't happen if they are taking remdedial courses which throws off that goal. Students staying longer mean fewer spots for other students.
FYI to the previous poster who asks if all schools are doing the fuzzy math, I don't have the official answer, but I can tell you that when our children went to an alternative school they did only "fuzzy math", and now that they are in a traditional school, they still do "fuzzy math", but they combine it with a lot of traditional math and old school repetition.
Deidre
Fuzzy math proponents intentionally painted the District into this corner. Perhaps they sensed their support was waning. By securing middle school first, they necessitated the later adoption of fuzzy math for high schools and elementaries.
Note that the District's Strategic Framework calls for students to be ready for algebra in the eighth grade, but CPM doesn't teach algebra. If algebra is so important, then why did we select a curriculum that doesn't teach it?
There is likely no one-size-fits-all math program but a hybrid would be nice. When schools allow kids out of 5th grade not knowing their times tables or how to do long division,something's wrong.
Can every school choose it's own math curriculum? Melissa, you mentioned that North Beach was using Saxon. Our elementary school is not using that one.
You might want to call North Beach and ask the principal how that happened. I think f you are unhappy with the math curriculum you might go to your PTA and say that you want to have it on the agenda and talk about it at a meeting (where, hopefully, the principal is present) and pass a resolution saying that parents at your school want a change. That works as a unified parent voice.
I think that given the outcome of the math/science WASL in the Legislature and that Terry Bergeson, the State Super of Public Schools, has finally gotten the message, we may finally see a movement away from purely Connected Math and get to a hybrid.
I recall that my sons' Spectrum teacher in 5th grade at Whittier had volunteers test every kid in the class on multiplication tables 1-12. We would just work through them, one by one, and when they missed any part of one table, we stopped. They got credit for the tables they passed but had to go and study again for the next time they were tested. Her expectation was that they would know them cold and they would be tested over and over again until they could all do all of them perfectly. I don't know if the other 5th grade teachers did this as well but I was grateful she cared enough to make sure this happened and I was happy to volunteer to make sure it happened.
I'm not sure if that only applies to schools already using another curriculum or if it extends to schools that might yet want to adopt one.
This is at the elementary level.
I'm confused -- do you mean CMP? I thought the eighth-grade CMP materials were supposed to be usable as Integrated 1 texts. That's what Washington has been telling us, anyway.
Helen Schinske
I asked Carla Santorno this question at the Community Conversation meeting at Mercer in the Fall and she said that although there is no algebra class per se, that they elements of algebra are taught in various sections of the CMP curriculum. This concept here and that concept there.
I thought it was a weak answer. If algebra is important, they should teach it.
My daughter is taking Integrated I at Washington and she is using a CMP text. It's total crap. They go through this charade of discovery in the class, and then I have to teach her the math as we go through her homework together. I have no idea what happens at the homes of students who don't have a resource like me, but it can't be good.
Thanks
However, he has been told that starting next year he will be required to A] use the New and Improved CMP books recently adopted even though he has not yet been given a copy, and B] follow the district mandated calendar which tells teachers exactly what pages to cover on what day all year, just like the 6th and 7th grade math teachers are required to do this year.
I have also spent the year volunteering/observing Int II and Int III classes. Charlie, just wait til you see Int II. While I was surprisingly pleased with the content and rigor of some of the Int II book, the geometry chapters made me apoplectic.
Evidently it is part of the move toward standardizing middle school math curriculum.
The message from the math dept. has been that they have a new standard curriculum and have to align with the offerings at other middle schools. They are also trying to align with the elementary spectrum programs that are working one year ahead.
They also prefer not to put 6th graders in classes with older students.
I guess the district feels it is easier to focus on mediocrity in academics instead of expecting excellence.
This news about Eckstein is very disturbing to me - how many other progams will be cut down or deleted in order to standardize cirriculum or close the achievement gap?
Deidre
I have believe this is coming from the district and Eckstein can't say no.
According to the Kellogg 8th grade Academic plan in math, the Course Summary and Goals: "In Math 8, students are expected to take an active role in their own discovery of mathematics and its applications. The program centers on mathematical investigations, includes a number of hands-on explorations with concrete models and uses cooperative groups as a learning structure. The Connected Mathematics materials are problem solving oriented, highlighting critical thinking and reasoning over memorization and drill. The course will require students to communicate their thinking, both orally and in writing."
Yup, bottom line goal is to communicate your thinking, not to have strong math skills. That's the hallmark of fuzzy math.
I think they are trying to align all the schools so that there is continuty across the district (which is good for parents because there isn't confusion over who offers what) but the problem, as has been pointed out by many here, is why put a limit on a student who can work further ahead? We know it can be done so why change it now? Maybe some schools don't want to work ahead (or don't have enough demand) and maybe the district wants to be able to better track schools.
Deidre
As to the anonymous who posted this question:
who exactly in this case is "the district," or is it even possible to find out? You can't talk to a nameless, amorphous force whose numbers are legion. Didn't some responsible official have to sign off on this, or does the district really work by invisible, untraceable osmosis among hundreds of bureaucrats, as laying it at the feet of "the district" seems to imply?
You got it. You figured it out. For all of the talk about making the District more open, honest, transparent, engaged and accountable, the Superintendent actually has not taken even one step in that direction. Any movement you have ever seen towards these values was made by the Board, not the Superintendent.
At our Student Learning Committee yesterday, CAO Carla Santorno gave an update on math adoptions. As you may know, the district (as required by our policy) staff appointed a math adoption committee a couple of years ago and they worked for some months to come up with a recommendation for elementary and middle school math textbooks. The board went ahead and adopted the MS textbook but Carla advised holding off on the elementary because the editors were revising their books and she wanted to see the new editions before landing on the elementary recommendation.
Yesterday, she said she is recommending that we adopt a combination of constructivist/traditional, namely Connected Math and Singapore Math. The committee had recommended a much more constructivist approach, called Investigations. Rosalind Wise did bring examples of the books to all 70 elementary schools and left them there for a week so that teachers and parents could peruse them. Opinion on Investigations vs. Connected Math was split 50/50, with parents favoring Connected Math as easier for them to understand (and therefore help their student at home). Carla is mindful that some teachers and students will need/want the support of more traditional materials so is recommending Singapore Math as the supplement.
She also clarified that schools which already have excellent test scores for all children (not just certain groups) would be permitted to continue using whatever text they are now using.
Having consistency of text materials and curriculum becomes most critical for the students in the district whose families are mobile, because switching from one school to another can lead to big gaps in their learning.
I hope this clarifies.
Because textbook adoption also involves training teachers, her plan is to roll out the new materials for half the elementaries next year (2007-08) and half the following year.
A motion will be brought to our next SLC meeting to be introduced to the board soon and Carla is asking executive to schedule a special public hearing to ensure that we hear from everyone on this issue. Because of deadlines for ordering materials, the Student Learning Committee is recommending we add a special board meeting for the vote.
Everyone is welcome to attend SLC, 4:30-6:30 Tuesdays in the Stanford Center, to observe the discussion. Please feel free to email or phone the board with your input.
Thanks for the update!! I'm so relieved to see that Carla is making an effort to move back to more traditional math. If the proposed combination curriculum of Connected Math, and Singapore is adopted will it be used in elementary, middle and High schools?
Thanks again,
Deidre
Brita, thanks for the head's up on the Singapore/CMP hybrid recommendation. (Although I am a little confused, as CMP is a middle school curriculum, not an elementary one.) Sigh. Am I the only person in Seattle who thinks this is a terrible idea? I'm working on a longer response that explains why I think it is wrong and what I think ought to be done instead, but it isn't complete. Perhaps I will ask Beth if I can contribute it as a post rather than a comment here?
The "letting schools with good test scores do their own thing" bit, does it include middle schools, like Eckstein? Are they going to backtrack on requiring them to change textbooks and teach topics in a certain order? Given that they are full and over-enrolled, they don't have to worry so much about a mobile population, ain't no room for nobody to show up mid-year.
I just had coffee with a friend, a woman whose older child is an 8th grader in Integrated II (child went from 6th grade honors right to Int I in 7th grade without any hideous gaps ruining their academic life because child had good (private) elementary math education and there is so much overlap and wasted time in the CMP series). She also has a rising 6th grader. The letter from Eckstein to the incoming student said that they are no longer testing kids for math placement. Given her older child's experience she found this alarming. She called the 6th grade counselor who had not heard a thing about it. As for Eckstein not even offering Int II or III in the future? That had not been mentioned. The kicker is that her kids attended private elementary school and she has been so happy with Eckstein, she has convinced quite few parents of her younger child's private school classmates to give Eckstein a try. So much for listening to your market.
Let me doublecheck--I may have the name of the elementary constructivist math text wrong. The one being adopted is NOT 'Investigations'.
Brita
Why would teachers be romantic about Constructivist math? Why do pendulums swing? Many see the alternative as tediously mind-numbingly boring drill and kill that they hated
themselves in school. Many want their kids to have more fun, be more engaged. Many also strongly believe that when a child has discovered something for himself, they will retain it longer. Think of it as a 'kids have to touch the stove to understand hot' argument. Yes, there are elements of truth to it, but is this true for the whole body of arithmetic, algebra, geometry, probability? I don't buy it.
However, here's the thing is about constructivist mathematics. It can work, it can work well if two things are true: Adequate class time and adequate teacher training. Adequate training also presupposes strong mathematical literacy. The ironical thing about maintaining the approach as part of a hybrid approach is that you lose the time necessary to make it work. So the discovery portion of the curriculum can become superfluous and add to the confusion instead of removing it. Perhaps a limited discovery portion can aid learning, but only if the teacher is strongly knowledgeable in the process and the mathematics, carefully selecting the elements of discovery to use.
It is not enough to say we will do a hybrid of constructivist and traditional math. The teacher needs to be very clear what constructivist goals to work toward, not simply do some of the constructivist exercises some days and some traditional work on others. Or will they do some topics in the constructivist manner and some in a more traditional manner? How can you make a discovery process work with a traditional approach? (Well, I would claim that the traditional approach does involve discovery, but the success of it completely depends on how well the teacher understands the mathematics and how the discovery unfolds.) The theory of TERC and CMP is that teachers can simply follow the lesson plans step by step and thus ensure discovery, without having to understand it all themselves. I think this is flawed, that teachers who make such a Socratic method work must have a deep understanding of the material themselves. It is even more flawed when the teacher deviates, uses a hybrid and has to choose which constructivist pieces to include and which to omit without a deep understanding about how the exercises fit together.
A separate problem with CMP and similar programs (and our State EALRs) is they pile on too many topics, on the philosophy that kids should be exposed to lots and lots of fun topics in mathematics. However, what really ends up happening, many of the kids never really end up getting the salient ideas of each topic. Every spiral back to the topic has to start fresh, since it has been so long since they've seen it before, since they never really mastered any of it last time; so each time they see it anew it bores and confuses and frustrates the same kids over again. Having to go at a fast enough pace to cover so many topics also means that while the kids may have constructed their own thinking about a topic, they don't get the next step, the essence, an understanding of and the mastery of the most efficient algorithm. What people may be thinking about when they say they want a hybrid approach is to maintain the constructivist aspect, doing all that thinking of the topic, spending all that time writing about their thinking (argg!) and then having the teacher make sure they understand the most efficient algorithm and that they then have plenty of practice in this algorithm. Honestly, do the schools really devote all the time necessary to do that? Do elementary school teachers really have the expertise to do this right? In my experience, the answer to both questions is a flat-out no.
Singapore. How many reading this have actually seen a Singapore text? Have you solved the problems in it?
Here's the thing I found out about Singapore. One main reason it seems to work is that it teaches a different problem solving paradigm. By using a specialized visual spacial methodology, it teaches students at a very early age to solve what we consider complicated multi-step arithmetic and algebraic problems. When I investigated Singapore years ago, I was told that one must start at the beginning, otherwise it would not make sense. One must devote a lot of time to setting up the paradigm. It is rigorous. And there is exactly one way to do the multi-step problems --- a way that teachers and parents are not familiar with. Isn't the lack of parent familiarity with the curriculum one reason for dissatisfaction with constructivist math?
My son at the time was at the 3rd grade level in math, according to individual achievement tests. Those were lean years, so even though the Singapore books are inexpensive, I didn't want to spring for kindergarten and first grade books so just ordered the second grade ones. (They were not available locally at the time so I couldn't browse first. Are they now at Math n' Stuff?) With my background, how could I not figure out how to do second grade Singapore math? Well, I did sort of figure it out. But it wasn't easy and I never got fluent in it. I never tried to teach it to my son. Without starting with kindergarten level problems, I doubt I would have been capable of explaining the method well enough.
Singapore works well because the kids learn very specific ways to set up and solve problems. The philosophy is diametrically opposed to constructivist math where kids discover that there are many paths to solutions. Singapore works because even though the problems are challenging, even if the kids don't understand what the steps mean, as long as they learn to set it up correctly, they will get the correct answer. And every time they do a problem, every time they set up the very particular visual display of information, they are (even if only unconsciously) becoming so fluent in the fundamentals of arithmetic and algebra that even if they cannot express it in their own words yet, they are nonetheless on the path to deep understanding.
How many elementary school teachers are going to be able to do the Singapore style problem solving? How are they going to do this sort of structured approach part time, while also seamlessly blending in a completely different approach? Yes Singapore is sexy, yes some schools and some districts are getting great results. Are they doing it as an add-on or for the full math curriculum? How did they start? Did they start with first graders and work up or did every grade adopt it simultaneously? How much training did teachers get? What training will Seattle elementary teachers get? How will parents react when once again they will not be able to help their 3rd grader with their homework?
Saxon? I am not a fan of Saxon. I would have hated to have been taught with it and I would have hated to have had to teach from it. However, it is not without its supporters, and for good reason. It is incremental, comprehensive and rigorous. Its biggest plus is that a teacher who is not particularly strong mathematically can be successful with it. I'd hate to require Saxon, but I do think there's a place for it. Some kids and some teachers do wonderfully with it.
Solutions? I read somewhere, probably on the internet (don't you just love when people say that? How credible of me! Even though I cannot site the source, I strongly believe what I am about to say.) about a study that claimed that it doesn't matter which math curriculum is used, any can be successful, as long as the teacher is fluent in it, completely comfortable with it. Mandating a hybrid Singapore/Constructivist curriculum is not going to make that happen.
The reality is that most elementary school teachers are not strong in math. And kids show up with a wide variety of backgrounds. Every elementary school ought to have a full time math specialist who works with all the classes, all the teachers, coordinating volunteer tutors, coordinating and analyzing pre and post tests, helping the teachers flexibly find the right curriculum for their particular situation. A curriculum that will ensure that those particular kids with that particular teacher will learn arithmetic and mathematics.
Computation: Elementary math standards ought to be focused almost entirely on computational competency. Skip the "explain your reasoning" aspect. If the kid can compute the area of the carpet or add fractions with unlike denominators that shows they understand. Period. There's plenty of time to explain reasoning in advanced classes, don't confuse kids by pushing explanations before they are completely fluent in actually solving the problems.
Pre and post testing. Give pre-tests and actually use the results to determine what each student needs next. Kids who show competency can be nudged just a little to mastery, kids who demonstrate mastery can move on. Probably this means ability grouping. If multiple classrooms teach mathematics at the same time, the math specialist would be able to coordinate some fluid ability grouping to ensure that all kids are advancing mathematically.
Consistency? Unified schedule? Yes, I think that the district can and should be able to mandate something along these lines to ensure that all schools are performing and that student mobility doesn't hamper success. But that does not mean insist that every class teach exactly the same thing from the same text every day. In semester or quarter long chunks, the district can mandate when kids ought to have achieved computational competency in various topics. (And kids who are ahead ought to be allowed to work ahead, but that's a whole separate discussion.) It would be great if the district gives a benchmark test to all students once a semester or so, as long as the benchmark is simply computation and not based on a particular curriculum. If the third grade teacher knows, for example, that on a particular day the district will administer and grade an assessment of her kids' ability to add fractions, multiply three digit numbers and calculate perimeters of rectangles, then she along with her school's full time math specialist, can use whatever tools they want as long as they demonstrate success.
Since I was asked, I will respond. I know nothing of Singapore or Connected Math. I'm sure they have their good point and bad points. I would need to be trained in either or both of them to be able to effectively teach them. I got zero training when RB hired me on how to teach College Prep Math. I have basically spent the past two years making it up on the fly and hoping for the best. This does an incredible disservice to my students, most of whom are below grade level and are struggling to catch up.
What I can say is that my students come to me with absolutely no number "sense". They do not have the ability to make the leap from 1/2, to .50 to 50%. It completely baffles them. I take that to be an indictment of the "fuzzy math" being taught at the elementary and middle schools. When my students get to me, with my "old school" ways and mostly "old school" curriculum, they really struggle and I have to step away from the curriculum and teach how to add, subtract, multiply and divide fractions. This wastes valuable instruction time since these are skills that the students should have mastered years earlier.
I don't really know what curriculum would be best. I do like College Prep Math. What I do know is that students need to master the basics of arithmetic and basic math before anything else can be done. The fact that so many students get to RB without these basic skills is a crime of huge proportions.
I haven't had to do much supplementing of Integrated 1 at home this year, but suspect that's probably due to the teacher adding more formal explanation and problem-solving to the mix, as well as to my daughter figuring things out for herself. But I must say I'd welcome a switch to a curriculum with a single textbook that one could look things up in. It's just so dippy having to check on the internet to see whether your kid memorized the quadratic formula correctly.
I've gotten terribly annoyed with the kind of math teaching the WASL has apparently fostered, but I do have to say that I think the math section of the WASL, while not yet a very good test, is actually now *better* than the reading and science WASL questions I've seen. I suspect the amount of fluffy, WASL-ese writing required on the math has gone down over the years as well.
Helen Schinske
LA Times Essay on Algebra
Thoughtful articles on Singapore Math
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Helen Schinske