Missing Math Curricula
Last year the State of Washington re-wrote the state Math Standards and the Grade Level Expectations. You may remember that the State first released the revised standards and performance expectations for grades K through 8 (approved by the State Board of Education on April 28, 2008) and then, after some delay, the revised standards and expectations for high school on July 30.
Seattle Public Schools delayed the adoption of high school math materials for the release of the new state standards. This delay was entirely unnecessary and now, over six months later, we still don't have a material adoption decision.
But it's actually worse than that.
Seattle Public Schools has yet to adopt a revised math curriculum. That's curriculum - not materials.
Let's be very clear about this. The curriculum is the set of knowledge and skills that the teachers are supposed to teach and the students are supposed to learn. For example, in Grade 3, students are expected to be able to round whole numbers through 10,000 to the nearest ten, hundred and thousand. So by June of the third grade students are expected to be able to round a number like 3,467 to the nearest ten (3,470), the nearest hundred (3,500) and the nearest thousand (3,000). The materials are the textbooks (and other media) used to support the learning and teaching.
It is the Board's duty to adopt curricula. The Board has yet to adopt any revised math curricula following the revision of the state Standards. This may be because on the WASL this year students will still be tested on the old standards and grade level expectations, so in preparation for the test the District will continue to teach to the old Standards. That, however, would be the most egregious proof that the District is devoted to teaching to the test rather than teaching to the Standards or to what is best for the Students. It is far more likely, however, that no revised curricula have been adopted because no one on the Board knows that they should be doing this work and no one on the staff cares whether the Board does it or not. The K-12 Mathematics Program Manager, Anna Maria delaFuente, has made it clear that she believes that the curriculum is set by the State - not the Board.
So let's set aside, for the moment, the Board's negligence and indolence in failing to adopt a revised math curriculum and focus instead on the District staff's efforts to align instruction with the revised curriculum (as set by the State).
According to the Strategic Plan: "A Math Project Team will develop an implementation plan and timeline for action during summer 2008. Alignment of the elementary and middle school instructional materials to the new State Performance Expectations will be completed this summer." This work is supposedly done.
Is it? Part of the State Standards for Grade 5 is this: "5.1.C Fluently and accurately divide up to a four-digit number by one- or two-digit divisors using the standard long-division algorithm." As we all know, this skill is not among those covered by the Everyday Mathematics textbook. Perhaps it is covered by the Singapore Math supplemental material. It is valuable to note that in the Fifth Grade, division is covered in Section 4 of the EDM text and that the District's pacing guide shows that the students will be working on Section 4 for eight days of instruction from November 10 to November 26. Can anyone with a fifth grader confirm that their student was taught the standard long division algorithm during the two weeks leading up to Thanksgiving?
So what's going on? Why is it that the revision of the state math standards for high school had such an impact on our choice of materials but the revision of the state standards for grades K-8 didn't impact our choice at all? Why is it that the Board has not adopted an updated math curriculum? How, in the absence of an adopted curriculum, can we adopt materials? Is the math instruction in Seattle aligned with the new state standards or not? And if it is, then where is the long division in the fifth grade? What - exactly - is the District aligning math curricula to? How has math instruction in Seattle changed in response to the new math standards and grade level expectations adopted by the state?
I see a lot of flowery statements and lot of assurances that work has been done, but I can't see any of the actual work (the instructional guide is not available to the public) and I can't see any evidence of the work. It is very hard for me to share in the District's confidence in the absence of this evidence.
Seattle Public Schools delayed the adoption of high school math materials for the release of the new state standards. This delay was entirely unnecessary and now, over six months later, we still don't have a material adoption decision.
But it's actually worse than that.
Seattle Public Schools has yet to adopt a revised math curriculum. That's curriculum - not materials.
Let's be very clear about this. The curriculum is the set of knowledge and skills that the teachers are supposed to teach and the students are supposed to learn. For example, in Grade 3, students are expected to be able to round whole numbers through 10,000 to the nearest ten, hundred and thousand. So by June of the third grade students are expected to be able to round a number like 3,467 to the nearest ten (3,470), the nearest hundred (3,500) and the nearest thousand (3,000). The materials are the textbooks (and other media) used to support the learning and teaching.
It is the Board's duty to adopt curricula. The Board has yet to adopt any revised math curricula following the revision of the state Standards. This may be because on the WASL this year students will still be tested on the old standards and grade level expectations, so in preparation for the test the District will continue to teach to the old Standards. That, however, would be the most egregious proof that the District is devoted to teaching to the test rather than teaching to the Standards or to what is best for the Students. It is far more likely, however, that no revised curricula have been adopted because no one on the Board knows that they should be doing this work and no one on the staff cares whether the Board does it or not. The K-12 Mathematics Program Manager, Anna Maria delaFuente, has made it clear that she believes that the curriculum is set by the State - not the Board.
So let's set aside, for the moment, the Board's negligence and indolence in failing to adopt a revised math curriculum and focus instead on the District staff's efforts to align instruction with the revised curriculum (as set by the State).
According to the Strategic Plan: "A Math Project Team will develop an implementation plan and timeline for action during summer 2008. Alignment of the elementary and middle school instructional materials to the new State Performance Expectations will be completed this summer." This work is supposedly done.
Is it? Part of the State Standards for Grade 5 is this: "5.1.C Fluently and accurately divide up to a four-digit number by one- or two-digit divisors using the standard long-division algorithm." As we all know, this skill is not among those covered by the Everyday Mathematics textbook. Perhaps it is covered by the Singapore Math supplemental material. It is valuable to note that in the Fifth Grade, division is covered in Section 4 of the EDM text and that the District's pacing guide shows that the students will be working on Section 4 for eight days of instruction from November 10 to November 26. Can anyone with a fifth grader confirm that their student was taught the standard long division algorithm during the two weeks leading up to Thanksgiving?
So what's going on? Why is it that the revision of the state math standards for high school had such an impact on our choice of materials but the revision of the state standards for grades K-8 didn't impact our choice at all? Why is it that the Board has not adopted an updated math curriculum? How, in the absence of an adopted curriculum, can we adopt materials? Is the math instruction in Seattle aligned with the new state standards or not? And if it is, then where is the long division in the fifth grade? What - exactly - is the District aligning math curricula to? How has math instruction in Seattle changed in response to the new math standards and grade level expectations adopted by the state?
I see a lot of flowery statements and lot of assurances that work has been done, but I can't see any of the actual work (the instructional guide is not available to the public) and I can't see any evidence of the work. It is very hard for me to share in the District's confidence in the absence of this evidence.
Comments
The Extra Practice follows the sequence in the Primary Math.
The division algorithm for dividing a 3 or 4 digit number by a 1-digit number is taught in grade 3 (3-digit by 1-digit in US edition, a few 4-digit by 1-digit in Standards edition). The basic concepts and using the algorithm are taught in about a week, with division by 2, 3, 4, and 5, and then it is reviewed with division by 6, 7, 8, and 9 over the next 3-4 weeks, and used in word problems. In grade 4, it is briefly reviewed (more 4-digit by 1-digit) and used throughout. Division of decimal numbers by 1 digit is taught also. In grade 5 students presumably know how to divide by 1-digit,it is no longer taught. Division by 2 digits is taught, in a little over a week, just concentrating on that. After that, there are word problems that use it, and in the second half there is some division of decimal numbers by 2-digits.
So, the supplementary books for Primary Math 5, the Extra Practice, do not have practice for division by 1-digit, except as encountered in word problems. The ones for grade 3 have a lot more practice of division by a 1-digit number. There is some practice for division by 2-digits in the Extra Practice 5. Then there are word problems with division both by 1-digit and 2-digits.
Standards edition of Primary Mathematics for grade 5 includes division by a decimal number with 2-digits such as dividing by 0.42.
The EDM alignment with Extra Practice only refers to pages in Extra Practice for 2 lessons on division. This does not reflect the time spent on division in the regular Primary Math program, with division of a 3-digit number by 1-digit in 3A.
Interesting, because I have not seen Singapore Math being used in my childrens' classrooms. When asked at curriculum night, the teacher said they had no training in Singapore Math (meaning they won't be using it).
EDM on it's own does not meet the new math standards. I have had to preemptively teach my children standard algorithms before they learn the unconventional EDM methods. I would be interested to hear if other parents are supplementing at home.
Adoption Process Key Dates
August 26 Tentative timeline drafted
October 1 Board presentation about timeline and process
October 4 – 15 Committee applications (staff) posted and publicized
October 22 – November 10 Committee applications (family/community) posted and publicized
October 27 – November 18 Committee applications reviewed and scored
November 25 Committee and process submitted to IMC; approved
November 26 All committee applicants notified of status
December 4 (4:00 – 7:00 PM)
@ Cleveland High School Committee meeting #1: Norms, goals, review of potential criteria
December 11 (8:00 AM – 3:00 PM)
@ Cleveland High School Committee meeting #2: Cultural relevance criteria; development of comprehensive screening criteria
December 16 (4:00 – 7:00 PM)
@ JS Center (Library & Rm. 2778) Committee meeting #3: Completion of comprehensive criteria; development of initial criteria
January 6 (4:00 – 5:30 PM)
@ JS Center Library IMC reviews initial and comprehensive criteria; suggests revisions and/or approves criteria
January 6 Initial rankings of high school mathematics materials expected from OSPI
January 8 (8:00 AM – 3:00 PM)
@ JS Center Rm. 2765 Committee Meeting #4: Standards review; OSPI rankings review; practice with screening tools; inter-rater reliability; begin initial screening
January 8 – February 4 Initial screening (done individually by committee members)
January 31 Final rankings and recommendations for high school mathematics materials expected from OSPI
February 5 (8:00 AM – 3:00 PM)
@ JS Center Rm. 2778 Committee Meeting #5: CORE only (grades 9 – 11); narrow to top three choices; schedule and plan for site visits
February 10 (8:00 AM – 3:00 PM)
@ JS Center Rm. 2778 Committee Meeting #5: ADVANCED only (Pre-Calculus, AP courses); narrow to top three choices; schedule and plan for site visits
February 9 – 27
@ JS Center Public Review; site visits by committee members; student focus group
February 9 – March 12 Comprehensive screening (done individually by committee members)
March 5 (4:00 – 7:00 PM)
@ JS Center Rm. 2765 Committee Meeting #6: Reports from site visits
March 12 (8:00 AM – 3:00 PM)
@ JS Center Rm. 2778 Committee Meeting #7: CORE only
Final recommendation for grades 9 – 11
March 17 (8:00 AM – 3:00 PM)
@ JS Center Rm. 2772 Committee Meeting #7: ADVANCED only
Final recommendation for Pre-Calculus and AP courses
March 18 – 31 IMC reviews final recommendations; assuming approval, forwards recommendations to Chief Academic Officer and Superintendent for approval
April 8 School Board Work Session
Mid-April School Board sub-committee (if needed by policy)
April 22 School Board Meeting Introduction of recommended adoption selection
May 6 School Board Meeting School Board vote
May 7 Books ordered; assuming School Board approval
The three HS material finalists are CMP, Key Curriculum Press and Prentice Hall. None of them use the integrated approach to math. They all offer Algebra I, Geometry, Algebra II, and Calculous.
All incoming 9th graders will begin using the new materials this year. The problem according to both of the math teachers that I spoke with is where to place kids currently in HS that have already begun IMP. They don't know whether the district will require kids who have begun IMP to continue and complete IMP, or whether they will transition them to the new curriculum? I have an 8th grader taking 9th grade math so I am following this very closely. Will they give him credit for taking INT I as they have done in the past? Will he be grandfathered in and be doomed to INT II and III in HS? Or will he transition to the new curriculum and go to Algebra I with no credit for the INT I class he took this year? Or will they give him credit for one year of HS math, and put him straight into Geometry? So many questions and so few answers...
Starting in 2009, as the story goes, the middle schools that now offer Integrated I and Integrated II will offer the first two years of high school math instead. The classes, both in syllabus and materials, will be the same as the high school course. And - if their teacher is certified to teach at the high school level - the students who take these classes will be able to receive high school credit for the classes upon request.
This is completely different from the current status. Right now, middle school students taking classes with the same name as the high school math classes are not necessarily getting the same curriculum as is taught in the high school class. The District claims that they don't know what is being taught in any of these classes. Students can request high school credit for the classes, but it will be automatically denied without any consideration. The Board may allow students and families to resubmit their petition for credit in the fall, but it remains unclear if the Board will consider granting credit for any high school classes taken in middle school prior to the 2009-2010 school year.
Although this is the story that they are telling now, the actual results may vary.
I wasn't really asking if will he get credit on his HS transcrips, I know that the district does not do this as of yet. What I was asking is will the HS he goes to recognize that he has completed INT I and place him in INT II (or it's new equivalent) as they have been doing thus far? Or will they not give him credit as it doesn't match up with the "new materials" and have him start 9th grade in Algebra I, even though he took integrated I?? This wouldn't necessarily be a bad thing, but I would like to have the option as to his placement.
Discovering Algebra on the other hand is defective. While it rated #2 on the Preliminary State Ranking (behind Holt, which did not make the SPS final cut despite its #1 ranking) this ranking is done by correlation with topics covered. The fact that Discovering Algebra does not develop algebraic thinking in a coherent manner is not counted against Discovering Algebra at this time.
Consider that in the Elementary Ranking Bridges to Mathematics was highly ranked in the preliminaries until it was later found mathematically defective and removed from consideration. I taught from Discovering Algebra (piloting it in 2000-2001). DA is the worst book I have used if the intent is to have students learn authentic algebra. If the goal is to become familiar with the graphing calculator's power and do a bunch of statistics that is DA's forte, unfortunately it is a lousy algebra book.
EDM and the standard long division algorithm at grade 5. EDM does nothing to teach the Standard Long Division algorithm. EDM does a lot with partial products and estimating.
CONSIDER ... the following optional one day projects ( which I believe are the only place that EDM uses long division)...
There are optional projects in 4th, 5th & 6th grades for the standard US algorithm. OPTIONAL 1 DAY PROJECTS. Now are CAO Santorno and Math Program Manager Anna-Maria dela Fuentes claiming that EDM teaches the standard division algorithm?
https://www.wrightgroup.com/support_info.html?sid=325
Teacher's Lesson Guides: Long Division Algorithms
These pages are prototypes for the Everyday Mathematics, Third Edition Teacher's Lesson Guides. They demonstrate instruction for the U.S. traditional long division algorithm for Grades 4, 5, and 6. Other instructional pages for the rest of the U.S. traditional algorithms will follow for all other operations, in their respective grades.
Grade 4
* Project 11: Long Division, Part 1
* Project 12: Long Division, Part 2
Grade 5
* Project 12: Whole Number Long Division
* Project 13: Long Division with Decimal Dividends
* Project 14: Decimal Long Division
Grade 6
* Project 13: Long Division
-----------------------------
On May 16th 2007, CAO Carla Santorno said that should the WA State math standards change the SPS could easily adapt to those changes.
Charlie has pointed out that the curriculum changes were to have taken place by September 2008. So will CAO Santorno ever be held responsible for this failure to perform? Remember she largely unilaterally recommended EDM for Adoption and she is the primary person responsible for not implementing the Singapore Supplement as prescribed by the School Board.
Where is this alignment that shows how EDM is used in a way that supports the Grade level math performance expectations?
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What are a great many of those 9th graders going to be doing next year when they are totally unprepared to succeed in Prentice Hall Algebra I?
We need to be adopting some one year intervention materials.
SPS math continues to be a colossal mess. Keep in mind that D44.00 and D45.00 are still neglected as students without required necessary skills are socially promoted contrary to existing school board policies.
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Just remember that everyone is held accountable. (Right?)
Grade 4
* Project 11: Long Division, Part 1
* Project 12: Long Division, Part 2
Grade 5
* Project 12: Whole Number Long Division
* Project 13: Long Division with Decimal Dividends
* Project 14: Decimal Long Division
Grade 6
* Project 13: Long Division
Correlations
* Everyday Mathematics®, Third Edition: Correlations
------------------------------
You might be thinking that grade 6 should be project 15 but no on the EDM site it is project 13. (but then again the links do not work so no big deal)
Go here:
http://www.k12.wa.us/CurriculumInstruct/Mathematics/default.aspx
Select the .pdf for k-8 standards and page through to find grades 2 and 3.
I have been reading this thread with interest (as you can probably imagine). I do need to correct one thing:
adhoc wrote:
The three HS material finalists are CMP, Key Curriculum Press and Prentice Hall. None of them use the integrated approach to math. They all offer Algebra I, Geometry, Algebra II, and Calculous.
This is not correct. The three finalists are College Prep Math (CPM), Curriculum Press (Discovering Algebra) and Prentice Hall. I think a case can be made the CPM is an integrated approach to math.
The reason that I am being so anal about this is that there is a curriculum called CMP (Connected Math Project) and it is important to make this distinction. Conneted Math is used in the middle schools and it is not a good curriculum. It really does not teach much math and I have been told does not really line up well with the new state standards. Since I don't follow what is happening in the middle schools,I will have to take that person at their word.
I understand how confusing this can be, but it is very imporant to keep this straight. We use CPM at Rainier Beach. We have the newest version in Integrated 1 (called Algebra Connections) and Integrated 2 (called Geometry Connections) and we like how deep it goes into the subjects and how it meshes well with the Complex Instruction training we took over the summer. Now, as to how it meets the new State Standards, I have no idea. I am leaving that to the adoption committee to figure out.
I've looked at the "Discovering... " texts and there is little opportunity for practice. It reminded me quite of bit of the middle school math that I experienced student teaching 5 years ago, Connected Math.
I can't get into specifics in this forum, but, it is VERY obvious in my classes that kids who can't do basics can't do much else, despite the decades long claims of the discovery-groupwork-solves-everything crowd.
I'd prefer the Prentice Hall to the College Prep Math, HOWEVER
I really really hope that the "Discoving..." failure texts are NOT adopted.
Bob Murphy
We have three current board members who listened to staff at the last adoption speak of rigor and mathematical fluency and then produced a 7-0 vote to adopt a text book series without the standard algorithm for long division. A book series that has little cohesion in the presentation of material from day to day and week to week. Grade level coherence without day to day coherence is absurd. EDM has an incredible number of learning goals at each grade level.
A long as the board refuses to realize that the staff has done nothing to correct ongoing problems in k-8 math the future of k-12 can hardly be fixed with a good materials adoption at the high school level.
As Charlie points out there is nothing in the way of math leadership that points to things getting better. There are all kinds of empirical evidence that shows the district has been in math "la la" land for a decade. It seems from their actions (or lack thereof) that the SPS leaders wish to have math remain there.
The school board pays no attention to whether the pacing plans are influenced by the posted grade level math expectations (they are not thus far) but is ready to spend a few more millions on a math adoption.
Are these folks ever planning on fixing k-12 math? Oh I know it must be that it takes more time to evaluate the results and all is well.
If so, do Dan Dempsey or MathTeacher or other high school math teachers here have an opinion about those two textbooks being better than the "Discovering" books, also published by Key?
Does the district have to choose a single publisher for all this, or could they take Prentice for part of them and Key for the better ones? Just wondering.
Thanks.
It is two separate decisions.
The Core is one decision and
the Advanced is another.
I share your scepticism about how this process runs. This high school adoption appears to be run just like the failed elementary adoption and the failed middle school adoption.
You are definitely right about the easy choice ... no one has elected to teach much meaningful real math with k-8 adoptions so why start now?
This cannot pass without comment.
JTW wrote:
I have a premonition that they will choose CPM because it appears most similar in style and approach to EDM and CMP2... bad news for our kids. Having observed the previous two math adoption cycles I suspect their main criteria is choosing the one that appears to be easiest to teach.
As the only person on this blog who teaches math using College Prep Math, I have to say the JTW is wrong, way wrong in this assertion.
Of the 3 finalists, Key Curriculum Press (the Discovering Series) is the curriculum most like Everyday Math and Connected Math Project. College Prep is a melding of Old School (there are practice problems and actual math in the textbook) and the Reform Math (Big Ideas, Complex Instruction). Prentice Hall is the curriculum that is the most "Old School."
All of these curriculua have pluses and minuses. I have been told by the representives from RB who are on the adoption committee that the curriculum that lines up best with the new state standards will be the curriculum that will be recommended to the school board. Given the IMP and CMP did not make the first cut, I will take them at their word.
As for the assertion that the curriculum that will be chosen is the one that will be easiest to teach, I have to assume that JTW is not a teacher and has never been a teacher because it does not matter what curriculum is chosen, teaching is hard and teaching math is even harder. There is no such thing as something easy to teach.
There is an extrordinary amount of time needed to prepare, execute and modify the lessons that were taught. By saying that JWT is implying that the math teachers of the SPS are lazy, don't care about teaching math to the students of Seattle, and are not capable ot teaching math to ALL students. Many of the best, most dedicated, and passionate math teachers in Seattle are on the adoption committee. They have taken their responsibilty seriously and have spent many long hours trying to decide which curriculum will be best for the high school students of Seattle.
You many not agree with the choice of curriculum (I probably won't either), but to say the reason a curriculum will be chosen is because it will be easy to teach is an insult to the teachers of mathematics in the high schools of Seattle and implies that they don't care about math and their students. Let me assure you that nothing could be further from the truth. If you want to find out, come spend a day with me. I'm in room 268 at Rainier Beach. I get there around 6:30 and leave either at 4:30 (on days I teach Evening School) or 5:30 till 6:00.
I look forward to meeting you.
When I commented that College Prep reminded me of EDM/CMP2 it was for these reasons: They all have heavy calculator use, lots of group work, little definition of mathematical terms or procedures on how to work problems, lack of book organization for reference, and cartoony illustrations separating paragraphs (which learners like my kids find distracting). CPM appears to spiral similarly to Integrated.
When you refer to Prentice Hall as "Old School" I take that as a compliment. I am reminded how little training our high school teachers had in math (I'm an old guy but made it through two years of college math). One teacher I kept in contact with was retired army. Yet our generation understands math better than the young and I think it was because we had the basics covered in our books, so the quality of teacher mattered less. I can still remember the left side of each page introduced the new concept for the day, defined mathematical terms, demonstrated how to do the problems, and on the right side of the page was a moderate amount of daily practice. There's no reason teachers can't enhance something like that with classroom activities and applications to reinforce the concepts. But what the SPS has adopted instead recently, are books so weak that it requires special teacher training to implement them in the classroom. On top of the teacher's BA or MA and math endorsement! As a result the quality of teacher presentation can vary widely, and has undue influence on the student's ability to understand concepts. There's no back-up plan if they didn't get it, to look up in their textbook. They really need that, whether they had a sub or were absent that day, or to help English Language Learners that might have missed something important that day during the verbal classroom session in English. Thankfully we didn't have calculators in the bad old days, or we'd never learn the self-discipline required to memorize facts. If you don't know your times tables quickly it can be impossible to follow an algebra lecture on the board.
I hope this clarifies my point of view. Regretfully I must decline your invitation to meet personally due to my own work and family commitments. However I do sincerely thank you for doing the tough job of educating our kids, and for posting on this blog so we all can learn.
The District is choosing between three different sets of materials, not curricula. The curriculum is the set of knowledge and skills that students are expected to acquire. The textbooks and other media are the materials used to support teaching and learning that curriculum.
It is critical that we speak precisely and ask others, particularly those from the district, to do the same.
So the adoption committee will not recommend the curriculum that lines up best with the new state standards, but the textbooks that are best aligned with the new standards.
I'm sorry if this seems petty, but I assure you it is not.
That said, Mr. Rice has re-stated what we have been told from the start: the primary criteria will be alignment with the new State Standards and Performance Expectations. It's good to hear.
While teaching is a challenging craft and art, and teaching math particularly so, the District's choice of K-8 materials appeared dominated by a pedagological criteria rather than curriculum. The decision to follow reform math appeared to come before any other decisions.
Folks outside of math education are suspicious of reform math and believe that its appeal (for educators) lies primarily in how it does not rely on the teacher's understanding of math. It appears - to those of us on the outside - that reform math sidesteps real math so as to be less demanding on the teacher, particularly those who don't have a firm grasp on the mathematical concepts.
This may be true or it may be false, but it is a common perception in the community, particularly among folks who do understand and appreciate mathematics.
Oh, I would say the opposite: that reform math demands far too *much* from both the teacher and the student, because it teaches in such an inefficient way and requires so much writing in the responses. (And you really have to understand math well in order to lead a discovery session that's worth anything.) That said, of course not all teachers or students respond to those demands. I remember getting my kids' graded TERC lessons back and noticing that any old verbiage was often accepted as an explanation, as long as there was enough of it. Didn't have to make sense.
Helen Schinske
I have also had the exact situation where my son got full marks based on the amount of verbiage, even though it didn't make any sense.
Additionally, although it's touted as promoting verbal skills with math, Reform math is just the opposite. Kids who struggle with verbal skills end up spending much more time on the reading and writing and then there is simply less time available to synthesize the mathematics. A traditional textbook can be useful to someone who knows limited English as they can follow the mathematics in the examples and find the clearly delineated algorithms and rules.
A traditional text is more useful to parents helping their child. And a traditional text teaches the skills kids will need in any future learning endeavor: when you get stuck, how do you effectively use the resource available to find the information you need? The reform math texts are not useful as resources, so do not reinforce this useful skill. When I started tutoring a girl in PreCalc, that was exactly the skill she was lacking. Stuck on a problem? Skim the chapter to find a similar example. Almost immediately her daily migraines went away.
Early 1200s: Fibonacci spread the use of Zero (and/or Arabic numerals) to the West, freeing mathematical thinkers to a higher level of abstraction.
After four hundred years or so of the very best mathematical minds working furiously hard, two geniuses discovered The Calculus simultaneously. Four Hundred Years of many people's lifetime achievements and we expect ordinary high school kids to discover all of it on their own in four years? Would we use the same approach in any other field of endeavor?
A math teacher once told me that kids have to discover the math themselves or they won't remember it. Yet he coaches math team and often takes kids to regional and even state. He does this by drilling them, by teaching them "short-cuts" and algorithms for problem solving where even *he* doesn't know the mathematics behind the algorithms. He does not see the disconnect.
Teaching mathematics well is a challenge. One must be fluent in mathematical thinking and one must be flexible and able to explain things in multiple ways. One must be fluent in mathematics years beyond what they are teaching because students *will* find patterns and make conjectures. A good teacher must be able to reinforce the good conjectures and dispel the errors in reasoning that lead to incorrect conjectures.
The tag line from math camp (I heart NSF) I attended so many years ago,
Find patterns, make conjectures, prove things.
That's the best definition of mathematics I know. Reform math agrees and actually tries to package it up to make it easier on the teacher, but fails miserably. Good "traditional" pedagogy *does* motivate understanding, it *does* motivate discovering and synthesizing the mathematical thinking behind the algorithm. It does it more efficiently and does not rely on students and teachers all working a higher level of mathematical sophistication.
Consequently everything can be half-learned or un-learned but the student and the class are swept along with the current of the pacing guide to another topic which is disassociated with the previous topic. The student quickly learns not to be concerned by the amount of the material they didn't understand. It's a de-contextualized swirl of nonsense, busy work, and elaborate explanations of the obvious followed by mysterious, inexplicable magic tricks (Voila! The y-intercept! Pulled out of nowhere like a rabbit from a hat) that students are told they are supposed to understand, but then told that it doesn't matter if they don't.
This "discovery" method isn't really easier - it's impossible. And, because it's impossible, no one expected to achieve it. And, since no one is expected to achieve it, no one really tries to achieve it. And there is nothing easier than not trying at all.
Conversely, "fuzzy math" rewards good guessing and teaches teens in groups to make up their own rules as they go along. Self expression is valued over precise reasoning.
Without real math in the schools, do we risk raising a generation of kids who can't reason clearly because they never had to learn how? Because they sure aren't being taught proper grammar or spelling, either.
I was back downtown with an open mind but still couldn't find examples of actual algebra in the College Prep Mathematics (CPM) "Algebra" textbook.
No wonder American students can score lowest in math ability among developed countries, at the same time as scoring highest in math self-confidence (Washington Post, Oct 17, 2006).