tag:blogger.com,1999:blog-7691251033406320222.post1604296221961751767..comments2024-03-26T04:19:38.862-07:00Comments on kitchen table math, the sequel: Another reason to distrust the spiralCatherine Johnsonhttp://www.blogger.com/profile/03347093496361370174noreply@blogger.comBlogger65125tag:blogger.com,1999:blog-7691251033406320222.post-9473675468575071002011-11-29T10:57:23.208-08:002011-11-29T10:57:23.208-08:00I'm not a big fan of Parker & Baldridge, e...I'm not a big fan of Parker & Baldridge, either; I agree that it is fairly thin on content. More worrisome, even though the authors explicitly deny (in the introduction) any intent to teach pedagogy, the book is just <i>filled</i> with monolithic and unsubstantiated claims about "the way children learn" and "the right way to teach" math.<br /><br />But you know, you can't really judge what goes on in a (college) classroom from its textbook. In my classes at Oakland U. the official text is Billstein. The manner in which I "follow the text" is (how to put this delicately) rather hypothetical. That is, the list of topics we go over roughly correlates with the chapter and section headings in Billstein, but the organization and presentation within those topics is <i>radically</i> different. And I know that much the same is true at MSU, UM, and WSU, as I have first-hand knowledge of faculty at those institutions.<br /><br />In any case my point was not about textbooks. It was a response to your claim that "<i>other than Wu's class, there are no *math courses in elementary ed* at the undergrad level in our nation at this time, and merely a handful of pedagogical math methods courses in education depts that have any math content for k-6 at all</i>". That's just outrageously false, as all of the courses I listed are <i>content courses</i>, not <i>methods courses</i> (which preservice teachers <i>also</i> have to take <i>in addition to</i> their content courses), taught not in education departments but in math departments by honest-to-goodness real-life mathematicians.Michael Weissnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-22908901908261950782011-11-28T21:08:03.747-08:002011-11-28T21:08:03.747-08:00Michael,
Parker and Baldridge are good texts, but...Michael,<br /><br />Parker and Baldridge are good texts, but they aren't what I meant. They serve a good purpose, no doubt, and I am happy to see those courses being taught with those texts, but they aren't mathematically deep. They aren't math textbooks. Perhaps I need to describe the difference differently?<br /><br />Liping Ma talks a great deal about the understanding of US teachers vs. Chinese ones. She makes a great deal out of their ability to discuss place value. The US teachers talk just fine about tens and ones, and on first pass, it seems like she's making a big deal out of nothing. Intuitively, place value is easy, right? Swap ten ones for a ten, etc. But she keeps digging and finds out that they can't speak deeper about place value. Much like a college student who dimly understands but who says "yeah, right, that's what I said" when a professor corrects him because he can't see what he doesn't know, the US teachers didn't have a deep understanding. Parker and Baldridge help teachers get to a certain level, but not beyond that. They are not demanding enough of the math for it to go beyond that. Wu's book does. <br /><br />We can debate whether everyone needs to go past Parker and Baldridge or not some more, but what I was speaking of is a vastly different course than the ones you showed me. <br /><br /> The Wayne St. course might be taught by a mathematician, but Mathematics for Elementary Teachers: A Conceptual Approach is not a mathematically deep book. It draws on the NCTM standards, which don't inspire confidence. "an emphasis on learning via specific, realistic examples and the extensive use of visual aids, hands-on activities, problem-solving strategies and active classroom participation." is not an emphasis on mathematics.<br /><br /><br />I looked at length at U Mich's math dept site. While the course you link to is in a math dept, only one version of the undergrad math concentration --one for a secondary level cert--requires the first course in that sequence. That appears to be an alternative to receiving a math major, not in inside a math major. This concentration has more math in it than some, but again, it's not for elementary certs.<br /><br />The listings for that concentration look a lot like inquiry courses, iirc: "The students are engaged via constructing collective explanations of key mathematical topics."<br />Not sure that's the same idea at all.<br /><br />It'd be nice to see real syllabi.Also nice to know how many ugrad math majors actually take these courses as electives.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-69659582872368211672011-11-28T20:12:54.569-08:002011-11-28T20:12:54.569-08:00That my complaints are identical to others is not ...That my complaints are identical to others is not a statement against interest. I've met many parents of children who hit the wall in algebra after having come from Saxon. Many of them scored well as proficient procedurally up until algebra, yes. But that's not the only result that matters. The students understand none of why they do what they do, and collapse later--at algebra, or maybe a bit farther. Most can't do STEM college work. They can't even explain place value to me, let alone fractions or decimals. <br /><br />I've met more whose children collapse before then. Their kids hate math because of how it's taught. Those results matter too.<br /><br />I can teach a child to ride bicycle with training wheels. But they are hobbled by it. It minimizes their risk, but prevents them from learning how to lean, so they can't handle the vehicle at real speed.<br /><br />Worse, I haven't seen at all that Saxon works when the teachers are weak. That is precisely when I see a terribly bad result, one where everyone is struggling by pre algebra.<br /><br />I guess we will have to agree to disagree. Given my current bookshelf of 30 or so books I promise myself I'll read but haven't yet, I doubt I'll get to yours. So thank you for the offer, but it might go better to someone else.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-79633448901935065102011-11-28T17:16:49.095-08:002011-11-28T17:16:49.095-08:00Allison,
Stephen Hake was hired by John in 1983 b...Allison,<br /><br />Stephen Hake was hired by John in 1983 because he had been using the same methodology in the middle school grades that John had introduced with his Algebra series in 1981. Stephen's program was thus refined with John's methodology and with his editorial input.<br /><br />Your complaints/arguments are identical to many who haven't used Saxon materials at all or as John had asked them to be used. He discovered (yes, there is "discovery" in math education) that what worked for kids didn't always make sense to adults. That's what many teachers slowly admitted as they became committed to Saxon Math.<br /><br />John's mantra was always, "Results matter!" That is, is the student proficiently ready for the next level? Did the program carry him/her when the adult didn't, such as with weak teachers and/or absent parents? (A textbook series is often the one constant in a child's life of learning today.) My opinion on any program, therefore, is unimportant until I see the results of that program on the student, not only at the end of one year, but at the end of high school. Is that student ready for the workforce or college without the need of remedial education? The fact is the academic results of those who have used Saxon are legend, especially compared to the garbage we've seen published since 1989 (not including Singapore Math).<br /><br />I will be happy to send you a free copy of his biography, which gives many testimonials by teachers and administrators as well as factual research results, plus an explanation of his philosophy and methodology. You have to promise to read the book, however. If you agree, send me your mailing address to nakonia69@saxonmathwarrior.com.Nikinoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-13797644520297038142011-11-27T18:53:10.331-08:002011-11-27T18:53:10.331-08:00And don't forget, other than Wu's class, t...<i>And don't forget, other than Wu's class, there are no *math courses in elementary ed* at the undergrad level in our nation at this time, and merely a handful of pedagogical math methods courses in education depts that have any math content for k-6 at all. </i><br /><br />Okay, that's just manifestly untrue. What on earth are you talking about? Here are four Universities in one region in one state, all of which have mathematics courses for elementary teachers that are taught in math departments, by mathematicians, completely separate from the methods courses which are taught by the ed schools. None of them match your description.<br /><br />Michigan State University:<br />http://mathdata.msu.edu/CP/RW/S201_007.html<br />http://mathdata.msu.edu/CP/RW/S202_001.html<br /><br />Oakland University:<br />https://files.oakland.edu/users/grossman/web/MTE210/<br />http://www2.oakland.edu/sehs/mde2/syllabi/Syllabi%202009/El%20Ed%20syllabi%202009/MTE/MTE211-F09.html<br /><br />Wayne State University:<br />http://www.clas.wayne.edu/unit-inner.asp?WebPageID=2087<br /><br />University of Michigan:<br />http://www.google.com/url?q=http://www2.soe.umd.umich.edu/elem_standards/syllabi_pdfs/Math%2520385.pdf&sa=U&ei=G_fSTrqBJcKh8QOT6fT9Dw&ved=0CAQQFjAA&client=internal-uds-cse&usg=AFQjCNETrF2jk5xzHk01Vf78zge9KRceFg<br />http://www.math.lsa.umich.edu/ibl/489.htmlMichael Weissnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-86408582611557800942011-11-27T17:12:20.873-08:002011-11-27T17:12:20.873-08:00SteveH said
"My son was bored with the standa...SteveH said<br />"My son was bored with the standard pace of Singapore Math. When I taught him algebra and geometry at home using the Glencoe series, I could never take them at the standard pace."<br /><br />We kept the pace up in the Singapore books by just doing the workbooks, not the texts and certainly not the extra practice books. That was not our original plan (we bought all the texts and workbooks), but the problems in the workbook were straightforward enough that the texts were only consulted about once a year (usually to figure out the notation used in a problem statement).<br /><br />I found that the Singapore texts did a good job of introducing new material while practicing the old, gradually increasing the complexity of multistep problems from year to year. Even now that my son is in AoPS Calculus, I'm still pleased with our decision 10 or 11 years ago to start him on Singapore math rather than the curriculum his school was using.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-36326126678677222342011-11-27T12:05:11.662-08:002011-11-27T12:05:11.662-08:00Niki said:
-- You quote some Saxon lessons to show...Niki said:<br />-- You quote some Saxon lessons to show how "unlinear" they are. What you don't explain to those who have never used Saxon is those topics are "introduced," with 5 problems out of 30 on that particular topic found in their written practice/homework. <br /><br />Hi Niki,<br />There's a difference between constant repetition and coherence. My objection is with the idea that distributed practice makes up for a lack of coherent structure. I quoted the exact order by which topics are "taught" in Saxon Intermediate 4. That order is the problem, and no repetition of material in previous lessons or future lessons will fix it.<br /><br />The approach in current Saxon books above grade 3 is one that is bewildering. Every day, a different concept, as if *the concepts in mathematics do not build on each other.*. Yes, the procedures are given and practiced. But they are given without explanation of what it meant, and given in such an order as to imply that math is like a cookbook where the recipes are in alphabetical order by ingredient--as if there is no notion of a purpose to what is being taught.<br /><br />Mathematics education is like building a house where you can work and live comfortably-- a place where once the structure is solid, allows you to spend time roaming around, getting work done, playing, resting, etc. The building of the house must be done from the ground up, bit by bit. You don't put in the windows before you build the walls. You don't build the cabinets before you put on the roof. <br /><br />Saxon's order is as if to say that we practice nailing up some of the frame, and tomorrow, we move on to nailing on the roof. We distribute practice on nailing, you see, and that's what is important. <br /><br />But a structure built this way will not be load bearing. It may LOOK like a house, but it is NOT a house.<br /><br />What I find even more bewildering is how anyone could read page after page of lessons ordered in that fashion and not notice a problem. It's an emperor-has-no-clothes moment--- one must be pretty sophisticated to not notice the obvious.<br /><br />Now, Saxon's name isn't listed as the author of those books; Stephen Hake and others are. It may be that these books are miles from the original content. It happens quite a bit--Dolciani's books have been ruined in that way (see e.g. "Mathematics: Structure and Method" or "Thermal Physics" by Kittel and whomever else is now listed.) So it may be that all sorts of Saxon defenders haven't seen what's currently published under their moniker; I don't know.<br /><br />As to the value of distributed practice, I would add that it also comes at the expense of just teaching the material. A lesson where 5 of the 30 problems are new and 25 are review is unhelpful to teaching the new. 5 is not enough to ground the concept. It should be far far far more. Review is not the place to explore the content. By only showing 5, and then reviewing a smorgasbord of prior work for 25, little depth can ever be explored and understood by the students.<br /><br />I have more complaints about the procedural work of Saxon, and the weak or nonexistent reasoning offered, but that seems best for a different post.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-69066727517334331912011-11-27T06:05:02.241-08:002011-11-27T06:05:02.241-08:00Let me also say that I never pulled out the big gu...Let me also say that I never pulled out the big guns (of competence) with my son's schools. I've always tried to be constructive - with very little effect. It's very difficult to draw a line in the sand while your kids are in the school. Also, it can take years to figure out what's going on. Catherine drew a line in the sand and I give her very high marks for that. It would be interesting to hear if she would do it differently if she had to do it again.<br /><br />Even after my son graduates from high school, it would be a difficult thing to do in our small town. (I think it must be easier in larger towns or districts.) People are extraordinarily funny when it comes to K-8 public schools. I don't think they want the issues clarified. Parents who have different ideas of K-8 education just keep quiet. If they can afford it, they send their kids to other schools - and they still keep quiet. The issues are VERY personal. Full inclusion is very personal. Even teachers know that differentiated instruction doesn't work unless you lower expectations. You have to believe that the more able kids "will do just fine". It's a dream world. Increase the range of abilities in a classroom but talk about how teachers can get all kids to learn at their best levels. The sorry excuse you hear when it doesn't work is that "public schools have to teach ALL kids." Apparently this has to happen in one age-tracked classroom.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-24606274761963872512011-11-27T05:09:40.391-08:002011-11-27T05:09:40.391-08:00"In particular, the rather slow-moving drill ..."In particular, the rather slow-moving drill is not particularly suitable for gifted math students, who can progress more quickly with less boredom (and, perhaps, more understanding) with the Singapore c<br />curriculum"<br /><br />My son was bored with the standard pace of Singapore Math. When I taught him algebra and geometry at home using the Glencoe series, I could never take them at the standard pace. We would cover a whole chapter in an hour or so. I would give him problem sets and he would go off and do them on his own.<br /><br />No curriculum is satisfactory for advanced students, and you don't even have to be gifted. Now that my son is in a regular high school math class, he deals with the slow speed perfectly fine. At least the content is proper. <br /><br />In terms of K-6, Saxon makes it easier for schools to be competent at a proper level. The needs of gifted students are another issue. Schools have to allow for true acceleration.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-22020516846951050282011-11-27T05:01:21.442-08:002011-11-27T05:01:21.442-08:00"... EM doesn't bother to explain how pla..."... EM doesn't bother to explain how place value works in the lattice method, and presents the algorithm as a way to multiply."<br /><br />Yes, the lattice method is just thrown in there. Everyday Math goes out of its way to not teach the standard algorithms. They introduce partial sums and partial products, but they never go to the full, most efficient (standard) algorithm. Their goal is NOT any sort of full understanding of what's going on. Their goal is to give the basic concepts of what's going on. They don't believe in the need for mastery because kids have calculators. However, real understanding of what's going on involves hard work. Having a conceptual understanding is not enough. Don't buy their argument that they care about understanding. They have an extraordinarily simple idea of rote learning and understanding. They see little linkage between mastery and understanding. That is one of their biggest flaws. You might get away with that with basic math skills, but it fails miserably when you come to manipulating rational expressions.<br /><br />As I've always said, they use calculators as avoidance tools rather than magnification tools. Calculators, used properly, should allow one to tackle more complex problems and to raise expectations by focusing on more complex ideas. Schools use them to do the opposite.<br /><br /><br />"This is not nitpicking, this is a direct attack on the poor quality of material in the teacher's manual, and is reflective of a cavalier attitude toward truth and accuracy..."<br /><br />Exactly, and that should be the focus. Don't get drawn into an argument over the merits of the lattice method versus the standard algorithm. I could come up with a detailed analysis of why the standard long division algorithm teaches so much more understanding and number sense, but they really don't care. The want the students to select a favorite algorithm and make it his/her own. OK, but what, exactly, is the level of mastery they require? While my son was taking EM, I don't remember that ever happening. Perfectly capable kids got to fifth grade without knowing the times table using any sort of technique.<br /><br />It's an issue of competence, not pedagogy. If you argue too much about pegagogy, you fall into their trap. Focus on the top end algebra in 8th grade path, not the low state profiency to nowhere. If they dispute that, ask them to define (back through K-6) the content, skills, and grades necessary to get to algebra in 8th grade.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-70838947230250688902011-11-27T04:35:15.524-08:002011-11-27T04:35:15.524-08:00"The very philosophical foundation of Everyda..."The very philosophical foundation of Everyday Math is flawed, and must be rejected."<br /><br />Yes, I agree. The key is that you have to define the issue, not them. They will start talking about understanding and vague ideas of differentiated instruction, but you have to counter by asking for details. They will talk about balance, but what, exactly, does that mean? Do they ensure mastery of the skill part of that balance each year, or do they "trust the spiral"? If they trust the spiral, how do they know it works? <br /><br />Do they point to the What Works Clearinghouse? I've had that thrown in my face. Even the WWC says that they really don't have enough data. And what do they use to claim that something "works". It's a relative improvement, not an absolute one. The WWC really does not want to be seen as irrelevant.<br /><br />Do they point to students who have been successful with Everyday Math? Ask for a questionnaire to be sent home to parents so that you can subtract the benefit of parental teaching/reteaching. Do teachers send home notes to parents asking them to practice math facts with their kids. If so, that's outrageous.<br /><br />I would suggest that you never argue over the standard algorithms. They are well-prepared for that. If it does happen however, ask them to prove mastery of ANYTHING. They will probably claim that the spiral allows kids to learn when they are ready. Of course, this means that if they don't learn, then there is something wrong with the kids, not the teaching. Ask them if they really think the spiral works by definition. What, exactly is their plan for ensuring mastery? Ask them when they do that for each skill. Our schools try (try!) to ensure the mastery of adds and subtracts to 20 in third grade. These kids are now so far behind by third grade that they will never catch up.<br /><br /><br />The discovery learning argument is kind of old. No one can argue against discovery. It's too vague. However, it's neither necessary or suffient. Ask them if it is possible for a student to discover things while listening to a teacher explain things. Ask them if it is possible to discover things while working alone on a homework set of 25 problems.<br /><br />What they really want is NOT discovery. Discovery is really a justification for full inclusion classrooms with the teacher as the guide on the side. That's what they want. Discovery is only a cover for that. They just want a happy learning environment to make them feel all warm and fuzzy.<br /><br />If your focus is on results, you have to define what those results should be on an absolute basis. I would focus on the key 7th grade (or whenever) math tracking decision. Usually it catches parents by surprise, and by then, there is nothing they can do about it. It's at that point where some parents figure out that their kids are perfectly capable of getting on the higher track, but the schools have not prepared them properly. Ask the high school to provide statistics of the highest math class (and grade) of kids who do not get to algebra in 8th grade.<br /><br />Schools are so concerned about STEM that you should ask them what level of math and grades they think are necessary for students to have that opportunity in college? Ask them what specific degrees they are talking about. Look at college math requirements for these departments. Do they require differential equations? How many high school students will be properly prepared? How many of these kids have been helped at home or with tutors?<br /><br />Don't ever concede EM's success. It is fundamentally flawed. The only way it could be successful is by reducing expectations and slowing down the coverage ... at the expense of more able kids. Institutionalized low expectations.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-61663327524798144412011-11-26T19:46:01.293-08:002011-11-26T19:46:01.293-08:00Never having used the lattice method for real calc...Never having used the lattice method for real calculations (although I have played with it a few times), the question I have is how can anyone say it is "very efficient and powerful", as the EDM Teachers Reference Manual does? If we look at the operations performed in the standard algo and Lattice method, the Lattice always has more operations (defined below). If I can support this, and it is very evident that it takes longer to draw a lattice as the problem becomes larger, it therefore disproves the EDM Manual assertion that "The authors have found that with practice, it is more efficient than standard multiplication for problems involving more than two digits in each factor." If there are more operations in the lattice method, AND you need to draw the lattice as opposed to two lines in the standard algo, the lattice method has to take longer. <br /><br />This is not nitpicking, this is a direct attack on the poor quality of material in the teacher's manual, and is reflective of a cavalier attitude toward truth and accuracy (see post above under ammunition).<br /><br />And so to the proof (for n x n lattice):<br />Operations involved:<br />1. multiplications<br />2. additions<br />3. carry in multiplication process<br />4. carry in addition process<br />5. writing multiplication results<br />6. writing additon results<br /><br />There will always be equal values for multiplications (a nxn digit multiplication will always involve n-squared multiplications), carry in the addition process (there will always be 2(n-1) additions), and writing addition solution (the answer will always have at most 2n digits).<br /><br />For the other operations, the lattice requires 2n-squared (2 x n x n) additions, 2n-squared numbers to be written for multiplication results, and zero carrying in the multiplication process.<br /><br />For the other operations, the standard algo requires (n(n+1)) + (n-1) + (n-2) + (n-3) + .... (n-n) addtions, as well as the same for numbers to be written for multiplication results, and (n-1) squared for carrying in the multiplication process. I tried to simplify this but failed (should have paid attention in series class), but doing it by hand for 3x3, 4x4, and 5x5 showed that the lattice method used 2,3, and 4 more operations. When you go to higher n's (yes, I used a spreadsheet), you add three operations to the difference for each increase in n (so for the 6x6, the lattice uses 7 more operations; for 7x7 it uses 10, etc.),.<br /><br />So it is not as easy an quick as the standard algorithm, but I will agree that there is nothing inherently wrong with it and that EDM does not teach to mastery. <br /><br />Brian BTN<br />Brian BTNBrian BTNhttps://www.blogger.com/profile/01369503806460632099noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-3322930295578040202011-11-26T19:05:45.797-08:002011-11-26T19:05:45.797-08:00The lattice approach to multiplication was include...The lattice approach to multiplication was included in the original (draft) version of EM as a sidebar to highlight how place value works in another algorithm. It was not intended for students to use the algorithm in calculations. Currently, EM doesn't bother to explain how place value works in the lattice method, and presents the algorithm as a way to multiply. It is inefficient, particularly with numbers of three digits or more, and with decimals. The standard algorithm on the other hand is efficient while underscoring how place value works. <br /><br />A video done by M.J. McDermott a few years ago demonstrates that the lattice method may not be as easy and quick to do as other algorithms: http://www.youtube.com/watch?v=Tr1qee-bTZIBarry Garelickhttps://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-9610861607195242542011-11-26T17:10:16.974-08:002011-11-26T17:10:16.974-08:00Two thoughts:
1) The Saxon approach, though popul...Two thoughts:<br /><br />1) The Saxon approach, though popular with some home schoolers, is not a panacea. In particular, the rather slow-moving drill is not particularly suitable for gifted math students, who can progress more quickly with less boredom (and, perhaps, more understanding) with the Singapore curriculum.<br /><br />2) There is nothing inherently wrong with the lattice approach to multiplication. It is mathematically well founded and is as easy and quick to do as other algorithms. The problem with Everyday Math is not that they chose bad algorithms, but that they don't teach the algorithms they chose to mastery.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-21243608703352161562011-11-26T15:06:55.585-08:002011-11-26T15:06:55.585-08:00SteveH/Niki:
Thanks for the input and feedback. ...SteveH/Niki:<br /><br />Thanks for the input and feedback. Two comments and one bit of ammunition. <br /><br />The first comment ties into what Steve said, "They have to understand that their basic assumptions of education are wrong." I read this to agree with the statement I made to the Board of Education, i.e.,<br /><br />"The very philosophical foundation of Everyday Math is flawed, and must be rejected." I am going to focus my push on showing that the major tennants of EDM are wrong: <br />1. repeated partial learning (I like that term and the implications), <br />2. discovery learning (ask the BoE if they want to get operated on by a doctor who did "discovery learning" in surgery class in med school), <br />3. ignoring the basics and the standard algorithms (or forcing teachers to supplement, which has to be occurring inconsistently across a district - a great lead in for a discrimination law suit).<br />4. inch deep, mile wide; although the standards may be hard to fight (or at least that will be the next battle).<br /><br />My second comment ties to Niki's thoughts on "Those monied fingers..." In the long version of my prepared comments to the BoE (which got cut because I only had three minutes to speak), I was going to comment on the ability of the insiders (monied fingers) to use jargon to confuse the issue:<br /><br />"It is very easy to get caught up in, or confused by, the jargon used by the current day equivalent of Eisenhower’s Military-Industrial Complex, i.e., what I call the Publishing-Educational-Governmental Complex. This Complex does not consume the results of education; they sell the tools for that education. I would posit that the effort to sell has overridden the desire to produce good results."<br /><br />My focus is going to be on results, not research. What do the middle school teachers say? What do the college professors say? What do the parents say? What are we producing out of high school, whether they go to college or to work? They need to know the basics and the algorithms, and EDM is failing in that regard.<br /><br />Ammunition:<br />One interesting "reason" I have discovered for EDM's success is that they must have a large number of schools using the program with incredibly small class sizes. On the front page of the EDM website (ABOUT) is the statement: "It is currently being used in over 185,000 classrooms by almost 3,000,000 students."<br /><br />If I use my long division, which they obviously did not, to work this out, I come up with at most 16.22 students per class. I don't know about you, but even in Greenwich our class sizes are 20-21, if not more.<br /><br />Brian BTNBrian BTNhttps://www.blogger.com/profile/01369503806460632099noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-77786339735882163872011-11-26T09:03:05.193-08:002011-11-26T09:03:05.193-08:00Brian: There are many of us working on local or li...Brian: There are many of us working on local or limited levels who are trying to bring common sense changes to math education. I've long maintained we're like sparklers, however, and we need to become a candle with sustained light on the subject. <br /><br />Parents, understandably, leave the problem when their children are out of the education system, so there's a high turnover rate among those of us in the "math wars." To try and organize a group that could consistently counteract NCTM's immense power seems highly improbable. <br /><br />For one thing, we would need big bucks from someone with a big megaphone. The National Science Foundation, for example, pumped $84million in grants to NCTM colleagues during the 1990's for them to write, implement, and embed unproven math curricula, which are still destroying American math education today. The NCTM-Federal Government fingers went very deep throughout the political systems at the state and local levels, as well as within teacher training programs. Those monied fingers will not be pried loose easily.<br /><br />That's why John Saxon's battle with NCTM and their political allies for 15 years is so important to recognize and honor today. To his great surprise, he became a multimillionaire as parents and maverick schools grabbed onto his traditional program, starting in 1981. He was vilified, ridiculed, and one "leader" offered to throw a party to celebrate his death. That hatred for him still exists today.<br /><br />I have two goals today at age 71. I want John Saxon honored for providing successful math experiences to thousands of children (and to their parents and teachers). He and his friend, Jaime Escalante, are true heroes. ("Waiting for Superman," the acclaimed documentary about public education, should be remade to show how Supermen are actually treated by the public education establishment.) Jaime, who died recently, has been memorialized through the movie, Stand and Deliver. I wrote John's biography to memorialize him, at least in book form. My dream is for him, finally, to be honored openly. (Go to http://saxonmathwarrior.com.)<br /><br />My other goal is to keep building my Emmanuel Academy, a K-8 tutoring program at my church, with the primary use of Saxon Math and Saxon Reading and Writing methods.<br /><br />Hey, being 71 means you have 50 years of work experience, so why not keep putting it to use?!Niki Hayesnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-84505798390219529092011-11-26T06:45:46.244-08:002011-11-26T06:45:46.244-08:00It seems to me that the best way to confront the m...It seems to me that the best way to confront the math problem in K-8 is to work down from the high school. For many years, our middle school used CMP for 7th and 8th grades. Parents complained that their kids were not prepared to start honors geometry as freshmen. Heck, CMP didn't even provide a proper introduction to algebra. In response, the school added more algebra to CMP. It still didn't solve the problem. This is a good approach because one can clearly see and define a specific curriculum gap. The school can't deny it. They can't say that it isn't important.<br /><br />Eventually (I don't know the details), our school finally realized that they couldn't push differentiated instruction through 8th grade. They had to separate the kids in 7th and 8th grades for math. They had to offer the exact same honors algebra course in 8th grade as the high school course and use the same textbook. This forced them to get rid of CMP, probably because the school was small and they couldn't offer two separate approaches to math. This pushed the problem down to the lower grades that used Everyday Math.<br /><br />This is where the push seems to end. Everything is based on doing well on the state tests, but the state tests are not good enough. I once tried to figure out the math behind the conversion of the raw percent correct scores on the state test into the "Proficiency Index" all schools use to see if they are meeting expectations. However, this has little to do with whether the schools are properly preparing kids for the top math track when they hit 7th grade. What the state tests do is to convert really bad raw percent correct scores into really nice looking percent correct proficiency indices. For more affluent communities, this is a really simple goal. Our town even points to the proficiency index to claim that it is providing a good education. They are wrong.<br /><br />It seems that the only way to push improvements into the lower grades is to focus on what the schools use as the criteria for getting into the top math track in 7th grade. If that is a specific test, then those skills can be tested and tracked specifically in the lower grades. Unfortunately, many schools base the decision on Everyday Math grades and a teacher's recommendation. In any case, one could try to force a school to define exactly what that means. Those expectations can be clearly defined and handed out to parents so that they can see if their kids are on the top math track in the lower grades.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-4012765756799172192011-11-26T05:52:12.580-08:002011-11-26T05:52:12.580-08:00I'm betting big that schools will be highly re...I'm betting big that schools will be highly resistant to polling parents about any kind of tutoring; they want to take credit for it and don't want to consider any alternative explanations.momof4noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-18090969507926089492011-11-26T05:04:09.971-08:002011-11-26T05:04:09.971-08:00Schools will point to kids like my son who are suc...Schools will point to kids like my son who are successful without ever asking what went on at home. In two different K-8 schools my son was in I tried very hard (constructively) to get them to see the issues; to get them to define some sort of process that would ensure mastery of the basics. It never happened. They have to understand that their basic assumptions of education are wrong.<br /><br />If possible, parents need to get schools to send out questionnaires to parents to find out exactly what kind of teaching/reteaching they do at home. I'm talking about things other than going to museums or making sure that kids have done their homework. I'm talking about teaching the basics. We've talked about this in the past at KTM. It's really annoying for parents to get notes sent home asking them to practice basic math facts with their kids. I'm sure that if you eliminate the kids who got help at home, Everyday Math would show very little success.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-7716202322386395102011-11-26T05:03:29.899-08:002011-11-26T05:03:29.899-08:00Everyday Math and its ilk give spiraling a bad nam...Everyday Math and its ilk give spiraling a bad name. I call it repeated partial learning. It doesn't deepen the learning for kids who have mastered the material (probably from their parents), and it doesn't get the job done for those who didn't figure it out in the first place. It's really circling. One parent I knew complained that her three kids (in different years) were covering the same material in pretty much the same way.<br /><br /><br />"Texas may finally step forward from most other states with our mandate that requires the teaching of standard algorithms. This prevents the use of fuzzy methods as the primary source of instruction (Everyday Math's lattice method, for example)."<br /><br />The problem really isn't about the standard algorithms versus EM's individually-selected choices, like the lattice method. It's about ensuring the mastery of anything. The major fundamental flaw of Everday Math is that it tells schools and teachers to just go through the motions; to "trust the spiral" without any proof that it works. Teachers don't have to worry if kids don't learn the times table by fifth grade. The "spiral" will take care of it.<br /><br />The whole goal of Everyday Math is to give schools some sort of pedagogical basis that allows full inclusion. The Holy Grail for many educators is to find some magic way to track kids by age and hope that they all get what they need. They talk about differentiated instruction, but there are no specific goals.<br /><br />When my son was in fifth grade, the school and parents had a meeting to talk about EM because there were many rumblings. They talked a lot about the "balance" between critical thinking and mastering basic skills. Nobody seemed to be willing or able to define exactly what that meant, even though perfectly capable kids had somehow gotten to fifth grade and were struggling with the times table.<br /><br />The fifth grade teacher had a choice, to trust the spiral, or to slow down the coverage and spend more time ensuring mastery. She chose the latter, but sent out a letter at the end of the year claiming victory over understanding and critical thinking. My son had a lost year.<br /><br />They want to avoid drill and kill, but what they are really doing is changing math into something that it isn't. They don't want math to be a filter, so they think they've found a perfect way to pump them along. The problem is that they pump along the problems until it's too late to do anything about them. The kids get separated into different math tracks (usually in 7th grade) and for those in the lower tracks, almost any possibility of a STEM career is over. By 7th grade. No amount of Project Lead The Way in high school will fix the damage. The problem isn't student motivation. The problem isn't some subtle difference in spiraling. The problem is basic school competence.<br /><br />The worst part is that those students (and their teachers) will really think that it's their limitation. Kids will say that they just don't like math or that they are somehow genetically not capable of math. They are not math brains. Teach badly and then blame the students, genetics, peers, poverty or society. Pump kids along until you can't see the cause anymore.SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-63797029073420395642011-11-25T18:48:32.155-08:002011-11-25T18:48:32.155-08:00Niki:
We here in Greenwich CT are facing a simila...Niki:<br /><br />We here in Greenwich CT are facing a similar issue relating to the timing of a curriculum review and any possible change in text books (if you can call EDM a textbook). Our public schools have their next math curriculum review scheduled for 2014, which means a possible pilot in 2015, and maybe adoption in 2016. Since CT adopted the Common Core States Standards, the Connecticut Mastery Test will become CCSS compliant in 2014. <br /><br />I have started a push to get a curriculum review moved up to NOW! See my blog at<br />http://greenwichmath.blogspot.com/<br /><br />I highlighted many of the same issues you noted above (calculators, spiral,inch deep/ mile wide, non-standard algorithms) to our board of education when I spoke to them (for the three minute time limit). We shall see if anyone was listening.<br /><br />I would love to hear more about your work.<br /><br />Thanks<br /><br />Brian BTN (by the numbers)Brian BTNhttps://www.blogger.com/profile/01369503806460632099noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-12042934856270082822011-11-25T17:32:03.114-08:002011-11-25T17:32:03.114-08:00I was selected to serve on the Texas Education Age...I was selected to serve on the Texas Education Agency's committee this year to help rewrite our state's math standards. I had asked for grades 3-5 because those are the children with whom I work now as a paid tutor at the local Catholic school (who uses Saxon Math)and am most familiar with the concepts they must learn. <br /><br />I decided to testify before the State Board of Education last week as they looked at the final draft from our 80-member TEA committee. Strangely, I was the only one from the rewrite committee to be there.<br /><br />Here's what I told them:<br />1) Texas may finally step forward from most other states with our mandate that requires the teaching of standard algorithms. This prevents the use of fuzzy methods as the primary source of instruction (Everyday Math's lattice method, for example).<br /><br />2) We also are prohibiting the use of calculators in K-5 math classrooms. (John Saxon started fighting the NCTM in 1985 and their support of calculator use in early grades. It's only taken 26 years to get that message across.)<br /><br />3) HOWEVER, I said we have created a document that is a mile wide and an inch deep. It must be pared down. That is, the 4th grade has 43standards. At (realistically) 150 days of seat time instruction out of 185 days, that gives teachers 3.5 days for students to master a concept. And then they must move to the next concept/standard.<br /><br />4) In addition, in an effort to add "rigor" to instruction, we have pushed harder concepts to lower grades. I explained that is not "rigor." It's just making the lessons "harder."<br /><br />5) We will therefore see a massive frustration index among our teachers and those training them. Trying to cover too much has been a complaint for years, so I don't think our new standards will improve on that situation. Weak teachers who don't know their math content will become even weaker.<br /><br />I withstood 30 minutes of questions by the SBOE members, some of whom said we should push adoption of the new standards from 2012 to 2017, when the new textbooks would roll out based on the new standards. I insisted that meant 5 years would be lost in teaching students standard algorithms and how to master mental arithmetic (no calculators).<br /><br />It will be interesting to see the final decisions made by TEA and our state board.Niki Hayesnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-33109282324063659822011-11-25T17:10:29.521-08:002011-11-25T17:10:29.521-08:00Allison: You quote some Saxon lessons to show how ...Allison: You quote some Saxon lessons to show how "unlinear" they are. What you don't explain to those who have never used Saxon is those topics are "introduced," with 5 problems out of 30 on that particular topic found in their written practice/homework. The other 25 problems in that written practice are review--or are a "spiraling"--of all the previous lessons before that assignment. <br /><br />THAT is the difference between Saxon's spiraling--a constant repetition of pieces of a concept so that it is mastered by the end of one year--and the fuzzies' spiraling which is based on repeating lessons on one concept for two or three years.<br /><br />Saxon's method has been justified by researchers who label it now as "shuffling" different topics so students do get the incremental development and continual review (practice) that John designed.<br /><br />Saxon Math cannot be used episodically by teachers to shore up a student's particular weakness because it is designed to be the whole cake, not one ingredient. For that reason, John hated chapters, which he called "hunk" learning that required students to swallow a big hunk prior to moving to a new chapter. That's why his daily lessons are written in a manner that has constant repetition and APPEAR not to be linear by those individuals used to working with chapter formats.<br /><br />I really do encourage you to read his biography. It's titled John Saxon's Story, a genius of common sense in math education. You might get more insight into a program that more than half of our 1.5 million homeschoolers are using. It's also the one I taught on the Spokane Indian Reservation and brought, as the principal with teacher approval, to an 80% white Seattle elementary school. Great success was experienced in both places, mainly because Saxon is a skills level program, not a grade level one. My 5th grade Seattle kids, for example, were using the 76 book by the end of the year. <br /><br />Most of all, the kids learned not to be afraid of math--even to love it. The valedictorian on the reservation thanked me during graduation for teaching her algebra, which had allowed her to enroll in college. It wasn't I who taught her, however. It was Saxon Math. <br /><br />By the way, I am the one who wrote John's biography.Niki Hayesnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-79249990897725405742011-11-21T04:57:55.924-08:002011-11-21T04:57:55.924-08:00"I've been pondering the question of what..."I've been pondering the question of what an ideal K-16 curriculum would look like if there were no state requirements, ..."<br /><br />I see two issues. In K-8, I just hoped for basics that would lead to algebra in 8th grade - better, if we could have what kathyiggy talked about (minus the EM in the early grades).<br /><br />Beyond that, my son takes private music lessons from a music professor. Many kids do sports outside of school. Last year, I thought it would be nice to have my son take private chemistry and physics lessons. I never followed up. We have to play the high school/GPA/SAT game. I also know that somewhere in our state is an open club for kids who want to prepare for the FIRST Lego League competition. <br /><br />The question is how can you increase these opportunities and get them to fit in with the schools. I think kids would find a lot of support from the community. The one thing that really strikes me about the rise of the internet is how much people are willing to give of themselves for free. <br /><br />Is there anything happening in college towns for academics? Our university has a preparatory program in music for the community. Some colleges must provide true acceleration options for kids.<br /><br />Our high school is looking into allowing students to take college courses, but the problem is scheduling. The other problem is providing an academic path to get there, but I think they will leave that up to the students and their families to figure out.<br /><br />Many kids would be so much further along in lots of subjects if they were given the chance. (I just had to look up when to use further versus farther.)SteveHhttps://www.blogger.com/profile/03956560674752399562noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-39493981602110987182011-11-20T21:31:56.624-08:002011-11-20T21:31:56.624-08:00The issue of scheduling is huge, especially if stu...The issue of scheduling is huge, especially if students also are in drama or music classes. At my local high school, with 2700 students, there are three sections of AP English, two of AP Chem, 1 of AP government, etc. If you are taking things out of order, you need to really plan it out, and the high schools generally don't make it easy to figure out how to do that. It is easier to just make everyone move in lock step.ChemProfnoreply@blogger.com