tag:blogger.com,1999:blog-25541994.post618697511798653080..comments2024-03-02T15:23:18.091-05:00Comments on D-Ed Reckoning: Effective Mathematics Instruction The Importance of CurriculumKDeRosahttp://www.blogger.com/profile/06853211164976890091noreply@blogger.comBlogger17125tag:blogger.com,1999:blog-25541994.post-30793656953939492412009-03-22T21:16:00.000-04:002009-03-22T21:16:00.000-04:00Ability grouping happens all of the time in school...Ability grouping happens all of the time in schools. The reason it is frowned upon, is because these groups were historically static, keeping children on the same track with the same other students at the same rate of learning.<BR/><BR/>The newest term is invitational groups, based on specific skills. So, if you had a class with a portion of fifth graders that needed decoding work, you could work with that group for just that skill. Students could move in and out of these groups as skills were brought up to grade level (mastery is such a false term). This flexible grouping allows for students to spend most of their time in independent practice and inquiry, while meeting for specific skill work that is needed. <BR/><BR/>In ability grouping, students are usually given a large assessment that measures a general level. If students are grouped based on this assessment, they will not receive specific skill work, rather, they will progress at a learning rate at this level with similar peers. This just puts children on a bell curve in a smaller group. This approach is better than the whole class model, but still not efficient or effective for each child.<BR/><BR/>A teacher that wants to effectively group students homogeneously will look at the results of a large assessment, and then get more information about students at levels of need by conducting authentic assessments such as interviews, "kid watching," running records, informal reading assessments from student chosen text and teacher chosen text. This will allow the teacher to get a better view of the whole child.<BR/><BR/>As far as constructivism, it is a misnomer that it is a pedagogical strategy. Contructivism is Piaget's theory on how students learn. When appied to education, it is very effective and takes a masterful teacher and classroom manager. It is not an easy philosophy to be successful with because our students are tested, schools are organized and designed, and the culture of the public is in line with traditional practices. In mathematics, children should learn the same content as traditional courses yet not rely on the same strategies, such as memorization of an algorithm. Instead, they should be coached to acquire more and more sophisticated problem strategies that are elegant and efficient and practiced. Children should have strategies for solving a multi-digit multiplication problem that are based on their own construction of knowledge that are accurate and work well for the child. <BR/><BR/>A child that has been in an effective constructivist setting should view each problem and devise a strategy that is most efficient for that problem (and accurate, logical of course). So for math facts, memory is typically the best first strategy. If memory is not sufficient or developed around these facts, a child should still be able to construct an accurate response in a reasonable amount of time.<BR/><BR/>The hardest thing to see is the role of the teacher. Teachers should be like facilitators, coaches, and learners all in one. When working with a math concept, a teacher can control the direction of the class by having clear learning targets and seeking out mathematical thinking from students to meet these targets. So, for a multiplication lesson, if I wanted to see my class move from counting on fingers to using an algorithm, I would provide time for my students to work independently and together on a situation or problem(s), and then look for a progression of strategies that students were using that I could teach from via student presenting. I would allow the students to share and discuss a few strategies, and use this work to help my class see the connections, and practice the more efficient strategies. <BR/><BR/>This teaching keeps all students in their zones of proximal development and allows them to accelerate by seeing and practicing strategies that are on the cusps of their learning edges.<BR/><BR/>We have a long way to go as educators as far as professional develop goes, but many great things are happening in progressive education that cannot be ignored.Travis Burkehttps://www.blogger.com/profile/00146492112611506427noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-88866229551715631692007-04-04T15:42:00.000-04:002007-04-04T15:42:00.000-04:00re: GroupingI wish this were just a matter of sema...re: Grouping<BR/><BR/>I wish this were just a matter of semantics, but the politics of hurt feelings has a powerful lobby. So, we must be careful with our word choice. <BR/><BR/>Joanne hit the nail on the head. These are skill based groups. These groups can be formed without assessment of fuzzy measures such as potential and readiness, or, ideally, even their age. Rather, their membership should be based on what skills the child has attained at what rate they can acquire new skills.<BR/><BR/>Skill based groups should be unique for each subject area, including art, music, gym. Such grouping should allow fluid movement between groups throughout the year. The name "skill based" should remind teacher and student that their task is to demonstrate skill mastery through any number of measuarble objectives.<BR/><BR/>An art teacher I once worked with defined talent as the outward representation of acquired skills. Anyone could learn these skills. Some will master them faster or with a greater degree of perfection than others, but we can all improve our skills. The physicist Richard Feyman knew this when he sought out someone who could teach him portraiture.<BR/><BR/>There should be no shame associated with skill based grouping, whatever it is called. I believe that by ensuring all subjects are so grouped, almost everyone is going to find themselves in a variety of levels as compared to their peers. Most importantly, the requirements for advancing to the next group should be clear and explicit, with all children given the opportunities to stretch themselves or be comfortable as they choose.dweirhttps://www.blogger.com/profile/01579315039135326834noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-51566980030376138232007-04-04T15:14:00.000-04:002007-04-04T15:14:00.000-04:00Rather than "ability" or "capability" grouping, wh...Rather than "ability" or "capability" grouping, why not call it "readiness" grouping. There are all sorts of reasons for being ready, or not ready, for a particular level of instruction. Prior instruction, missing school because of illness, innate ability, emotional upset -- the list goes on.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-25541994.post-42341850162068763062007-04-04T12:30:00.000-04:002007-04-04T12:30:00.000-04:00The sad part about school today is the fact that t...The sad part about school today is the fact that the people trying all this new, progressive pedagogy like constructivist math don't have a clue what basic education is really about. They spend so much time playing games and doing tricks that the students don't learn the fundamentals.<BR/><BR/>I have seen from experience the damage done to children who do not learn the critical fundamentals at the early grades. Being a fourth grade teacher for four years, I have seen the disaster "progressive" education has done to some children. I personally have a student who is in my EIP (Early Intervention Program- a class limited to 14 low performing regular education students) class who has been retained once, been in the second and third grade "taught" by two supposedly "good" teachers and the child cannot decode at all. She was never taught it. It is not a learning disability. I am now trying to teach this child basic decoding, AFTER BEING IN AN AMERICAN PUBLIC SCHOOL FOR 5 3/4 YEARS. <BR/><BR/>I have encountered NUMEROUS students who, even to this day, do not know basic addition, subtraction, and multiplication facts entering the fourth grade. Fifth grade teachers lament the fact that students do not know basic facts. <BR/><BR/>I think what the problem is the lack of SYSTEMATIC instruction. In many places, like my current school, some teachers are allowed to do what ever they damn well please. Unfortunately, the student suffers under tutelage of "all high and mighty." These all high and mightys are either the ones who insist on games and gimmicks or are too lazy to properly teach and subsist on busy work and worksheets.<BR/><BR/>I have used a program with similar coomponents like DI (Voyager Time Warp). I like DI it because it's simplicity, but effectiveness. It takes the mystery out of instruction. It is consistent. It works for both the fresh rookie and the experienced veteran. It engages students. No child is left behind. If these teachers had been using DI instead of doing their own thing, these kids would be able to read now.<BR/><BR/>ThomasAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-25541994.post-17264056942160360892007-04-04T11:06:00.000-04:002007-04-04T11:06:00.000-04:00When I was in Junior High School, there were 5 lev...When I was in Junior High School, there were 5 levels in 8th grade math. I was in the second highest group, and performed rather poorly there (I believe because of my teacher's rather strict insistence on memorizing formulae -- when we had a substitute for about a week, my performance suddenly shot up).<BR/><BR/>The teacher decided that due to performance I should be moved down a level -- in 9th grade there were only four levels, so I was moved into the third group (even though those who had been in the third group the prior year went into the second group in the revised system -- I'm not sure, I think there was some confusion somewhere). Yes, being moved from the "pretty smarts" to the "pretty dumbs" did bother me for a bit, though I never actually heard any comments on it from other students.<BR/><BR/>I had no idea at the time, but this ended up being one of the best things that happened during my high school career.<BR/><BR/>We went over things laboriously and repeatedly. Over and over, again and again long after I knew the material. Immediately I aced every test, of course, which wasn't a great motivator but made me feel good anyway.<BR/><BR/>It's also worthwhile to note that it helped me develop more sympathy for those with lesser abilities.<BR/><BR/>By early 11th grade, I would correct the teacher regularly. By the end of 11th grade, I would see proofs of problems the teacher wasn't aware existed. In 12th grade, I started coming in to school early, talking to the calculus teacher for 15 minutes or so about his lesson, and then going out and helping kids doing their calculus homework in the hall. My base of knowledge was solid enough that picking up new information was a breeze.<BR/><BR/>I disagree with stevenh on changing it to "capability" grouping. In fact, to my ears this sounds even worse -- it's like saying the kids will always be at the lower rungs. Children do progress at different paces at different times, and have spurts in their intellectual growth just as in their physical growth. Ability grouping is just that -- current ability grouping. Joanne, I understand your concerns, but the reasons behind the differing ability are not necessarily at issue (except for the kids). It's not "innate ability" they're being grouped by. No one can judge their innate ability anyway.CrypticLifehttps://www.blogger.com/profile/05313033952671292402noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-58963192565482930512007-04-04T10:35:00.000-04:002007-04-04T10:35:00.000-04:00I don't think I buy the arguments against ability ...I don't think I buy the arguments against ability grouping. The arguments against it seem to argue that kids will be put into a "slower" group because they haven't been taught the material earlier, but this doesn't have to be the case.<BR/><BR/>Ideally kids would be grouped into levels based on current "level" and "speed". For example...<BR/><BR/>For example, imagine a program that had several levels (roughly equivalent to grades) 1, 2 3, 4, 5<BR/><BR/>Now within each level there would be three groups corresponding to the pace upon which that group is able to get through the program... i.e. a for slower kids, b for average, c for faster kids.<BR/><BR/>This means my 3rd grader might be placed in level 2, but he could also be placed in group 2c which would have him up to grade level within a year… and beyond it in another year.<BR/><BR/>Also note, because of the grouping, even kids in the slowest group would still move at a pace that ensured they were progressing trough the level in one calendar year.<BR/><BR/>Summary: I want ability groups based on "potential" not on simply current level.<BR/><BR/>Yes... some kids will move through the system exponentially quicker... so what... at least the kids who struggled a little more would move through the system at a quicker pace than they do now and not get left behind. <BR/><BR/>Right now our system takes all kids through to about 6th grade level at the same time. 1/3 are held back from what they are capable of… 1/3 are just right… and 1/3 are completely left behind with no way to catch up.<BR/><BR/>My daughter is sinking in reading in her current 1st grade class, but she is still tested and expected to read books way above her current level. She is slowly learning to hate reading, homework is torture for her, and she has recently taken to calling herself a dummy. I would much rather she get placed in a class that is on her level and moves at a pace that she can master what she needs too. <BR/><BR/>(Note: she also needs to get out of a classroom that promotes whole language)TurbineGuyhttps://www.blogger.com/profile/09781298806992944235noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-66113084653085103092007-04-04T08:30:00.000-04:002007-04-04T08:30:00.000-04:00"I think "ability" grouping is a poor term. There ..."I think "ability" grouping is a poor term. There are many reasons why some kids have trouble with reading or math that have nothing to do with innate ability. For example, they may have been taught poorly."<BR/><BR/>This is why many don't like tracking in the lower grades. It's quite understandable. When schools have such trouble with curricula and teaching methods, who can trust their ability to correctly place students. It may just allow them to ignore real problems and blame it on the students.<BR/><BR/>But just because schools are bad at teaching and selecting curricula doesn't mean that ability grouping shouldn't be done. Perhaps it would sound better if you called it capability grouping. It won't make their teaching problems go away, but it will sure help those who are ready and willing for more.<BR/><BR/>Look at it this way, if you don't separate kids by capability, then that doesn't guarantee better teaching methods and curricula either. Perhaps cpapbility grouping would get parents to question why their child is not in the faster paced group. Schools would have to justify their decisions. Without grouping, it's like Sergeant Schultz ..."I see nothing! NOTHING!"<BR/><BR/>By high school, everyone does abiliity grouping, but by then, everything looks like external reasons.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-25541994.post-58881466183011619722007-04-04T01:54:00.000-04:002007-04-04T01:54:00.000-04:00Success for All groups students by reading perform...Success for All groups students by reading performance so that the teacher can focus on the skills the whole group needs to learn. I reported on a number of Success for All schools. Teachers said student behavior improved significantly. Poor readers, they thought, had been living in fear of being called on to read in class. So they kept their classes in an uproar to hide their incompetence. In a small group of readers with similar skills, students felt safe from humiliation.<BR/><BR/>I think "ability" grouping is a poor term. There are many reasons why some kids have trouble with reading or math that have nothing to do with innate ability. For example, they may have been taught poorly.Joanne Jacobshttps://www.blogger.com/profile/06801487780819716845noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-28311707563915656652007-04-03T13:34:00.000-04:002007-04-03T13:34:00.000-04:00Anon:Even though there may be a race/class compone...Anon:<BR/><BR/>Even though there may be a race/class component in many districts, I went to a lily white suburban school (a local apartment manager was regularly threatened by the locals about what might happen should she rent to any of those **** [insert racial slur here]) with a solid tax base of mostly middle class housing. This school was as culturally homogenous as you can get outside a rerun of some old sitcom.<BR/><BR/>Even in the absence of stereotypical low-performing minorities, abilities grouping had to be abandoned.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-25541994.post-17269010745913757572007-04-03T13:20:00.000-04:002007-04-03T13:20:00.000-04:00Why is "ability grouping" the great unmentionable?...Why is "ability grouping" the great unmentionable? Because the racial and ethnic makeup of the groups is politically intolerable.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-25541994.post-66566909330509557402007-04-03T11:31:00.000-04:002007-04-03T11:31:00.000-04:00I like Engelmann's take th best:"The notion that t...I like Engelmann's take th best:<BR/><BR/>"The notion that the lower performers are humiliated if they are in a homogeneous group with other lower performers is actually backwards. They will suffer far more if they are placed far beyond<BR/>their level of skill and knowledge, because they will receive an uninterrupted flow of evidence that they are dumber than all the other children in the group"KDeRosahttps://www.blogger.com/profile/06853211164976890091noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-61241575311281836532007-04-03T11:19:00.000-04:002007-04-03T11:19:00.000-04:00shortwoman,Don't forget that the struggling studen...shortwoman,<BR/><BR/>Don't forget that the struggling students learn just by being in the presence of the advanced students. Osmosis, you know.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-25541994.post-84623176497104309652007-04-03T01:55:00.000-04:002007-04-03T01:55:00.000-04:00Ooh! I know! Pick me!!!Abilities grouping is con...Ooh! I know! Pick me!!!<BR/><BR/>Abilities grouping is considered "bad" (even though if we were honest with ourselves we would know it was necessary) because even in second grade kids know if they are in the "smart", "average" or "dummy" class. And believe me, those are the words we used in the 70s. <BR/><BR/>Can't have little Johnny thinking he's a dummy. It would be bad for his self-esteem. Maslow's Pyramid is more important that math you know.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-25541994.post-26162279937213759482007-04-02T23:22:00.000-04:002007-04-02T23:22:00.000-04:00crypticlife,Apologies, I misread your post... It s...crypticlife,<BR/><BR/>Apologies, I misread your post... <BR/><BR/>It sounds like your 1st grader has the same problems that my 3rd grader has. I am willing to bet that he could survive in Algebra, but is stuck doing stuff he mastered last year.<BR/><BR/>Why oh why is Ability Grouping such a dirt phrase?TurbineGuyhttps://www.blogger.com/profile/09781298806992944235noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-61246907072011820332007-04-02T22:12:00.000-04:002007-04-02T22:12:00.000-04:00crypticlife,Somehow even with a back to basics cur...crypticlife,<BR/><BR/>Somehow even with a back to basics curriculum, I doubt that your son would learn to "multiply, divide, square numbers, work competently with negative numbers (including multiplication/division), and do multiple-digit addition/subtraction" in 1st grade.<BR/><BR/>My biggest issue with my 1st graders classroom, is that they aren't required to master the addition (and subtraction) facts. It is so annoying to see kids counting on their fingers while adding 7 + 3.TurbineGuyhttps://www.blogger.com/profile/09781298806992944235noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-73593717577203559122007-04-02T15:08:00.000-04:002007-04-02T15:08:00.000-04:00Sadly, my son is in a first grade TERC (i.e., cons...Sadly, my son is in a first grade TERC (i.e., constructivist math) classroom. As such, his ability to multiply, divide, square numbers, work competently with negative numbers (including multiplication/division), and do multiple-digit addition/subtraction is largely ignored. However, should he make a counting error when counting up 30 or 40 blocks, it's a mark against him.<BR/><BR/>American primary educational philosophy seems to labor under a strange view that kids can't learn math. Teachers seem to think kids in other countries, particularly Asian countries, are simply innately good at math. This is simply untrue (in fact, Richard Nesbitt in his book The Geography of Thought cogently suggests that Westerners may think more reductionistically (i.e., in a more math-friendly fashion))CrypticLifehttps://www.blogger.com/profile/05313033952671292402noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-75641757293803196062007-04-01T19:27:00.000-04:002007-04-01T19:27:00.000-04:00Are these changes in the department of education s...Are these changes in the department of education something to be worried about?<BR/>http://www.leadertalk.org/2007/04/sweeping_change.htmlAnonymousnoreply@blogger.com