This article explores how a school district in Decatur discards the traditional notions of “curriculum” and goes for the student-centered, small-groups, guided instruction approach. Like most such articles and efforts that purport to do away with traditional approaches, the first thing to get attacked is the use of textbooks:
“Your curriculum is based on the learning standards and how you teach, the strategies you use,” Mahoney said. “A textbook is just a resource.”
This is one of those maxims that starts in ed school and persists beyond. It has been repeated often enough over the years that it has now taken on a life of its own and accepted by the education establishment as the absolute truth. And the general unquestioned consensus is that something that’s so organized, sequential, and linear, and contains problems that students have to practice is not something to plan a course around. (Extended discussions of this topic usually end with another maxim: “Research shows” that this is true.)
Which might explain why the textbook industry, faced with the maxim that textbooks are just resources, produce math books with sparse explanations, a sequence of topics that makes little sense, a dearth of word problems of any consequence–or explanations of how to solve them–and problems that do not scaffold or provide much in the way of practice and learning. Key pieces of information that are not discussed in the body of the lesson are hidden in discovery type problems at the end of the problem set, ostensibly for the brighter students to conform to the current fad and practice of individualized and differentiated instruction.
Well, don’t tell anyone but in my eighth grade algebra class, I managed to secure multiple copies of Dolciani’s “Modern Algebra: Structure and Method” published in the 60’s that served many students well over the years despite claims about research on textbooks and traditionally taught math, and what such research shows. And that’s what I use instead of the textbook I’m supposed to use–part of the”Big Ideas” series of math textbooks by Larson and Boswell. The students told me they like the Dolciani books much better and even like the problems. One parent also told me this, having voiced the same concern about the “Big Ideas” textbook that I described above.
But the watchword in classrooms across the country continues to be “individualized” and “differentiated” instruction. This last term appears to be falling out of favor to be replaced by “guided instruction”:
“The idea behind guided math is small groups,” said Teri Cutler, math coordinator for the district. “Research is showing that teaching a whole group, 20 to 30 kids at the same time, is no longer as effective.” Classrooms will have stations, just like they do in guided reading, and students will work independently or in pairs at those stations while the teacher meets with a small group of children who are at similar levels. Every 15 minutes or so, kids switch to a different station. Every student gets independent time on learning activities and time with the teacher for specific instruction.
“The good thing about guided math is, the teacher can group them by ability,” Cutler said. “Some are really struggling and can have that time with only those students at their level. Some are ready to move on to the next level, and can have the chance to excel and move on as well. It’s so much better for students that they can have that time in a small group with the teacher.”
Again, another idea that sounds great. But I’ve been in classrooms where the students work in stations. I was an assistant to teachers in such classrooms and tried to work with the students in each of the groups. There is only so much time that one can spend with a student and frequently I was in the position of having to repeatedly explain to students what they were supposed to do, and provide explicit instruction for those students who weren’t able to discover what they were expected to discover. The idea that students move at their own pace and learn what needs to be learned in such a set-up is a seductive one.
But like most efforts, they are based on the assumption that traditional methods simply do not work–practice is “drill and kill” and mind-numbing, and textbooks are only resources. What isn’t done–in practice and in articles such as these–is to find out what the successful students are doing that’s different than the strugglers. Successful students often get help at home, or outside via tutors, using methods held in disdain by the education establishment. And in fact, parents are exhorted to help their students at home, to learn things like math facts and other essentials for which no time is built in to the classroom. Classrooms are the province of the “fun stuff”: the discovery activities that students used to do at home.
Those who don’t have access to such help are at the mercy of ineffective practices that are touted as “the answer”. And of course, if a student doesn’t succeed, there’s all sorts of excuses: The teacher isn’t teaching it right, or the student just isn’t trying, or the parents aren’t teaching their kids the math facts and other essentials at home. That last one is a popular one; along with “there’s no cure for the ravages of poverty.”
traditional math 
Last December I spent several full days reviewing old curricula and math textbooks at our university archives. I did this, because our own province, British Columbia, is undergoing a radical, massive change in our schools, creating a new curriculum designed on 21st century learning. The educrats want us to believe that in the world of technology and innovative strategies, the requirement for old textbooks and teaching whole class methods are no longer effective in the new world learning environment.
They could not be more wrong.
When reviewing these old textbooks – dated all the way back to 1895 to the current day, 2 things became evidently clear: they were much more straightforward, explicit and filled with understanding every step of the way. Second, they were much more serious about teaching math effectively on the assumption that the TEACHER was the one in charge, and that expectations and high standards must be maintained in order to train kids to deal with the real world. Whereas the rhetoric surrounding 21st learning today “talks” about having kids collaborate and solve real world problems, back then kids were actually “doing” it.
In contrast, the newer textbooks are filled with gibberish, cartoons, and very little time dedicated to rigorous practice, mastery of facts, and zero understanding of anything relevant. In short, what kids learn today from their textbooks is all over the map, with no firm foundation set to prepare them for higher order mathematics.
What’s even more concerning though, is how our new curriculum de-emphasizes the use of ANY textbooks. The Ministry has given their consent to allow teachers to use whatever resources they want, however they want. This is akin to having doctors being trained and treat patients based on what the internet says will work, or perhaps on the latest flyer advertising an untested medicine.
Without rigorous standards in place, with endorsed resources and textbooks approved for classroom use, one can only surmise how quickly this house of cards will come crashing down. Question is, are you willing to risk your kid’s future on that?
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“guided instruction”: Versus unguided instruction?
“The idea behind guided math is small groups,” Really?
“Research is showing that teaching a whole group, 20 to 30 kids at the same time, is no longer as effective.”
Guiding small groups rather than larger groups is more effective? Wow, what an idea!
” students will work independently or in pairs …”
Guiding themselves?
“The good thing about guided math is, the teacher can group them by ability,”
OK, put them in larger equal ability groups, set up walls up around them to keep down the noise, and then give them the full time guidance of their own teacher. Instead, they have mixed ability classrooms, separate them into equal ability stations, and then give them only a fraction of the teacher’s time.
Hello! Anyone home? I haven’t even gotten to textbooks yet. If these students spend lots of time self-guiding, how, exactly, is that done?
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Isn’t it ironic how grouping kids by ability level in whole classes is bad, yet doing so inside classes is good?
I find it quite insulting that people would describe my whole class teaching as “unguided”. What do they think I do all day, if it isn’t guiding them?
An interesting question that is worth asking advocates of this method — would you operate it with adults? Because I have been to quite a few sessions as an adult learner, and I have never once met a person that broke us into groups and taught us separately. Because it would be a mental way to do things. Yet, apparently, it is meant to work with kids!
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Yes, and also interesting that direct and explicit instruction from a teacher is considered bad, but if a student instructs another student directly and explicitly, that’s celebrated as a great thing. I once brought that up in a discussion forum and someone gave me some explanation of how explanation from a peer has a certain type of “affect” that explanations from an older person does not. I didn’t understand and still don’t.
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My view is that this is an academic turf thing. I’ve seen it in other areas, like psychology, where people think that their area of knowledge is of primary importance. These ideas dominate K-6 because that’s all they have. They don’t have subject expertise. They call facts “mere” and skills “rote.” It’s all about what they were directly taught and learned by rote. I saw it disappear in high school (mostly) where teachers are certified in their subjects and kids are grouped by academic level.
K-6 pedagogues want full inclusion and social promotion which tracks kids by age. This is made worse now because low ability kids are not sent off to other schools. This can be good, but they don’t follow the model of high schools which are full inclusion environments and not full inclusion academic classes. You can’t increase the range of ability in an academic classroom and somehow magically get better results. If, however, they start separating kids by levels and classrooms in K-6, then those kids who get their “math facts” and other basics at home will clearly define the upper levels. They don’t want that to be too obvious, so they have to mix them in the same classroom, but then separate them by level. The levels are no secret to the kids or teachers – only to the parents.
I can’t tell you how many times I’ve been told that kids will learn when they are ready. This completely removes any analysis of good versus bad teaching (or non-teaching) approaches and puts the blame completely on the kids and parents. They just point to the kids who are successful without asking us parents what we had to do at home.
I’ve never heard any explanation as to why separate ability grouping is OK in high school, but not OK in K-6, especially now with full inclusion and much larger ranges of ability. That range increases every year if you track by age. So now they want to hide tracking with internal class grouping where the kids have to teach themselves for most of the class period. Claiming that it’s better academically is nonsense.
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A couple of comments: Parents would not accept this type of grouping at all. There would be massive outcry.
There are children who come into Grade 1 with little knowledge, but go on to equal or surpass those who have had much parental input.(over time)
Teachers have lost much autonomy over time and poor ideas are forced upon them.
Children who have had a good deal of teaching at home still have much to learn from mixed classrooms, particularly in terms of compassion, gratitude, understanding and patience with others.Valuable lessons and probably best learned at a young age.
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Ability grouping inside a classroom is still tracking. While some kids may naturally catch up in terms of reading or very basic skills by fourth grade, this is not guaranteed and does not apply to all subjects and skills. It rarely, if ever, happens naturally in middle or high schools. Schools clearly understand the need for ability grouping with the larger range of full inclusion. They just want to hide it from parents. It’s not hidden from the kids or teachers, and the higher level groups will be filled with students who get help from parents at home to ensure mastery of facts and skills.
Compassion, gratitude, understanding and patience with others do not require mixed ability academic classrooms. I saw those social benefits happen in my son’s full inclusion middle and high school environments. Why do these social benefits require mixed ability academic classrooms in K-6? The real reason is that schools don’t want to be open about the problems of full inclusion and the tracking that happens with in-class ability grouping, unless it’s just silly enrichment rather than acceleration.
The fundamental problem is that tracks become permanent and there are no ways to bridge the tracks. This jump is possible in K-8, but much more difficult in high school. However, the solution in most K-6 schools is to use spiral (repeated partial learning) curricula that denigrate facts and skills and assume that kids will learn naturally when they are ready. This is fundamentally wrong and increases the academic gap and difficulty of bridging tracks. We parents who create the best students are forced to push and ensure mastery of facts and skills at home. K-6 schools assume that kids will achieve their potentials naturally at some point in time. That does not happen. Now they want to add in-class ability groups and somehow claim that it isn’t tracking.
Either K-6 schools have to admit that they were wrong about mere facts and rote skills, or they have to provide other solutions. They don’t mind it when others do what they don’t want to do in class. We parents get notes telling us to practice math facts at home, and many educators like the idea of flipping, where students watch direct instruction videos online before they come into class to do the fuzzy group stuff. They don’t mind computer-based tools that do the job. In the music world, students have mixed-ability band, chorus, or orchestra “classes”, but turn to private lesson teachers for individualized instruction and a focus on skills. Virtually all music students who make it into All State take private lessons. Music is an area where there are many cases of students who cross the tracking divide at different ages with the help of private teachers who focus on skills. This track crossing is NOT POSSIBLE when K-6 schools denegrate facts and skills, and offering in-class ability grouping just hides the problem.
Unfortunately, outsourcing mastery of facts and skills is backwards, and music is an opt-in subject. We need schools that push and ensure facts and skills IN CLASS, but then offer private teachers to help bridge those skills gaps for late bloomers. Schools can then have opt-in after-school clubs and competitions that offer enrichment and advanced levels of study. As it is now, schools want both the classroom and the after-school programs to be fuzzy and engagement-driven, as if group engagement, not individual expectations and pushing, will solve everything. That’s not how it works.
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Steve I agree with you about the poor math. Most of the rest are not decisions that come from schools. They are enforced from above, are traditional and some actually have come about from parental pressure over the years. Schools at k to 6 do not have mixed Kto6 classes because they are trying to hide things from parents. Mixed classes exist for multiple reasons that I won’t go into here. Children from poorer resourced homes can catch up and overtake other children. That is the reality I have seen, even in math.
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“Most of the rest are not decisions that come from schools.”
Not in any school I’ve seen. “From above?” What other “above” is there other than the local school district? States do not require full academic class inclusion and fuzzy student-centered group learning in class. Schools can offer classes that go beyond minimial CCSS expectations. I’ve gotten the impression that many teachers want us parents to side with them against administrations, but that won’t fix things from my perspective.
“… some actually have come about from parental pressure over the years.”
Some parents love full-inclusion mixed-ability classrooms, but they don’t insist on fuzzy math and student-centered learning. Parents don’t tell teachers that it will create better academic learning by focusing on understanding and problem solving over mastery of skills. Parents don’t tell teachers to “trust the spiral.” All of the K-6 teachers I’ve met seem to go out of their way to make sure we parents don’t interfere. I called them preemptive parental attacks, and attacks they were. Our son’s first grade teacher told my wife and I that he had “a lot of superficial knowledge.” Another told us parents about the glories of explaining in words why 2 + 4 = 4 for MathLand.
“Children from poorer resourced homes can catch up and overtake other children. That is the reality I have seen, even in math.”
How, specifically, does a school help them do this? This is not calibrated and you state it as if it’s some sort of justification for the fundamental difficulties of mixed-ability academic classrooms. That one can possibly self-IQ-fix the problem does not mean much. Tracking in class is still tracking. Apparently, schools know the problems of mixed-ability classrooms. Grouping in class is just more politically acceptable than separate classes. Still, in-class ability grouping does not fix the fundamental educator failures of low expectations and not ensuring yearly skills. It does not provide any specific ways to help kids bridge any tracking gaps. How many kids never bridge those tracks because of these systemic flaws? I’ve tutored many kids in high school who are quite capable, but were never able to bridge the K-6 math gaps that were created – not by “above” or parents or anything other than the pedagogical and anti-math beliefs of K-6 schools.
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I agree with everything Barry has written. There are far too many people climbing the career ladder, trying to get out of the classroom as quickly as possible and spreading this pernicious stuff.The only person who benefits from this is the ladder climber and he/she will never be held accountable.
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In my experience, the general rule solving problems is “take a complex problem and break it into simpler pieces and then solve the simpler pieces in a logical, sequential manner.” As a child, I was taught how to solve a huge variety of simple problems. Every year, I would be introduced to carefully selected complex problems and I would learn how to break them into simpler problems that I already knew how to solve.
It’s frustrating that experts encourage elementary school teachers (who really don’t know any better) to use big, conceptual, context-rich problems as a vehicle to teach simpler concepts. It’s a backwards philosophy.
The whole point of a textbook is to introduce concepts in a logical, linear, sequential manner. Students practice simpler concepts frist, and then have the foundational knowledge to tackle more complex problems.
It used to be that anyone who had a good idea could provide (much appreciated) activities to supplement, enhance, and add some “spice” to the textbook, but the textbook was still the foundation which gave the teacher a structured, logical sequence to follow to teach a subject. Now, if children aren’t working in groups on applied problems every day, teachers are accused of being unimaginative or lazy. At least that’s how it is in my district.
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