What’s direct instruction and why don’t teachers know about it? In response to Zig Engelmann’s book and D-Ed Reckoning’s posts, Dennis Fermoyle of From the Trenches of Public Education is curious about a teaching method he’d never heard of.

Picking up the ball, RedKudu adds that her teacher training taught her to avoid “teacher-centered instruction” — and therefore direct instruction.

In the teacher-centered classroom, knowledge is “transmitted from professor to students.” Note the verb “transmitted.” Sounds impersonal, like meaningless data moving through a processing system. Students are “passive.”

In the learner-centered classroom, students “construct knowledge.” Note how much longer the description is. Note the money words like “synthesize,” and “integrate.” Students are “active.”

“Direct Instruction” is a specific teaching program developed by Engelmann and Wesley Becker.

Direct Instruction (DI) is a model for teaching that emphasizes well-developed and carefully planned lessons designed around small learning increments and clearly defined and prescribed teaching tasks. It is based on the theory that clear instruction eliminating misinterpretations can greatly improve and accelerate learning.

Without the caps, it’s the idea that teachers should teach students what they need to know rather than setting up experiences that will (or won’t) enable students to figure things out on their own.

If there are teachers reading this blog who’ve used Direct Instruction, I’d also be curious about your experiences with it.

This is what we’ve been using in college courses which have large enrollments. In my opinion, its success depends on the maturity of the students. They might sleep through my class or they might take detailed notes and ask questions during or after class. It’s up to them whether they sink or swim.

Wouldn’t this fall more into the traditional school model? English used to be a set of dictations and diagramming. Math was math facts. I mean you find something that works and duplicate, go for it. It appears that the experiences are good in some ways but don’t seem to be a dependable teaching model.

I moved back to a modified form of lecture several years back, at the request of my students, who didn’t feel they should be paying for me to come in and “facilitate.” Their request shocked me at first, but what they said made sense–I was the one with the Ph.D,; they were the ones trying to earn a B.A.

I teach literature, so I’ll spend the first couple of weeks on very short pieces and model close reading. As we move to the end of the first couple of weeks, I’ll go into a more Socratic style of lecturing.

But I’ve pretty much abandoned student-centered learning. It’s bullshit. My colleagues who still use it are sending me students who still need to be taught.

And this isn’t just in large lecture courses. I do this in classes as small as 20.

I have used Reading Mastery, Engelman’s DI program for teaching reading. At first I did not like it because I did not enjoy teaching from a script. I became a convert when I saw how effectively it taught students how to read. I think sometimes we forget that things which are boring for teachers are exciting for little kids. It would have been more fun for me to work with storybooks and whole language, no question, but I had to remember that the lesson aim wasn’t to entertain me as a teacher — it was to teach students how to read.

The students really enjoyed the program once I got the kinks worked out of my presentation. Keeping it fast paced and active is crucial!

I observed the program work effectively with students from all walks of life. Low income, high income, ELL, gifted, you name it.

The potential pitfall of DI is that you need solid classroom management skills. If you can’t get the kids to sit still, respond on cue, and attend to the teacher for 20 minutes then you are completely sunk. These behaviors are challenging for students who are used to more constructivist lessons, but I believe that they can be taught.

One more point: I don’t think it is accurate to call DI “teacher-centered” instruction. I see the point, because the teacher is leading a class, but DI has a very high student response rate.

The students are reading sounds, words, and stories aloud. They spend more time talking than the teacher does. They respond individually and in the whole group. The teacher does provide immediate error correction and feedback, which could be considered “teacher-centered,” but the kids do most of the talking in a lesson.

I was also trained to avoid teacher-centered instruction, but I think that training sets up a false dichotomy between constructivist and direct instruction. Constructivist training taught me that students should be actively engaged and participating in the lesson. I liked DI precisely because it made that happen.

Many homeschoolers are familiar with Englemann’s book “Teach your Child to Read in 100 Easy Lessons” and/or the PC-Quicktime based computer system “Funnix”. Both of which work to teach even kids who “canâ€™t to sit still, respond on cue, and attend to the teacher for 20 minutes” without being ” completely sunk ” Of course when a homeschool kid spins in circles while staring at the ceiling during recitations or quizzes, it doesn’t disrupt any body else’s learning.

Since the lessons are so strictly scripted there is little “prep” or “lesson planning” needed. Which one might think would be popular with teachers.

70 to 80% of the time I do DI. My students don’t know enough about the math they should be perfect at in order to complete activities in the constructivist method.

For example: I wanted the students to findthe mass and volume of five selected metals and then plot that data on a mass vs. volume graph, find the slopes of the lines (find density of the metals) and then compare the order of the densities to the metal’s position of on the Periodic Table to show the trend of density of the elements.

The students ALL have taken Algebra I and II and Geometry with very good grades in all (I have all honors classes and in 11th or 12th grade).

They could not find the mass of the samples using electronic scales (didn’t know about the tare), or the volume of the metals (didn’t know about finding volume by diffence), could plot a graph on paper (they used graphing calculators), couldn’t find the % error from a provided equation, on and on. They couldn’t DO the constructivist method of ‘discovering’ the trend of the elements in the Periodic Table since they did not know how to do the math and science in the classes they already passed with wonderful grades!

When the University of Maryland science professors held a meeting with the science department heads in Prince George’s County this past fall, they told the science folks for my county that is was assumed that students from the county didn’t know anything about math or science.

I do DI almost all the time. I directly teach the lower level skil the students should have learned years before before I put the students in the lab. This is very slow-at first. Since we use math all the time in chemistry (ha! Who’d a thunk it!) the student start getting very good at these skills. They then start getting the point of the labs.

These students have been so abused academically by my county with constructivism. DI should be first and foremost. When basic skills are mastered then, and only then, can you put students in an environment to discover things using the tools they have.

I also use the DI programs to homeschool my son after school. I do think some teachers might need to read over scripts the day before to ensure they don’t add “errors” to what they teach. This is especially true if you are new to the DI program. It also helps the teacher be more fluent and natural with the script and possibly do some acting or help “punch it up.”

It is amazing how much time teachers get for prep. Imagine how much less time they would need to develop curriculum if it were already there.

And to add to matters, why don’t DI teachers develop their own curriculum with multimedia, scripts, and activities. It is now simple and possible with things like wikibooks.org where teachers can collaborate to design curriculum according to Zig’s DI rubric.

Anna and Miller (above) expressed the core of what my school uses in a DI model. Our version is actually called EDI – Explicit Direct Instruction. It includes a clear presentation at the beginning of each class period about what will be studied and learned that day. Then many short direct instruction moments followed by testing for understanding by randomly (considered very important) calling on students to answer questions about what was just taught.

Homework also , must only be on the topic taught that day, and only assigned if the teacher expects 80% correct completion of the assigned work from 80% of the students.

I’ll be honest, I don’t know how much other classes are strictly following the model. I think that for the introduction of new material it works really well provided… students are interested in the material to begin with. No method or teaching sequence on earth can convince a student that the material will actually be useful to them in the future unless they already believe that.

Still, I think that EDI (our direct instruction model) as benefited my moderately-interested students.

I hear a lot that teachers should like DI because it cuts down on lesson prep time, and I don’t really understand that argument. I enjoy my job. I like planning lessons. I don’t think I’d be much of a teacher if I didn’t.

That’s actually something I don’t like about DI — I miss using my brain and my creativity to figure out how to present material to my students. Like I said, I don’t enjoy teaching from a script. Sometimes it’s hard to feel like a professional when you are teaching out of a box and a consultant is guiding every vocal inflection you make.

A lot of resistance to DI from teachers comes from this. We like crafting lessons. We like having that responsibility. We are insulted when others assume that we’re so lazy we’d like a script, or so irresponsible and incompetent that we need a script. I try to convert other teachers to DI, but it’s often an uphill battle because of these issues.

I don’t mean any of this to take away from DI — like I said above, it works and I am a strong DI advocate. It’s just that it goes against the grain for most teachers, and takes away a lot of what they like about their jobs. I think that has a lot to do with why DI is unused despite being so successful. It doesn’t matter how wonderful your system is if its intended implementers resist using it.

Wouldnâ€™t this fall more into the traditional school model? English used to be a set of dictations and diagramming. Math was math facts. I mean you find something that works and duplicate, go for it. It appears that the experiences are good in some ways but donâ€™t seem to be a dependable teaching model.NerdMom – the instructional method being discussed is Direct Instruction (note initial capitals) – a particular form of teacher-centered teaching. The traditional school model failed a large proportion of students. Direct Instruction includes, amongst other things, careful presentation of material so that kids know the earlier material they need to understand later stuff, continual checking by the teacher to see if kids are making any errors, and plans for corrections if they are.

It also includes a lot of teacher training and monitoring of performance so as to make it a dependable teaching model – unilke traditional school models.

When I began teaching, I used to carpool with a veteran math teacher. She told me how education theory and philosophy was subject to trends and that such trends were fueled, in part, by the bordome of teachers and the financial ambitions of educational consultants and pretty much everyone else who draws a school district paycheck without actually teaching students. Like the auto and computer industries, they rely on planned obsolescence for their livelihoods.

Now, fifteen years later, it does seem that the traditional method of instruction has become the radical new idea.

Direct instruction can be — and always has potentially been — a powerful tool. I think the best at it are teachers with strong personalities, charisma and articulateness, quick on their feet, passionate and with at least some sense of humor.

Teaching students through discovery can also be powerful but in order to be so takes an awful lot of planning. You have to really know and understand your students and plan accordingly and sometimes be a bit overbearing to ensure the discovery really happens.

The idea that some method of delivering instruction is good or bad, in or out, is mercenary and born of ignorance. Good teachers find a way. They try things out. They listen to and observe their students and are open to anything and everything.

Think of Miles Davis or the Beatles — how many different approaches they took to creating music.

We too ought to see ourselves as artists. The great ones never worry that they are or are not in fashion.

Although my primary focus is currently on WHAT we teach rather than HOW, I must strongly endorse Mr. Strauss’ reasoned and thoughtful comments. Good teachers have always blended successful methods of the past with the best of what is currently known about the different ways that children learn. No single style can possibly meet the needs of our more and more diverse learners we encounter every day. There ssems to be considerable confusion about the technical meaning of DI as developed by Mr. Engelmann. One would need to thoroughly study his rationale and approach to make an informed judgment and I suspect many are responding to the ‘label’ rather than its substance just as many react to ‘discovery learning’ as if it is a method to be used all the time. Effective math leasson I’ve observed for the past 10 years included the essential components of instructional/learning theory:

1. Motivated the lesson (a ‘hook’)

2. Articulation of the objectives of the lesson (what students will know and/or be able to do at the end of the lesson) – this must be carefully thought out during planning and conveyed clearly.

2. Connected current learning to prior learning

3. Reviewed the necessary prerequisite skills for success

4. Provided clear explanations both orally and in writing (on board, on handout or in an electronic presentation)

5. Maximized student involvement via questioning, promoting of dialogue or an activity

6. Assessed what was actually learned (e.g.,responses to questions or requiring students to complete a specific task).

When you remove all the labels, Joanne, it comes down to this: How do we know that the objectives of the lesson were achieved? When I am transmitting parcels of information directly to students, I am still engaging their minds by asking many many questions of different taxonomies to check for their understanding as well as checking if they are still conscious! When I propose a challenging problem and give them a few minutes to work on it in small groups, I am still monitoring their progress carefully and asking guiding questions.

If DI includes all of rhese components and allows children to explore at times and tackle unstructured open-ended questions for which there is no clear blueprint for solution, then I applaud DI and I guess I’ve been using it all along. If ‘Discovery Learning’ includes all of these components, then I guess I’ve been using it all along and I applaud that too.

Again, as Larry so ably expressed it, good teachers FIND A WAY that works for most of their students most of the time. There will always be some in the class who are not able to grasp the material for a myriad of reasons, often having nothing to do with the child’s ability. Rather than continue this general debate, perhpas we should be looking at REAL examples of effective teaching and then we can applaud these efforts and use them as models for the rest of us, rather than debate the category into which the lesson falls. Oh well, this will never happen, because real examples and pictures would obviate all of the rhetoric and we’d have nothing to blog about!

Again, as Larry so ably expressed it, good teachers FIND A WAY that works for most of their students most of the time.The evidence does not bear out that this eclectic or “techer knows best” result is working or has ever worked. There are simply too many children who have not and are not learning what they are expected to learn.

Rather than continue this general debate, perhaps we should be looking at REAL examples of effective teaching and then we can applaud these efforts and use them as models for the rest of us, rather than debate the category into which the lesson falls.I think you misread the question. DI (as opposed to di) is a curriculum, not a general category, and it is a real example of effecting pedagogy.

I think the confusion on the part of many commentors and bloggers shows how little is known of DI.

KDeRosa writes: The evidence does not bear out that this eclectic or â€œtecher knows bestâ€ result is working or has ever worked. There are simply too many children who have not and are not learning what they are expected to learn.

You have a point. Teacher autonomy can be disasterous. I work in South Central Los Angeles where, if you can keep the kids in your room and keep them from harming each other then you are considered a good teacher. I’ve seen teachers use their autonomy to do great things with great results (how about a 30% increase in test scores in a single year!) and I’ve seen other teachers babysit students, turn their classrooms into pulpits for miseducation.

Direct Instruction (as opposed to direct instruction), attempts to mitigate — as do all prescribed curricula and, for that matter, state standards — the wide disparity in effectiveness among teachers.

But at what expense?

The National Institute for Direct Instruction suggests paying for its product with instructional materials funds. That means less money for actual instructional materials for teachers. It also requires teachers to be out of their classrooms, away from their students, for trainings. It might be worthwhile to do that for teachers who are not already effective in their classrooms but leave the rest of us alone, please….

The National Institute for Direct Instruction suggests paying for its product with instructional materials funds. That means less money for actual instructional materials for teachers.The NIFDI implements whole school interventions. The curriculum it uses, however, is commercially available like any other curricula. I don’t see how substituting one set of books for another amounts to “less money for actual instructional materials for teachers.” In the end the teachers are teaching from a curriculum just as they were before.

It also requires teachers to be out of their classrooms, away from their students, for trainings.I think that most of this is done before the school year starts and during in-service days. This seems to be par for the course when changing curricula.

It might be worthwhile to do that for teachers who are not already effective in their classrooms but leave the rest of us alone, pleaseâ€¦.Again, the evidence bears out that the number of effective teachers teaching lower performers is an exceedingly small. I do agree, however, that there is no need to change what effective teachers are already doing if the student performance bears this out.

Larry – I agree that shoving something down the throats of teachers is not effective. I would suggest having states split their schools so there are typical developmental/discovery school and also the traditional and/or DI type schools that teachers AND parents can pick from.

Anna – DI allows a teacher to do MORE for science, additional reading, and supplementary activities. If your teaching is more effective, then the students have MORE time to apply concepts through teacher created activities. Not sure if my theory makes sense to you.

I’ve been working on some open source curriculum and it is really, really difficult and time consuming. I hate to have to do this for each subject for even a kindergarten class. If you apply the principles of DI (http://directinstruction.org/wiki/index.php/Direct_Instruction_Approach_Specifications) then you have a lot of work to get even a simple Kinder science program out the door:

http://directinstruction.org/wiki/index.php/Free_Direct_Instruction_Science_K

I would rather have a good outline to work off then spend my time supplementing by designing activities.

Just my 2 cents.

Thanks for pointing all that out, KDeRosa.

And forgive my assumption that Direct Instruction was a methodology and not an entire curriculum, materials included.

I suppose it addresses the needs of English language learners, gifted students, and students with learning disabilities.

You said that “the evidence bears out that the number of effective teachers teaching lower performers is exceedintly small.” (That’s depressing).

How small is that?

And to what evidence are you referring?

And does this data include high schools?

I’m really curious.

To KDeRosa:

I do not claim to have any expertise in DI.

However, I have probably been observing effective math lessons for 3 decades and, I beg to differ with you, good teachers usually do find a way to help children learn. Their lessons are highly organized, well-planned and practice both the ART and SCIENCE of pedagogy. I suspect that many commenter and ‘experts’ out there fail to recognize these two attributes of great teaching. The focus of many commenters is on the failures of teachers to teach effectively. This is demeaning to the majority of quality educators out there who somehow help most children learn to read and develop math skills despite many obstacles, not the least of which is the endless supply of new ‘designer’ curricula and methodologies that might currently be in vogue.

I also didn’t read any reactions to the components of an effective math (or any other content) lesson. I would like to read or see models of effective lessons that do NOT incorporate many of these basic components. I contend that lessons that reflect these will be effective, ie., students will learn, regardless of any other methodology.

I will certainly make it a point to become more knowledgeable about the curriculum and pedagogy of DI before attampting to characterize it further.

“Their lessons are highly organized, well-planned and practice both the ART and SCIENCE of pedagogy.”

I’m sorry, but the “ART and SCIENCE of pedagogy” does not make sense. A pedagogy is a method of teaching. Two examples are Direct Instruction and Discovery Learning. Those two are opposites. Are you saying neither is right and an eclectic method is better?

I may have missed it but it seems to me you either directly teach concept FIRST then apply the principles in an activity

OR

You have students try to figure out the concepts while you are “guide on the side”

2 VERY different ways of teaching.

I suppose it addresses the needs of English language learners, gifted students, and students with learning disabilities.The only difference between learning disabled students and gifted students is the pace they can proceed through the curriculum. Otherewise, the instruction is identical.

ELL kids are a special consideration. But bear in mind that many low-performing ELL kids know so littlelanguage concepts in their native language that teaching them is English from day one does not present a problem.

How small is that? And to what evidence are you referring? And does this data include high schools?I don’t have a precise number but if you know that your typical title I school performs at the 20th percentile you see that almost no students are performing at grade level in these schools. yet soem exceptional teachers do exist; hopefully, they’ll chime in.

This is not to say that there aren’t lots of good teachers out there. There are. Just that it’s difficult to be an effective teacher in the absence of administartive support.

Dave:

The focus of many commenters is on the failures of teachers to teach effectively. This is demeaning to the majority of quality educators out there who somehow help most children learn to read and develop math skills despite many obstacles, not the least of which is the endless supply of new â€˜designerâ€™ curricula and methodologies that might currently be in vogue.29% of school students are failing to meet the basic level of reading in grade 8 as measured by the NAEP. Source http://nces.ed.gov/nationsreportcard/pdf/main2005/2006451.pdf (figure 12)

32% of school students are failing to meet the basic level of mathematics in grade 8, as measured by the NAEP. Source http://nces.ed.gov/nationsreportcard/pdf/main2005/2006453.pdf (figure 12)

Clearly a lot of teachers are failing to help many children learn to read and develop reading skills. This is not good for those students.

Direct Instruction, thanks to Project Follow Through, has a strong evidence base that it can improve the performance of students. See http://psych.athabascau.ca/html/387/OpenModules/Engelmann/evidence.html This makes it unlike many fads.

I am impressed by your efforts to teach students learn to read and develop maths schools. I am puzzled however as to how you think you’d be demeaned if all teachers were provided with an effective curriculum and methods of teaching and if school districts were reformed so they supported you, rather than put obstacles in your way.

As for your points of an effective maths lesson, may I link to a sample DI maths lesson script at http://www.specialconnections.ku.edu/~specconn/page/instruction/di/pdf/math_sample_lesson_a.pdf

?

Effective math leasson Iâ€™ve observed for the past 10 years included the essential components of instructional/learning theory:1. Motivated the lesson (a â€˜hookâ€™)

This is the one point of difference I think. In DI, kids are motivated by specific praise for learning things. The curriculum is presented so they will learn things. Some kids may learn slower than other kids, but they’ll learn something. So the motivation is doing something you’re good at.

2. Articulation of the objectives of the lesson (what students will know and/or be able to do at the end of the lesson) – this must be carefully thought out during planning and conveyed clearly.The objectives are clearly articulated at the top of the lesson. During the lesson the objective of a new section (ie one that isn’t review) is conveyed to the students. For example, the start of Exercise 2 tells the teacher to tell the students that “You’re going to learn about units of weight.”

2. Connected current learning to prior learningYes, this is the essence of DI. For example, in the lesson on weights children are first asked to say how much they weigh.

3. Reviewed the necessary prerequisite skills for successYes, when material that has been covered before is being repeated before it is built on.

4. Provided clear explanations both orally and in writing (on board, on handout or in an electronic presentation)Yes, instructions are given both for what the teacher to say, and for what the teacher is to write on the board. Questions like “What’s 50 minus 10 are just given verbally.

The instructions have been tested to remove any ambiguities, on the basis of experimental evidence that if there are two ways to interpret an instruction some kids are going to pick the wrong interpretation.

5. Maximized student involvement via questioning, promoting of dialogue or an activityYes, from a quick read through counting sentences, at most the teacher only says 7 sentences before asking another question of the students or asking them to do an activity (and those 7 sentences were short ones explaining the rules of a game to the students, and that counted the one that said basically “lets go”)

6. Assessed what was actually learned (e.g.,responses to questions or requiring students to complete a specific task).Yes, students are continually being asked to give their answers (at the same time, so the teacher can tell the difference between students who don’t know and students who are just a bit slow in getting their thoughts together).

If an assessment indicates a problem, then that’s when a teacher needs to identify the source of the problem and fix it. This is where I think your list is a bit limited – surely it is important not just to assess what is actually learned, but if you find something that hasn’t been learned (and should have, in that lesson), then surely it’s vital to re-teach it until it is learned?

KDeRosa and Tracy W:

I’d like to believe that I’m open-minded and able to rethink a position in light of new information. The more I read about DI, the more I can appreciate its effectiveness, particularly with disadvantaghed children. Reading the sample lessons (thanks, Tracy)was eye-opening. The lessons were fast-paced, requiring excellent preparation on the part of the teacher, incrementally developed and incorporate spiraling. I can see the immediate error correction and feedback. I can certainly appreciate how this could lead to mastery of the content presented.

I can also appreciate why many educators and teacher groups might initially resist its scripted nature. My initial reaction was also negative because I didn’t fully appreciate the history of the program and, in particular, its original target audience.

One of the problems for me is that, although I have worked with K-8 teachers and students, my primary experience has been at the secondary level. Most of my observations have been from PreAlgebra through Calculus. Mr. Engelmann’s materials are K-6 oriented, I believe, so I need to learn much more about them before drawing conclusions. However, if one measure of a program is in the performance of children on standardized assessments, then DI needs to be taken very seriously.

The other issue for me is that I’ve also worked with many children (including some K-6 students) who are able to ‘connect the dots’ very rapidly and ask questions and make observations that are unexpected, i.e., ‘outside the box.’ Part of the ART of teaching for me (this is for Dickey45) is to be able to react instinctively to these ‘teachable moments’ rather than tell those students to see me after class for enrichment. Of course, DI might allow for this by moving these more capable children into a different group so they can work at a faster pace, but I’m not sure this addresses the need for DEPTH of learning or understanding.

Also Dickey 45: Blending (I don’t like the term eclectic) discovery and direct instruction is very possible! I do both in every lesson I teach. I often move from lecturing and direct transmission to providing a provocative problem for which there is no obvious solution and vice versa. There is no doubt that children who come to my class unequipped with the basic ‘tools’ require a much more structured approach but that doesn’t prevent me from asking them to think more deeply. I need to break it down in greater detail for these youngsters until they have enough repetition to draw a general conclusion but many do get there! (Read the anecdotal evidence I have been providing for these lessons on my blog).

Again, I need to understand more before evaluating DI materials, as if my opinion would make any difference anyway.

One thing is for certain. Those who believe in DI are truly DIsciples! I hope they will read my thoughts in the same open-minded way that I am trying to bring to this. In the end, we really all do care about children and their learning. That is our common ground!

I often hear that DI is not appropriate for some kids, like high performers. Here is Engelmann on the the results from Project Follow Through, the largest educational experiment in U.S. history:

Not only were we first in adjusted scores and first inpercentile scores for basic skills, cognitive skills, and perceptions children had of themselves, we were first in spelling, first with sites that had a Headstart preschool, first in sites that started in K, and first in sites that started in grade one. Our third-graders who went through only three years (grades 1-3) were, on average, over a year ahead of children in other models who went through four yearsâ€”grades K-3. We were first with Native Americans, first with non-English speakers, first in rural areas, first in urban areas, first with whites, first with blacks, first with the lowest disadvantaged children and first with high performers.

From The Outrage of Project Follow Through, chapter 5, p. 7

I’d also point out that there was a discovery model that took place in PFT, along with a whole language model, an open education modeland parental involvement model. In short, most of what is fashionable today was tested in PFT. And, all of these fashionable models performed worse that the control group.

thanks, Ken, for those detailed statistics…

Pls consider the following and give me your thoughts:

4th grade classroom, students have demonstrated mastery of basic multiplication facts and some conceptual understanding of multiplication as arrays and repeated addition.

On the board, the teacher writes a column of 15’s (there are ten in all)

15

15

15

…

15

——

She instructs students to find the sum mentally but not to raise their hands with any answers at that moment. After a minute, she directs students to discuss thier ideas in small groups of 3-4. She tells them to compare their results, not just the sum but HOW they did this. After 2 minutes, she leads a discussion, inviting students from each group to share their ideas. She comments and adds other ways, insuring that students see at least 4 methods. She asks, “Which method is easiest for you? Why?” etc… This does not take more than 15 minutes in all.

Ken, where is there room for this type of creativity and discussion in DI? I think there is value in this discussion because it may help many students deepen their conceptual understanding of place value, multiplication, etc. I do think some teachers would prefer to include some probing questions of this nature in addition to the materials prescribed by DI. I also believe that statistical results may not reveal how students would perform on these open-ended types of questions, which are not typical of NAEP or some other standardized assessments. I would be interested in seeing how children in a variety of settings would handle this type of question. Because of their strong knowledge base, DI students should do well but the proof would be in performance. There seems to be a feeling among many experts that younger children are not capable of much abstraction or higher forms of conceptualization. When I was a K-5 math staff developer, I saw they were, provided they were routinely exposed to these kinds of questions along with mastery of facts. As always, I look for a ‘balanced’ solution, a statement that incites some to riot! Again, my understanding and appreciation of DI is evolving. I can see why many are impressed. I can also understand why some established programs would be unhappy with DI’s outstanding results in PFT. Ken, I’m just not there yet when it comes to the need to improvise or respond to the individual needs of certain types of learners. Your comment regarding high achievers dosn’t dispel my doubts. Basically, your response was, “Look at the stats for all learners!” I’m looking for more. I’ve worked with high achievers and I know they need to experience some non-routine thinking and be encouraged to probe and go deeper. Perhaps the answer is that DI works for most but other options can be offered as well.

Dave Marain

Dave,

I do not believe that exercises like these represent a good educational bang for the buck. If you were to spend only 15 minutes per class enagaged in exercises like this you would be spending about a quarter of your instructional time on these kind of activities. High perrformers can spare such time, but I do not think that average and low perfomers have such a large amount of time to spare. Even assuming that they do, is this a good use of instructional time? For the student that knows how to translate the coulumn of numbers into the math problem 15 x 10 and knows the skills to solve such a problem — this activity is trivial and a waste of 14 minues and 50 seconds. For the student that does not know how to do this, the question I have is “why not?” if these skills have been previously taught. For this student, I do not believe this is an efficient way to teach these skills at this point. Moreover, I do not think that engaging in such an exercise represents an exercise in student creativity any more than having students solve word problems. But that’s just my opinion.

In any event, the DI math curriculum offers optional group activities that are similar to this activity. So to the extent that such activities represents “balance” there you go.

The DI math curriculum is not geared so that the students pass standardizrd tests. The curriculum is geared to teaching students the skills they need to succeed in algebra. In this respect, all of the problems presented in the curriculum are of the “do it” open ended variety. If you want to get a good idea what the end product of the DI curriculum is, here is the fifth grade posttest. A student who has been through the DI curriculum should be able to complete this test with at least an 80% accuracy rate. High performers should be able to get to this levelby the third of fourth grade grade. Many eighth graders would not do well on a test of this rigor and, not unsurprisingly, many eighth graders fail to learn algebra because they never learned the skills that the DI students are capable of learning by the fifth grade.

Being able to pass a test like this requires a high degree

ken–

More ‘bang for your buck’ is an expression that would definitely ring true for central school administrators and board members who often relate to the ‘business model’ of education and for whom the ‘bottom line’ is maximizing district scores at minimum cost to the taxpayers. From that perspective, adding a column of 15’s may be a ‘waste of time.’ From the perspective of math educators and mathematicians like Liping Ma who has called for a more ‘profound understanding of fundamental mathematics’ the following scenarios may not be:

One child who didn’t recognize 15 x 10 = 150, explained that she added up the 5’s to get 50, then moved her finger to the next column and counted on by 10’s: 60-70-80-90-…-150. Ken, you might argue that’s the result of not learning her skills well enough and you may be right. A different view is that she demonstrated an understanding of place value that many 4th graders do not have. Actually, I will never convince you of that! Another child for some reason, said that he counted by 15’s up to 75 and then doubled it to get 150. What an inefficient method and waste of time, right? Another student demonstrated his understanding of place value and emerging sense of the distributive property by explaining that ten 10’s = 100, ten 5’s = 50, then added the sums. Several students just visualized the standard algorithm in their minds, getting 50 in the one’s column, pictured writing the zero and carrying the five to the next column, counting 5-6-7-8…-15.

About 7 of the 20 students mutliplied 15 x 10. Guess that class wasn’t trained properly, right? I do not believe in having these kinds of dialogues every day for 15 minutes! I do believe that when students see other ways of approaching a question, their understanding deepens. Certainly, some children will be confused by being shown alternate methods and these students need to be shown one straightforward approach in the clearest possible manner. But this is not true for all students. Let me share a dialogue I had with one of the SAT students I taught last night. Won has been in this country for about a year and he is clearly an outstanding problem-solver with very strong skills (and he expresses himself in English surprisingly well). After reviewing a challenging problem asking for the least value of y satisfying some inequality involving 2 variables, Won raised his hand and showed us a much simpler method: “Just make x and y equal”, etc… I asked Won if his teachers in Seoul allow students to discuss different ways of solving a problem and he just smiled at me and said, “No, they tell us how to do it.” Guess that supports a more direct model, right? I asked Won how he felt about following the teacher’s method and he replied, “Oh, I usually did it my way anyway and he only checked my final answer, so it was ok.” Is Won merely the exception to the rule and he’ll learn math despite the methodology. Let me guess what you might say!

One of my daughters who is a regular and special education elementary teacher told me that several years ago she taught from a scripted program for reading and spelling for a special population of children. She expressed that these children absolutely learned with this program provided the teacher strictly adhered to it. She felt confined by it but recognized its value. However, she noticed htat some children soon became bored and were able to move at a faster pace but that she couldn’t simply give them more advanced materials to work on their own nor could she move this subgroup to another class. Yes, Ken, this is an implementation problem, but probably not uncommon. Here’s how she put it to me: Dad, for children who come to us one or more years behind, this type of program helps them to catch up and that’s really good. She also said that many children may only be able to learn in this kind of structured environment, but she did not feel that it was appropriate for other children and, in fact, she thought that one of her goals was to prepare her students to move into the ‘mainstream.’ Just one point of view.

No matter how I argue my points, I know you will have a counter-argument because of your intimate knowledge of DI and because you have seen it work. I can’t argue those results. But statistics often don’t tell the whole story and everyone knows how we can prove almost anything we want by by how we present the data and by the assessments we use. I looked at the 5th grade posttest and, while I was impressed with some of the required skills, I saw questions that used some models and terminology that are non-standard and inherent to the program. I also did not see too many questions that got at assessing conceptual understanding or applying the skills in other contexts. I may not have seen enough to form a real judgment however.

In the end, there is probably room for more than one approach. HOWEVER, AS I’VE STATED REPEATEDLY, THERE ISN’T ROOM FOR DIFFERENT ESSENTIAL CONTENT IN MATHEMATICS. THE CORE MUST BE STANDARD.

Let’s talk about profound understand, Dave

I think we all agree that this is the desired goal of education. Where we disagree is in the means of achieveing it. I would argue that doing well on a well designed standardized test may not be a valid indicator that a student has PU (thestudent may or maynot have PU, we don’t know), but I do think that a student’s inabilitgy to do well on such a test is a good indicator that a student does not possess PU. So, simple standardized tests tell me that many students lack PU and have failed to get over the initial hurdle. I also know that DI students are more likely to pass this initial hurdle.

Another problem I have is the automatic assumption that activities like the activity you described somehow build PU. I do not think there is evidence suggesting that this is the case. On the flip side, I disagree with the implicit suggestion that DI does not build PU. The common misunderstanding is that DI teaches by rote of purely procedurally. This is not true. Teaching by rote is inefficient. The object of DI is to teach so that students can generalize from what they are taught and apply taught knowledge to new situations. The ability to egneralize leads to PU.

Also, altenate methods are taught in DI. Foe example, in addition to the typical procedure for subtracting by nine, the student is taught that subtracting by nine can also be accomplished by subtracting by ten and then adding one.

she did not feel that it was appropriate for other children and, in fact, she thought that one of her goals was to prepare her students to move into the â€˜mainstream.â€™Not all scripted programs are good. And remember, the only reason the script is there is to ge the teacher up to speed as quickly as possible. This statement may be accurate as it pertains to the progema your daughter is teaching, but it is not accurate as it pertains to DI. The reseaarch shows that high performing children perform better in DI programs even more so than low performers. The point is that all children benefit from clear effective instruction.

In the end, there is probably room for more than one approach.I don’t disagree. But it is my opinion that these altenate approaches should be held to the performance standards set by DI.

Ultimately, a student will have more room to exercise his creativity if he has a large skill set at his disposal. Presently, it appears that DI reliably confers the largest skill set in the quickest amount of time. instead of diluting the model with something that is not as effective, wouldn’t it be better to use DI to give the kids a good skill set and then proceed into algebra and geometry and have them exercise their creativity there? Just my two cents.

“4th grade classroom, students have demonstrated mastery of basic multiplication facts and some conceptual understanding of multiplication as arrays and repeated addition.

On the board, the teacher writes a column of 15â€™s (there are ten in all)

15

15

15

â€¦

15

â€”â€”

She instructs students to find the sum mentally but not to raise their hands with any answers at that moment. After a minute, she directs students to discuss thier ideas in small groups of 3-4. She tells them to compare their results, not just the sum but HOW they did this. After 2 minutes, she leads a discussion, inviting students from each group to share their ideas. She comments and adds other ways, insuring that students see at least 4 methods. She asks, â€œWhich method is easiest for you? Why?â€ etcâ€¦ This does not take more than 15 minutes in all.”

The way it really works:

4th grade classroom, students have demonstrated mastery of basic multiplication facts and some conceptual understanding of multiplication as arrays and repeated addition.

On the board, the teacher writes a column of 15â€™s (there are ten in all)

15

15

15

â€¦

15

â€”â€”

She instructs students to find the sum mentally but not to raise their hands with any answers at that moment. Most of the students breath a sigh of relief, because they have no idea of the answer. After a minute, she directs students to discuss thier ideas in small groups of 3-4. She tells them to compare their results, not just the sum but HOW they did this. The kids form groups and immediately start goofing around. Luckily most of the groups end up with at least one kid who can figure out the problem because their parents tutor them at home.

After 2 minutes, she leads a discussion, inviting students from each group to share their ideas. No one answers at first, but she calls on a kid anyway. He mumbles something about doing it in his heaad. She comments and adds other ways, insuring that students see at least 4 methods. The students furiously copy what she is doing on the board, but not quite sure what she is talking about. She asks, â€œWhich method is easiest for you? Why?â€ etcâ€¦ This does not take more than 15 minutes in all. Most of the kids didn’t quite understand the lesson, but thats ok… they will spiral through the curriculum and hit it up several more times over the next year. Eventually 50% of the kids will master the concept.

Meanwhile over in Sir Zigs class across town. Zig has demonstrated to his students that that if you have the same list of numbers, you can count up how many numbers there are and its the same as a multiplication problem. The kids quickly calculate 10 x 15 and shout out the answer. Zig gives them several other simular problems, to test their mastery. After 5 minutes, he is sure that they understand. All the kids seem to get it, and he compliments them on how smart they are. It seems like they can spit out the answer almost as fast as he can write problems. This has not taken more 15 minutes. Now that 100% of the kids have mastered this concept, he can move on to something else. He makes a mental note to revisit this concept tomorrow morning, to reinforce it. Eventually, 90+% of his kids will go on to pass the state proficiency exam.

More â€˜bang for your buckâ€™ is an expression that would definitely ring true for central school administrators and board members who often relate to the â€˜business modelâ€™ of education and for whom the â€˜bottom lineâ€™ is maximizing district scores at minimum cost to the taxpayers.In my district we have

noadministrators who believe in using time efficiently.Not one.

The need to respect children’s time, the reality that childhood is brief, is never mentioned.

I’ve been copied on emails written by administrators saying, “Having students rush through curricula isn’t a priority for me.”

There it is in black and white.

“Isn’t a priority.”

Maybe high-scoring districts are different. However, I haven’t seen or heard such views applied to kids scoring 1s and 2s on the state tests, either.

My 7th grader, who needs instruction in punctuation – punctuation! in 7th grade! – just made a collage for his ELA class.

And he’s got one of the best teachers, a teacher who also teaches the SPED kids.

Rory,

Don’t you realize that if that’s “the way it really works,” you are at fault. You obviously have failed at classroom management; you haven’t maintained “clear and consistent expectations.” If you had, the kids would be involved in spirited and productive discussions.

What? That’s unrealistic? How negative. You probably tell your students they can’t all play professional ball, too.

Wow, that was amazing reading, Rory. Unfortunately not in a usual sense of that word. You seem to have a very low opinion of your students, and I feel sorry for them. Here is Roger’s comment again, maybe it’ll make you think:

Donâ€™t you realize that if thatâ€™s â€œthe way it really works,â€ you are at fault. You obviously have failed at classroom management; you havenâ€™t maintained â€œclear and consistent expectations.â€ If you had, the kids would be involved in spirited and productive discussions.