A word about fractions

This story begins with a tweet that I read.

This tweet poses a nice engaging situation where addition of fractions would be a very useful tools. But, addition of fractions involves common denominators. And, then I began to remember my students attitudes toward fractions, which can be summed up by the following…


… clearly fractions are so difficult that it requires someone with the reputation of Chuck Norris to be able to deal with them effectively.

Except, they aren’t. Or maybe they are, but they certainly don’t need to be. The logic that says that 2 min + 31 sec doesn’t equal 33 of anything is perfectly understandable to most. It’s the exact same premise as requiring common denominators to complete a fraction addition problem. And THAT is confounding to many. It seems like an arbitrary rule that math teachers invented to trick students.

And the teaching of it carries with it some strong opinions, too. I remember during my undergrad, one of my professors asked this:


One of my classmates changed his major that day. He got so angry that it we would be discussing the possibility that a student could write that equation and could be thinking something mathematically accurate. Dude literally stormed out of class and I never saw him again.

It is possible, by the way:

About the same time I was reading the IES Practice Guide for teaching Fractions. Are you familiar with the IES Practice Guides for mathematics? The Institute for Educational Studies gathers high quality research studies on educational and catalogs them in the What Works Clearinghouse.

The Practice Guides are documents that synthesize the multiple research studies that exists on a certain subject and operationalize the findings. Recently, I explored the IES Practice Guide for Fraction Instruction K-8.

I’d encourage you to check it out. To summarize, making fractions and conversations about portioning and sharing things a common part of math conversation from the beginning can help take the natural understanding that kids have and build fractions into that context. That will give us a chance to use math talk as a tool for students to need more exact language. My preschool son right now uses “half” extremely loosely at the moment. (I’ve drank “half” my water could really mean anything quantitatively.) In order for him to effectively communicate, he’s going to need to develop a more precise definition of “half”. That will require him adding additional fraction vocab to his toolbox.

As teachers, this gives us a chance to build in some more effective language, clearly defining the fractions as numbers. As such, encouraging a lot of conceptual sense-making about the different operational quirks that are required to effectively compute when fractions are involved. (If fractions aren’t numbers, but instead are just made-up, goofy ways of writing numbers, then the rules for computing them are goofy and made-up, too.)

The practice guide provides some tangible steps to achieve this. I’d encourage you to check it out. Lots of steps forward to take in the area of student comfort and effectiveness with fractions.

Zooming In, Zooming Out: On Education Research (and Religion)


U.S. Navy photo by Chief Photographer’s Mate Chris Desmond. (RELEASED)

Feedback. Various researchers have stated that effective feedback should be of the “what’s next?” variety. Good feedback helps people see “what’s next?”

But what if the feedback is corrective? Is the revision of the previous attempt implicitly the “what’s next”? What if it wasn’t implicit? What if the teacher explicitly told the student to revise? Then does it become better feedback? What if the feedback isn’t directly related to the content, but instead the organization of their work? Does that reduce the quality of the feedback since the correction is toward a non-content goal?

What if? What about that? How about this?

These have been the conversations in which I’ve found myself several times over the last few weeks. My mind has been racing. Not only to understand the intense scrutiny with which we are examining teacher moves, but also to convince myself that these types of conversations are valuable.

Lines of questioning like I mentioned above are like zooming really far in on a certain single aspect of teaching and for a moment exploring it in isolation. Treating it like it is the only factor that matters in order to understand that one thing completely. As though, for a moment, all that mattered was good feedback. Or formative assessment. Or opportunities to respond.

The fact is that these different aspect of teaching and learning don’t exist in isolation. That’s one of the unrelenting truths of the classroom. Opportunities to respond and feedback depend on the quality of the classroom management. Good feedback depends, at least partly, on effective working relationships with students. And good formative assessment is quite dependent on the skill of assessment writing.

So, does the essential interconnectedness of these different elements of good instruction mean that we shouldn’t separate them out and examine each one? Well, not so fast. It’s true that lines of questioning like that can go on for a long time and in the end, we’ve created some pretty well-defined boundaries around things like feedback, or formative assessment, or opportunities to respond. But, I think we need to suspend our disbelief for a moment to understand that these types of conversations ARE important.

I repeat: These conversations are important to have and I believe more practitioners should be having them. There are a variety of terms that we use as educators that are common AND really poorly defined. Feedback is an excellent example, but also terms like “mastery”, “high standards”, even words like “compassion” get used with widely different understandings and thus widely different corresponding behaviors.

But these are words that have meanings and corresponding behaviors that will improve students’ lives and school experiences when done properly (and will have limited effects when done poorly.) There isn’t always an A-for-effort when it comes to teacher moves. “I tried to give good feedback” is noble, but “I gave good feedback” is more effective for student learning. And switching from the former to the latter will require locking down what effective feedback is and what it is not. This is true for any number of teacher moves from instruction to assessment to classroom management to communication.

But we can’t stay zoomed in. I credit a colleague for saying, “Education research is about constantly zooming in and then zooming out. Getting narrow and then widening your view. You work to create definitions, then you zoom out to see those definitions in context.”

This discussion isn’t entirely different from the back-and-forth required to become effective practioners of most religions. Most of the religions that I am even surface-level familiar with have this same back-and-forth between the experiential, spiritual, the perhaps undefinable side with the clinical, dogmatic and well-defined side.

For example, some religions practice fasting from food and drink for different times of the year. Further, some fast from meat and dairy on the ground that for a given time, they shouldn’t eat “animal products.”

What about eggs? Eggs aren’t meat or dairy, but they are clearly an animal product.

What about fish? Depends on how you define “meat.”

What about honey? Are bees animals? Is honey a “product” of that animal?

What about soy milk? It’s not an animal product, but it’s feels kinda like cheating. Is the goal to make do without milk? Or simply to not consume the animal product?

And when should do children start this? Should infants suspend nursing during the fasts because it’s milk? Or are infants exempt? If infants are exempt, what about their mothers who are needing to keep their diet somewhat consistent to stay well-nourished to feed their infants? When would the religious leaders guide the parents to start having the children begin fasting?

See? It all gets very clinical quite quickly. By asking such questions, we’ve allowed ourselves to zoom all the way into the nitty gritty details about this one aspect of the spiritual experience. And quite frankly, that’s okay as long as we remember that the  clinical exists to enable us to serve the bigger picture better. The point of fasting (at least as far as I’ve understood it) is to be able to pray better. That’s what we see when we zoom back out.

And being willing to help practitioners dig through the nitty-gritty can be a way to honor the sincerity of their devotion. They want to do the very best job they can and they have questions. That’s okay. It’s okay if they want to zoom in and examine the different elements of the work they are trying to do. We should encourage them to do that inasmuch as it is providing effective supports to their efforts toward the bigger-picture goals.

And this brings us back to the classroom. Classroom teachers should be encouraged to zoom in on the finer details of their work, too. The zooming in provides definitions and supports techniques. The zooming out provides context. Zooming in is where the fine-tuning occurs. Zooming out is where we learn how those updated practices look amidst the sea of other factors. Do we really have time? What will that activity look like the way my desks are configured? When will I be able to provide feedback to the second and third step of the project for each group?

It takes both. Neither is good enough on their own. They aren’t enemies, but rather they complement one another. And when we gain an appreciation of the place, value, and role of the zoom-in and the zoom-out, then we can start to use them both to make our work better and better.

The EdTech Conundrum

Imagine you were the CEO of a brand new EdTech start up with a brand new device that was ready to revolutionize education. (Or at least so your marketing team would have us believe.)

You unrolled your plan to get your device into the hands of students and put it into action. So, here’s my first question. What are your indicators of success? Profit? Devices sold? Number of districts implementing your device? Number of teachers implementing your device? These all seem fairly reasonable.

Do you know what almost certainly wouldn’t be one of your indicators of success? The degree to which your device is improving student outcomes.

So, let’s bring in an article: Education Week’s Popularity of Ed Tech Not Necessarily Linked To Product’s Impact. In which author Benjamin Herold builds a case that there is a fundamental conflict between the traits of Ed Tech that best sell and the traits of Ed Tech that best impact student achievement.

Among the traits that sold best, according to the article, “a promise of cost savings for schools, no requirements for face-to-face training, and an ability to be easily integrated into existing teaching and learning practices.” That is, light on financial commitment, light on PD, and light on classroom disruption.

It’s tough to argue with cost, but the latter two start to expose a weakness that are probably contributing directly to why these EdTech innovations aren’t having that much of an impact: They aren’t innovating. If you are integrating devices that don’t require educators to update what they do in the classroom, then don’t expect for any significant changes in learning outcomes.

The author, quoting Andrew Calkins, adds “Practitioners [in traditional schools] find it easier to adopt technology tools that readily fit within their existing models,” Calkins said. “That’s why tools and platforms that demand a lesser degree of disruption might have found greater purchase in the marketplace.”

It is easier, more comfortable, and less stressful on people and resources to integrate tools that integrate into existing school systems, traditions and practices. But this is fundamentally problematic in school communities where existing systems, traditions and practices had reached their capacity for student achievement. If the systems are working as well as they are going to work, then a tool that makes the system function better isn’t what’s needed. What’s needed is a new system.

And that’s a much tougher sell. And it probably explains why we continue to be somewhat disappointed with the way our technology is faring within our desire to improvement. This is why frameworks like SAMR serve such a valuable purpose. They provide structure and language to the act of transitioning from one educational paradigm to another. This highest level of SAMR doesn’t force a particular type of classroom action or behavior, but simply asks the educator to consider what is possible now that wasn’t possible before the technology was available.

And this becomes the ultimate value of the technology and it also explains why we’ve had such a difficult time having our hopes realized. Technology has the potential to fundamentally restructure the way our schools function. And unfortunately, we won’t see the value of some of these tools until we let them do just that.

If education REALLY needs a game-changer, then…

So, I got a “what-if”…

What if teachers only taught half their day?

Follow me down this rabbit trail for a minute. It started with a video. This one. Watch it if you haven’t already.

It’s kind of long, sorry about that.

So, technology isn’t a game-changer. That’s because it doesn’t change the game. It’s a different strategy to bring to the same game. Instructional technology is just that: INSTRUCTIONAL. You don’t change the game by changing INSTRUCTION.

You change the game by changing LEARNING. That’s where the revolution comes from. It’s fair to say that one definitely leads to the other and it certainly isn’t valuable to separate those two practically Siamese educational activities. Teaching and Learning.

So I began to ask myself, what produces high amounts of learning? Well, at the risk of oversimplifying: good teaching. And good teaching rests on foundation of good lesson-planning and good lesson design.

In fact, according to L. Dee Fink of the University of Oklahoma, “designing and managing an instructional event” is the “most crucial” quality in “ensuring whether or not students have a significant (rather than a boring or trite) learning experience”.

That having been said, take a look at The University of Michigan Center for Research on Teaching and Learning’s Guide for Effective Lesson Planning. Many seasoned teachers look at that list of super important items and chuckle to themselves at how no one in the teaching profession has time to put that kind of detail into their lessons.


We have created a situation where the people who have the most impact on the learning don’t have the ability to do the thing that research suggests will have the largest impact on the learning.

Well, what are they doing instead?

Well, here’s an infographic. (I’m not sure if infographics count as “citing research” or not, I’ll let that come out as critiques as my peers review my blog posts, but I think the point is well made.) In a typical work day, teachers spend the majority of their time instructing students, which might seem like a no-brainer except they have to teach them something. The typical processes include using instructional materials (which have to be chosen or designed) and giving assessments (which need to be chosen or designed, and then graded and returned with feedback.) Without those things, we don’t see learning. And learning is the goal.

Which means this super-important lesson design work, which has to be done for high amounts of learning to occur, is not given sufficient time within the typical teacher’s day. Most days it isn’t given ANY time in the teacher’s day. Or it is given time that is supplanting family time, relax time, or hobby time. That isn’t just me being sympathetic. Those things keep teachers from getting burned out.

So, you can’t really change the job of teaching. It is all of those things and not because we chose them to be.

But our culture doesn’t need teachers who lesson plan. It needs teachers who lesson plan WELL. It doesn’t need teachers who assess learning and give feedback. It needs teachers who assess learning WELL and give GOOD feedback. It doesn’t need teachers who reach out to reluctant learners. It needs teachers who reach out to reluctant learners PERSISTENTLY and EFFECTIVELY.

Those things take time. Time our teachers don’t have because of the way our education system requires its teachers to work.

So, enter my original “what-if”. What if teachers only taught half the day?

Secondary teachers would teach three classes. or elementary teachers would teach either the morning or the afternoon. Secondary folks might have 75-80 students instead of double that, in some cases.

Then, the other half of the day, they are collaborating, researching best practices, lesson planning, giving feedback, observing each other teach, making contact with parents. Young teachers could experience real mentorship. Teachers could really reflect and really collect, look at, and examine student data.

I know, I know, I know. Money, money, money. I understand that this plan isn’t a cheap one. I get that. I don’t think this plan is going to be the next one tried. But it is simple. It is elegant. And it probably would work. And if education needs a “game-changer”, then we need to think about ACTUALLY changing the game. This plan does that.

There are teachers out there doing amazing things right now. Imagine what those folks would do if you gave them that kind of time. They wouldn’t be amazing anymore. They might just be revolutionary.

Why I’m not THAT worried about the future of math education…

A New York Times article by Elizabeth Green has made its social media rounds lately. “Why Do Americans Stink At Math?” has been tweeted/shared a couple million times by now, with good reason.

It’s actually a really good article with some good story-telling and relevant history, and all the data and examples to back up the title. It’s worth a read. (It isn’t a quick read, mind you, but a good read.)

As far as I can tell, the thesis of the article is in the middle of the piece:

The new math of the ‘60s, the new new math of the ‘80s and today’s Common Core math all stem from the idea that the traditional way of teaching math simply does not work.”

The “traditional way” that Ms. Green speaks of is summed up a bit later in the piece.

Most American math classes follow the same pattern, a ritualistic series of steps so ingrained that one researcher termed it a cultural script. Some teachers call the pattern “I, We, You.” After checking homework, teachers announce the day’s topic, demonstrating a new procedure: “Today, I’m going to show you how to divide a three-digit number by a two-digit number” (I). Then they lead the class in trying out a sample problem: “Let’s try out the steps for 242 ÷ 16” (We). Finally they let students work through similar problems on their own, usually by silently making their way through a work sheet: “Keep your eyes on your own paper!” (You).

Green goes on to say that quite often teachers recognize the limitations of the traditional model, but have a hard time reforming it largely because of poor resources and ineffective training. From later in the piece:

Sometimes trainers offered patently bad information — failing to clarify, for example, that even though teachers were to elicit wrong answers from students, they still needed, eventually, to get to correct ones. Textbooks, too, barely changed, despite publishers’ claims to the contrary.

So, here we go. Sounds like a big problem, right?


I’m not that concerned. Ya know why?

First off, I don’t want to give the impression that I think that Green is writing untruths or is exaggerating. That isn’t where I’m taking this. American math education needs some serious work. But see, that’s where I get encouraged.

Let’s look at a specific bit of content. How about volume and surface area of prisms?

So, my textbook provides this:

Prism Clip

taken from Holt’s Geometry, 2009 Edition, Pg 684


These practice problems fit in with the “I, We, You” model that Ms. Green described in her article. Right on cue, the textbook appears to be pitching to our education system’s weaknesses.

But those weaknesses have entered a brave new world where teachers who have found models that work are not only willing, but also able to share them freely for anyone and everyone who might be looking.

For example:

Andrew Stadel’s “Filing Cabinent” is, by content standards, just another prism surface area problem. But, the situation he sets up is anything but ordinary.

Timon Piccini’s “Pop Box Design” asks a relatively simple question in a context that is approachable by practically everyone.

Dan Meyer’s “Dandy Candies” pushes the envelope on video quality, pushes the same content, and includes it in a blog post that discusses a competitor to “I, We, You.”

All those fantastic resources are available… for free. And the creators can be reached if you have a question about them.

A movement has begun. An (ever-growing) group of math teachers decided that it was one thing to discuss reforming math education and it was quite another to effectively reform math education. The group is getting larger. It’s inclusive. It’s welcoming. It’s free to join. And it doesn’t expect anything from those who join. Everyone does what they are able. Some share lots. Some steal lots. Some do both. The bank of resources is growing.

And this isn’t legislated reform. There is a genuine desire for this. I spoke in Grand Rapids, MI this past spring and was amazed that the crowd that was willing to gather to hear someone talk about reforming math education. Nearly 100 folks crammed into a room to have, what ended up being a rather lively, discussion about how to engage all learners, push all learners, and keep as many learners as possible interested in meaningful mathematical tasks.

2014-03-14 12.38.33

They had to turn people away from a talk on effective math lesson planning.

So, Ms. Green is certainly right. Americans stink at math. But there is a growing group of teachers who are aware of the problem, interested in seeing it solved, and now, more than ever, there are places they can turn to, people they can reach out to (and who are reaching out to them). And it is all available for free on technology that practically everyone already has.

So, forgive me, but I am quite optimistic about where this might take us.


Testing at the speed of… change.

I have a question:

Will the problems the public education system be solved by employing standards-based solutions like Common Core (or some other standard-based curriculum)?

This seems like an interesting question. A lot of follow-up questions would be needed.

1. What are public education’s problems?

2. What’s causing the problems?

3. What do we do about problems that aren’t solvable under current law?

4. Are certain standards-based solutions better than others?

5. What will education look like when all its problems are solved?


I don’t want to sound like a skeptic, but, here in Michigan, we’ve been at this for a while.

In Novemeber 2005, the National Governor’s Conference decided that high schools weren’t rigorous enough to prepare students “for an increasingly competitive global economy.” In Michigan, this led directly to the development of the Michigan Merit Curriculum.

The results weren’t good. By 2011, the state set the proficiency “cut scores” at 39% of the MEAP Test questions correct. (Got that? The Michigan Department of Education was cool writing a test, giving to every student in the state, and calling “proficient” any student who could get 40% of the test right.) This, of course, showed that 90% of 3rd graders were proficient in mathematics statewide. By 2012, when the cut score was raised to 65%, statewide proficiency dropped to closer to 40%.

So, after all this, apparently, the people of Michigan wanted Common Core. So, along with that, we passed some other laws to try to get Arne Duncan’s Race to the Top money (We failed, by the way. Then we failed again. Then we failed for a third time.)

After all that, we’d changed a number of laws, including approving the Common Core standards. However, a lot of those laws were designed to appeal to Arne Duncan and his several billion dollars, which never came.

So, we have a department of education that has approved Common Core. By January of 2012, the state was gearing up for the Smarter Balance Test. We even had school districts running trials and pilot testing situations (my district included), even as the state legislature determined that it didn’t have the funds to support Common Core.

Bear in mind, these changes had all come quite quickly. If this upcoming junior class (class of 2016) is to take the Smarter Balance Assessment, it would have done so after an education that included no standards (from kindergarten to 2nd grade), Michigan Merit Standards (3rd grade until 7th grade), and Common Core Standards (since 8th grade). Keeping in mind the implementation dip that is going to accompany the transition periods, it’s really any wonder why we have any expectations for this group beyond simply finishing the test.

And the speed of change wasn’t being lost on people. Common Core dissent is gaining publicity and some think that is makes for some pretty compelling television. So, Michigan is stuck having blazed a trail that isn’t exactly popular and isn’t exactly funded.

Moreover, in the past month, a new set of questions is brewing in Michigan: What test will those students be taking next year? The public pressure is mounting. Business leaders and education groups support it, but there is a lot of apprehension over the online nature of the test. (And Bill Gates suddenly isn’t a huge fan of high-stakes testing anyway.)

So, it looks like we’ll stick with MEAP another year, except we might steal some of the Smarter Balance questions. We currently don’t have a test written, or dates to plan on. The only certainty we have is that we can rest assured, there will be some test we will have to give.

I started teaching in 2006. This has been my experience for the entirety of my career. All of this flurry over which standards, which test, which questions. For what? People are yelling, negotiating, quitting their jobs over all of this. But we still don’t have an answer to the original question.

Will the problems the public education system be solved by employing standards-based solutions like Common Core (or some other standard-based curriculum)?

Oh, and don’t forget. We need to grow consensus on those five questions BEFORE we get to the original, bigger question. Here’s the problem. We aren’t prepared to try to build consensus on those five questions, at least not in the right way. Discussions like these require cooler heads. (Every been in a meeting when people start to get worked up? All progress stops until everyone calms down.)

Oh, and there’s these other questions that are going to come into play.

6. Should kids who fail to meet a proficiency standard move on with support and accommodations? or be held back to start the program all over again?

7. What are the academic grounds on which a student should be eligible to be a varsity athlete? What level of participation is acceptable if the student doesn’t meet all the standards?

8. What is the acceptable age at which a young person, or their family, should be able to freely opt a student out of the state’s preferred education program without penalty? What are the conditions on which an opt-out application is accepted?

All of these questions I have seen people yell and scream in disagreement with each other. Yelling. Over athletic eligibility and the disagreement over social promotion vs. retention.

Education is filled with passionate people. We don’t need any more passion. We need more wisdom. We need calmness. Patience.

I would love to see the State of Michigan (or any state) just stop all of this madness until it can issue a research-based negotiated document answering those 8 questions with rationales, just so that we know that those answers have been factored into any plan to move forward.

I hate to sound like a skeptic, but until we are prepared to clearly build consensus on those eight questions, all of our “fixes” are much more likely to make the problems worse, not better.


My (imaginary) conversation with a baseball sabermatrician

Baseball’s gets most of the benefits of a very talented group of statisticians. They spend their times trying to figure out the value that each action of a baseball player adds to their team’s chance of winning a game. Every possible action. In fact, ESPN just issued an article regarding the value of a catcher who frames pitches well.

So, I’ve been wondering why education can’t get in on a little bit of that action. A while back, I appealed to Sabermetricians hoping to get some of that talent to play for our team.

Today, through some Twitter conversation with school data aficionado Andrew Cox (@acox) I got an idea of what the conversation might look like if a Sabermatrician responded to my appeal.

We’ll call our statistician Timmy. I’ll play the part of Andrew.

Andrew: Thank you for calling. I have been looking forward to this conversation for a while now.

Timmy: It’s no problem. I’ll do whatever I can to help. But first, I need some information from you.

Andrew: Anything. Just name it.

Timmy: Well, I need to know the goal of the education system?

Andrew: The goal?

Timmy: Yeah, the goal. You know, like baseball’s goal is to win games. The most successful team is the team that wins the most games.

Andrew: Yeah, well, that sort of depends on who you talk to. This article lays out 11 goals (some more explicit than others). President Obama says this. Thomas Jefferson says this. These folks say we should teach entrepreneurship

Timmy: Well… okay. So, you’re saying that education as a whole doesn’t have an agreed upon goal?  Who makes the decision of what a school goal is?

Andrew: Well, school boards make a lot of decisions. Increasingly, it seems like legislators are getting a larger say.

Timmy: I see, well, Okay, okay. So, are schools doing anything to measure how strong the long-term retention is for it’s students?

Andrew: um… while I can’t speak for schools nationwide, I am not aware of any K-12 school districts that are doing anything to measure the long-term retention of the content.

Timmy: Well, that makes it tricky to figure out the practices that contribute to that.

Andrew: I agree.

Timmy: Well, okay. Goals might be tough to define. I understand. It’s a diverse system. What about the means?

Andrew: The means?

Timmy: Yeah, like, in baseball, the means of reaching your goal of winning is to maximize the runs you score and minimize the runs your opponent scores. So, what are the means of reaching the goals of the educational system?

Andrew: Yeah… the means.

Timmy: Yep.

Andrew: Well, it kind of depends on which goal the school has.

Timmy: I’m sorry, I know I come from the baseball field, but isn’t learning the goal?

Andrew: Yes, absolutely.

Timmy: So, what practices maximize that?

Andrew: Well, these people say effective use of formative assessment and differentiated instruction. These folks have all kinds of advice. Some of that advice matches these folks’ advice.

Timmy: Okay, there some things to work with there. Some of that’s teacher stuff. Some of that is student stuff. Some of that is parent stuff. Some of that is administrator stuff.

Andrew: Yup. That is pretty much true.

Timmy: How can you tell if those things are actually happening in a classroom or in a student’s home?

Andrew: That can be tricky business. Principals have a hard time get into the classrooms to support instructors. And you can’t really ask to do walkthroughs on students’ homes. 

Timmy: So, what data do you have?

Andrew: We have TONS of demographic data. We have attendance and behavioral data. We have test scores.

Timmy: I’m sorry, do you really need to contract me so that I can tell you that there is value added to a kid’s experience by showing up to school and not getting in trouble?

Andrew: No… no, we knew that one.

Timmy: One thing that helps baseball statisticians is that every play is recorded from at least 3 camera angles. So, why don’t you just put cameras in each classroom to get a real sense of what teachers and students are doing?

Andrew: Some think that would be usefulLawyers say that’s risky. 

Timmy: Well, Andrew. If you don’t have a goal, you can’t really isolate the means, and we can’t really observe any of the practitioners in any real detail, then what do you expect do get done with your statistics?


Doggone it, Timmy. That’s a great question.