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Finding the Statistical "Good" in Schools

On Education and Learning

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Ever have someone lump you into a group into which you didn't belong? Feels pretty bad, doesn't it? Why, then, do so many of us do this to the folks who educate our kids? This week, in our ongoing weekly series on education and learning, we'll be exploring some of the ways in which statistics can help us to not do this, along with some ways in which statistics can legitimately guide us in evaluating our kids' educations.

Statistical Accuracy in Different Sized Groups - Using the Onion of Emergence Personaity Theory

Chapter Nineteen

Personal "Statistics"

For weeks now, you've been hearing me rake statistics through the proverbial mud. Statistically based grade assessments; bad. Fractally based visual assessments; good. This week, however, we'll be doing the very opposite. We'll be looking at the good in statistics. And believe me, it's been there, all along. Right in front of our noses. Or at least, right in front of our eyes. Given, of course, you know where to find it. You see, this good exists only in certain situations. Primarily, those which involve big groups of numbers.

Why look for the good in statistics? Because I recently had a very compassionate conversation with a fellow who is a professional statistician. This fellow is warm, human, and sees the good in numbers. By his own admission, though, he's recently made what he sees as some pretty big mistakes in his personal life. Why? I think, because he used his professional knowledge of statistics to guide him in some very personal decisions. Rather than following his head and heart.

Does it sound like I am implying his mistake came from his not using his head and heart?

In truth, I am not saying this. At least, not entirely. What I am saying, then, is that he should have used both. He should have used both his knowledge of statistics and what he felt in his head and heart.

How can you do both though? Aren't statistics pretty much the opposite of human intuitions, as in, they're "cold hard facts"?

At times, yes, statistics can be cold hard facts. At other times though, like when we need to take our nation's temperature with regard to how well we're teaching our eight graders math, these numbers can stir up some pretty strong personal reactions.

Are you curious as to how we're doing? Not well. Thirty two percent of our eight graders, nationally, can't do basic eight grade levels of math. And only six percent of these kids achieve advanced levels of math (NCES Digest of Education Statistics, 2005).

Feeling anything? I sure am. Why? Because by eight grade, a full third of our kids probably hate math. And probably will for the rest of their lives. Translation. We're failing these kids. And failing ourselves. This based on our national statistical evaluations for the years 1990 through 2005.

Now what though? So maybe we're failing to get these kids to like math. Aren't some people just "bad at math?" Moreover, can we even trust what these numbers imply?

My opinion? Yes, we can trust these numbers. Moreover, we should trust these numbers. As well as what these numbers imply; that for all our advances in education, we are currently failing a full third of our kids in the area of math.

Now consider what this failure means. It means that a third of our kids will probably grow up to be poor money managers. Or at least, they'll probably hate doing things like balancing check books and budgeting for vacations. They'll also probably feel pretty bad about themselves for being like this. In fact, many will feel downright stupid, or angry, or ashamed. Or at the very least, be reluctant to be in situations wherein they may be asked to understand numbers. Like budgeting money with a spouse or colleague.

What other kinds of activities am I talking about?

  • Coaching a son or daughter with homework;
    ("You need to ask you mother to help you, son. You know I'm bad at math.")
  • Applying for mortgages or college loans;
    ("What does all that fine print mean, sir, and how long will we have to pay this?")
  • Enlisting the help of a financial advisor;
    ("How can we know he's not duping us? Maybe we should just wait to open a retirement account.")
  • Shopping for food and interpreting the sale prices;
    ("Why'd you buy this size, honey? You paid twice as much for the laundry detergent."
  • Evaluating fellow employee performance fairly;
    ("Ah, you know that guy is just a screw up. So what, his numbers say he's doing okay. You know how numbers lie.")
  • Discussing with your husband how much life insurance you need;
    ("Do we have to talk about this now. You know how I hate talking about money.")

Now stop.

And breathe.

Now consider what this implies.

It implies that failing to teach kids eight grade math will permanently affect their self worth. As well as their ability to see themselves as being as good as others who can do math.

It will also likely affect their desire to go on to college. As well as their willingness to seek advancement in their careers.

Aren't these conclusions too personally biased to be accurate though? I am, after all, emotionally involved.

Okay, yes. I admit it. My conclusions are personally biased. And I do feel emotionally involved. More to the point, though, I should be emotionally involved. Why? For one thing, because my feelings are a part of what drives me to write this weekly column; I feel personally invested in making a difference in how kids feel about learning. Including about math.

In addition, I see being openly honest as the basis for trust in personal relationships. Thus, if I want you to personally relate to me, I must be personally honest with you. Including about what may appear to be some statistically unsound opinions. And biases.

Admittedly, these opinions and biases are not enough though. I might, indeed, be too personally involved to make a clear decision. So how do I account for this possibility?

I research my personal feelings to see if statistics and I see eye to eye. And you know what? When it comes to teaching our kids math, we do agree. Being bad at math does affect people's overall feelings of being as good as others. This based on my personal research on math over the past two years. So much for the common wisdom that emotionally charged personal feelings have no place in research.

Now for the killer idea.

From what I've just told you, we know we are failing to teach a full third of our kids normal everyday math. Moreover, I feel confident these statistics accurately reflect the problem. The thing is though, these statistics are based on something I've been railing against for weeks now. They're based on the very same test grades I say may injury our kids' love of learning.

Doesn't this mean that I'm now contradicting myself as to whether we should rely on grades to measure our kids progress in school?

Not really.

Are you curious as to why? Let's see.

Statistics vs Real Life

Despite what people say about how statistics can lie, most people believe statistics to be true. And trust them. At least, initially.

That this happens has always felt a bit unnerving to me.

Yet these same people, when asked whether they think statistics distort the truth, will readily admit, this, too, is possible. And quite probable, in fact. At least, most people will say this. At least, some of the time.

So the fact is, people both do, and don't, trust statistics.

What interests me here is the order in which these two experiences occur. Do, first. Don't, second. Which means, this order may be one of the things which biases us away from hiring new teachers; those with no known track record.

What I mean is, can you imagine hiring a teacher who has no statistical evidence for that they can successfully teach? Remember, we first trust stats then personally question them in hindsight.

So what makes us do this? And what are "statistics" anyway?

My answer. Statistics are numeric representations of life created in order to uncover patterns we normally do not see. Patterns which, if used wisely, can help us to make better decisions.

In a way, they're the lean, mean, predicting machine. Madam Zola's scientific counterpart. The pocket protector's reason for existence.

Of course, the key to understanding what is going on here lies in how we describe these patterns. They are, "numeric" patterns. And while numeric patterns can, and often do, reveal truths we normally do not notice, the validity of these truths depends largely on the size of the sample group. Which you already know; in general, large groups, large validity. Small groups, small validity. At least with regard to the conclusions we can draw. As well as with regard to the predictive power of these numbers.

Okay. So what I've just said you've already heard many times. In fact, even statisticians themselves remind themselves of this idea. Sp where's the problem?

The problem lies primarily in how we apply statistical truths to individual lives. In essence, we tend to overlook the large group validity requirement and apply our results to personal decisions.

Let me say this again. Statistics are a terrific way in which to find repeating patterns in large groups. Especially if we visually plot these statistical repetitions in ways that reveal visually identifiable repetitions. However, while statistics are great when applied to large groups, they literally suck when applied to individual cases. Which is why statistics fail to help you to win the lottery. And fail to predict the weather on individual days. The Farmer's Almanac, remember? A whole book of statistics applied to individual cases.

With regard to statistical grade averages then, for instance, for all the schools in a given state, do these numbers accurately reveal patterns of failure and success? At the state level, yes they do. Moreover, based on the patterns these numbers reveal, we can then know where to focus our efforts so as to best improve our schools.

Unfortunately, knowing where we need to focus these efforts, in no way, tells us how to make these efforts. Why not? Because knowing which schools have problems in no way reveals the nature of these problems. Let alone the nature of individual kids and how we can change their problems.

Moreover, the further away you move from the group level, the less statistics help. And statisticians readily admit this. Why, then, do we act as if we can focus on grades more than children and still help children?

My thoughts? The bias, remember. We trust stats first. Then mistrust them second. We literally place our human trust in the numbers, then, we second guess this trust.

What can we do then? To see, we'll need to explore some real world examples. At least, some examples which include some real world characteristics.

Why qualify what I've just said with, "which include some real world characteristics?" Because what I'm about to tell you is an imaginary story, not a real one. A thought experiment, if you will. In this story, we'll consider how statistics can help us to know where, in our schools, we need to focus our attention. And how once we know this "where," we must forget about these numbers and focus on what our heads and hearts tell us. Why? Because as I've been saying, statistics cannot guide individual efforts.

At the same time, we'll also need to explore how we can address these problems, essentially by using warm, human fractal recognitions to guide our efforts.

Then later, we'll need to let go of these individual efforts and return to the cold hard truth of statistics. Why? Because warm, human fractal recognitions suck at showing us the big picture. And because statistics are better suited for measuring these kinds of over all efforts.

Thus, to measure how our individual efforts turn out, we'll need to refocus on statistics.

As for telling you an imaginary story rather than a real one, know I'd much rather be telling you a real story.

Why not tell a real one then?

The truth. It's against the law. In reality, I could easily be sued for telling you a real story. Thus, I'm going to have to do what the science fiction writers of the forties and fifties did. I'm going to have to use an imaginary story in order address a social issue. Hopefully, this will not prevent you from seeing my points.

Seeing the Good in Statistics

Where will we begin then? Let's begin by grounding our imaginary story with this week's real life statistical example; our dilemma with teaching kids eight grade math. Can you guess which states statistics say need the most help? And which need the least?

Know that what I'm trying to point out here is how we base most of our warm human guesses on a fractal sense of what we picture about the question. What I mean is, we base most of our human biases on our personal, inner visual patterns; on what we picture in our heads.

Thus, picturing a state like California, for instance, might make many people guess this state is doing fine. Above average, even. They do, after all, have a lot of socially active folks. Seriously, they do. And most of us can picture this.

Conversely, picturing a state like North Dakota, a state we don't hear much social squawking from, might bias us toward guessing that the kids in their state fall into the low range as to how well they are doing in math. Why would they be interested in teaching their kids about math anyway? Don't they mostly make their livings from agriculture and tourism?

Yes, they do. Agriculture. Number one. Tourism. Number two. (Notice. I'm using more statistics.)

So what is the truth here?

The truth is, California is the fifth worst state in the country. At least as far as how well eight graders do in math. Forty three percent of their eight graders cannot do eight grade math.

At the same time, the kids in North Dakota are at the very top of the pile. Of all the kids in the United States, these kids do the best in math. At least in the math we normal folks use to live by and manage our everyday lives.

Which state is the worst?

Mississippi. At forty eight percent.

Think this is bad? Compare this to the kids in our nation's capitol; Washington, DC. Sixty nine percent of these kids cannot do eight grade math.

Sixty nine percent! Makes you wonder what those politicians are thinking, doesn't it!

Seeing Statistics Fail

So if you were in charge of directing our nation's schools, what would you do about this problem? Got any thoughts? For instance, would you make state wide efforts to improve elementary school math instruction?

If you did, know that your efforts would most likely fail miserably. And most likely would waste your state's time, money, and heart felt energies in places wherein most of your state's kids would not need this help. And yes, the statistics I am referring to do accurately tell us a lot of kids in California need our help with math. However, they do not tell us which kids need this help. Only that "California" kids need this help.

Okay. Big sample size. Big accuracy. So how do we effectively narrow down our focus? For instance, should we continue to use statistics, knowing they will eventually fail when the group gets to be too small?

I think we should. Why? Because school sized stats are still relatively big samples.

So how would you use this idea to figure out which California kids need our help? And why would you choose to ignore the fact that statistics will eventually fail?

Because our inner visual guidance system has failed us once already. Our personal judgments regarding states, remember? We're also dealing with what is still a big group here, numbers wise. Thus, what we need here is some more cold hard facts. Don't you agree?

Quite honestly, at this point, I'm going to stop telling you a story. Why? Because I don't think I need to play this out to the bitter end in order for you to see my point. Suffice it to say that if we were to use statistics, we would see that inner city kids, in general, need more help. No surprise. And still a valid conclusion. But what then?

At this point, our friend and ally, statistics, would begin to come apart at the seams. Why? Because saying an inner city kid needs help with math does not say how to best help this individual kid. More important, we need to remember why statistics fail here. They fail because the thing we've been basing our statistics on; average grades, will fail to help us to access the human factor within these grades. We can know, in general, only that these is a human factor hidden within these numbers.

So say we have an otherwise bright inner city kid who is too distracted to study because his mother is a drug addict. A simple example to visualize.

Now play this out in your head. What do you picture? Will tutoring this kid in math improve his proficiency?

Of course not. We all can see this. Thus even with tutoring, this kids will still likely fail to achieve a normal eight grade level in math, this despite the fact that the methods being used here to tutor this kid would in most cases success for other kids.

What's the answer then?

The answer is to use fractal geometry to both define the personal problem and guide the personal solution. Translation. We need to visually examine this kid's personal connections and look for any malleable patterns. Beginning with discovering which of the numeric symbols he literally can and cannot picture. And how he feels when he cannot picture these symbols.

And do what would you then do with this information? For instance, would you do therapy on this kid? Or perhaps, try to reach his soul by giving him art classes, or karate lessons?

Obviously not. Besides, we all know, schools are not therapist's offices. Nor are they spiritual advancement centers. Nor should they be.

So what could we do?

I've already told you. At least, in theory. We need to focus on what he can and cannot picture, especially in and around math.

What would this look like in the real world though? Unfortunately, we're out of time and space for this week. Which means, if you want to see how fractal geometry would discern usable solutions for this kid, you'll need to read next week's column.


Closing Comments

So what have I been saying this week? For one thing, that we need statistics. To me, this is a given. As well as that statistics should have a respected place in our children's educations as well. The thing we need to be clearer about, though, is where this place is. In other words, "what should we be using statistics for?"

My answer? Making generalizations about big groups. Things like the state wide math achievement levels of all eight graders. And the number of kids in the United States interested in going on to college versus the mean family income.

What we should not be using statistics for though, is to guide our personal efforts to help these kids. At least, not at the individual level. Why not? Because at the individual kid level; meaning, with two or so people, we need personal warmth and insights to guide our efforts, not cold hard impersonal facts.

In a way, what I'm saying here is, while you certainly can drive a carpet tack into the floor with a five pound sledge hammer (statistics), you might not like the look of what will be left of the floor. At the same time, while tack hammers (human interactions) work great on individual little carpet tacks, they suck at driving big metal spikes into landscaping railroad timbers.

We need to reserve our five pound sledge hammers (statistics) for driving big metal spikes into landscaping railroad timbers, rather than using them for installing little carpet tacks. At the same time, we should not be trying to use tack hammers (personal human interactions) to drive big metal fence posts into the ground. Finally, the whole point is, we should learn to be more aware of which tool we are using where.

For example, when I was in eight grade, I studied Latin, and these studies were grounded in my learning the foundation principles; Latin grammar and syntax. The next year, New York State decided immersion was better. Thus, in my first year of Spanish, my studies were focused on learning how to parrot Spanish phrases. Most of which, I never really understood. At least, how they were supposed to be spoken in real life situations.

Why the state wide switch between eight and ninth grade? Statistics. You see, the statistics of the day told schools that most kids learn foreign languages better if they are immersed in this foreign language first. And statistically, this idea is still true. Unfortunately for me and for the small group of fussy kids to which I proudly belong; meaning, to the Asperger's style learners, this way of learning languages is a total waste of time. Why? Because fussy kids simply cannot navigate, let alone tolerate, the lingual vagueness of parroted phrases. These words simply make no sense to us. At least, not without first being taught the rules by which people come up with these fussy phrases. As well as the rules as to where these phrases are best used.

My point? Statistically, kids in New York were found to do better when their lessons in foreign languages centered on learning how to parrot phrases rather than on learning how to make, and use, these phrases. At least, at the beginning of learning a language. However, since this statistic lumped me into a group to which I, in no way, belonged, being in these classes essentially killed my love of learning languages. Including my desire to learn my native language; English.

My dislike of languages then continued unabated for the next forty years. Until I discovered, almost accidentally, how language students, and all of us really, learn and communicate on a continuum which extends from fussy to fuzzy; from precision to vagueness; from facts to feelings; from statistics to children. At which point, I became consciously able to choose which style would be best for me to use. One case at a time. One language at a time.

No surprise, this is when I began to, for the first time, feel personally drawn to learn a foreign language. In this case, Greek. Certainly no easy language to learn.

And what have I chosen to focus my learning efforts on? On learning to see the overall beauty in the language as a whole, both visually and aurally.

And how exactly have I been doing this? One letter at a time. Personally and with genuine curiosity.

So, am I blaming my life long disinterest in languages on a failure in my education? Actually, I'm not. And in truth, it doesn't really matter to me why this failure happened. It matters only that I use what happened to make the world better for children. Beginning with that I am learning how to be just like them. Before they lost their love of learning, that is.

Until next week then. I hope you're all well,


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