I've spent the last three weeks with a group of brand-new high school students. These mostly fifteen-year-olds have taught me a great deal about the failings of the American educational system. Of course I'm not the first to point out that we in the U.S. are not accomplishing what we say we want to in K-12 education; many others have said it before me and many more will continue to say it after me. The rather lengthy list of items in my "references" section attest to that fact. So why am I taking the trouble to write a blog entry about it? Frankly, because I am so shocked at just how *bad* it really is.

Don't get me wrong. I knew it was bad. I just didn't know it was THIS bad. And I didn't realize our nation's progress has been so meager.

Let me clarify. I know we have made wonderful strides with certain student populations. The kids who come from an environment where Maslow's first couple of levels are adequately met and who have supervision, support, and love from family and community are doing better than ever. The kids who, frankly, would have been fine regardless of their school experience are doing great. It's the rest of them that I'm talking about now. The kids in my classrooms are mostly black, from less-than-ideal homes, with less-than-necessary income levels, and who've experienced very, very little success in math in their first 8 years of school. With *those* kids, we're failing miserably. It's also clear that we've been failing them for years.

My last couple of decades in colleges and universities all over the United States have shown me that not only is it possible, but it is *likely* that students in the aforementioned population will enter higher education with significant gaps in their mathematical understanding (if they even enter higher education at all). Year after year, semester after semester, I would see young adults enter my classroom without the level of *numeracy*, mathematical fluency, that I expected from a country that talks as much about education as we do.

I went to high school to try to get some answers. In my first several weeks, I've observed several well-meaning but misguided efforts that, rather than fixing the problems, actually help to exacerbate them. In this blog entry, I discuss three of these ill-conceived strategies.

**Reason # 1: "Interactive" notebooks**

Students in high school don't know how to take notes. They also don't know how to listen very well, nor are they very good at picking out the important bits from the stuff they do hear. This is a HUGE problem. Perhaps it's always been a problem, I can't speak to that definitively. What I do know is that it's a problem now and it's a problem I've seen get worse in the last two+ decades I've been in the field. What I also know is that teachers have been trying for years and years to fix this problem. Many different silver bullets have been aimed at this target, most missing wildly. The newest of these is the so-called 'interactive notebook'.

Before you flood my inbox with angry emails because you are an interactive notebook lover, let me qualify: I am in favor of the *intent* behind the idea, it's the *execution* that I take issue with. For those of you who haven't heard of the newest pony leading the educational bandwagon, the interactive notebook is, well, just a notebook. But it's a notebook that students "interact" with by gluing stuff in it, writing stuff in certain ways in it, and organizing stuff in a very regimented, prescribed, and, I'll just say it, artificial and stilted way.

Here are some "tips" for interactive notebook use that I've gleaned from other teachers who seem to love them: (links to these teachers' sites are in the references)

The purpose of the interactive notebook is to enable students to be creative, independent thinkers and writers. Interactive notebooks are used for class notes as well as for other activities where the student will be asked to express his/her own ideas and process the information presented in class.

Interactive notebooks are characterized by "right side input" and "left side output":

An interactive notebook is a personalized textbook. It's a working portfolio: all your notes, class work, questions, & quizzes in one convenient spot.

I mean, it sounds great, right?

It *would* be great if the hype were true. If students were all thinking deeply about the material being presented, analyzing it and synthesizing it, then recording it clearly and creatively for their own edification, I'd be all over this interactive notebook thing. But they aren't. No. Not even close. Instead, it's a sad picture of students dutifully cutting out the rectangular piece of partial notes from the handout given by the teacher, gluing it precisely in the location and with the orientation dictated by the teacher, and mindlessly "filling in" the blanks with what the teacher says. It's a parade of specific, creativity-killing instructions ("fold the paper in half horizontally, then again vertically, label each quadrant with a capital letter A through D in a clockwise orientation..."), with the token individual aspect thrown in ("write two sentences that describe how you feel about polygons"). With the student population I am referencing in this blog, there is no "interactive" component to the notebook. Instead, it's more akin to force-feeding a prisoner who's on a hunger strike. They swallow, but they hate it and with every spoonful learn to hate the environment even more. Hell, if these students *had* the behaviors in place that would allow them to listen, synthesize, and record their responses, questions, and new insights, then they wouldn't be in predicament they are!

Here's another part I take umbrage with: it's all a thinly-disguised way of having the teacher take all the responsibility and do all the work. Have you seen the plethora of YouTube videos all aimed at teachers helping them know how to spend their entire summer "getting ready" to do interactive notebooks with their students? Here's a math problem for you: how many trees are killed for every classroom that's creating these notebooks? Do you have any idea how many copies are made? How much paper is wasted? (Not to mention glue.) How is it a good practice to glue paper on top of perfectly good paper? Not to mention, *why* are they 'writing textbooks' when we have many good quality textbooks that have already been written? (Even more upsetting, these textbooks are now sitting idle and unused in many a classroom cabinet; all while students and teachers busily re-create the wheel.) Plus, and this is a biggie, they don't do what they say they will do: there is NO evidence that, after a year of "interacting" with these notebooks, students go forth and are more creative, better organized, or more capable of taking good notes, coming up with their own personal connections, or in general being better learners!

Instead, I would venture that what gets created is an entirely new breed of student, the one I saw in my classes. The student who, as I'm teaching and leading them through an example of the concept just discussed, is just sitting there. When I direct, "Since you probably won't remember all of this, it might be a good idea to write it down", this new breed of student angrily responds, "You didn't say we'd need to write this down!" and then snaps, "Do you want this in my binder or in my notebook?" When I express surprise at the anger and indifference at the location, the irritated response is, "Well you need to make up your mind!" Obviously, this new breed of student has clearly received the message that the teacher is the decision-maker, the determiner-of-where-and-how-things-are-written, and, most disturbingly, the one who is responsible for the entire learning experience. If learning doesn't happen, the fault clearly and completely lies at the teacher's feet. This. Is. Wrong.

**Reason # 2: Product, not process**

Students in high school are a product of what we emphasized in elementary and middle school. In the U.S., that means getting the right answer. To a multiple-choice question. On a standardized test. That everyone takes at the same time. In the same way. On the same day. Now this might not be a horrible thing if (a) getting the right answer = knowing the concept / being able to perform the skill and (b) the questions we ask are the ones we value and that actually assess what we say we want as a result. But it's not. Nope. Not even close.

Instead, the unanticipated result is a population of student who have no idea how to pose questions or make connections between the various bits of disconnected "knowledge" they are given. We have a classic cart-before-the-horse scenario going on in U.S. schools right now: we are assessing students [aka 'collecting data' (more on that in a minute)] *before* we are teaching them the stuff they are assessed on! In fact, my observation is that the entire classroom time is spent on assessment and very, very little on actual *instruction*.

Let me give an example of what I mean. I put this bit of information on the board for my 9th grade Algebra I class and just waited and observed to see what they'd do with it:

One year, an airline saved $40,000 by eliminating 1 olive from each salad served in the first-class section.

I was hoping to see shock or disbelief, to witness curiosity, and to hear my students thinking about this surprising statement and generating questions like (1) *Wow, how many salads did they serve?* (2) *How many jars of olives would I have to buy at the grocery store to equal $40,000?* or similar ponderings. Sadly, I saw and heard none of these things. Instead, most students didn't even bother to read the information (despite it being prominently displayed on the SmartBoard in front of the room) until I directly pointed it out to them, "Class, if you haven't already, read the statement on the board and think about what it's telling you, what questions you have, and how you might proceed in answering those questions." Once they did look at the statement, there was .... nothing. Abject apathy. No curiosity, no idle, "hmmm, I wonder...". Just blank stares, loud sighs, and non-verbal cues indicating utter contempt. Frankly, I am STILL depressed about it. It is so tremendously disheartening to see an entire group of 15-year-olds who are so completely over it, who have given up on learning, and who have absolutely no interest in obtaining knowledge simply because it's what humans do. Somehow, in 8 years of our educational system, we have eliminated that natural human tendency from people who are only 15! That. Is. Wrong.

**Reason # 3: Data-driven design**

If you ask practically anyone in the United States what he or she would like to see our kids being able to do after completing our K-12 educational system, they would say stuff like, "Contribute to society" or "Be able to solve difficult problems" or simply "Do useful, high-quality work and live a good life." Please note I include the caveat "practically anyone" because you will NOT receive these types of answers from people who are in the educational assessment business, or politics, or hedge-fund managers who think they are educators -- these are all exceptions to what the "typical" American would like for their nation's youth. These people have goals for our K-12 system that sound like this: "The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form with 80% accuracy." or "The student will represent verbal quantitative situations algebraically and correctly evaluate these expressions for given replacement values of the variables 90% of the time." Do YOU see a 1-1 correspondence between the items in the first list and the ones in the second? Neither do I. That's because there is NO RELATIONSHIP between them. What we *say* we want our students to be able to do and what we *test* are not aligned. Not even close.

The result of this tremendous misalignment is obvious: you cannot hit what you don't aim at. Consequently, we are NOT creating a generation of students who are independent thinkers, creative problem solvers, and skilled at being lifelong learners. Instead we are creating a population of people who have no idea what to do if the question isn't multiple choice, if all of the necessary information isn't obvious, given, and written in bold, and if they aren't told first, in minute detail, how to proceed. It's sad. Tragic even. And it makes me MAD.

As a mathematician, of course I love numbers and I trust them. I know the power of data and the importance of making informed decisions based on facts, not emotions or intuitions or guesses. So you might conclude that I'd be a fan, a supporter even, of "data-based instruction" -- but I'm not. Again, like the interactive notebooks, I am in favor of the *intent*, it's the *execution* I'm opposed to. Because of well-meaning but misguided and poorly implemented legislation like No Child Left Behind and Race to the Top, the execution of this so-called data-driven instruction is a thinly veiled attempt at CYA ("cover your ass") on the part of the schools. The only motivation is to prove, via the data, that the school / district / state is worthy of the money. And if the numbers don't come out right, it's the teachers fault. That's sad. And. It's. Wrong.

**The Consequence?**

Johnny (a.k.a. Mary, Bobby, Dashawn, Jaynaya, etc.) can't think. He doesn't have the basic mathematical understanding of how the operations work, the nature of numbers, and the fundamental "rules" of the game of math. She doesn't have the "self talk" skills to decide what to do when she doesn't know what to do. He doesn't have the confidence to just read the problem, take it one step at a time, and TRY. She doesn't have any tools in her problem solving toolkit aside from learned helplessness and the response, "I don't know" when posed a question.

I don't know about you, but this depresses the hell out of me. Have you experienced similar responses from your students? What strategies or techniques have you found that are helpful in trying to turn the tide? As always, I'd love to hear from you.

**References:**

Site where the great graphic of Rodin's *The Thinker* came from - Thanks University of Louisville for the great pictures AND the fabulous information!

A nice case against "textbook school mathematics"

"Why Johnny Can't Add without a Calculator" article

"Why Johnny Can't Read, Write, or Do Math" article

"Why Can't Johnny Do Math?" article

Everybody Counts: a report to the nation on the future of mathematics education

"A Nation at Risk Turns 30" report on how far we've come

"A Nation at Risk 30 years later" videos

Interactive notebook pages

How to use interactive notebooks in math class

Interactive notebook wiki

Setting up your interactive notebook Slide Share

One of the big "players" in the educational assessment game: Pearson

Fabulous video by Sir Ken.

The Solver Blog

Author: Dr. Diana S. Perdue