Teach the Facts!

Warning, an edu-technical polemic, wrought by frustrations with new students and their skill deficits, follows...

Teachers, it’s 10-12 weeks until testing, do you know where your kids are…in their facts?

Everyday, as I focus on teaching math, I grow more and more convinced that the facts are the sine qua non of elementary math. We have invested hugely in building facts fluency at our school and I cannot fathom how this is not done at others. I suspect the rhetoric of “drill and kill” has given some teachers a handy excuse to escape the need for students to be absolutely fluent in their facts. Certainly, students should be taught the facts in fun and engaging ways that do not poison their enjoyment of math. Automaticity in arithmetic is a standard, not an instructional practice; students should have lots of fun developing their fluency in the facts but teachers must make sure they achieve complete competency.

I have also heard some teachers say that they believe their students will develop their facts fluency through their daily use embedded in higher-level material. They liken developing facts fluency through math to developing oral fluency through wide-reading. This is a tempting but erroneous analogy. A fifth-grader unable to fluently multiply is not simply slowed but crippled. Following a reading analogy, arithmetic is more akin to decoding than fluency. You would not expect a student to read a 5th grade story without knowing phonics, you cannot expect a student to even understand much of 5th grade math without multiplication. What sense does it make to teach that one-fourth is equivalent to two-eighths, if the “4 x 2 = 8” fact is not automatic in the students’ minds? Likewise, the most difficult aspects of area and volume are not memorizing formulas, it is doing long-division by two and multiplication with multiple digits. Next year, if I teach 5th grade again, I plan to start with algebra and coordinate geometry, teaching no number sense standards until my students have mastered their facts. I suspect that “lowest common denominators” and “simplest form” will cease to be such a struggle when students can intuitively perceive the links between the numbers and I suspect that long division will be much less of a challenge when the students can easily subtract.

Further, I was recently told by our second-grade teachers that about 40% of their students had mastered subtraction. Funny, little more than that had mastered those facts when they came to me in fifth grade. Teachers: do not be deceived by students who can “quickly” subtract on their fingers, or speedily count multiples to finish a ten or twenty question fact exam. The arithmetic bar must be set at automaticity, instantaneous recall, not conceptual understanding. It is good for students to know that four times five is 5 + 5 + 5 + 5, but they must also know that four times five is twenty, without stopping to think.

Our math curriculum, and I suspect most, offers no remedial lessons for the majority of students who rise to fourth or fifth grade without being fluent in subtraction and multiplication. It certainly offers none of the resources needed to track students’ progress, an equally essential element. But that does not excuse teachers from preparing and including activities and lessons that teach the facts, and from taking the time to assure that all students learn them. Teachers, if there is only one thing you force yourself to go outside of the curriculum and do, I suggest that this be it.

Ups and Downs

Say what you want about teaching, it is never boring. Every day is filled with more highs and lows than I suspect most business people see in a month. The problem is that at the end of the day the ups fade but the downs follow me home, hanging around until the next day brings a chance to redress them or replace them with more. Here’s Tuesday.

7:40 – Down – N--- and R--- get bored.

My Newcomer’s group used to be the highlight of my day, even at 7:20 in the morning. But several of the best in the group didn’t come back after Winter Break and these bloody cold mornings make anything hard to enjoy. I’ve also started to feel a lack of enthusiasm among the remaining students, culminating in two students preferring to stay outside and play soccer instead of coming to class. The principal caught them and dragged them in and they complained they were bored. I feel bad because I know that reflects badly on my preparation. Spicing up Newcomer’s, another big item to add to the task list. The problem with before/after-school classes is that they add a lesson to prep, while simultaneously taking away the time to do it. If only I worked 16 hours a day like those demi-god KIPP teachers.

9:10 – Up – M--- writes a summary.

M--- continues to be my all-star. She is a brilliant young lady, terrifically hindered by the fact that she speaks only a year’s worth of English. Yet she maximizes her language and pushes herself to the head of the class with ferocity. Even in writing ---that’s writing in English, mind you--- she is one of the most participative students. She has memorized all the writing frames and she knows the organization of a three-paragraph essay backwards and forwards. In math, she has gotten tired of dominating the class and now quietly tutors her neighbor, an English Only student who is probably two years behind her. This week, M--- wrote a beautiful summary of a Calvin and Hobbes strip I had the kids read. Perhaps only a sentence or two was grammatically accurate, but her sequencing of the story and the structure of her essay was vastly superior to most of the students in the class.

11:20 – Down – J--- and V--- check out.

You may remember B---, the student who undertook a personal revolution earlier in the year. I am pleased to report that she has continued this transformation, attending extra classes and slowly but surely mastering her facts. But now, I have watched the opposite occur. Two of the top fourth grade math students have slowly descended into inattentiveness and apathy. They are not focusing in class or turning in homework, they stopped acing tests and now even passing them. I should have called their parents weeks ago. I know that these girls cannot come from absentee or undisciplined families, that a single phone would probably be enough to turn around their behavior. My busy-ness and lack of Spanish-skills is an insufficient excuse, but it is reality at the end of each day.

12:30 – Up – F--- masters perimeter.

F--- is one of my newcomers, although he has been here for a few years. He is in the process of referral for special services because of his severe difficulty learning to read and acquiring English vocabulary. He is one of the students that easily gets dismissed, by myself as well as others, as needing more than a mainstream teacher can provide. On Tuesday, F--- asked me if he could just work on the computer, instead of attending to the grade-level material, as he still needs to learn the majority of his facts. I was tempted to acquiesce but, by the grace of God, I decided to keep him in the lesson. And today, he learned. At the end, as we were practicing on our whiteboards and I saw the right answer on F---‘s. I didn’t see any work, however, and asked him to explain his answer. He did!

2:30 – Down – V--- loses control, I lose control.

V--- is one of the most charismatic students in my afternoon class. Obviously very bright and deeply scarred, his life is an endless alternation between his feelings of success and anger. Lately, he has been alternating less and just staying angry. I suspect he is “just” growing into the depth of issues his childhood traumas has provided for him, but he takes the whole tenor of the class with him. As goes V---, so goes O----, G----, C---- and A---. I seem to have no control over this domino effect. Nothing is more frustrating to me than this feeling of cascading failures. V---‘s angry disrespect and confrontation-seeking sets a low bar for behavior expectations and, even after booting him out of class, I have to struggle to raise it again. This incessant disorder devastates everyone’s affective level and makes learning impossible, leaving me to watch as the class V--- disrupts falls farther and farther behind.

D--- Triumphant

Edu-technical background :

Every week all the 4th and 5th grade students at my school take a multiplication test. We have used all our teacherly powers to affix status upon this event. It is labeled “The Principal’s Challenge” and The Man himself comes to each class to initiate it. On Friday, the class that had the most students with a perfect score receives a banner to display in their room all the next week. Every student who aces the test receives a t-shirt saying “Multiplication Master” that they are allowed to wear on Friday. At this point, we have moved from having 3 students in 4th and 5th grade ace the test each week to having 60. Overall, better than 90% of our 5th graders and 80% of our 4th graders have attained mastery (80+/100) of multiplication. Needless to say, as each class tries to achieve the banner and as more and more students show up in the t-shirts, it becomes increasingly apparent who the laggards are. This brings us to D---.

The story:

D---, in all likelihood, suffers from fetal alcohol syndrome. He does not look like the other children, he does not act like them and he certainly does not learn like them. He cries constantly, he picks his nose, he licks his shoes and, until the recent acquisition of a hearing aid, he talked at the top of his lungs. Due to years of parental obstructionism and professional ineptitude, he was only qualified for special education this December. He is paranoid, from years of bullying and abuse. He incessantly believes people are stealing his stuff and making fun of him and he is often right. Yet, he is constantly in search of companionship and tries, each morning anew, to befriend kids who have despised him for years.

A long time ago, I realized that my morning work, a sheet of 120 multiplication problems to be completed while homework was checked, was not a possibility for D---. Sitting next to other students meant endless distraction, an interminable cycle of D---‘s misbehavior, other students’ bullying, and D---‘s sobbing tantrums. Even sitting in the very front, facing only me, the world was filled with too much excitement, too many stories to tell the teacher and too many carefully arranged stacks of my papers to dig into and disorganize.

I eventually gave up on D--- completing the morning work and making any progress in learning his multiplication facts. He was too low even to join my after-school “facts club.” One afternoon, however, D—‘s other teachers and I looked up fetal alcohol syndrome online, in search of strategies to help us help D---. As though written directly for me, the website essentially said, “Students with F.A.S. can’t complete worksheets. They are much better off learning basic skills on the computer or with flashcards, where there is a high degree of interactivity.”

The next day, I put D--- on the computer during morning work. Wholly engaged by Multiflyer, hands down the best facts-teaching game ever, D--- would happily work at hundreds of multiplication problems. At first I only let him work during the multiplication period, but then, as he never does his homework, I let him stay on the machine during the homework correction too. Eventually, as our class progressed farther and farther past D---‘s capabilities, I just let him work at the facts. He explored different games at multiplication.com and only occasionally misused the time.

After a few weeks of this intense practice, D--- told me that he was going to pass the Principal’s Challenge. When he only got thirty or forty problems out of the hundred, he tried to fill in the rest as we corrected the test. The other kids caught him, called him out, and D--- sobbed. He cried to me about how he thought he could do it and how desperately he wanted to pass. I told him to keep practicing. A few weeks later, D--- got fifty-two correct. He came rushing up to me as the class counted out our perfects. The class laughed at him but, undeterred, he said that next week, he would pass the test.

Last week, just as the five minutes finished up, I walked by D---‘s desk and saw something I never believed possible. As my eyes quickly scanned the paper, I did not immediately find it awash with ridiculous guesses. In fact I found myself tracking back and forth across the rows of problems as I looked for an error. I picked it up, telling D--- that I would correct it myself. Unable to tell if he had done well or wrong, D--- assumed the worst and put his head down.

D--- did not ace the test, but he got over seventy problems right. It was a spectacular improvement, from twelve at the beginning of the year, and I announced it to the class. We were all amazed and the reconsideration of deep-seeded contempt was tangible. Most of the students in the class did not get seventy correct at the start of the year and for D--- to be within a few months progress of them was inconceivable. Ecstatic, D--- ran to the phone to call his mother, ran to the other classes to show his other parents, and came back to my class to call his mother again.

Evaluation Song and Dance

I just finished typing up a real, honest to goodness lesson plan. That might not shock you, given that I am a teacher, but I realized that it’s been a little while. Don’t get me wrong, I do a weekly plan that includes every objective of every hour of every day, as do most teachers at my school. But very rarely do I sit down to do a piece-by-piece script of a single, one-hour lesson. In fact, I only do it when I am told to do so, almost exclusively for evaluation.

That’s the funny thing about evaluation in teaching or, at least, novice teaching. We are expected to do things for the purpose of evaluation that are entirely impractical to expect a regular basis. The result is a process far more akin to artistic performance than professional assessment.

First, we compose two- or three-page lesson plans, demonstrating our satisfaction of this standard of the teaching profession or that best practice. Generally, they require a good hour of our time to articulate and format. I know parents and professors would like to believe we do this for every cherished moment with the children but… get real. Even assuming half an hour, if I were to do this for every lesson for a whole week, I’d spend nigh on 20 hours a week in planning alone! (Maybe if I worked the mythic 16-hour KIPP day, this would be achievable.)

Then, almost always, we are evaluated at carefully appointed dates and times. Consequently, we are able to assure that we will be teaching our best possible lesson and be at our most obscenely over-prepared, well-stocked with carefully differentiated materials, painstakingly made hands-on activities, key cross-disciplinary connections, and deeply meaningful realia, --- all the trappings of a great teacher, all impossible for the new teacher to have on hand with the daily frequency we wish we could.

When it’s show-time and our evaluator arrives, we know what we’re expected to do and we are careful to do it. Knowing that we need to be demonstrating standard four, we’re careful to push our children up Bloom’s taxonomy and don’t worry about neglecting the comprehensible input, because that’s standard seven. Or perhaps we’ll focus on meeting the needs of our English Language Learners and leave our Special Populations behind, or perhaps we’ll integrate some technology and leave out the insuring of equity for all learners.

When the process is over, all our evaluation reveals is our understanding of the expectations, our ability to meet them on cue. There is no real assessment of our daily, meaningful implementation of best practices. There is no evaluation of what is actually experienced by our students.

My solution? First, instead of submitting a single, ad hoc lesson plan, we should submit our regular weekly plans. We should submit the plan before we had the training on X, Y, or Z, and then after, showing how that professional development changed our regular plan and our everyday practice. Then, we keep submitting those plans, creating the expectation that we keep incorporating those improvements. For observation-based evaluation, we set aside dreamy best practices possible only with limitless time and boundless resources. They are useful as aspirations but not as standards of evaluation. We need to establish expectations that should be visible in any meaningful lesson. Informed by our actual lesson plans, our evaluator comes in at two or three appropriate times, unannounced, over the course of a week and stays for an hour, assessing our success in meeting those expectations. If you observe three of my writing or math lessons in a week and there’s a best practice I’m not doing, it’s safe to say I don’t do it. Likewise, if I don’t meet the needs of a subgroup of my students one time in three, they’re going unmet.

Teachers don’t need to be evaluated on what they can do, given unlimited prep time and warned well in advance, they need to be evaluated on what they actually do, every day. I’m sorry to say it but it’s true: my students don’t experience my highest potential, they experience my daily practice. They experience how many hours I have to plan and prepare and how many I need to set aside for sleeping, eating and me. My teaching and my students’ learning is tempered by reality, mine as well as theirs, and good evaluation should reflect that.