Taking credit where no credit is due

“There is no abstract art. You must always start with something.
Afterward you can remove all traces of reality.”
~ Pablo Picasso (1881 – 1973)

No Child Left Behind (NCLB) has finally been repealed, but the end of this law came with too little reflection. The current administration touted their success in removing what had become an uncomfortable and unpopular reminder of America’s academic challeges, but the truth is that No Child Left Behind originally was slated to end in 2014. By 2014, all students in America were expected to be at a 100% passing rate on their state tests. That did not happen. That could never have happened. By the year 2014, the federal government had an awkward law that had failed its mission abysmally, and masses of employees and paperwork that remained and remain behind, ghosts in the Overlook Hotel of educational bureaucracy.

El Chapo in my life

This post has no point to make exactly. But as I look at the news articles about the capture of El Chapo, I realize that I know something curious that I ought to share. El Chapo is otherwise known as Joaquín Archivaldo Guzmán Loera, the Mexican drug lord who heads the Sinaloa Cartel, a criminal organization that has made uncountable dollars in drug sales and other illegal activities.

Here is what I know: El Chapo has become a folk hero to many young, male students who idealize him. When he was on the run, these students would tell me confidently that he would never be caught. They loved stories of his near escapes. They idolized him. A few years ago, earlier versions of these students were all wearing Scarface t-shirts, at least when school uniform policies did not stop them.

Here is what I speculate, admittedly without data to back me up: I believe these students can see themselves as Scarface or El Chapo. The “Drug Lord” path to success seems attainable. They can imagine themselves on top of an organization that deals in drugs and weapons. That path sounds exciting, too, much more dramatic than engineering, for example. Probably because I worked in an area with gang activity, teaching a population filled with legal and illegal immigrants, I have heard many El Chapo stories at lunch and after school. El Chapo has a large fan club.

Eduhonesty: As we try to level America’s academic playing field, we run up against obstacles that don’t often get aired. The El Chapo fan club is one of these. Try selling chemistry and calculus to a kid who dreams of heading a drug cartel. In my experience, that kid will smile at you indulgently. Oh, Ms. Q., you are so cute, that smile says. I know you have to say that stuff. My mom says it, too. But you and my mom just don’t get it. I am going to be a Latin King!

The truth I never tell

“The worst form of inequality is to try to make unequal
things equal.”

~ Aristotle

America has been mired in political correctness for years. Teachers dare not suggest that students in urban schools might be actually… different. Our students are all the same, you understand. Some of them just know less and need a little extra support.

I’d like to state unequivocally that we are lying when we try to believe this more-palatable version of the facts. For the kids on the bottom of our academic heap, that little bit of extra support might as well be a Bandaid on a third-degree burn. Regular readers will know that I believe the only chance for our academically-disadvantaged students consists of a longer school day and longer school year. We have documented that inner-city students may start school with only a little over half the vocabulary that nearby suburban kids bring to the classroom. We have documented that those kids who are already behind tend to fall farther behind, absent intensive interventions.

But I’ll skip the school-year issue for now. I’d like to go back to the current grouping fashion. I vividly remember my first attempted group project, a Spanish presentation on different Spanish speaking countries. I’ll grant that any teacher’s first group work will have hitches, probably a few major hitches, but let me describe that experience. Presentation day arrived. Group One could not present. Two members were absent, I believe. Given that my roster had 35 kids but my classroom usually contained around 28, I should not have been surprised. No Child Left Behind attacked absenteeism as well as grades, recognizing that the much higher rates of absenteeism in impoverished and academically-disadvantaged districts creates many problems for students. High rates of absenteeism are excellent predictors for dropping out of school, not to mention the havoc that missing school creates for grades. But having one-fifth of that Spanish class absent was no rare occurence. I tried to move on to Group 2. They also had members absent. All members of Group 3 were present, but they had not expected to present; they did not have their posters or other visual materials. Group 4 was completely unready. Etc. We presented those countries to the class in spurts over the next week and a half. I rewrote my lesson plans as I went along.

I learned and I got better at structuring projects. But I’d like to tell a truth that never seems to hit the airwaves. It’s extremely difficult to do group work effectively once the absenteeism rate climbs up above 10% on average. In a lower-performing high school, in lower-level classes, that rate can hit 20% on cold, snowy days, as students who are waiting until they are old enough to officially drop out decide to stay home to play video games.

These pockmarked classes do not require a few academic nips and tucks. Only major surgery can rescue such classes. They also don’t need more group work and more team efforts. Group work wastes ridiculous amounts of time when a group can rarely form any version of a quorum. When members of the group only turn up half the time or less to work on projects, other members end up shouldering changing burdens. If the student assigned to explain the geological terrain of Costa Rica only turns up one day out of three, some other student will probably attack the terrain question — or the group will end up presenting yet another substandard effort in a year of substandard efforts. If students are supposed to teach each other, planned learning may slip through cracks in an already cracked lesson plan. Costa Rica’s terrain may forever be lost in the mists of half-glimpsed paragraphs that other group members merely skimmed, if they looked at Costa Rica’s terrain at all.

Teachers can find ways to work around these problems to some extent. But frequent group work still probably will do more harm than good in a school suffering from high rates of absenteeism. Individual work may be less fashionable according to modern educational theory, but plans that include reading book sections and then filling out worksheets will result in greater learning, at least for those motivated students who are clinging to their dreams while the kids on either side of them regularly leave empty holes in diminished classrooms.

Eduhonesty: Gloves off. Just because group work produced great results in Redmond, Washington, we cannot assume that same strategy will produce similar results in Detroit, Michigan. Classrooms in Detroit have far greater disciplinary and attendance challenges. That attendance and disciplinary data is out there, buried in academic and governmental documents. The truth we need to acknowledge is this: In many classes, frequent grouping will slow students down, rather than “enriching” their learning experience.

P.S. Again, we have to approach our students on a class-by-class basis. I’m all for early experiments with group projects. But if class dynamics pose too many challenges, teachers and administrators should remember that worksheets work. We too often accuse past educators of being boring presenters of stagnant material, of lecturing when they should have been asking critical thinking questions. But we don’t talk about the lack of learning from that past time, because learning was not particularly lacking. In fact, despite all sorts of test manipulation, the evidence suggests our students are no better at math today than they were thirty years ago. From a document titled “NAEP 2012 Trends in Academic Progress, Reading 1971–2012 | Mathematics 1973–2012” at https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2013456:

“Results from the 2012 NAEP (a test that has been given to America’s students since 1973 as part of government tracking of educational trends) long-term trend assessment show improvement in the mathematics knowledge and skills demonstrated by 9- and 13-year-olds in comparison to students their age in 1973, but no significant change in the overall performance of 17-year-olds.”

Sadly, the news is even worse when we look at reading scores. According to the same publication, seventeen-year olds in twelfth grade scored 12 points lower in 2012 than in 1971.

Theory and practice, and the dark side of grouping

“In theory, there is no difference between theory and practice; In
practice, there is.”

~ Chuck Reid

What are the costs and benefits of group work? In this time when the benefits are touted everywhere, I’d like to pause to consider costs. As we continue to endorse regular and even daily group work, we need to examine the differences between theory and practice. My school demanded daily group work last year. Overall, I do not believe that policy benefited students.

We spend too much time looking for magic cures. How will we pull up scores? Districts try techniques that worked in specific studies with specific student groups — without considering whether the needs of their students match the conditions in those studies. More grouping will never be a magic cure for lower academic performance, especially when students are thrown into those groups too often and too soon. An underappreciated problem in groups comes from those students I will call “sloughers.”

An old adage says, “More hands make for lighter work.” That’s true — especially if you are one of the sloughers. My daughters sensibly disliked group work because they usually got stuck with a disproportionate amount of the work. The students who care most about their grades often end up doing most of the work. The students who care least naturally do the least. Those less-motivated students volunteer to find pictures or draw lines on the Martian calendar while other students do the math necessary to create that calendar. The students who know the least may also be kept from adding real contributions. A group may quietly encourage Anne-Marie to find pictures because they do not trust her to do any mathematical calculations.

Many readers of this blog are teachers, and I can hear the voices saying, “That’s why you have to structure group work carefully!” A strong teacher can control to some extent for unfair distribution of labor. For example, every student could be required to turn in pages of calculations to show they did their own work. But even then, a regrettable amount of copying may occur, especially when one teacher has over thirty students.

We also say “Two heads are better than one.” I’d say that’s not necessarily true in group work. If my slougher lets an academically stronger or academically more motivated student do most of the work, my slougher will not be better off for working in a group. The results and benefits of regular group work depend on the learning levels of students in the group, social-emotional dynamics, and the motivation of individual students. Collaboration often works well in studies and in theory, but collaboration requires structure, time management skills, communications skills, and the ability to delegate tasks effectively. Even with strong teacher supervision and guidance, many students may struggle to work effectively in groups.

The counterargument to my above contention might be that we should oblige students to work in groups for exactly those reasons. Our students need to learn to delegate, manage time, and communicate. I’d agree with that position, provided we also remember that the extra time we use to work on delegation, time management and communication will be taken away from teaching core content. We teach collaborative skills at the expense of content. Those collaborative skills will be useful in later life, but they do carry a hidden cost: The time spent teaching group work has been taken from time that might have taught content.

Other challenges are worth noting. If no one in the group understands the material well, groups can even lead each other astray. A teacher can start with a group that mostly understands rotation and orbits, and end up with a group that has created its own unique solar system and vocabulary, one where Mercury’s days merge into Mercury’s orbit and nobody quite knows how anything works. An assertive student can easily teach his or her group to do ratios wrong while the teacher is working with another group across the room. When that happens, a teacher has to correct the misunderstanding — knowing that unlearning and relearning mistaken mathematical processes can be much tougher than doing the process right in the first place.

The last adage I’ll throw into this post will be “The more the merrier.” Unfortunately, this adage often proves true in group situations. Grouping students will make many students happy. Sloughers get to share the load, as much of it as they can give away. Other students create their own version of a recess or break. They enjoy group work for the social opportunities that circling their desks can provide. While the teacher helps Group D across the room, Group A may be quietly catching up on Jasmine’s date with Deryan last night. Sloughers can be talented at giving an appearance of work from across a room, while exchanging notes and whispered comments on Jasmine’s new manicure.

Eduhonesty: I actually like group work, a fact that may not be obvious from this post. I enjoy creating projects that encourage independent thought. I believe in teaching collaborative skills.

I do object to mandates from above that require that work, however. Each class deserves to be taught according to what works best for that class. That will depend heavily on subject matter and student learning levels. In particular, when an entire class demonstrates academic weakness in one area, letting that class’s students teach each other will likely prove a losing strategy. Students cannot teach each other what they do not know. They should not be forced to try simply because we want them to try out their teacher chops on one other.

America’s teachers have their boots on the ground. They can see the terrain around them, and each classroom’s terrain is unique. Teachers can assess what works and what does not work. They can see who works and who does not work. Especially after teachers have been provided with professional development on grouping, they should be left alone to choose how to present material to their students. That may be frequent group work, occasional group work, or relatively little group work. Let the teachers decide.

No free lunch

This post is a response to reader concern about the “humiliation” suffered by children who received cheese sandwiches in the previous post. Yes, being given a cheese or peanut butter sandwich because your parents have not paid their lunch bill most likely will embarrass the kids with those sandwiches. Kids should not suffer for their parents mistakes.

But school districts should not have to shoulder $50,000 of unpaid lunch bills, either, as the district in question did last year. Suggestions that the district call parents individually sound good on the surface, but who will make those calls? What work will not be done because of the many minutes lost to those phone calls? Do we want our schools to become collection agencies? That $50,000 represents tax dollars collected from Americans who expect their tax dollars to pay for education — not defaulted lunch obligations. Again, every expenditure we make in education comes at the expense of alternative purchases. The money spent on the new copy machine may prevent or postpone the purchase of a computer program designed to teach astronomy, for example. Schools operate on fixed budgets based on tax dollars collected and distributed to their districts. They can make some purchases on credit but, like families on budgets, they can only run so far and so long on credit.

By middle school or high school, students should have a basic grasp of economics. They should have learned that there is no free lunch — not unless you qualify for one after taking a means test, that is. They should realize that failing to pay your bills will catch up to you. As life lessons go, those cheese sandwiches are a gentle way to make a point. No one went hungry unless they chose not to eat.

Siding with the school all the way

Under the banner “Controversy,” Yahoo Parenting printed the following article: “High School Calls Out Kids With Lunch Debt, Serves Them Cheese Sandwiches,” by Melissa Walker on January 7, 2016. The article is at https://www.yahoo.com/parenting/high-school-calls-out-kids-with-lunch-balances-203559666.html Here is how it starts.

High school senior Sierra Feitl was in the lunch line on Monday when the girl in front of her was told to return her tray of food. “They were like, ‘You owe $25.60; I have to take the tray from you,’” Feitl told NBC affiliate WTHR. That day, all students who had hit a $25 debt limit with their lunch balances were given an “alternate lunch” of a cheese or peanut butter sandwich and milk.

The Kokomo school district in Indiana sent parents letters at the end of last year to alert them to the new debt policy, which went into effect on Jan. 1. It reads: “Once the $25.00 charge limit has been reached, an alternate meal will be provided to the student. The parent and/or guardian of the student will receive an automated phone call and/or email explaining that the student has reached his/her charge limit.”

Jeff Hauswald, superintendent of Kokomo School Corporation, told WTHR that the rule follows federal regulations and aligns with other surrounding districts. Last year, the district had to foot the bill for more than $50,000 worth of unpaid school meals.

Finances aside, Feitl objected to the way the students were treated, and she snapped a photo of the cheese sandwich to post to Facebook with this message: “If you owe $25 or more on your lunch account, this is what Kokomo High School provides you for lunch. Two slices of bread and two slices of cheese. Absolutely mortifying. My heart goes out to the kids that I go to school with that get their only meal a day at school.” Her post has been shared nearly 800 times, and there is a heated discussion in the comments.

Eduhonesty: I like Sierrra Feitl. She perceived an injustice and she went into battle. But she’s wrong. For one thing, the kids with free and reduced-priced lunches were not the target of these cheese sandwiches. This policy was for regular, paying customers according to a later part of the article, for those parents who did not qualify for free lunches. The government will pay for lunch if you are truly poor. While I have not been able to confirm this fact, my understanding is that, according to a school spokesman, only 10% of the kids with lunch account deficits qualify for any assistance.

That $50,000 the district paid for unpaid meals last year? That money was taken away from other alternatives. That was $50,000 that did not go to purchase new computers or books, an extra teaching assistant, or new musical instruments. That money that parents owed and did not pay took away $50,000 from this year’s students. My cafeteria in past years has taken the same approach, given those same cheese or peanut butter sandwiches to kids. What else can you do when the parents don’t pay what they owe? The kids can exert pressure to get the lunch money to come in. Without that pressure, a school district ends up saddled with a debt that takes money away from future student needs.

Yahoo should never have generated this controversy, or should have provided more information when they let Sierra’s cheese sandwich pictures loose on such a huge source of internet information. I imagine the kids are avidly following this story about their own district and the comments now contain many versions of “life is hard when your parent is a dead beat.” Negative comments relating to parent irresponsibility abound. If the kids felt bad before, I suspect they feel worse now.

If they are embarrassed, though, maybe that’s not such a bad thing. We should be teaching lessons beyond the core curriculum. The lesson here is that if you don’t pay your bills, that behavior will come back to bite you — a highly useful lesson that should be learned before cars are repossessed and young adults get ready to sign on the bottom lines of those many mortgage documents.

Abby nailed this one

“Dear Abby” recently received a letter from a woman who was deciding whether or not to move to a better school district for the sake of her daughter. She knew her district was substandard, but loved her neighbors. Those neighbors were best friends, vacation and carpool buddies who shared their lives. The parents were friends, the kids were friends, and even the dogs got along well. Reading between the lines, the woman wanted Abby to respond with something like, “Good friends are precious. Stay where you are at.” But Abby stepped up to the plate. She unequivocally responded to “Heavy Decision” that her daughter’s education needed to come first. I’d add that maybe “Heavy Decision” should consider a plan that moves both families to better schools if possible.

I have given this advice to students’ parents in the past and I want to blog my view:

Parents should move into the best school district they can afford. A two-bedroom apartment in a great school district most likely will be a better move than that house with a picket fence in the wrong zip code. I taught bilingual classes in a middle class district that performed up to par for the state and in a district that consistently underperformed state schools by a wide margin. Here’s the piece that does not receive enough attention: I got almost all my homework back at that middle-class district. The kids in my bilingual classes absorbed the culture of the school around them. That culture included working at home at night. The kids in that middle-class school took college seriously. Because my bilingual students listened to their classmates, they knew they were supposed to go to college, even if their immigrant parents had no experience with education beyond high school or sometimes middle school. In contrast, in the 89% poverty, lower-scoring school where I taught, student efforts never matched up to those from my middle-class school. Homework completion was spotty, even after mandatory Friday after-school sessions were added for students who had not done the homework. The homework that came in did not demonstrate the same commitment and effort. Blow-off efforts were regrettably common. So were drop-outs, and babies born to mothers in high school or even middle school.

Adolescents mimic the “cool” crowd around them, but “cool” differs from school to school. In some schools, academics become part of being cool. You may not need “A” grades to be cool, but you are expected to keep up with fellow students, to be part of the crowd. Where I live, failing classes will get you an enormous amount of academic support, as well as contempt by fellow students. In the financially- and academically-disadvantaged district where I last worked, academics never carried close to the same weight. You could be an academic disaster and still be “cool.”

In addition, because the school itself had fallen so far behind, classes necessarily did not offer the same opportunities. Despite my view that we are drowning in testing, our test data tells us a great deal. If the average academic level of a middle school math class falls in the fourth grade range, even a strong teacher will be held back by the need to present remedial instruction regularly. In a stronger school, less time will be required for remediation so more grade-level work will be presented and expected. I can teach more math and teach that math faster if my class enters at grade level at the start of the year. Remediation takes time away from grade-level instruction. The studies tend to show that students who enter school behind often fall further behind with time. I suspect necessary remedial instruction forms part of that picture. The opportunity cost from regular remediation will be all the material that cannot be taught while school minutes are being employed to fill in the gaps from earlier years.

Other intangibles should also be considered in choosing a school district. A district that sends a large percentage of graduates on to college will be a district that provides helpful guidance on college opportunities. The college fairs in stronger districts are often larger and more informative. Colleges and universities cannot afford to attend college fairs at every high school across the nation. These institutions of higher learning will pick schools that have previously provided them with students. That poor district’s high school college fair provided access to information about state schools, as well as local for-profits, trade schools and the military, but the Ivy League was conspicuously absent. Ivy League schools do recruit where I live, however.

Eduhonesty: Looking to move? I’d go to your state’s school report cards before I went anywhere else. I’d find the best schools in my area and then see what I could afford. If the best I could do was an apartment, I might still make that choice. My local high school was chosen as one of the top 100 schools in the nation by U.S. News and World Report a few years ago, in part because almost every student in the high school goes on to college. That’s an educational advantage that may be worth a tiny kitchen and lack of a garage.

Stumbling along

“Men occasionally stumble over the truth, but most of them pick them-
selves up and hurry off as if nothing ever happened.”

~ Sir Winston Churchill (1874 – 1965)

Here is the truth that we keep stumbling over: Unless we offer longer school days and school years to the students who have fallen significantly behind, we will never level the academic playing field. No magic exists to catch kids up in a standard school year, especially since the kids who have fallen behind tend to do less homework than their counterparts, rather than more. An equal school year tends to be unequal when that homework piece is thrown in — with the advantage going to the kids who were out front to start.

When we debate teaching techniques, disciplinary methods, and even extra tutoring, we are stumbling away from the truth. A few extra hours of tutoring per week may still leave students spending less time on academics than those more fortunate counterparts who attend more academically demanding schools. This fact tends to result in calls for raising the bar and increasing academic demands in our lower-performing schools. While upping our demands may prove useful sometimes, a child who enters school with only half the active vocabulary of another child will not catch up simply because the bar is raised. I can give all the rigorous homework I want. The number of papers turned in depends on how well my students can read and understand that homework. If the work’s too hard, the work won’t get done.

We can’t raise the bar to get out of this mess. We have to lengthen the school year.

Intriguing thoughts on our ADHD students

From NPRed, I recommend http://www.npr.org/sections/ed/2016/01/04/459990844/were-thinking-about-adhd-all-wrong-says-a-top-pediatrician. The article is titled, “We’re Thinking About ADHD All Wrong, Says A Top Pediatrician.” The following block quote contains a concept I support:

From Diagnoses of attention deficit hyperactivity disorder are up around 30 percent compared with 20 years ago. These days, if a 2-year-old won’t sit still for circle time in preschool, she’s liable to be referred for evaluation, which can put her on track for early intervention and potentially a lifetime of medication.

In an editorial just published in the Journal of the American Medical Association Pediatrics, Dimitri Christakis argues that we’ve got this all wrong. He’s a professor of pediatrics at the University of Washington and the director of the Center for Child Health, Behavior and Development at Children’s Hospital in Seattle.

Parents, schools and doctors, he says, should completely rethink this highly medicalized framework for attention difficulties.

“ADHD does a disservice to children as a diagnosis.” — Dimitri Christakis

Here’s why. Researchers are currently debating the nature of ADHD. They have found some genetic markers for it, but the recent rise in diagnoses is too swift to be explained by changes in our genes. Neuroscientists, too, are finding brain wiring patterns characteristic of the disorder.

But the current process of diagnosis amounts to giving a questionnaire to parents and doctors. If they identify six out of nine specific behaviors, then the child officially has ADHD.

“If you fall on this side of the line, we label and medicate you,” says Christakis. “But on the other side of the line, we do nothing.”

This process is, necessarily, subjective. But there’s an awful lot of infrastructure and, frankly, money behind it, especially in our education system. A clinical diagnosis of “chronic or acute” attentional difficulties gives public school students a legal right to special accommodations under the Individuals with Disabilities Education Act. But a child who falls just short of that diagnosis is left without any right to extra support.

Christakis says that, instead, we should be thinking more about a spectrum of “attentional capacity” that varies from individual to individual and situation to situation.

Eduhonesty: I like the idea of placing ADHD on a spectrum. We have too many yes-no diagnoses as it stands. Many people are neither depressed nor not depressed. Many people are neither autistic nor not autistic. We acknowledge the autism spectrum, the kids with autistic characteristics who function adequately or even excellently in school. The same can be said of ADHD kids. One of my daughters once teetered on the edge of an ADHD diagnosis. I could have tipped that girl into medication and accommodations. But she was doing too well in school, despite erratic performance in a gifted program. She would eventually graduate magna cum laude from college and enter an Ivy League graduate program.

How much attention deficit qualifies as too much attention deficit? We all have drifty moments. Some kids may drift frequently and yet remain educationally functional. If the boy who blurts out random thoughts on firetrucks understands the week’s math, gentle reminders to get back on task may be all the help that’s needed. I was a strong but somewhat ADHD student in high school, and I still remember chasing a dandelion seed across my Spanish classroom, catching it, and exclaiming, “Lookie, Señor!” I did not come back to the moment until the class and teacher broke down in laughter. The either-or nature of ADHD diagnoses has always bothered me.

Attentional capacity seems a sensible approach to attention issues. I’d like to go one step further, too. Different does not mean deficient. In the end, an ADHD student who is frequently performing at or above grade level should probably be left alone. That student may be a handful in the classroom and at home, but sometimes the genetic dice roll combinations that are not easy to force down into a chair for hours. The inability to sit for prolonged period should not be viewed as a defect. I struggled to sit quietly through the years, but I now have two graduate degrees.

I will end by noting that many kids can easily sideswipe learning while watching fire trucks. These students are able to keep up with their classes even if they need extra management and occasional modifications. We are likely better off leaving those students alone who are not quite keeping up with the crowd in terms of overall grades, but who are testing at or near grade level on annual tests. Regularly forgetting to do or bring homework should not, in and of itself, result in a possibly prejudicial school placement. Viewing ADHD as a spectrum behavior rather than an on/off disorder would help kids who could benefit from a little extra help without falling into the full machinery of the state.

Computers will never be a cure-all

(Continuing the thread on America’s lack of mathematical prowess today)

A frightening number of teachers and administrators have told me that today students need a different, new kind of education. They need to be taught “retrieval skills” so they can access information.

One administrator said to me, “just give them calculators” when I was discussing the fact that my students could not do a number of basic mathematical operations. Many were arriving in middle school unable to divide double-digit numbers.

American education has gotten lost — lost and lazy.

Can I find the answer to the following problem online?

37 – 12x + 7 – 4x = 115

I can probably find that answer quickly. A kindly math geek will bail me out on some answers site. Or I could text my cousin who loves math and get the answer in just a minute or two.

Do I understand variables any better than I did before? Quite possibly not. With luck, my cousin will explain her reasoning and show me how she got her answer.

As far as the calculators go, I have no problem with students who can divide using their calculators as a shortcut to get division answers. The dividing itself only matters insofar as it represents a mathematical concept, one that will be needed later in many different forms for many disparate calculations. In simple terms, more complex mathematics will be filled with situations where students will need to break down an equation into smaller pieces in order to reorganize those pieces and change their form to get a targeted result.

Eduhonesty: Except for specific computer programs designed to practice and drill math skills, mathematics should be learned offline. Retrieval not only does not serve our students’ mathematical needs, that retrieval can prevent learning — especially when the emphasis in class is placed on grades rather than mastery.