# Common Core Crazy? Making sense of the viral common core math rounding problem

## Perhaps you have seen the Facebook post by an angry mother who  is upset about her daughter’s Common Core-based math problem. There’s a larger lesson here, but it’s not about the Common Core.

Carole read 28 pages of a book on Monday and 103 pages on Tuesday. Is 75 pages a reasonable answer for how many more pages Carole read on Tuesday than Monday?
And the student responded,
Yes, 75 is a reasonable answer because 103-28 = 75
for which she was deducted a point for not estimating the answer of 70, since that appears to be the lesson about what is a “reasonable” answer. The teacher marked:
-1 [pt] Estimate 100-30 = 70
For background on Common Core math methodologies, see Key Shifts in Mathematics

### Right math lesson, wrong question

Other blog and news sites have taken this on, for and against the question. I think this is a horrible question, but not because the exercise of rounding is worthless. It’s a poor assessment question because,

1. The answer, “75” is both accurate and reasonable.
2. It doesn’t lead the student into a larger methodology or purpose. Either the student missed the purpose of this exercise or the teacher didn’t set that expectation.

### Aligning Assessment Purpose with Expectations

This question seems to me to be assessing student understanding of the word “reasonable” more than the mathematical process of rounding. If the teacher had already defined a rounded answer as a “reasonable” one, then the student got it wrong.

However, had the teacher just thrown this question out there, how possibly could that child have known to round when faced with the word “reasonable” on an arithmetic problem?

Clarification of what is excepted of the child is due here.

Unfortunately, many teachers engage kids in processes without telling them why it’s important, where they’re going next, and how to apply it forward.

Kids need context, so when they say that they like lessons to be “broken down” what they’re asking for is clear statement of purpose, context, and relevancy. Don’t assume anything,  teachers!

And parents, when teachers are vague or opaque, clarify it for your child.

### The Problem here is that the Question stopped short of a fuller lesson

This should have been a 3-part question:

1. Use rounding to create an “approximate” answer.
3. Explain why or why not the approximate rounding answer is “reasonable.”

As a history teacher, I spent a lot of time teaching simple mathematics to 9th and 10th graders who struggled with dates and time. It was always a good teaching moment when looking at dates.

### Rounding as History math

If I were to ask students, “How many years ago was 1492 from today?” they’d go running for a calculator.  So I instead asked them, “About or approximately how many years ago was 1492 from today?”

My goal, just as that of the Common Core rounding problem, was to help students learn how to look at dates and make approximate statements on how long ago it was or the time between them.

We would start with why that’s important, anyway. Okay, so Columbus first sailed to the Americas in 1492, which launched a series of outcomes that led to today’s world. We want to 1) develop an understanding of how close or far from us that was in years; and 2) investigate both time and change. So, we will:

1. calculating approximately how many years ago 1492 was
2. measure that in centuries
3. count how many family generations that makes
4. use rounding to calculate an accurate measurement of how many years ago Columbus first reached the Americas.

After letting them try out their own methodologies, I would offer the process I like to use:

• every 100 years is a good tape measure for time in history.
• 100 years = a century

Then I’d use rounding to approximate our two dates to their nearest century:

• Today = 2017 = about 2000
• Columbus = 1492 = about 1500
• I can do that math more easily now: 2000 – 1500 = 500
• Therefore 1492 was about or approximately 500 years ago

(Here we can work on how many centuries and family generations ago it was –for generations, we’ll assume 20yrs per generation = 500/20 = 25 generations –> wow, only 25 generations, that is, parent –> child, was not that long ago, was it!)

Now let’s use our rounded answer, 500 years ago, to make a mathematically correct answer:

• Since 2017 is 17 years further away from 1492 than 2000, we need to add 17 years to the rounded total
• Since 1492 is 8 years further away from 1500, then we need to add 8 years to the rounded total.
• Therefore, 17 + 8 = 25 years to add to the approximate answer:
•  500 + 25 = 525 years = (2017-1492)

To reinforce this lesson, I would work with another date from the 20th century, say a parent’s birth year, 1974. Same process works, but with the one little switch that 1974 is closer to 1492 than 2000, so:

• We already know that 1492 is 8 years further away from 1500, so we will need to add 8 years to the rounded total.
• But, 1974 = 26 years closer to 1492 from 2000
• Therefore we have to subtract 26 from our total (as opposed to adding the 17 years to 2000 for the year 2017)
• So, we will be adding 8 and subtracting 26:
• = +8 + -26 = -18 (or, 26-8=18)
• We next subtract 18 (or add -18) from our rounded total:
• = 500-18 = 482 years between 1492 and 1974.

The lesson could then be enhanced by working with 1975 as the round instead = 475 years. So we have -1 for 1974 and + 8 for 1492 = -1+8= 7;  then 7 +475= 482 years between 1492 and 1974.

### Teachers, Don’t Cut Short the Lesson!

What have we learned:

1. Approximations and rounding is a valuable tool.
2. We can use approximations to quickly ascertain accurate math answers.
3. Rounding can help us think in different time or math units such as centuries and generations.

So you see, my problem w/ the Common Core question is not that rounding is an invalid exercise but that rounding must be taught as a distinct skill and why it is useful.

Teaching should always be clear about purpose and be applied and extended for new knowledge.

– Michael

# Dan Bozzuto on Effective Teaching, Learning & Standardized Tests: Student Success Podcast no. 27

### Dan Bozzuto explores the difficulties to replicate great teachers, the inherent problems with standardized testing, and some great ideas on how to address both.

Part 1/2, featuring Dan Bozzuto, award winning educator and inspired classroom teacher. Dan considers my question, “are good teachers replicable?” which takes him to standardized tests and other obstacles to student learning, including to question the very purpose of modern education.

This podcast is just a start to the essential questions of modern education, which Dan and Michael will carry forward in an upcoming Part 2 interview with Dan Bozzuto.

Student Success Podcast No. 27, published July 19, 2016 (recorded on Aug 9, 2015).

### It’s hokey, trite, and boring:  long live the great American high school graduation ceremony & hopes and dreams for students and parents!

As a teacher I grew cynical about graduation ceremonies. At my school the faculty blessedly sat well behind the podium, mostly out of view. When one of our kind ever “went to the dark side” and joined the administration, we’d always riddle them with texts during the ceremony about having to behave and offering to pass along some Hot Tamales, the faculty currency during these tedious events.  We ran bingo contests with student names, competed as to who could eat the most Hot Tamales at a time, bet on the length of the speeches, and otherwise fooled around worse than the children had done in our own classrooms.

I no longer go to graduation ceremonies for a living, but the other day my wife and I sat through a ceremony for a family member. Since we were in the audience, I had to behave. At least, I thought, the faculty of this school had to behave, too, as they were seated on the main floor by the students in full view of everyone. Ha!

Then I had to figure out how to survive it myself. My wife had banned all thoughts of listening to a podcast, so I put the phone on airplane mode and, unlike half the people around us, sat isolated from the outer world with only a graduation before me. So I begged my wife for a pen. She sighed, reached into that magic bag she calls a purse, and produced one. I spent the rest of the ceremony employing the advice I give students on how to survive a boring class by jotting notes on the program, deconstructing the events.

My first notes regard how many times the principal bragged about grade inflation. Well, he didn’t put it quite like that, but he bragged over and over that 103 kids, about a third of the class, graduated with honors. I pondered how the rest possibly managed to get below a 3.5.

The clue was “Weighted GPA,” which is education-speak for honors-classes bonus where a C is a B, a B is an A and an A is a 5.0 on your 4.0 scale GPA. There were certainly kids taking honors courses (AP/ IB, etc.) that did not make a 3.5, but for those kids not taking honors, a 3.5 is truly a 3.5, whereas for the honors kids that’s just a C.

My next notation reads, “7 or 8 Vice Principals!!” and is underlined three times. I was already shocked by the number of faculty — they streamed in like the Persian army of old.

Then the principal got to introducing the administrators. What should have been a quick, “Here’s Ben, our Vice Principal of Student Affairs” and “Meet Lucy, our Academic Vice Principal,” turned into a directory of all the administrative positions you never heard of. I attempted a quick mental calculation of the administrators times their bloated salaries divided by the county residents, but then I just got angry.

Next came introductions to the County Superintendent of Schools, a Director of Curriculum (was the County Director of Honors Programs unavailable?) and a couple Board of Education members. My notes read, “Memo to self: NEVER RUN FOR BOARD OF EDCUATION!”

The Superintendent took the easy route and had the kids write her speech. She just read off a list of quotations on the meaning of high school that the school had students send her. Our family graduate made the list with one I felt was rather apropos to my own take on the ceremony about not letting the haters get you down.

A Board of Education member then gave a speech she had to have pilfered from a web search on “trite graduation speeches,” featuring Robert Frost, of course, and his “The Road Not Taken.” I can’t remember if she got the title right, as it’s usually called “The Road Less Traveled” by most graduation speakers. And, of course, she read the poem.

Really? You read the poem? Okay, it’s only four stanzas, but make that four incomprehensible stanzas coming over a basketball stadium loudspeaker to an audience most of whose last breath of poetry came precisely at their own high school or college graduation ceremony, likely hearing this same poem.

She next delivered the standard tripe about daring to take the road “less traveled,” even though the poem states that both roads are equally traveled:

Worst of all, and here I take offense on behalf of Robert Frost and all thinking English teachers, she assured the kids, heh, don’t worry, even if your road is the wrong one it’ll be alright because, “you can always turn around and go back the other way later.”

What’s horribly wrong with that misreading of the poem itself is precisely what’s wrong with an education system so full of backstops and “safety nets” that magically protects students from their own bad choices.

It starts with turning zeroes into 60% Fs, dumbed-down summer school and no-competition sports, and ends with the absurdities that we’re all winners no matter what we do – and one third of the graduating class receiving honors.

### Nobody Better Than Anyone Else

But even those students are all equal among themselves, as the word “Valedictorian” didn’t make it into the program. The student speakers were the class president and another student whose title or honors went unmentioned. My notes here read: Memo to school: VALEDICTORIAN IS THE PERSON WHO DELIVERS THE VALEDICTORY.”

Usually, that’s the kid with the highest GPA but not always. I learned afterwards that the selection was based upon a speech contest, which is fine. Nevertheless, the word “valedictorian” did not appear in the program or the event, and no mention was made of who was no. 1 in the class. I guess we can distinguish a third from the rest, but not the one-percenter from even that top third.

“The Road Not Taken” ends with a “sigh” as the narrator considers that he may, in the future, look back upon the choice he is making today with regret:

I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I,
I took the one less traveled by,*
And that has made all the difference.

The job of educators is to guide children into making positive choices. By dumbing down both negative consequence and positive rewards, we are developing fragility in our children, not robustness.

There’s much pedagogical discussion about the benefits of failure, but clearly it’s not being implemented here. This school has a multitude of administrators whose job is to make sure as many kids as possible “earn” a 3.5 and as few as possible don’t somehow manage to fail out. With one-third the class earning honors, largely due to the grade inflation of the GPA “honors bump,” what’s the other two-thirds to do but ponder why they bothered at all?

The problem is that the failure is too easy and too little sanctioned. There is no pain in failure if summer school is easy and all stigma is removed. Worse, in offering no positive alternatives to academic failure, we merely make anything possible and that will too often be seriously bad choices. Our Board of Education speaker is only creating more future sighs of regret.

And let’s clarify here and now that a very few, if any, of the kids will be a trail blazer. I wish a normal life upon them all, one that, when they get to be my age, they don’t look back upon and sigh, as Robert Frost’s narrator knows he will one day, and wonder what might have been on that other road. The lie our speaker told is that each of us is unique and special and, by the way, we won’t be held accountable for our screw-ups. Maybe you’re the one. Good luck. But for the rest of us, let’s just see what we can do to make our paths — which are never really just a straight choice between this and that, and are instead a series of turns and cross steps — as safe and happy as possible.

### A sigh for who didn’t make it – and applause for those who barely did

I know there were kids who didn’t make it through to their senior year and were not there that day. I also know there were kids who walked that stage but have not yet earned their diploma. For the ones who have fully graduated and who earned every bit of it — and not just the one-third of the class who benefited from grade inflation, I congratulate you, and I trust your road will be a well-planned, well-traveled, and safe route to happiness.

I rather love the kids who struggled, who got screwed by a teacher or two, possibly deservedly but mostly not, who dug a few holes, and who can’t remember what’s due when, but who fought back and graduated. God bless the 103 honors students, but the others are my heroes.

Yet, it’s the kids NOT on that stage who need to learn the meaning of the Frost poem. Those who weren’t there, dear Board of Education speaker, are your audience, and you might do a better job of helping them avoid the lesser roads they unfortunately took — and can now very little work back from.

Honest, I’m not a buzz kill, and I congratulate the students and their families on this graduation. That’s wonderful and it’s an important rite of passage in our country. My cynicism is for the hordes of Principals and Vice Principals and Superintendents and Boards of Education who could use a refresher on the meaning of “The Road Not Taken.”

– Michael

* The “one less traveled by” isn’t a unique, different path, rather, it’s the narrator’s future rationalization for a regretted choice of today — and it couldn’t be a more inappropriate sentiment for a graduation ceremony.

# Introducing “Tips for Teachers”: building efficiencies to free you to teach (and not waste so much time doing everything else)

## The number one teacher complaint is time.

Introducing “Tips for Teachers,” a series of blog posts, videos, lessons, and ideas from School4Schools.com LLC on helping teachers get through their routines and days more efficiently – so they can focus on what they love and what they’re there for: teaching kids.

#### Tips for Teachers will focus on teacher processes and the use of technology to build efficiencies in every day tasks.

Some coming posts include:

• Using Outlook to get in control communication, tasks, calendars, and email management.
• Using OneNote for organization, brainstorming, and task management, as well as some of its other cool features such as email integration and whiteboard.
• Power of a WordPress teacher or class website.
• Using an SMS system for student reminders and increased workflow.
• Grading by voice recording and sharing feedback with students and parents by voicemail propagated through email.
• How to make a simple, quick voice to text reader to use in the classroom or to help kids read texts you assign.

#### Teachers, get your time back!

Check back for these and more coming Tips for Teachers, and follow us on Twitter, Vimeo, or Facebook.

Or subscribe to Tips for Teachers here:

### Some background thoughts on why I’m so concerned about teacher efficiencies

by Michael Bromley, founder and president of School4Schools.com LLC & the A+ Club

Schools throw huge resources at teachers: Learning Management Systems (LMS) , smartboards, software, copy machines, computers… but how many PD days were ever spent learning how to use them, and if there were any, what follow-up support was there?

My ten years of classroom teaching was always tainted by administrative disdain for my time. We were given tools and expected to use them – without real ongoing support on how to actually use them.

For example, if your school provided you with the Microsoft Office Suite, I’m guessing there was never any PD attached to it, much less any serious guidance on how to use it effectively. Just look at how much a business will spend on teaching its professionals how to use Microsoft Office. A quick Bing search yields \$2400 a day for training of 12 employees, or a four-day intensive course for \$480 per student. Or, what about a \$20 per month subscription to Lynda.com? Nope, not for schools. They’ve got too much money to spend on other things and none for your personal efficiencies and time.

Sure, at my school we had a couple demonstrations on a new system (never anything on MS Office, which most teachers thought consists of Word and PowerPoint.)  I was even asked to show other teachers some of my use of technology during a staff meeting or a PD or two.  But there was never any follow-through and no ongoing individual attention to helping teachers use these tools or build efficiencies. (Some of these same administrators even asked me privately to show them some of my tricks.)

Our tech guy knew hardware but wasn’t much help on how to actually use the things as a teacher. The best support we got was from the students helpers who could actually make a sound system or video work. Meanwhile, every time I dropped through the teacher lounge, I’d be asked to show another teacher how to do this or that on the school LMS or some other computer thing.

It’s something about education that its resources are seen through the lens of budgets and allocations, but not actual use.

### Here are two stories to demonstrate it

1. When my daughter started attending my school, I was suddenly not just a colleague but a parent.  Now I saw my colleagues” grading habits, their assignment postings, and I heard the good and the bad from my daughter every day on the way home from school.

One of the most shocking things I discovered was how little her teachers used the very basic LMS program, Edline. It was a total waste (such as the teacher who put up assignments but had them repeated every day of the year, including weekends).  Assignments and grades were posted randomly if at all, and so many answers to my questions as a parent that could have been answered through Edline turned into email and hallway chases. And I was in the same building with them every day, so what about the frustrated parents who couldn’t get the answers I could only get through a personal shakedown?

I told our principal and facilities vice principal about my observations and how I personally had to spend minutes  every day that turned into hours every week helping my colleagues do simple things on Edline that nobody had bothered to show them before and how the school should really help its teachers learn how to use the system. The two of them laughed at me. Literally. They laughed, and I walked away.

So it was back to helping my colleagues one at a time and day to day figure out how to easily and meaningfully put up their assignments and grades for students and parents.

2. When my school replaced blackboards with whiteboards,  I purchased my own projector to take advantage of the ready-screen whiteboards represented. The school had one or two projectors that we were always taken, so I got my own. Now my kids had the benefit of my desktop in every class, and I had the benefit of prepping to it rather than hoping I could get one of the other projectors.

A couple years later the school got a donation for smartboard systems that used ceiling-installed projector that interacted with a device attached to the whiteboard.  Cool stuff. They put it in my classroom — yep, and left it at that.

The audio wires weren’t installed properly, and the tech guy couldn’t figure them out. So I bought my own little amplifier and set it up myself. The VCR system just didn’t work right, so I bought all my videos on Amazon and ran them straight from my computer. And so on.

The smartboard system had a magic wand that worked by interacting with a static electric field that was projected across the white board projector area by the attached device. However, the two 8-foot whiteboards were connected by a metal band that ran down the middle of that projector placement. Static-electricity field + metal band = I could only use half the smartboard screen at a time. The kids and I laughed it off every day, but it was a true annoyance that was daily wasting my time and impacting my lessons.

Moving the projector was an option, but I knew that would be difficult as it was a permanent installation in the ceiling. Why not, then, just cut one of the 8-foot whiteboards in half, move the other one to the middle and the two 4-foot pieces to the side? I asked the vice principal of facilities (the one who laughed at my idea for a PD to instruct teachers on how to use Edline) for help. He was furious. How dare I question what the donors had given me! Alright,  whatever.

### See horse. See cart. The wrong one is in front.

Here’s the problem: administrators perceive teachers as service providers for the wrong set of clients. Students and families are not their clients, policy, pedagogy and the Department of Education are. If focus were upon students and parents as the real clients, schools would be very, very concerned about every aspect of a teacher’s day, especially how their teachers use their precious time to support their clients. Instead teachers are providers of pedagogy, test results and public policy.

### What would I do as an administrator?

Good teachers know who their real clients are.  Everything else is backup and resource for the core aim of teaching.

My dream school is one in which kids truly are first, and in which teachers drive their teaching and not the school. The school’s job would be to support, guide, and help execute what the teachers themselves decided they can do best. Just dreaming here, but isn’t that what we believe we’re supposed to do with kids — and if so why, then, don’t schools approach teachers the same way?

Anything we can do to make a teachers’ day go a little quicker, a classroom a little more productive and effective, and to help along a teaching process or to lessen a frustration, I figure there is at least one kid who learned just a little more that day and one parent who felt good about it.

Yes, it is “all about the kids,” but it’s helping teachers help kids that concerns us. In our A+ Club student support program, we help kids help themselves. Through Tips for Teachers we hope to help teachers help themselves help kids, one efficiency at a time.

– Michael

# High school students getting smarter, or high schools getting easier?

### Or just another case of grade inflation?

Bad news from the National Assessment of Educational Progress: as of 2009, a majority of high school students scored “basic” or “below basic” in reading and math skills.*

(*Kudos to the Wall Street Journal for not using “progress report” in its article or headline; here for the rest who fell into that trap.)

Hmmm: in the early Nineties, 74% of  high school students graduated. These days, it’s 81%. Clearly, the additional 7% of graduates aren’t driving those proficiency scores higher.

The report also informs us that based on SAT scores, only 43% of high school students are prepared for college.  Whether or not that number has been extrapolated to the entire graduating population is unclear. If not, the prepared-for-college students represent 43% of the only some 45% who take the SAT (as of 2007).

All of this means… Continue reading

# AP Exams! Are these classes really all that “advanced”?

### Welcome to the Advanced Placement exams. But is it really the blank check it’s supposed to be?

AP exams start in a week (May 5 – 16), so, yea.

(Oh, and btw, we can help you prepare: we have experienced high school teachers to work with you  — real teachers, that is, not the just anybody’s who work at “tutoring” sites.)

So, you suffered through the class all year — supposedly it’s “college” level — and now you have to spit it back for a few hours. Best of all, it’s not for a grade. So if you didn’t prepare it doesn’t matter… right? The College Board says it’s good for you (AP Exam benefits) and I’m sure it is. It’s good for your teacher, too, because teach gets to pretend it’s a real class for a change. Continue reading

# Liddy Allee-Coyle on teaching as a two-way street: the power of honesty & respect for students

## Liddy Allee-Coyle on teaching as a two-way street: the power of honesty & respect for students

Student Success Podcast No. 18, Mar. 19, 2014

Today’s Guest: Liddy Allee-Coyle, Master Teacher, Ithica City School District

In this interview, Liddy discusses her work as a teacher coach to champion the student-first classroom in which students have trust with their teachers and their learning and  “choice, relevancy, and a reason” for learning.

As Liddy says, “Every kid wants to know why… if we answer that ‘why’ we get more buy-in.” Liddy’s ideal of relevancy for students is learning any lesson as practice for further learning and not necessarily that particular lesson, “to be life-long learners.” Continue reading

# Dr. Jonathan Plucker: Excellence Gaps and the national imperative for equity AND excellence

## Dr. Jonathan Plucker: Excellence Gaps and the national imperative for equity AND excellence

Student Success Podcast No. 17, Feb. 28, 2014, recorded Feb 24, 2014

Today’s Guest: Prof. Jonathan Plucker, University of Connecticut

For background, please see the first Student Success Podcast interview with Dr. Jonathan Plucker, Talent on the Sidelines: the Excellence Gap with Dr. Jonathan Plucker or this blog post: Student Success Blogpost: The “Excellence Gap”: income & race disparities persist

Dr. Jonathan Plucker rejoins us to update progress and events since our previous interview in October, 2013 regarding “excellence gaps” as demonstrated by his study, “Talent on the Sidelines.” Continue reading

# Agenda books and schools: making good little secretaries

### Why are we teaching kids to use 1970s technology?

Ever hear of Day Timer? Yes, the personal agenda book still exists, but only for a few old school types. Except in schools, where the kids are supposed to use agenda books, and it’s all their damned fault if they don’t.

Seriously. At the A+ Club, we hear from teachers all the time that Johnny “just needs to do what all the other students do and write down the assignments in his agenda book.”

If it were up to me, every kid would have exchange email and  Outlook working seamlessly on their computers, tablets, and phones, and everything they need to do would be posted there automatically. Continue reading

# “Roam schooling” & online tutoring: learning without barriers?

### Is online tutoring & digital learning really going to work?

Fluff or substance? Revolution or fad? Where is online tutoring and digital learning going to take us?

When I was in K-12 school in the 1970s, mostly, education was being turned over. The students had no idea, as it was just happening to us. But what is education today was largely defined by the research, theories, experiments, and, mostly, fads of that period. Continue reading