All posts by Michael Bromley

Founder and President of School4Schools.com LLC & The A+ Club, Bromley taught Social Studies for seven years at Archbishop Carroll High School in NE Washington, DC. Bromley is a historian, published author, entrepreneur, and dedicated teacher. School4Schools.com LLC and The + Club are Bromley's expression of enthusiasm and love for students.

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.

Click here for the Facebook post by Larisa Yaghoobov Settembro

The problem asked was,
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.
  2. Use your rounding technique to develop a mathematically accurate 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:

I’d start with defining a century as a common time unit:

  • 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

3.14: A Pi day celebration from a math idiot

Is math just for math people? Are you just not wired for math? Well, you and your math-struggling student can celebrate Pi day, too!

I was awful at math in  high school. So bad, in fact, that I  didn’t qualify to take math in college.

Felt great at the time, but looking back on it, what a shame. The only math I could do as a kid was “breaking a twenty” as a cashier at my job at the drug store. I could make change like a champ! Now, cashiers don’t even have to know any math at all, since the machine does it all for them.

So do we really need math?

Sadly, some universities think we don’t:

Wayne State drops math as general ed requirement

What a shame — and I know why they’re doing it, although they’ve got an excuse for it:

This decision was made largely because the current (math) requirement is at a level already required by most high school mathematics curriculum,” the school wrote.

Yes, and that’s precisely why so many colleges have to teach remedial math to freshmen — and that’s the very problem that Wayne State is avoiding.

Now math at Wayne State will only be required of kids who don’t need help with it.  By dropping math for the rest, they’re giving up on those kids just as my college gave up on me.

Now This is Me, Missing Math

Well now into my middle age, having built a couple businesses, written a couple books, raised a couple kids, planted a couple trees, you know, a full life  — and now working with students in the A+ Club across the country, I contest that we all need math.

Higher math skills would have allowed me to engage in more subjects at college that I find fascinating such as Physics and Chemistry. Higher math skills would today allow me to make better analyses of my finances and businesses. Higher math skills would allow me to understand the statistics behind many of the studies I read on education and behavioral economics. And lacking those skills bars me from conducting studies of my own.

I became a math illiterate for the very same reason I see so many middle, high school and college students struggle with it today:

  1. They found math difficult and thereby highly aversive;
  2. Consequently, they avoided engaging in the independent practice required for advancement in math;
  3. Consequently to that, they never got the feedback and direct help they needed in order to engage in that so very important independent practice (see Help for students struggling with math: “guided” v “independent” practice);
  4. Repeat until the student is no longer required or allowed to take math or just gives up.

A Pi Day Plea: Parents, help your child like math!

I can only urge parents not to let math slip by your child. It kills opportunity and, worse, it becomes an excuse for not being able to do those other things that require math.

Even if you don’t like math yourself, you can engage your child in math by turning it from judgment into positive reinforcement.  See my post for how to help your child with math even if you don’t know math by engaging in Socratic questioning to guide students in explaining it themselves: How to know if your student is really learning: “if you can’t teach it you don’t know it”.

Your child can succeed in math, and it doesn’t take expensive tutors to get there. What’s required, though, is ENGAGEMENT, because,

Math is a process not a skill

What my parents and I didn’t know when I was in high school was that math is not a skill set. My brother was and is a math whiz, it just came to him easy, which made it enjoyable.

Me, not so easy.

Having scored higher on the SAT math than on the verbal sections (and I’m a writer), I should have known that, yes, I can do math.

The reason I didn’t LEARN math was that I didn’t DO math. Hated the homework, thereby hated the class, thereby didn’t get teacher feedback, thereby didn’t learn, and thereby did poorly on tests.

Happy Pi Day to you and your non-math student

Let’s not use Pi Day as a punishment but as reminder that we all can do math.

When I work with a student who struggles with math, I, who knows nothing about their algebraic formulas love hearing the kids explain to me something that they DO know about it. They always know something — and, yes, now I find myself learning a thing or two myself!

Please also see this marvelous advice from my math teacher friend, Speaking math constantly with Joy Ferrante.  Joy’s advice is for parents of smaller children, but it holds for all of us at any age — to learn math we must do some of it, and we can.

– Michael

Understanding and Overcoming Procrastination: a presentation by Michael Bromley

From the Sycamore School Lecture Series: Parenting 21st Century Kids:

On March 1, 2017  at the Arlington, VA Central Library, Michael Bromley presented:

Understanding and Overcoming Procrastination

Michael Bromley discusses strategies to help ourselves and our children overcome the urge to delay. Michael is a high school teacher, historian, published author and founder and president of School4Schools.com LLC & the A+ Club

Please click on the below image to open the full slideshow.  This slideshow is not narrated: for audio explanation of these ideas, please go to the Student Success Podcast: Procrastination Primer part 1.

A presentation by Michael Bromley from School4Schools.com LLC & the A+ Club copyright 2017

NoteSlideshow Copyright 2017 by School4Schools.com LLC.  This slideshow is for personal use only ** not for distribution ** Please contact School4Schools.com for permissions and more information.

More events from the Spring 2017 Sycamore School “Parenting 21st Century Kids” Lecture Series:

Wednesday March 15th 7:30-9 p.m.
Navigating Technology: How to help children address cyber bullying & manage electronics

Brooke Carroll, Ph.D. will lead an interactive discussion regarding parenting our tech-connected children. Brooke is an Educational Consultant & former Head of School at Seneca Academy; she has over 30 years’ experience in education. Location: Arlington Central Library

Wednesday March 22nd 7:30-9 p.m.
Ways to support your anxious child

Christina Tripodi Mitchell, Psy.D. is the Founder and Clinical Director of The Child & Family Practice of Washington, DC & is a Clinical Professor of Psychology at The George Washington University. Location: Arlington Central Library

Wednesday March 29th 7-8:30 p.m.
Promoting Executive Functioning & Study Skills at Home

Ginny Conroy is an expert in applied behavior analysis and recently opened her own practice Social Grace; she works with children and families to provide individual & group social skills and educational advocacy.
Location: Westover Library

Click here to Register for the Sycamore School Lecture Series: Parenting 21st Century Kids

Here to learn more about the Sycamore School.

How to know if your student is really learning: “If you can’t teach it you don’t know it”

We hear it all the time. Students say, “I get it when my teacher shows it to me, but I can’t do it on the test.” Then parents tell us that their child “doesn’t test well.”

When children say, “I get it when my teacher shows me,” what they’re really saying is that they didn’t learn it for themselves.

Turning New Knowledge into Prior Knowledge

The process of turning “New Knowledge” (NK) into “Prior Knowledge” (PK) is what I call “internalization.” When our brain receives new information, it looks to store it somewhere meaningful. If there is no related PK to connect it to, then the NK remains just that, unrelated, unconnected information that has no lasting memory.

However, when the NK finds a comfortable home, it is connected to meaningful PK and can now begin the process of internalization, that is going from NK to PK.

Kids get this. Continue reading

Five tips on how to “study better” for an exam: extending memorization for brain memory and recall

memoryWhen students say they don’t “test well” or that they “don’t know how to study,” parents and teachers often respond with suggestions — and criticism — to, well, just “study harder.” Great. But what does “study harder” actually mean?

We can see how “studying harder” might actually work if we divide learning into the two distinct parts of:

  • Factual Knowledge
  • Application of Knowledge

The first is straight memory, while the second requires its application, by which we mean extension through comparison, analysis, evaluation, and so on. Thereby “studying harder” requires development of first, factual knowledge, and, second, using it. Continue reading

Laptop, Tablet, or Desktop? Google Docs or Office 365? Which technology is best for high school and college?

What’s best for school, a laptop, tablet, or PC?

Heading back to school always feels like a fresh start. And like a new set of clothes, getting a new device just makes you feel good.

But for high school and college students, freshmen especially, the choice of technology can really impact academic performance. The wrong choice can make school difficult or, worse, become an excuse not to do well.

Into the start of the 2016-17 school year, I thought it’s time for an update from previous posts here on the topic. The technologies haven’t changed much, but there are more options — and most importantly, more affordable ones.


Here for previous posts on the best technology for school:
College bound: desktop, laptop or tablet? PC or Mac?
The Best Computers for College: desktop, laptop or tablet? PC or Mac pt 2


What has changed significantly, though, is the “cloud.” Continue reading

Student web searches on why I have to do homework & how a misguided SEO program taught us a lot about students

essay revision and draftingSearch engine results reveal much about ourselves, something worth reminding both teens and their parents. Not only can a search history flag a teen’s behavioral choices, such as being frustrated over grades and homework, it tells us what’s going on in general.

And web searches can even predict the future, such as a Bing analysis of web searches that accurately predicted the onset of pancreatic cancer before diagnosis (see article here).

With teenage students, their web searches certainly tell us what’s on their mind, usually something tied to popular culture, music, sports, movies, etc. When it comes to academics and school work, which are our concerns, here at the Student Success Blog, we have accidently discovered an interesting little indicator of student standing and cries for help in some of the search engine requests that have led to clicks on our site. Continue reading

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).

Continue reading

ADD: a reminder for parents what “Attention Deficit” really means

Parents of a student who has been diagnosed with “Attention Deficit,” commonly known as “ADD” and “ADHD,” get a reminder every hour of every day that by, “attention deficit,” ADD is more than some inability to focus.

Wikipedia defines “Attention Deficit Hyperactivity Disorder” (ADHD) as:

characterized by problems paying attention, excessive activity, or difficulty controlling behavior which is not appropriate for a person’s age.

The key words here are, “paying attention,” something that I am reminded of as I jumped up from my living room chair at the smell of my burning breakfast. My wife would remind me that I always burn the roast. I remind her that she should remind me when I put something on the stove.

A wise, wonderful person, my Belgian host-mother during my student exchange year to Tournai, Belgium, told me (in French), “Michael, you try to do too much at once.”

My own mother wouldn’t disagree, especially during those numerous emergency visits for another round of stitches needed because I wasn’t “paying attention” again. Continue reading

Sleepers Awake: a celebration of J. Reilly Lewis, master organist, conductor & educator

J. Reilly Lewis, world-renowned conductor, organist, and expert on the music of Johann Sebastian Bach, and our dear friend, died unexpectedly last week.

A Friend to All

We called him our friend because, for Reilly, if you were a friend of Bach, you were a friend of Reilly’s — and if you were a friend of Reilly’s you could not help but be a friend of Johann Sebastian Bach.

We were both. We were both because Reilly was a true teacher who was passionate about his craft, welcoming and enthusiastic for his learners, and compassionate and patient for those who didn’t know it — like the best teacher, a friend to all.

Reilly welcomed his friends several Sundays each year at the National Presbyterian Church, whose organ he called one of the best in the world, and on occasional Tuesdays at the Church of Epiphany on 13th Street, for “Noontime Cantatas.” Reilly’s Washington Bach Consort is a premier musical organization in Washington DC whose performances are part of the permanent collection at the Library of Congress.

Reluctant Learners

A few years ago, the musical director at my high school and I brought a rather unwilling group of about a dozen or her Music Theory 9th graders  to a “Noontime Cantata.” Reilly loved nothing more than for students to attend his concerts.

The value in it for the kids was the trip itself, hanging out with their friends and missing their other classes. The cost in it was to have to sit through a classical music concert. These were Catholic school students, so they knew how to endure a mass. Still, classical music? Yikes!

I sat behind them in the upper level pews and shared a box of Altoids to help them stay awake. There weren’t enough Altoids in the world to hold up their nodding heads. If the violins didn’t push their eyes to the back of their heads, the chorus closed the gap between their chins and chests. Most of them were fast asleep by the end.

They were good sports, they were brave, and they had behaved.

We awaited for the audience to depart, then relocated to the main pews while the school bus returned. I did my best to give them a little history lesson of the church, why the stained glass, why the design, how this church held community in DC during times of distress such as the Civil War.  Poor kids, they bravely sat through my attempts to engage them in some learning while we were sitting there waiting for the bus.

A Private Lesson from Reilly

Then a little man in a tuxedo walked up to the group, and with the brightest, happiest voice, loudly welcomed them and thanked them for coming to see his concert. The kids turned to him and smiled back gently, reluctant to engage, but curious.

Reilly asked them a few questions about their school, if they’d seen a concert like this before, and one or two bravely, if quietly, answered.

Then, with that wisp of mischievousness that made him so compelling as a person, performer, and teacher, Reilly said, “Do you want to see the organ?”

Again, the kids were hesitant but polite. Reilly said, “Come on!” and led them up the isle and onto the alter, where a beautiful organ sat with all it’s confusing keys, knobs and pedals. Reilly sat at the bench and ushered us to come around him.  The kids were now well past curiosity and jostled for the best view. My father and I stood back and smiled at each other, not fully aware yet of the magnificent treat before us.

Reilly turned to the kids,  “Do you want to see how it works?” He had them by now, of course, deliberately teasing them with a couple keys and different sounds from the pipes.

Suddenly, he launched into a full blown performance, with his hands and feet racing about the keys, magical, like nothing they had seen before, not CGI from the movies, not beats and rhymes from their friends and music videos. This was special, and their eyes lit ablaze.

I looked over at my father who had seen countless performances – but never from just over the master’s shoulder! He was as mesmerized as the kids, and more for knowing for what a special moment it was.

After a bit of pure showmanship, Reilly wrapped up, not having shown off, but having shared the fun.

We thanked the maestro who with genuine enthusiasm thanked the students for being there. The kids returned the thanks with equal enthusiasm.

The bus had arrived, and these 9th graders climbed into it not with the shared pain of sleeping through a classical concert but with the joy of a unique and wonderful experience that they talked about the ride back to school.

RIP J. Reilly Lewis

We will miss you, J Reilly Lewis, and we will think of you often as we aspire to love our work as you did yours and, more importantly, love sharing it with all — all of whom we will call our friends.

– Michael