Tag Archives: math

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

For math success: guided and independent practice empowered by effective feedback

Help for students struggling with math: “guided” v “independent” practice

At the A+ Club we often hear from parents that their child is struggling in math.

Sometimes it’s, “she never does well in math” or “he does his math homework but scores poorly on quizzes and tests.”

Why students struggle in math: guided v independent practice empowered by feedback from The A+ Club on Vimeo.

Guided practice” is when the teacher shows or “teaches” a new topic or skill.

Independent practice” is when the student engages it by him or herself.

Effective teaching develops learning through a deliberate combination of guided and independent practice, where each builds upon the other. However, if the two are disconnected b an absence of effective and direct teacher to student feedback, then learning doesn’t happen.

This is why kids often say, “I get it when my teacher explains it, but I can’t do it on my own.” When your child complains that he or she “doesn’t test well,” it’s because your child is not receiving effective feedback to empower the independent practice required for learning.

This process is the same for all courses and subjects, but it more frequently manifests in math classes because math learning is not as easily processed through “guided practice” as other subjects.

In our A+ Club academic program, we engage students in effective learning techniques and provide guidance and direct math tutoring and in all subjects for overall academic success.

– Michael

Speaking math constantly with Joy Ferrante

measuring-spoonsSpeaking math constantly with Joy Ferrante

Student Success Podcast No. 11, Dec. 18, 2013

Today’s Guest: Joy Ferrante

Joy discusses how parents can be deeply involved in their child’s math learning. We use math and other school subjects all day long — how often do we use those concepts and tasks to help our children learn? Calendars, cooking utensils, house addresses… anything can be turned into a useful, effective math lesson for children, and not just young children. Continue reading

Math success: believe you can achieve with Okera Hawkins

Math success: believe you can achieve with Okera Hawkins

Student Success Podcast No. 9, Nov. 29, 2013

Today’s Guest: Okera Hawkins

Co-founder of The A+ Club, Okera Hawkins, discusses what it takes to succeed in high school math. If there’ any single thing, Okera tells us, it is “confidence.” Getting there is a process — but it is a process that every student can engage and master. But they have to want to. Okera leads us through the pieces of success in math, including organization, asking questions, and math literacy.  Please enjoy this excellent and important interview. Continue reading