Common Core Common Sense: Myths About the Standards, Part 4

Common Core Standards

In recent months, there’s been a tremendous amount of buzz regarding an educational change called Common Core. And a ton of that buzz perpetuates down-right false information. There’s so much to say about this that I’ve developed a five-part series debunking these myths — or outright lies, if you’re being cynical. This is the fourth in that series (read Myth 1Myth 2 and Myth 3), which will continue on Wednesdays throughout August and into September. Of course, I’ll be writing from a math perspective. Photo Credit: Watt_Dabney via Compfight cc

Myth #4: The Standards Require More Testing

Perhaps the most controversial aspect of the U.S. education system is standardized testing. And for good reason. There are a myriad of problems with these tests–from their links to private companies to their use as teacher evaluation tools.

While I’ve said from the start that it’s not fair to judge the Common Core Standards based on their implementation in individual states, it’s also not fair to pretend that the standards and testing don’t go hand in hand. States aren’t abandoning standardized testing any time soon, so don’t hold your breath.

But what we do know for certain that the adoption of Common Core Standards does not mean more testing–in the long run. In fact, there is no testing requirement inherent in the adoption of Common Core. None!

However, as states move from previous standards to Common Core, there will be some changes in testing. First, student may take two sets of standardized tests–at first. In these situations, one test is the one aligned with the state’s previous standards. And students may take practice tests, based on the Common Core Standards. Usually this translates to more testing during one school year, with only one test score used for student placement or teacher and school evaluations.

Because the Common Core Standards focus on critical thinking, Common Core-aligned tests will probably look a little different than the all-multiple choice tests that we’re all used to. Students are required to show their work and may even be asked to explain how they came to their answers. Here’s a two-part example, which corresponds with the third grade math standards:

A. Fill in the blanks below to make a number sentence that represents the drawing:

Common Core

________ x ________ = ________
B. Put the dots below into five equally sized groups and write an equation that represents the drawing.

•  •  •  •  •  •  •  •  •  •  •  •  •  •  •  •  •  •  

Answers:
A. 4 x 6 = 24 or 6 x 4 = 24 or 8 x 3 = 24 or 3 x 8 = 24, etc.
B.   •  •  •      •  •  •      •  •  •      •  •  •      •  •  •      •  •  • 
3 x 5 = 15 or 5 x 3 = 15 or 15 ÷ 3 = 5 or 15 ÷ 5 = 3

There’s something going in the above problems that’s difficult (or impossible) to measure with multiple choice questions. First, students are asked to draw as a way of problem solving. Second, there are multiple correct answers.

(Psst. Want to test your third grade or fifth grade math skills? Take one of the Math for Grownups math quizzes. No one has to know your score. Promise!)

So while Common Core does not eliminate testing or prevent test results from being used inappropriately, if the tests are well constructed–and dang, that’s a big if–students have a much better opportunity to demonstrate critical thinking and the open-ended nature of mathematics. That’s not more testing, that’s better testing.

Got a question about the Common Core Standards for Mathematics? Please ask! Disagree with my assessment above? Share it! And if you missed Myth #1, Myth #2 or Myth #3, you can find the herehere and here.

 

Math at Work Monday: Samantha the Freelance Designer

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I had the pleasure of speaking with Samantha Volz who has the pleasure of working from her very own home every day. That is one of the benefits of being a freelance designer. In addition to graphic design, this artist also does photography. It seems she is creatively blessed with talent.  I was curious about how she uses math in her work. Let’s take a look at what she had to say:

Can you explain what you do for a living?

I’ve been working as a freelance designer since 2001.  I design marketing/advertising material for companies. In addition, I also design websites and other support files for social media applications. I am a photographer, painter, and artist as well.

When do you use basic math in your job?

I have to use specifications to set up design files. Set up bleed, trim and safe zones so that when the file gets to the printer, it is set up correctly and prints correctly. For instance, if I have a print sheet that is 8.5 by 11 inches for a trifold brochure, I need to divide the paper by three and adjust 1/8th of the 3 panel. Depending on how the trifold folds, I will need to adjust the panels 1/16th of an inch if a panel folds in. Then, on the layout in the software I have to consider set up for a printing press or digital printing if my graphics bleed to the edge I have to add at least 1/8th to 1/4th of an inch of graphics that extends past the actual final layout for being trimmed down to allow for machine error. So my final file that is handed over to the print vendor is 8.5 x11 with bleed 1/8th bleed on all sides. Total graphic coverage is 8.75 x 11.25 trimmed down to 8.5 x 11 and scored for folds indicated on the set up with 3 panels roughly 3.66 ” wide, again depends on the fold design chosen for that tri-fold brochure how it will read, flow and open up to reveal the information being provided.

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

Yes, I use a calculator a lot.

How do you think math helps you do your job better?

I could not do my job without it. It is how everything flows from the client to me, the designer, and then to the printer until it is produced as an end product.

How comfortable with math do you feel? Does this math feel different to you?

I am comfortable with normal addition, subtraction, division, multiplication, and fractions. Nothing too complicated.

What kind of math did you take in high school? Did you like it/feel like you were good at it?

I took honors math classes.

Did you have to learn new skills in order to do the math you use in your job? Or was it something that you could pick up using the skills you learned in school?

Yes, what I use now I learned in high school.

Who knew that the creative type still need to know their basic calculations and fractions?  Seems like everywhere you go, even in your home, math is sure to follow. I hope you enjoyed learning a little more about Samantha. Let me know if you have any further questions for her. 

 

Photo Credit: 55Laney69 via Compfight cc

Common Core Common Sense: Myths About the Standards, Part 3

Common Core Standards

In recent months, there’s been a tremendous amount of buzz regarding an educational change called Common Core. And a ton of that buzz perpetuates down-right false information. There’s so much to say about this that I’ve developed a five-part series debunking these myths — or outright lies, if you’re being cynical. This is the third in that series (read Myth 1 and Myth 2), which will continue on Wednesdays throughout August and into September. Of course, I’ll be writing from a math perspective. Photo Credit: Watt_Dabney via Compfight cc

Myth #3: The Standards Introduce Algebra Too Late

One of the reasons for Common Core is to be sure that when students graduate from high school they are ready for college and/or the job market. And these days that means having some advance math skills under their belts. But if you read the Common Core course headings, algebra is not mentioned until high school.

Up to this point, the math is referred to by the grade level, not subject(s) covered. So at first glance, this looks suspiciously like there is no mention of algebra in middle school. You have to dig a little deeper to learn that tough algebraic concepts are covered in the middle school standards. In fact, algebra is introduced (in an extremely conceptual way, with no mention of the word algebra) in kindergarten!

The Common Core math standards are divided into domains — or mathematical concepts. Here is the full list:

  • Counting & Cardinality
  • Operations & Algebraic Thinking
  • Number & Operations in Base Ten
  • Number & Operations — Fractions
  • Measurement & Data
  • Geometry
  • Ratios & Proportional Relationships
  • The Number System
  • Expressions & Equations
  • Functions
  • Statistics & Probability

Of this list, you can find algebraic ideas and skills in at least four domains: Operations & Algebraic Thinking, Ratios & Proportional Relationships, Expressions & Equations and Functions. (You can argue that algebra appears in others as well.) In kindergarten, students are introduced to the idea of an equation, like this: 3 + 2 = 5. They also answer questions like this: What number can you add to 9 to get 10? (Algebraically speaking this question is x + 9 = 10, what is x?)

Variables aren’t introduced until much later, in 6th grade, when students are expected to “write, read, and evaluate expressions in which letters stand for numbers.” At this point, students begin to learn the language of algebra, with vocabulary words like coefficient (in the expression 3x, 3 is the coefficient) and term (in the expression 3x – 6, 3x and 6 are terms). Also in 6th grade, they start solving simple equations and inequalities, like 4 + x = 7 and 5x = 15.

In 8th grade, radicals and exponents are introduced, and students learn to solve simple equations with these operations. In addition, they graph lines and put equations into point-slope form and slope-intercept form, and begin solving systems of equations (pairs of equations with two variables). They also make connections between an equation of a line and the graph of a line. Finally, functions are introduced in 8th grade.

All of that happens well before high school, leaving lots of time in high school to delve into polynomials, quadratic equations and conic sections.

But here’s the most important thing: under Common Core, students are given a tremendous amount of context for all of this math, as well as time to develop true numeracy. This can speed along algebraic understanding. For example, students who are fluent with multiples and factors of whole numbers and decimals will have a much easier time learning how to solve equations by factoring. That’s because they will have the foundation of factoring or expanding. They will be able to use the distributive property with ease and focus their attention on the new concepts being presented.

In other words, this slow build develops numeracy.

So don’t let the Common Core headings fool you. Algebraic concepts and skills are meted out throughout the grade levels, allowing students to truly understand foundational concepts and fluently perform basic algebraic skills well before high school begins.

Got a question about the Common Core Standards for Mathematics? Please ask! Disagree with my assessment above? Share it! And if you missed Myth #1 or Myth #2, you can find the here and here.

Common Core Common Sense: Myths About the Standards, Part 2

Common Core Standards

In recent months, there’s been a tremendous amount of buzz regarding an educational change called Common Core. And a ton of that buzz perpetuates down-right false information. There’s so much to say about this that I’ve developed a five-part series debunking these myths — or outright lies, if you’re being cynical. This is the second in that series (read the first here), which will continue on Wednesdays throughout August and into September. Of course, I’ll be writing from a math perspective. Photo Credit: Watt_Dabney via Compfight cc

Myth #2: The Standards Omit Basic Math Facts

While grabbing a latte at the local Starbucks a few weeks ago, I ran into a friend of mine. She was taking a break from teaching cursive to high school students at a nearby private school’s summer program.

“Kids don’t learn cursive in elementary school anymore, and so they can’t sign their names,” she explained. “Kids aren’t even required to learn their multiplication tables these days!” 

Well, I know for a fact that multiplication facts are covered in math classes across the country, including those in our fair city. But there’s this idea out there that third-graders are using calculators to find 8 x 2. While I don’t doubt that this has happened on at least one occasion, it’s not a trend in education. And math facts are a part of the Common Core.

The Common Core Standards emphasize critical thinking. And without a foundation in basic facts, students will not be able to apply critical thinking skills to problem solving of any kind.

Sure, there is no Common Core Standard that says students must be able to recite the multiplication tables 1 through 12 by heart. Instead, Common Core focuses on the concept of multiplication — which is pretty darned complex — encouraging teachers to illustrate multiplication with arrays (the picture below is an array), equal-sized groups, and area. The difference boils down to this: We grownups probably memorized that 8 x 2 = 16, while today’s students might figure it out on their own with a drawing like this:

• • • • • • • •

• • • • • • • •

 

The array above gives context to multiplication. Students can see for themselves that there are two rows of eight dots and 16 dots in all. The simple illustration even offers students a way to discover (or remember) the math fact themselves before memorization naturally occurs. In short, it’s much more meaningful than flash cards.

And while the example above is very visual, the idea behind it is flexible, allowing students with different learning styles to understand multiplication. A more kinetic (tactile) student can arrange 16 pennies in an array. A student with an aural learning style can count the dots out loud — in rows, in columns and in total. And so on.

There are plenty of other math facts included in the Common Core Standards, from the properties of number systems to formulas for area and volume. But I admit, you won’t find anything like, “Students will recite the value of π to the ninth decimal place.”

And this is a great change from more traditional approaches. Because, nothing sucks the life out of learning like memorization. Besides, can you remember the formula for the surface area of a cube? If not, could you figure it out or find it online? In my opinion, we want students to kick ass in the figuring-out option — to know that a cube has six sides that are exactly alike, and that surface area is figured when you add the area of each of the sides. Knowing those little details means that a formula isn’t necessary.

So yeah, Common Core hasn’t eliminated math facts. They’re just not front and center, leaving much more room for critical thinking. And that’s a good thing.

Got a question about the Common Core Standards for Mathematics? Please ask! Disagree with my assessment above? Share it! And if you missed Myth #1, you can find it here.

Math at Work Monday: Tina the Event Coordinator

 

math at work monday

Business is business, right? When it’s time to have those meetings and conferences, you want everything to run smoothly so you can concentrate on the task at hand.  Tina Speers has been ensuring that happens for four years as a corporate event coordinator.  She is the one making sure the projector runs like it should, and the refreshments are available on time.

Can you explain what you do for a living?

I have been an corporate event coordinator for four years. The majority of my job involves scheduling and planning events. I keep a Google calendar and plan the events and schedule rooms based on the needs of each group.  We also do virtual conferences, which requires IT skills such as basic knowledge of IP based systems.  I also stock our small cafe and make coffee on a daily basis.

When do you use basic math in your job?

Basic math is needed for the cafe.  Each item is 50 cents, or we have all day pricing.  I often need to make change (cafe is operated on an honor system).  I never use a calculator unless large groups pay per person for a certain amount of items.

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

If we need to make copies for our groups they are charged per page copied.  I often use a calculator because of the amount we charge.  A black and white copy is 05 cents and a color copy is 15 cents and we usual make copies in large volumes (at least 20 pages).  I also use basic math to complete the usage and metrics for the event center. We tally our guest totals by month.  I use a calculator for this because the numbers are usually large and uneven.

How do you think math helps you do your job better?

Math helps me do my job better because I am able to move fast when a guest is waiting for change.  I can’t imagine having to  use a calculator every time a guest needs change.

How comfortable with math do you feel? Does this math feel different to you ?

I am very comfortable with this math and it does not feel different or unusual in any way.  I mean,  I learned how to count change in first grade!  In general, I do not feel very comfortable with math unless it is very basic.

What kind of math did you take in high school? Did you like it/feel like you were good at it?

In high school I remember taking algebra, trig, and geometry as well as some sort of review class my senior year. I think it was actually called “Senior Review.”  I have not used any advanced math skills in my job. I took Calc I in college and barely passed.  I also feel I had a lot of bad math teachers especially in my middle school years.

Did you have to learn new skills in order to do the math you use in your job? Or was it something that you could pickup using the skills you learned in school?

I have not used any advanced math skills in my job.

Do you have a question for Tina? An event you need to plan? Send me your question and I will forward it to her.

Photo Credit: stevendepolo via Compfight cc