Math Education – Math for Grownups https://mathforgrownups.com Books to improve your math Mon, 16 Nov 2020 10:55:26 +0000 en-US hourly 1 https://wordpress.org/?v=5.4.4 What, Where and How to do Mathematics https://mathforgrownups.com/what-where-and-how-to-do-mathematics/ Mon, 16 Nov 2020 10:55:23 +0000 https://mathforgrownups.com/?p=1775 What, Where and How to do Mathematics What and Where is Mathematics….? Everyone is aware with the word math. But no one try to define what math is. If you are thinking that what the rubbish question is it, everyone knows what math is, then you are wrong. If we ask someone what math is? [...]

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What, Where and How to do Mathematics

What and Where is Mathematics….?

Everyone is aware with the word math. But no one try to define what math is. If you are thinking that what the rubbish question is it, everyone knows what math is, then you are wrong.

If we ask someone what math is? He probably said addition, subtraction, multiplication of numbers etc. or someone said solving algebra is mathematics. A few people can tell us exactly what mathematics is. It is not their fault. There is a fault of our systems, who do not develop the books properly. Some of teachers try to clear concept of mathematics but some of them not.

That is why many of us dislike the subject mathematics and suppose it to be hard or tough subject, but it is not. Mathematics is very easy subject if we found a teacher who try developing our concept. I taught by a teacher who never try to answer my question whether he always give me these questions as assignment from home. So, I never try to make question in front of him. But every time it is not the fault of our teachers, we are also wrong many times, we never give the proper time to mathematics, even not try to find something new. So today we try to understand definition of mathematics.

Every word has proper definition like Physics (Study of energy and motion), chemistry (study of molecules and chemicals), and biology (study of human and living things). But mathematics has not proper definition. Many philosophers try to introduce definition of mathematics. Some of said math is abstract science of numbers, some of said math is mother of sciences.

The math is too huge and cannot summarize in few words. Many philosophers claim that mathematics is a language of science which help each science branch to speak. Without mathematics every science field is mute. Like medical tell us about blood pressure but it cannot measure without the help of mathematics. Physics tells us about speed, but it cannot be measured without the help of mathematics.

Mean in every field you must use mathematics, even you cannot but a bus ticket without using mathematics. You cannot cock delicious food without using mathematics, you always put salt according to taste and quantity of food.

That is why philosophers said mathematics is a language, without it we cannot make conversation like other English French etc.

Imagine you are on the grocery shop and you are asked to buy 1 kg rice. How you tell the shopkeeper that you want to buy 1 kg rice? You look like a deaf. You have not any other way to tell him without using mathematics.

You can never think to live without mathematics. Mathematics is a necessary tool of life.

Once I was reading the history of mathematics, that how numbers were introduced? I read the story of Egyptians who invent the numbers first time 5000 BC. A herdsman compared sheep of his herd with a pile of stones when the herd left for grazing and again on its return for missing animals. In the earliest system probably the vertical strokes or bars such as I, II, III, IIII etc. were used for numbers 1, 2, 3, ….

After reading this story I come to know the exact meaning of “Necessity is the mother of invention”. But the mathematics is the mother of sciences said by mathematicians. But now a day mathematics is growing up as a language.

If we talk about painting, even mathematics is here. Exact amount of two colors makes a new color.

How to do Mathematics….?

We always listen from our math teacher if you want to perfection in mathematics then do practice, practice, and practice. Are you ever think that how to do practice? Many of us think practice mean do one question again and again. No…. Its not mean this. Its mean does practice of your concept.

How to practice of your question? When ever you learn a new question then first make question on it with teacher. Ask the teacher,

what is the purpose of this?

Why we are doing it?

At each step ask why we do as and why not?

We have a typically question with the math teacher to repeat the question. This is not a way to improve your math skills.

After getting the answers to your question,

open your note book any start solving this question

According to your thought and complete it in any cost

Even you are doing wrong

When you finish it then match your solution with the correct solution

Match the step where you did wrong

After pointing out each mistake in your solution go to math teacher

Asked him why we cannot do as I do

He will explain your mistake

Now start again a new question

Now at each wrong step your mind jerks you that it Is not write because you have taught by your math teacher that it is wrong.

When we made mistake by own hand and then get explanation of mistake, and then whenever try to make same mistake again, our mind never with us. Which is the sign of our mistake.

That is called practice. When each time you do new question by yourself by understanding each step, that why I am doing it or why not. Never hesitate to ask question by your teacher, if you are feeling hesitation you are not going to learn new things. Develop your habit to ask questions and always try that your question start with why, which, how etc. never say repeat it.

The last thing always sees the solution after the completion of your question. If you see solution at each point where you stuck, you are not going to learn new thing. When you make mistake, it will be resolved and you learn it, when you start copy paste you never get confidence to learn.

We always learn by our mistake.

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An Easy Approach to Mathematical Modeling https://mathforgrownups.com/an-easy-approach-to-mathematical-modeling/ Mon, 09 Nov 2020 05:16:54 +0000 https://mathforgrownups.com/?p=1718 In daily life we use mathematics to estimate our budget, calculate price, profit, loss etc. Doing this work is known as mathematical modeling. Basically, mathematical modeling is the part of our real life. Many of us know by the word “word problems”. In mathematics when a problem described by words it called word problem. If [...]

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In daily life we use mathematics to estimate our budget, calculate price, profit, loss etc. Doing this work is known as mathematical modeling. Basically, mathematical modeling is the part of our real life. Many of us know by the word “word problems”. In mathematics when a problem described by words it called word problem.

If we make mathematical model of our daily routine then it is very easy to maintain the time in work, game and for family. In this era of busy life, time management is a big deal. If we draw the mathematical model of time and spend time according to this, we can mange time easily.  

Not just the time, even we make a mathematical model of daily expenses we can also save a lot of money. Many of us are willing to take load from the bank but unable to calculate the mortgage of credit. If they are expert in solving word problems, then they can calculate their budget to know that are they able to return loan on time. How they can save money by paying installment in how many times?

I remember when I was kid, my mom gives me $15 pocket money for a month and asked, “How much you have to spent daily for covering the whole month?” Because I always spent the whole money before the end of the month. Now I understand that mathematics is too useful even for a kid. That time if I able to make equation of my expenditure then now I have too much money.

If mathematician does not develop the mathematical modeling, then physics was a theoretical subject, suppose how physicists find out the velocity with out modeling the definition into mathematical formula?

Many students have issue in solving word problem, but it is not a big deal. Just focus on some points in the statement and you will become expert in solving word problem. The way to write a statement in mathematical expression is called “Mathematical Modeling”.

Before solving any word problem, you must well verse in Mathematical modeling, draw your attention on the following points to make model of any word problem.

Focus on the following points in any statement:

  • What do you know?
  • What do you want to know?
  • What is the proper operation?

Example: Biden bought 2 kg tomatoes, 1 kg potatoes, 5 kg carrots and 3 kg apples from a market. How much weight he carries from the market?

Now according to above points find out the useful information. First see what we have given in the statement:

Biden bought 2 kg tomatoes, 1 kg potatoes, 5 kg carrots and 3 kg apples from a market. How much weight he carries from the market?

What do we know?

Weight of tomatoes= 2 kg

Weight of potatoes= 1 kg

Weight of carrots= 5 kg

Weight of apples= 3 kg

Now see in the statement what we must calculate or evaluate?

Biden bought 2 kg tomatoes, 1 kg potatoes, 5 kg carrots and 3 kg apples from a market. How much weight he carries from the market?

What do we want to know?

Total weight he carries?

The last thing we have to see, how to do? Which operation have to use? Since we want to know total weight so, total amount always calculated by addition.

What is the proper operation?

By adding weight of all.

Total weight=2+1+5+3=11 kg

Hence, Biden carries 11 kg.

If the word problems including more then one operation, then you have to focus on the following points:

  • Find out number of objects / people used in statement
  • Give name to each object / person
  • Breakout the statement into pieces according to object / person
  • Step by step write them with the given relation

Just do some examples to understand:

Example: If the sum of two numbers is 12 and difference is 2. Find the numbers.

According to our points, first see how many objects / persons are discussed?

If the sum of two number is 12 and difference is 2. Find the numbers.

Number of objects is two.

Now give name to both numbers. Let x and y are two numbers.

Now break into pieces:

If the sum of two numbers is 12 and difference is 2. Find the numbers.

The first when saying sum is 12:

So relation becomes

And second one saying difference is 2:

You can list this relation as you want, mean

or

Both are correct.

I take

So, we have two equations:

Both can solve simultaneously to get answer.

Adding both equation

Cancel the opposite terms and do simplification:

We get,

Put this one in any equation, I am putting in the first one

So, the numbers are 5 and 7.

Now what you think? It is easy now to solve word problems.

Consider if a problem consists of a single object / number and relating this object / number by itself then focus on the following points:

  • Name that object / number
  • Find out the relation between object / number
  • Write them in equal

Example:  If a number exceeds its square root by 56. Find the number.

According to our points, first see how many objects / persons are discussed?

If a number exceeds its square root by 56. Find the number.

Let x is that number.

Now break into pieces:

If a number exceeds its square root by 56. Find the number

As we know square root of 4 is 2. Number always greater by its square root so, in the above statement number is greater by its square root and according to statement number exceed by 56.

It can be solved now easily.

Rewrite the above equation:

Taking the square on both side of the equation:

By solving above quadratic equation, we get x=64 and x=49.

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Algorithms: Good for machines, bad for people https://mathforgrownups.com/algorithms-good-for-machines-bad-for-people/ Wed, 25 Feb 2015 07:15:56 +0000 https://mathforgrownups.com/?p=1443 This headline is a lie. It’s not that I think algorithms are bad. They’re not. Honestly, I think that’s how many of us move through our days without killing ourselves or someone else. We habitually take the medications prescribed by our doctors; we cook our eggs (and avoid salmonella); we follow the steps for safely [...]

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This headline is a lie. It’s not that I think algorithms are bad. They’re not. Honestly, I think that’s how many of us move through our days without killing ourselves or someone else. We habitually take the medications prescribed by our doctors; we cook our eggs (and avoid salmonella); we follow the steps for safely backing our cars out of the driveway; we put on our socks before our shoes.

Even certain mathematical algorithms are very useful, like the order of operations (or PEMDAS).

But in the end, I think that dictated algorithms are not so great for people, especially people who are learning a new skill, and especially when the algorithm has little to no meaning or context.

Don’t know what an algorithm is? Check out my earlier post defining algorithms. 

People Aren’t Machines

There are many different educational philosophies that drive how we teach math. For generations, teachers worked under the assumption that young minds were tabula rasas or blank slates. Some educators took this to mean that we were empty pitchers, waiting to be filled with information.

This is how teaching algorithms got such a strong-hold on our educational system. Teachers were expected to introduce material to students, who were seen as completely ignorant of any part of the process. Through instruction, students learned step-by-step processes, with very little context.

In recent years, however, our understanding of neurology and psychology has deepened. We understand, for example, that children’s personalities are somewhat set at birth. And that their brains develop in predictable ways. We are also beginning to realize that certain types of learning and teaching promote deeper understanding.

The result is a better sense of students as individuals. Instead of a class filled with homogeneous little minds, we know now that kids (and grownups) are wildly different–in the way they digest information and approach problems. (To be fair, this is closer to John Locke’s original theory of tabula rasa, in which he states that the purpose of education is to create intellect, not memorize facts.)

In terms of a moral, there’s not much I recommend in this Pink Floyd video, but I can certainly identify with the kids’ anger at being treated like cogs in the educational system. Besides, it’s cool.

A Case for Critical Thinking

Certainly critical thinking is not completely absent in the teaching of algorithms. It’s marvelous when kids (and adults) make connections within the steps of a mathematical process. But critical thinking is much more likely, when the process is more open-ended. Give kids square tiles to help them understand quadratic equations, and they’ll likely start factoring without help. Let students play around with addition of multi-digit numbers, and they’ll start figuring out place value on their own.

You can’t beat that kind of learning.

See, when someone tells us something, our brains may or may not really engage. But when we’re already engaged in the discovery process, we’re much more likely to make big connections and remember them longer.

That’s not to say that learning algorithms is bad. But think of the way you might add two multi-digit numbers without a calculator. Instead of stacking them up and adding from right to left (remembering to carry), you might do something completely different, like add up all of the hundreds and tens and ones — and add again. In many ways, you’re still following the algorithm, but in a deconstructed way.

And in the end, who cares what process you follow–as long as you get to the correct answer and feel confident.

Teaching Algorithms is Easier, Sort Of

So if discovering processes is so much better, why does much of our educational system still teach algorithms? Well, because it’s more efficient in a lot of ways. It’s easier to stand in front of a group of kids and teach a step-by-step process. It’s harder–and noisier–to let kids work in groups, using manipulatives to answer open-ended questions. It might even take longer.

But I say that based on what we now know about kids’ personalities and brains, we’re not doing them much good with lecture-style classes. So in the long run, it’s easier to teach with discovery-based methods. Kids remember the information longer and get great neurological exercise. This allows for many more connections. At that point, the teacher is more of a coach than anything else.

In the end, we all use algorithms. But isn’t it better when we decide what steps to follow, through trial and error, a gut instinct or discovering the basic concepts underlying the process? That’s where we have a big edge over machines. After all, humans are inputting the algorithms that machines use.

Photo Credit: teclasorg via Compfight cc

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We Learn Math Best Through Discovery — And Failure (Video) https://mathforgrownups.com/we-learn-math-best-through-discovery-and-failure-video/ Wed, 07 Jan 2015 07:24:29 +0000 https://mathforgrownups.com/?p=1457 What’s the best way to learn new math ideas? The answer might surprise you. But like learning a foreign language or that the little brake light on your dashboard means get to the mechanic — now! — getting the hang of math may require a little bit of discovery, rather than listening to boring lectures [...]

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What’s the best way to learn new math ideas? The answer might surprise you. But like learning a foreign language or that the little brake light on your dashboard means get to the mechanic — now! — getting the hang of math may require a little bit of discovery, rather than listening to boring lectures or reading books. And getting your Christopher Columbus on means failing a few times too. Here’s how discovery and failure play an important role in math education.

More videos are coming, so please subscribe to my YouTube channel: mathforgrownups.  Also, I hope you’ll share this video on Twitter, using #failureisok and #discovermath and post it on your Facebook page. Share the Math for Grownups love!

As always, I’d love to hear what you think. Ask your questions or share your feedback in the comments section. Were you surprised by anything in the video? What do you think about having to fail in order to learn? Share in the comments section!

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Back to School for Teachers, Students and Parents https://mathforgrownups.com/back-to-school-for-teachers-students-and-parents/ Wed, 10 Sep 2014 09:47:12 +0000 https://mathforgrownups.com/?p=1491 Now that Labor Day is behind us, it’s safe to say that most of country is back at school. In honor of this new beginning, I decided to share three of my most favorite posts for teachers, students and parents. Five Things Math Teachers Wish Parents Knew In this post, I asked veteran middle school teacher, [...]

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Now that Labor Day is behind us, it’s safe to say that most of country is back at school. In honor of this new beginning, I decided to share three of my most favorite posts for teachers, students and parents.

Five Things Math Teachers Wish Parents Knew

In this post, I asked veteran middle school teacher, Tiffany Choice, to share her advice for parents on how to help their kids succeed in math class. Her advice is golden, and stupid-easy to follow. In fact, none of her ideas involve learning new math methods. Huzzah!

Ten Things Students Wish Math Teachers Knew

I polled the high school and middle school students I know to get this great advice for teachers. If you teach math — at any level — do yourself a favor and take these to heart. Students aren’t asking for the moon.

Ten Things Parents Wish Math Teachers Knew

And there’s one more for teachers. Those of you who are parents see both sides of this equation. The homework wars are real, kids are stressed out and parents feel sometimes powerless to help.

If you’re a parent who needs even more support — and who among us doesn’t? — check out these bonus posts, where I outline ways that you can help your child become a master mathematician — or at least leave math class not feeling like a dummy!

Lowering Homework Stress: 5 easy steps for parents

Five Math Resources for Confused Parents

And of course, I’m around to answer your questions and give you support. Let’s get this school year off to a great, mathy start!

 Photo Credit: loop_oh via Compfight cc

Got a question or comment about any of the above resources, share in the comments section!

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Common Core Common Sense: Myths About the Standards, Part 5 https://mathforgrownups.com/common-core-common-sense-myths-about-the-standards-part-5/ Wed, 03 Sep 2014 06:09:31 +0000 https://mathforgrownups.com/?p=1389 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 last post [...]

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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 last post of that series (read Myth 1Myth 2Myth 3 and Myth 4), which began in August. Of course, I’m writing from a math perspective. Photo Credit: Watt_Dabney via Compfight cc

Myth #5: Common Core is Overflowing with Fuzzy Math

First, a definition: fuzzy math is a derogatory term for an educational movement called reform math. Therefore the claim of fuzzy math isn’t so much a myth as an attempt to insult  the way that many math teachers and education researchers advocate teaching mathematics to K-12 students.

Second, some history: in 1989, the National Council of Teachers of Mathematics (disclaimer: I was once a member) published a document called Curriculum and Evaluation Standards for School Mathematics, which recommended a newish philosophy of math education. The group followed with Principles and Standards for School Mathematics in 2000. School officials and curriculum companies responded by implementing many of the approaches offered by the NCTM and as a result, the way we teach mathematics began to change. This change is what advocates call reform math and critics often call fuzzy math.

Before the NCTM’s publications, math teachers focused on the math — in particular series of steps (algorithms) designed to get the right answer to a problem or question. With reform math, educators became more focused on how students best learn mathematics. Suddenly, context and nuance and “why?” were at least as important as the answer. And it is true that Common Core Standards for Mathematics are largely based on the NCTM’s publications.

If this is truly fuzzy math, then we don’t have a myth here. (Although, to be fair, there is a legitimate branch of set theory and logic called “fuzzy mathematics.” But somehow, I don’t think Common Core critics using this term have real math in mind.) I include the fuzzy-math criticism as a myth because it suggests that teaching math in a conceptual way is a bad idea.

Throughout this series, I have asserted that the best way for students to understand and remember mathematical concepts is by returning over and over to the concepts behind the applications. Why is 24 such a flexible number? Because it has eight factors: 1, 2, 3, 4, 6, 8, 12 and 24. Students who really get this will have an easier time adding and subtracting fractions, reducing fractions, simplifying algebraic expressions and eventually solving algebraic equations through factoring.

This is numeracy, folks.

Students will not become numerate (think literate but with math) without a solid, conceptual understanding of mathematical ideas and properties. Numeracy does not typically evolve from memorizing multiplication tables or long division or pages and pages of practice problems. (Disclaimer: some kids will certainly become numerate regardless of how they’re being taught, but many, many others won’t.)

Numeracy is a life-long quest concentrated between the ages of five and 18 years old. Grownups can gain numeracy, but isn’t it better for our kids to enter into adulthood with this great understanding?

If Common Core critics want to call this whole philosophy “fuzzy math,” so be it. Just know that the ideas behind reform mathematics are deeply rooted in research about how kids learn math, not some ridiculous idea that was made up in the board rooms of a curriculum development company or smoke-filled political back rooms.

In short, the problems with Common Core math are not found in the standards themselves. Instead, the application and heated discourse are clouding Common Core’s real value and promise.

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, Myth #3, Myth #4, you can find them hereherehere and here.

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Common Core Common Sense: Myths About the Standards, Part 3 https://mathforgrownups.com/common-core-common-sense-myths-about-the-standards-part-3/ Wed, 20 Aug 2014 06:04:13 +0000 https://mathforgrownups.com/?p=1374 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 [...]

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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 advanced 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 polynomialsquadratic 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.

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Common Core Common Sense: Myths About the Standards, Part 2 https://mathforgrownups.com/common-core-common-sense-myths-about-the-standards-part-2/ Wed, 13 Aug 2014 05:57:12 +0000 https://mathforgrownups.com/?p=1369 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 [...]

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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.

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3rd Grade Math Quiz https://mathforgrownups.com/3rd-grade-math-quiz/ Fri, 08 Aug 2014 09:35:53 +0000 https://mathforgrownups.com/?p=1476 [watupro 2] Photo Credit: jontintinjordan via Compfight cc

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[watupro 2] Photo Credit: jontintinjordan via Compfight cc

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Lowering Homework Stress: 5 Easy Steps for Parents https://mathforgrownups.com/lowering-homework-stress-5-easy-steps-for-parents/ Mon, 30 Sep 2013 05:25:10 +0000 https://mathforgrownups.com/?p=1288 Last week, I shared some unpopular opinions about homework. Mostly, here and on Facebook, people disagreed with me that three hours of meaningful homework was not too much. And looking back at that statement — which wasn’t exactly what I said — I see their point. Do I want my kid to be focused on academics for a [...]

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Last week, I shared some unpopular opinions about homework. Mostly, here and on Facebook, people disagreed with me that three hours of meaningful homework was not too much. And looking back at that statement — which wasn’t exactly what I said — I see their point. Do I want my kid to be focused on academics for a full 10 hours a day? (Assuming that for those seven hours of school, she’s being taught.) When it’s put in those black-and-white terms, no, I don’t think that’s reasonable. Nor do I think the debate is all that black and white.

Regardless, parents all over the interwebs are pissed off about the amount of homework our kids are assigned. Their complaints range from the truly anguished (“I tried for two hours to help my son with his math homework, but with his learning differences, I just can’t get him to understand!”) to the kind of petty (“Having to sign a reading log is busy work — for me!”). It got me wondering, what do we do to lower this stress, for parents and students?

So I came up with some ideas. Try them out at home, and let me know how it works for you. And if you have your own ideas, please share them!

1. Reset the Priorities

What is the point of homework? Is it meant to help kids practice what they’ve learned? Extend lessons from class? Finish up something that didn’t get done in school? Complete a long-term project from start to finish? Torture you and your kid?

If you know what you want your kid to get out of homework, you can better set the parameters. See, this is your kid, not the school’s. What you want your kid to get out of his or her education matters. A lot. Once you know your homework philosophy, find out what the school and teachers think. (They might feel differently from one another.)

Then you’ve got to decide what hill to die on. If getting the right answer is a big deal for your kid’s math teacher but a conceptual understanding is what you value, someone’s going to have to compromise. For example, I’ve told my kid that I don’t believe timed math drills are useful tools. (And that’s backed up by research, y’all.) We agreed that if her grade was negatively affected by them, I would go in and talk to the teacher. Stress was instantly lowered. If signing a reading log is arduous for you, give your child that responsibility. Or decide that you’re not going to figure everything down to the minute and shoot for an estimate instead.

When the stress gets high, go back to those priorities. Talk to teachers about assignments that don’t meet your homework priorities. And if necessary, allow your kid to blow off things that are not meaningful. (Yes, I just said that.)

2. Set a Flexible Homework Routine

Whatever this schedule is, it needs to work with your family. Kids who go to aftercare may finish up their assignments before they get home. (At my daughter’s school, that’s a requirement for most assignments and students.) Other kids may come straight home, have a snack and shoot some hoops before hitting the books. Still others may not start homework until after dinner or even get up super early in the morning to finish an assignment.

Most kids really do count on structure, and it’s important that they know what to expect. At the same time, the schedule should be flexible enough to make room for everyday life — like a good cry after a fight with a friend or a quick trip to the ice cream shop for an after-school treat. When they know they can “break the rules” from time to time, they’re less likely to test their parents all of the time.

It’s also important to pay attention to how the schedule is working out — especially from year to year. My daughter used start her homework as soon as she walked in the door. But when she got a little older, it was apparent that she needed 30 minutes or so to unwind, to do something that had nothing to do with school. Of course, as kids enter middle and high school, this schedule should be their own.

3. STOP Reteaching

I can’t emphasize this enough. Stop it. Right. Now.

You are not the teacher. When you reteach, not only do you risk making your kid furious and even more frustrated with the work, you risk confusing your kid. Big time.

There is a reason that long division is going the way of the dodo bird. There is a reason that teachers introduce algebra in earlier grades. There is a reason that kids learn how to find the least common multiple before they learn to add fractions. And you might not know what those reasons are.

I would never attempt to perform brain surgery on my kid. I wouldn’t try to fix the hybrid system on my car. That’s because I’m not trained to do these things. And while many parents do an amazing job homeschooling their kids, mostly, they’re achieving this with the whole picture — and a lot of professionally developed resources.

This is probably the hardest step. It also holds the most promise for lowering stress. I promise.

4. Ask Questions, Don’t Give Answers

Want to know how to accomplish the last step? It’s pretty simple, actually. When your kid says, “I don’t know how to do this!” respond with a question.

“What does the assignment say?”
“Can you explain to me what the teacher asked for?”
“What is confusing you?”
“How can I help you figure it out?”

This puts the responsibility back onto your kid — where it belongs — without taking on any of her stress. Keep asking questions, even if she can’t answer them. Don’t solve the problems for her, but look for her to find her own solutions.

5. Let Your Kid Fail

Kids learn from making mistakes. We don’t do them any favors by preventing them from failure.

I’d rather my kid fail a homework assignment than a test and a test than a grade. And I’d rather my kid fail at something when she’s 10 years old than when she’s 40 years old. Failure at a young age won’t keep her from experiencing later failures. But she will learn from those little failures.

For that reason, you should quit checking your kids’ homework for accuracy. Heck, when they get to be in middle school, you should probably stop checking to see if their homework is done. Give them the right structure for success — space and time to complete homework assignments, little reminders, etc. — but let them chart their own way. (My friend and colleague, Denise Schipani calls this African-Violet Parenting. I call it parenting by benign neglect.)

So there you have it, five steps for lowering the homework stress in your house. I can’t promise that you’ll never have another fight with your kid, but I can say that following these steps will help you keep your cool.

Do you have other suggestions? Share them in the comments section. 

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