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Now that school is out for the summer, I am going to take some time off from blog writing.  My articles will return on July 24th. Meanwhile, I hope you will go back and read some older postings that pertain to math.  Have a restful and rejuvenating summer vacation!

Featured Teacher

It's Me - Scipi

YEAH!!  After waiting for over nine months, I am the spotlighted teacher on the blog An Educator's Life Blog. 

The blog is by John Hughes, a sixth grade teacher from the great state of Utah.  While visiting his blog, you might also see what else John is spotlighting each week.  He has a great feature called Share the Wealth Saturdays where you can find many free and new teacher resources. Take a few moments to check it out by clicking on the bold blue letters above.

The Mathematics of a Hail Storm

Kansas had an absolutely terrible storm Sunday night.  The sky was a murky green (this is never a good sign), and the hail was the size of golf balls.  It broke three of our four basement windows; so, we had glass everywhere plus hail stones were coming into our family room like crazy.  We just stuffed the windows with pillows and tried to clean up.  Our neighbors have siding damage that looks like someone went through our neighborhood with a machine gun when instead it was the force of the hail.  When the storm let up, everyone was outside and most were thanking God for sparing our homes.  Hail was laying everywhere in piles; so, my husband, being the scientist he is, was examining some of the big pieces.  He showed me how the hail was formed.

 

He explained that hail is created when raindrops are lifted up into the atmosphere during a thunderstorm and then super cooled by temperatures below freezing, turning them into balls of ice. The faster the updraft on these balls of ice, the bigger they can grow. On the hailstones found in our yard, we could actually see several rings inside of them which indicated they were cycled through the thunderstorm more than once. What started out as a minute raindrop became a golf ball sized chunk of ice. According to Dr. Dick Orville of Texas A & M University, large hailstones have been clocked traveling more than 90 miles per hour. I don’t know how fast these golf ball sized ones were traveling, but fast enough to make huge holes in aluminum siding.

 

Let’s look at the math of concentric circles.  Concentric means two or more circles of different sizes that all have the same center -- like a bulls eye target. 

On the right is a picture of one of “OUR” hail stones. If you look closely, you can see four different circles, (a pattern) one inside the other.  That means it was recycled through the thunderstorm at least four times. 

AND it was not only hard, but heavy.  According to the Internet, the largest hailstone ever recorded in the United States occurred in 1970 in Coffeyville, Kansas which is about two hours southeast of Wichita.  It was a stone that weighed 1.6 pounds and measured 5.5 inches when it fell. YIKES!!  I am glad I missed that one.

 



Ice Investigation

 

 

Since ice seems to be the theme of this post, I want to mention my newest Teacher Pay Teachers resource entitled Ice Investigation.  This 20 page resource is a six lesson science investigation for grades 3-4 which uses ice cubes.  The inquiry guides the student through the six steps of the scientific method.  The unit consists of a three page student investigation organizer, a property word list, an optional student checklist, and a four point grading rubric for the teacher.  If you are interested, just click under the cover on your right. 

 

Divide to Conquer?

As presented in the posting of April 10th, there is another way to approach long division.  However, since many of you are required to present it the long way, here are a couple of ideas to make it easier for your students.

First of all, have the students use graph paper.  The squares help to keep the numbers aligned which seems to be a problem for many students.  If you don't have graph paper, you can download free templates at Donna Young's Free Graph Paper and make your own.  I like the idea of separating the problems with lines to ensure there is no cross over from one problem to another.

 

Secondly, try using the mnemonic of Does McDonald's Sell Cheese Burgers.  I've  see this acronym many times on Pinterest, but usually the C is omitted.

Check means that after the student has subtracted, they should check to see if the remainder is smaller than the divisor.  If it is equal to or larger, then they enough was not taken out of the dividend.  This is a step often skipped when long division is taught; yet, if the student doesn't check and make the needed correction, the answer (quotient) will be wrong.

In order to learn division, the student must first have a good understanding of multiplication. Students don’t need to perfectly know all of the times tables, but a majority of the facts or having a reasonably quick strategy to figure out the answer is necessary.

Start by practicing division using the number series the students can easily skip count such as 2 and 5. Then gradually move up to nine.  After that, move to division by double digit numbers using 10 since most students know how to skip count by 10.  Once the concept is understood, teaching division will become more about guided practice to help your child to become comfortable with the division operation which, in reality, is a different kind of multiplication practice.

Common Core Conundrum

As a member of Teachers Pay Teachers, I often read and share on their Seller's Forum.  As the Common Core State Standards (CCSS) become more "common", many teachers are asking about things being omitted or totally left out.  Let's start this discussion with what the Common Core supposedly is.  CCSS is a state-led effort coordinated by the National Governors Association and the Council of Chief State School Officers. The standards establish common goals for reading, writing and math skills that students should develop from grades K-12.  Although classroom curriculum is left to the states, the standards emphasize critical thinking and problem solving and encourage thinking in-depth about fewer topics.

With that said, this is the way I perceive these standards.  When I started teaching, (I've been at it for 30+ years) the curriculum was a nice, juicy apple. Included were subjects like spelling, geography, history, cursive writing in addition, areas such as effort and behavior were evaluated. I can't remember ever giving a state or national test, but I did have to teach art, music and P.E. The majority of the children went home for lunch where some adult was waiting.  Later, the arts were added to the curriculum and qualified teachers were hired to teach art, music and P.E. (Thank goodness!)

Then came the slicing of the apple.  One test was introduced and given each year.  (We gave the ITBS.)  Objectives were written that were different from the textbook, and more children were staying at school for lunch.  As time progressed, additional slices of the apple were removed as "before and after" school programs became necessary for children and free lunches became common place.  In addition, more than one test was required because now the district and the state wanted data.  History and geography became social studies, and phonics and spelling were replaced with the whole language approach.  I was directly a part of our district's benchmark test writing project where much money and time were devoted to the test that would reveal all, make teachers better, and students smarter.  Of course, none of those things occurred, and the money wasted could have been better spent on teachers who really make the difference in the classroom.  (By the way, all of those assessments are now gone.)

Many advocate that the CCSS will become the tool that can successfully turn around education.  Let's remember that these standards are merely the minimum each grade level is to master.  Think of the CCSS as the core of an apple; there is no "meat" on the core, just the left over part of the apple.  The basics are there; but teachers need to add the meat, but will they especially since the high stake tests that are imminent will most likely only test the core?  My question is: How much testing will be required; how often, and at what expense in money and time?  And who will pay the price?

I did some of my own reading of the CCSS, particularly those for the "key" grades of K-3.  Yes, the CCSS requires the multiplication tables be taught through 10, but does that mean a teacher shouldn't go to 12?  I personally want all of my algebra students to know the doubles through 25 because it makes finding the square root so much easier.  Since the multiplication fact is in the student's head, no calculator is required!  I also observed that money is not mentioned anywhere in the common core for grades K-3 except in second grade.  Covering that standard is going to be a daunting task for 2nd grade teachers if students have never seen it before.  (I did find the money standard in grades 4th, 6th, and 7th, and after that, money was considered Consumer Science.)  In addition, there is no standard for patterns in kindergarten which I find quite disturbing since all math is based on patterns.  Time and introductory place value have also been deleted.  If students do not get these basic concepts in kindergarten, it is obvious they cannot grasp the more complex ones in later grades.

As I read the many different responses on the TPT Forum as well as various articles about the Common Core, I realized that many teachers are viewing them as the all-in-all.  If that is all that will be taught, education is in BIG trouble.  I would suggest reading a rather thought provoking and eye opening article by Carol Burris, principal of South Side High School in New York. She was named the 2010 New York State Outstanding Educator by the School Administrators Association of New York State, and she is co-author of the book Opening the Common Core.

Personally I see several problems with the implementation of the CCSS.

1. Accountability: Only using test results to measure education, evaluate teachers, and to reward or punish teachers and/or schools is "iffy" indeed. Dr. Tom Heladyna wrote a must read essay about this very topic. Let's be honest, test questions are usually not asked in the manner you expect, and it all comes down to HOW students are asked to show what they know. Education is not a battery of tests.
2. Technology: Investing in and assuming that the digital world will do the teaching is a false assumption since much research indicates direct teacher instruction is what makes the difference for students. I suggest reading a dissertation by Binder and Watkins and/or an article entitled: What the Data Really Shows.
3. Teacher Training, especially in the area of mathematics.  Since the CCSS demands a more in-depth and comprehensive approach to subject matter, teachers will need a thorough foundation and a comprehensive understanding in every subject they are required to teach.  Having taught math methods at our local University, I instructed many who were already ill prepared to go "in depth" into mathematics.  What math they knew simply skimmed the surface.  This superficial knowledge was (and is) often revealed on the math section of the Kansas licensure test.  It is frequently failed by students seeking to be elementary teachers which then requires the candidate to retake that section until it is passed.  However, when the candidates does succeed, it in no way proves they understand or know how to teach mathematics thoroughly. 

My primary concern is that the Common Core will become so focused and fixated on a limited number of standards that little will be left of well-rounded education except a very inadequate and flimsy core.  If a teacher only follows the common core and nothing more, students will miss important building blocks in between. I believe education is an exciting and engaging lifetime journey, not a final destination or a binding contract with any government. I trust and hope parents (families) are the constant in this equation (a math word!) while schools and teachers are the variable. (both will change over time) 

How can any test adequately measure that?

 I would love to have your comments about this article.