Friday, October 30, 2009

Putting It All Together...

A couple of us got to talking and thinking last week.  This was not at a planned meeting, but one we chose to have in the hallway. (This is how most good meetings happen!) We have a decimal unit.  We have a fraction unit.  We try to deal with percents here and there.  Later in the year ratios and proportions units roll around and we have to re-teach the fraction stuff which we should have been working on all year but didn't have time for. One colleague said, "Why do we refer to these topics as units?"  His point was that we use all of these skills all of the time and they are all significantly interrelated.

We end up connecting the decimals to fractions and percents in the decimal unit.
We connect the fractions to decimals and percents.
We connect the ratios and proportions to fractions, decimals and percents.

So I'm sure you can guess the question.  Why not teach it all at the same time?

That's what we are going to do.

We started this week.  Here's the plan:

Start with teaching them the "how" of it all.  They will learn how to convert between fractions, decimals, and percents, to see the relationships.  They will become very proficient at this.  (They did a great job)

Next, probably the most important step.  Teach the "what" and "why".  What is it that you are doing and why would you ever do this.  They will use the newspaper, advertisements, baseball and football statistics to see how this all applies to most math they will ever do in their lives.  We will use percent circles, fraction bars, human beings, whatever it takes to make sense.

Money, money, money!  The students know all about it.  What better frame of reference!   We will even dabble into the stock market,  hopefully the stock market game at some point this year.

They will be experts at adding, subtracting, multiplying, and dividing fractions and decimals.  Fractions of a set, fractions of one, fractions of fractions.  They will be able to apply these skills to all problems that arise.

We will use current topics.  Today we listened to a Marketplace report from American Public Media which airs on NPR. This report about the assembly of the iPhone and the estimate of percent profit that each country involved in the design and manufacture earns.  This lesson involved estimation, converting percents to decimals, decimals to fractions, simplifying fractions, adding decimals, adding percents, and adding fractions.  This all came from a four minute audio news report.  Did I forget to mention a good practice in listening skills. I was really proud of them today!  This was followed up by a trusty old favorite "Maths Mansion".  This is a british television show that students love.  I can access it through Discovery Education.   The students learn in a fun and silly way how math works.  If you can watch it with your students.

By December 23rd they will be proficient and confident.  They will possess the tools to handle any problem thrown their way.  We will be sure stop and review but then push on!  It should be fun.

We are ready.
We will keep you posted!
Please check back for our progress.

Any suggestions...please, send them our way!

Saturday, October 24, 2009

More Science and Math!

Here is a link to a blog by Education Week about Education Secretary Arne Duncan seeing the need for more science in the curriculum because with No Child Left Behind, science is being "pushed" out of the curriculum.  I would use the word squeezed out!  This has happened in my school.  A link to the article is below.

Duncan said "I worry tremendously about the loss of science and engineering," Duncan said at one point. The main question, he added is: "How do we create the incentives so that students have a well-rounded curriculum?...We're thinking these things though."

Friday, October 23, 2009

What's the Problem? That's the Problem!

Oh, the age old problem...Word Problems!  Kids hate em.  They don't get em.  When you mention the two words the squirming in the seats begins.  The collective "Ugh!" ensues.  All of a sudden the teachers words sound like the teacher in Charlie Brown "Wha Wha Wha".  (If that didn't happen already.)

My goal this year in sixth grade is to break this vicious cycle of "Word Problem Phobia".  I want to get to the bottom of this.  I want to know exactly the reasons why each year there is a phobia, dislike, hatred for word problems.

I contend and tell the students that every single problem they will ever have to solve in their lives is a word problem.  That math they need to solve is connected to something, whether a trip to the grocery store, a home improvement project, or planning for a birthday party.  You never have to do a math problem just for fun, unless you want to.  (See last week's blog on Ken Ken's.)

So how will I get to the bottom of this?  How will this age old problem be fixed?  I'm not quite sure, but I will give it the "Old Intermediate School Try"!

Here's the plan:

~ Give them lots of word problems.
~ Not understanding what is being asked is the big problem.  Solving the wrong problem using the wrong numbers is the most common issue. So I will try to teach them specific reading strategies to help understand the problem.  We do this in reading, we will apply these same skills to math!
~ Teach them a system of how to organize the information and how to show the work for any problem.
~ The students will work together and help each other.  Isn't that how problems in real life are solved?
~ We will solve authentic problems that affect their daily lives.
~ We will use resources such as the wonderful book Comprehending Math by Arthur Hyde.
~ We will try to make it fun and exciting, not Charlie Brownish.
~ I will seek help from others.  Will you help me?  If you have any thoughts, ideas, suggestions, complaints, please let me know.  I am looking for input.

My next problem is to figure out how to get my kids to sleep. That's a serious word problem. (Ugh!)

Stay tuned. I will keep you posted.

Friday, October 16, 2009

Percents, Ken Ken's, and Graphing Away: Math Potpourri!

Another week down.  The theme of this week was powering through.  There is never enough time so we just did the full court press.

Problem Solving.  Check
Graphing.  Check
Ten Percent of any number.  Check.
Customary units of measure in ounces and gallons.  Check.
Couple of quizzes.  Check.
Metric linear measurement. Check

Looking back on it we did a whole bunch of stuff.   The most fascinating thing this week though was watching the students during independent working times.  They are talking about math.  They are asking for math.  They want problems to solve.  Some students are teaching algebra.  Some are very high level math students.  To watch them teach basic algebra to other students is amazing.  They want to learn!

One crew is on a quest to complete every Ken Ken puzzle around.  They started quite simple, but now they are doing the longer, much more difficult puzzles.  One character is even trying to make his own.  If you don't know, Ken Ken's are number puzzles in the form of Sudoku where you need to find the numbers in the boxes but by doing an algorithm such as adding, subtracting, multiplying, or dividing.  Click the links for more information.

Today's morning message problem came from my ride to work.  We were out of orange juice at our house.  I bought a 12 ounce container at Dunkin Donuts.  This container cost $1.70.  My regular half gallon orange juice container from Trader Joe's was empty.  The Trader Joe's juice costs $2.99.

How many Dunkin Donuts 12 ounce containers would I need to buy to equal one half gallon?
How much would that much orange juice cost?
How much less does it cost to buy a half gallon at Trader Joe's?
What is the price per ounce?

They started to work on the problem before our quiz today.  We are going to finish on Monday. I showed them both containers and one commented how math is part of every day. One said "How cool!" I told them that this is the stuff you can be thinking about while reading the cereal box at breakfast.  Each tiny piece of knowledge you gain will connect to another piece of information.

The thing I am most proud of this week was that every student can tell you how to find ten percent of any number.  Than to find twenty percent you just double the ten percent.  To find five percent you cut the ten percent in half.  To find fifteen percent, you add the ten and five together.  To find one percent you just move the decimal twice to the left.  A pattern will form.  It will always be a pattern. They will get to the point where they can find any percent of any number mentally.

No need for a tip calculator for these kids.

Next Week:  Unit test, Quick and easy decimal strategies, The facts reprised!

Friday, October 9, 2009

Just The Facts!

The students must know the facts.  Yes.
The students must have addition, subtraction, multiplication, and division mastered.  Yes.
The students must be held accountable for the facts every year or they will not retain them.  Yes.

The great facts debate was on this week.  The beginning of the year fact assessment revealed that students in general need to practice their facts.  Some teachers felt that they should already know them and basic facts are something we should not be teaching. Some thought they should just know them because they learned them in second and third grade.

We all know the purpose and the need for students to master their basic arithmetic facts.  We all know why they need to have computational fluency.  This is the foundation for being quick and accurate when calculating math problems.  Just as readers need to be fluent in their reading so they are able to comprehend the text, math students need to fluent to solve the higher order problems they encounter.

I posed this question to the class: "When was the last time you practiced addition and subtraction facts?"
The answers were overwhelmingly second and third grade.  As they were completing their facts tests I heard students mumbling, "I need to practice these."

I was glad to hear that.

I told the students that it is okay to not have the speed and accuracy yet.  I told them it is not their fault. I told them that they will master these facts.  I told them that they will be held accountable for these facts all year long. They will need to be quick.  They will need to practice.  They will be fine.

We can't expect students to know and retain information if we don't continually hold them accountable.  We need to have high expectations, but fair high expectations.  We need to bridge the gap from grade to grade and expect the facts to be a part of the curriculum every year.

There is a wonderful article from Scholastic on math fluency.  This article details why memorizing the facts is so important for higher-order math skills.  Here is an excerpt from the article detailing brain activity during math:

"Recent research in cognitive science, using functional magnetic resonance imaging (fMRI), has revealed the actual shift in brain activation patterns as untrained math facts are learned (Delazer et al., 2003). As predicted by Dehaene (1997, 1999, 2003), instruction and practice cause math fact processing to move from a quantitative area of the brain to one related to automatic retrieval. Delazer and her colleagues suggest that this shift aids the solving of complex computations that require “the selection of an appropriate resolution algorithm, retrieval of intermediate results, storage and updating in working memory” by substituting some of the intermediate steps with automatic retrieval (Delazer et al., 2004)."

I am looking forward to seeing their progress.  Let's get the brain shift moving. I can't wait for the students to feel the pride of being quick and accurate based on independently practicing the facts and being held accountable.

Tuesday, October 6, 2009

Math, The Way It Could Be?

Finally I have read an article with data (proof)  that there is a need to have math teachers just teach math in elementary school starting in fourth grade at the latest.  This month's "American Educator" magazine has the article titled  "What's Sophisticated about Elementary Mathematics?

The point of the article is that elementary schools need math teachers.  They need teachers who focus specifically on one subject to be able to get to the heart of the matter.  Students need to know the basics.  They need to know how to add, subtract, multiply, and divide.  They also need to know why and how everything works.  They need to be able to apply the math to their own life.  They need to understand algebraically at a young age how numbers and place value work.  They need all of this continually repeated.

When I taught in the lower elementary grades I always felt that math got less attention.  I taught it in the afternoon when the little ones were exhausted and sometimes falling asleep on the carpet.

Now there is a push in some places to have math specific teachers.  The teachers can focus on one discipline and dig real deep to build those crucial understandings and connections.  Lets get that push moving!  The students and the country depend on it!

Can we have a little bit of science too?