Math - Draw More Chickens, Write Fewer Numbers

Today I had the pleasure of being asked to work with 4th and 5th grade special education students.  Their teacher had explained to me that they were having trouble understanding multiplication.  Even though my new position is technically supposed to be helping teachers incorporate 21st Century Skills into lessons, I will never be able to pass up an opportunity to teach math.  I love it too much.

I started by asking them what multiplication was.

*Crickets*

I said, "OK.  When I say 'multiplication', what comes to mind.  There's no wrong answers.  Throw some words out."

One student said, "Times tables?"  Another said, "Skip counting."  After a pause another offered, "That line with two dots around it."

I'm guessing she meant the division symbol.

Here's the thing - I don't think the answers in most 4th and 5th grade regular education classes would be much different.  Kids think that math is about tricks we do with numbers, and that the key to being good at math is learning those tricks.  Special ed students, and lots of other kids think that because they are bad at memorizing rules, they'll never be good at math.  That's wrong.

Next, I told those kids that multiplication, and math, was not about numbers.  They looked at me like I had three heads.  At least I had their attention.  I reiterated, "You've been lied to your entire life.  Math is not about numbers.  And I'm going to prove it to you."

They were hooked.  Probably because they didn't believe me and they couldn't wait to see the head teacher crash and burn in a fiery mess.  Figuratively, of course.  Well, maybe literally for some of them.

So I told them, "Draw a picture of three chickens on your white boards.  I'm going to draw chickens, too.  Please don't laugh at my chickens.  I'm a mathematician, not an art teacher."

I'm a Mathematician, Not an Art Teacher

They were nice.  They didn't laugh at my chickens.

I said, "OK, each chicken just laid 3 eggs.  Go ahead and draw 3 eggs under each chicken.  You see, multiplication isn't '3x3'.  That's just the numbers and symbols we use to describe multiplication.  Multiplication is all about groups.  '3x3' just means that we have three groups of three."

The light bulbs started to go on.  They stopped looking at me like I was crazy, even if they didn't totally understand yet.

We modeled groups of airplanes with passengers.  Cookies with chocolate chips.  Flying saucers with aliens.  My flying saucers rocked.  Much better than my poor attempt at chickens.  Each time we talked about how there were repeated groups of the same number.  I only showed the multiplication problem in number/symbol form after we had figured out the answer to "How many do we have in all the groups."

I was pretty sure they understood, but I wanted to make sure.  So I told them, "Now, I'm going to give you a multiplication problem.  I don't care what you draw, but I want to see you express the problem as groups."  I gave them 7x4.

Some drew cookies, others drew flying saucers.  One kid drew seven tornadoes with four cars being mangled in each cyclone.  A bit graphic, but mathematically sound. All of them were able to model the problem without help.

For years I've talked about teaching math differently.  I've talked about the need to solve real problems, that there needed to be relevance behind everything that we teach - even basic facts.  I've talked about helping kids to understand before asking them to memorize.  Some were receptive.  Most thought I was crazy.  Many told me that I'd think differently if I didn't only teach the high math group.

They were wrong.  There's no reason that we shouldn't expect almost all students to have understanding of math the way we expect almost all students to learn to read.  We just have to stop expecting kids that have trouble memorizing to have no problems memorizing stuff that has no relevance to them.  In 40 minutes these special education kids went from thinking that multiplication was "the line with two dots around it" to being able to model multiplication problems.

Math isn't about numbers any more than writing is about the alphabet.  Numbers and symbols are just our way of expressing the quantities in the world around us just as the letters we use to write are the symbols we use to express our thoughts.  When we take away that context of that world around us, we take away students' understanding.

We'd never tell a student that they should do 40 letter manipulation problems for homework to get better at writing.  Or at least we shouldn't. (I'm not a big fan of spelling workbooks.)  That's not going to turn them into a writer.  Heck, it's probably going to turn them into a kid who hates writing.

Math is no different.  It shouldn't be about following rules to manipulate numbers.  It should be more about drawing chickens.

Should We Still Teach Cursive Writing?

A friend of mine posted this on Facebook a few days ago:

In the comments, I was one of the few who didn't agree that the lack of instruction in cursive was a huge problem.  Now that we are 12 years into the 21st Century, it's about time we start focusing on the skills our students will need in this century.  We need to be teaching kids to collaborate, create and innovate, communicate effectively, and think critically.  Not doing so makes school irrelevant to them.  What makes us think that someone would be engaged in a learning process that is irrelevant to them?

Cursive writing does not aid in collaboration in any way.  It doesn't help students become more innovative.  Cursive writers do not think more critically than those who print.  Today's communication is not done in cursive.  

We should be teaching students to communicate in the way they will need to in their world.  How much of your communication with your colleagues is done in cursive?  How much is done electronically?  

If we continue to teach our students things because "that's what we learned in school," we will continue to produce a generation of graduates without the skills they need to be successful.  It's time to prepare students for their futures and not our past.  

Friday's Five - Wisdom of Age, Wonder of Youth

Let me start this post by saying that I am amazed at the wonders of modern technology, invigorated by the natural wonder of kids, and appreciative for the wisdom of older generations.  I'm writing this post on my iPad at 36,000 feet while flying home from a visit with my grandparents in Florida.  Last night I heard wonderful stories about the jobs they had between my grandfather's service in WWII and the time he opened a jewelry store in New York. This morning I had the pleasure of explaining to my 6 year old why walking on the clouds he sees from the plane window would be impossible. Great stuff!

Photo Credit:  worradmu

Along those lines, I was wondering if it's possible to combine those 3 things (technology, wisdom of the older generation, and the wonders of youth) to create incredible learning opportunities for our students.  Here's five ideas:

1. Service learning projects involving local senior centers.  Students could read to seniors, help maintain the gardens, or help in other ways.  Afterwards, they could blog about their experiences and what they learned.
2. Invite senior experts into the school, or videoconference, to offer guidance on projects.  I am always looking for community members to help my students learn about real-word situations and problem solving.  There are plenty of situations where students can collaborate with retired members of the community.  My grandfather, for example, has Skyped in with middle school students to explain his experiences as a Jewish soldier liberating Concentration Camps during World War II.
3. Allow students to teach what they learn to seniors.  My grandparents mention often that they love when their community brings in college professors to give lectures.  Why can't our students do the same thing? My students would love to teach others how to use new technology, share their learning experiences, and present their projects with others.  It seems like a perfect match.
4. Invite local seniors in for a "games day" where they can teach their favorite card and board games to students.  The kids can then create descriptions and written directions of the games afterwards to publish on the class wiki or website.  In addition to being the catalyst for a great writing assignment, the interaction during the games would be great for everyone involved. 
5. Have children publish a biography of their grand-parent or other senior as a blog post.  They can do a series of interviews, and then compile a collection of stories from that person's life.  This way, the stories are saved forever, and students get a chance to learn a bit about their family history. 

Friday's Five - Developing Better Writers

When I've talked to college professors, high school teachers, local business owners, and others who deal with our young adults I'm often told that the ability of these young adults to express themselves in writing is sorely lacking.  Even in my fifth grade classroom I've seen an increase in students who struggle to write complete sentences, cannot use correct punctuation, and find it difficult to express themselves.  Some of the causes are probably an increase in "textese" and  the increased shift from a balanced curriculum to one that focuses solely on  math and reading during the last decade of NCLB testing.  Instead of looking at causes, however, let's look at five ways we can develop better writers in our classrooms and schools.

Photo Credit:  János Fehér

1. Make a commitment to have each student write at least one complete sentence per subject per day.  At first, this sounds like something that must already be happening in our schools.  It's not.  Think about the average math or science classroom.  Often there is very little writing going on, and even less that is written in complete sentences.  Instead of having students raise their hands to answer questions, make every student write their responses in complete sentences.  Then choose a few at random to share their responses.  In addition to building writing skills, you'll be using formative assessment to check the understanding of all of your students.
2. Get your students blogging.  When your work is being published to a wide audience, you are more likely to pay attention to the details of your writing.  The reading specialist and special education teacher in my building claim that their students' punctuation, capitalization, and spelling improved dramatically when they started blogging.  Blogging also is a great way to get students in subjects outside of language arts writing as well.  Asking students to share their learning ensures that they really understand the concepts being taught.  It's impossible to write about a topic well without understanding it.
3. Grade less.  Not everything that an author writes gets published.  Students need opportunities to simply write for the purpose of writing.  I can't tell you how many posts I start and then scrap.  If I were being graded on each of my posts I'd stop blogging.  I'm sure many of our students feel the same way.  Just like students sometimes draw for fun, we should encourage them to write for fun.  
4. Give opportunities for students to be creative.  In the past 10 years I've seen writing become much more formulaic in schools due to the rubrics on standardized tests.  We tell students, "If you do X, Y, and Z, then you'll get a '4' on the test."  I can't think of anything more detrimental to building a love of writing, nor more likely to destroy a student's ability to write creatively.  Allow students to illustrate their writings if they are artistic, write in verse if they enjoy poetry, or use web 2.0 tools to enhance their writings.  Give students writing assignments that lend themselves to creativity.  One of my favorite writing activities that I do with my class is to pass out cards with random narrative titles, main character descriptions, and settings.  I then ask my students to put together a good narrative using the elements they randomly received.  One student might have to write a story entitled "The Missing Day" that takes place in the old west about a pillow salesman, while another student gets "Elbow Soup" as a title, present day New York City as a setting, and an alien from the planet Oooff as a main character.  Since we spend a lot of time talking about how good narratives are composed in reading class, the stories they write are usually very good.
5. Build a love of reading.  It's very difficult to complete a job when you don't have access to the right tools.  Students who don't read much often are lacking the vocabulary and figurative language skills to write well.  Because of that they often have no confidence in their writing abilities and shut down any time they are asked to express themselves that way.  For these students, helping them find the motivation to read is supremely important.

How do you develop writing skills in your classroom?  Have you seen a change in the writing ability of students entering your class over the past few years?  What else can we do to show students the power of well-written words?