Every Day. Every Class. Every Assignment.

Nice. Show that we are more than that - every day, every class, every assignment. Pride, bravery, perseverance. Every day. Every class. Every assignment. We are Todd County.

Investigations Unit Training: December 8 and 9

SpringCreek Leaders Spill the Beans on Trapezoids

SpringCreek students have combined excellent camera work with very clear articulation to produce two fine examples of trapezoid geometry. Pay attention, now! Your teachers, Rain and Taleah, are about to take the stage...

I visited SpringCreek earlier in the week, and observed these students measuring other geometric shapes, like cylinders and spheres. I wonder if we'll see a report on the size of a basketball vs. the size of the hoop we try to toss it through? Hmmm??? Hint hint! ;-)

Why Can We "Add Zeros" When Multiplying by a Power of Ten?

Somewhere along their mathematical journey, every student is taught the "trick" of "adding a zero" to any number they multiply by 10. First of all, let me be clear - we know we aren't actually adding zero, right? Because if we add zero to any number, we end up with that same number thanks to the zero property of addition.

So if we aren't actually adding zero, or zeros as the case may be, what the heck is going on when we multiply by a power of ten?

Recently, I challenged the 5th grade teachers at South to have students answer this question. Mrs. Seger's mathematicians have risen to the challenge!

TCMS Adds One... No, Two... Hold On.. That's SIX New Videos!

Need to find the area of a trapezoid, and need it NOW??? The TCMS has you covered with SIX, yes SIX videos to give you plenty of practice. Enjoy!

Klein Answers the Call!

Nice work, Jesse! I liked the way you showed us how we could construct a parallelogram and use that to find the area of a trapezoid.

Trapezoid Challenge: Littleburg in the House!

Excellent! Wonderful presentation... We look forward to more from you!

The Super Ultimate Graphing Challenge!

Graphing Challenge

Great flash game for developing understanding of how graphs work. Can you stay within the blue field???

District Math Email Groups

Your cohort of mathematics teachers is just an email away!

To communicate with everyone at your (or any) grade level, open a new email message and click "To." Then in the search window, type "math." Now choose a group you'd like to share your thoughts or questions with!

Can the Middle Class Be Saved? - The Atlantic

Can the Middle Class Be Saved? - The Atlantic

It’s hard to miss just how unevenly the Great Recession has affected different classes of people in different places. From 2009 to 2010, wages were essentially flat nationwide—but they grew by 11.9 percent in Manhattan and 8.7 percent in Silicon Valley. In the Washington, D.C., and San Jose (Silicon Valley) metro areas—both primary habitats for America’s meritocratic winners—job postings in February of this year were almost as numerous as job candidates. In Miami and Detroit, by contrast, for every job posting, six people were unemployed. In March, the national unemployment rate was 12 percent for people with only a high-school diploma, 4.5 percent for college grads, and 2 percent for those with a professional degree.

Fastt Math: Status Unknown

I'm sure this will be on many a mind out there...

Despite my efforts to contact the tech folks, I have yet to hear anything regarding the status of the Fastt Math server. Stay tuned.

Clarifying Timeframes

Well, Chris has given me my first opportunity to blog! I've never done this before. But as Chris says, I need to practice my mathematical proficiency skill of communication.  I AM a lifelong learner!  I AM a lifelong learner!

We have been getting lots of questions about suggested timeframes on the curriculum guides.  Thanks for the feedback! We have changed the wording from weeks, to number of school days. School days are days in school when students are in math class (and that's every day! Right math lovers???). And please remember- these are suggested timeframes. Your mileage may vary.

We also added a bit of padding to the days in the first unit at every grade level. We know how important it is to set up your learning community and classroom routines. We wanted to give you plenty of time to determine what your students know, what your students need, as well as establish the managerial aspects of your classroom. This will free up your kid's attention from "What do I do when I have to go to the bathroom?" to "How many blocks do I have and how do I know?"

Matt Damon's Inspiring Back to School Speech!

Last weekend, concerned citizens held a "Save Our Schools" march and call to action in Washington, DC. Among their goals is a demand for a well-rounded education that develops every student’s intellectual, creative, and physical potential. Matt Damon and Jon Stewart were among the marchers - both having teachers for parents.

We're an embattled group, teachers. With a new school year about to begin, I wanted to repost Matt Damon's speech here. I hope you will find comfort within his public-school educated words.

"I flew overnight from Vancouver to be with you today. I landed in New York a few hours ago and caught a flight down here because I needed to tell you all in person that I think you’re awesome.

"I was raised by a teacher. My mother is a professor of early childhood education. And from the time I went to Kindergarten through my senior year in high school I went to Public Schools. I wouldn’t trade that education and experience for anything.

"I had incredible teachers. As I look at my life today, the things I value most about myself— my imagination, my love of acting, my passion for writing, my love of learning, my curiosity— all come from how I was parented and taught. "And none of these qualities that I’ve just mentioned— none of these qualities that I prize so deeply, that have brought me so much joy, that have brought me so much professional success— none of these qualities that make me who I am… can be tested.

"I said before that I had incredible teachers. And that’s true. But it’s more than that. My teachers were EMPOWERED to teach me. Their time wasn’t taken up with a bunch of test prep— this silly drill and kill nonsense that any serious person knows doesn’t promote real learning. No, my teachers were free to approach me and every other kid in that classroom like an individual puzzle. They took so much care in figuring out who we were and how to best make the lessons resonate with each of us. They were empowered to unlock our potential. They were allowed to be teachers.

"Now, don’t get me wrong, I did have a brush with standardized tests at one point. I remember because my mom went to the principal’s office and said, “My kid ain’t taking that. It’s stupid, it won’t tell you anything and it’ll just make him nervous.”

"I shudder to think that these tests are being used today to control where funding goes. "I don’t know where I would be today if my teachers’ job security was based on how I performed on some standardized test. If their very survival as teachers was based not on whether I actually fell in love with the process of learning but rather if I could fill in the “right” bubble on a test. If they had to spend most of their time desperately drilling us and less time encouraging creativity and original ideas; less time knowing who we were, seeing our strengths and helping us realize our talents.

"I honestly don’t know where I’d be today if that was the type of education I had. I sure as hell wouldn’t be here, I do know that.

"This has been a horrible decade for teachers. I can’t imagine how demoralized you must feel. But I came here today to deliver an important message to you: as I get older, I appreciate more and more the teachers that I had growing up. And I’m not alone. There are millions of people just like me.

"So the next time you’re feeling down, or exhausted, or unappreciated, or at the end of your rope; the next time you turn on the TV and see yourself called “over-paid”; the next time you encounter some simple-minded, punitive policy that’s been driven into your life by some corporate reformer who has literally never taught anyone anything…

"Please know that there are millions of us behind you. You have an army of regular people standing right behind you and our appreciation for what you do is so deeply felt. We love you, we thank you, and we will always have your back."

THE Fastt Math Champion!!!

This post is a month late... my apologies! Back on April 12 Mr. Hammer informed me that a Rosebud student had mastered addition, subtraction, multiplication, and division on FASTT Math. He wondered if she was the first in the district.

And... SHE WAS!!!

Huge props to Teana for this incredible accomplishment! Thanks also to her teacher, Mrs. Hammer, for giving Teana the opportunity to achieve this goal.














This just in! On May 19, Nathan down at Littleburg also met the ultimate goal: all 4 operations MASTERED in Fastt Math! Way to go Nathan! And thanks Miss Todd for helping him to get there!

Sentence Frames and Discourse

(Please continue to video after the break... ie. click on "Read More")

In many of my conversations with teachers both individually and in CWGs, the language issue is emerging over and over again. From 1st grade through 8th grade - the need for structure and explicit instruction in student discourse is overwhelmingly clear.

Years ago, many of us had the pleasure of attending a workshop at the Middle School by Jill Eggleton. For me, it was a transcendental experience and my instruction was forever changed. She convinced me of the importance of oral language in developing WRITERS, and she inspired me to use it daily - in every content area.

From "Linking the Language Strands"

Purposeful Listening and Speaking

Oral language is an integral part of the learning program across the curriculum. Students need to have purposeful interaction in the oral language function. It is important to allocate times that provide students with experiences in the different types of oral language.

It can be: transactional language that incorporates specific functional discussions, such as describing how to play a game, give directions or poetic language, such as describing a favorite character...

Or.... it can be describing your solution to a math problem!

After the break here, you can see first graders engaged in purposeful discussion. Also notice the sentence frames behind them. Yay sentence frames!!!

Eyrie Cam!

The Raptor Resource Project brings you the Decorah Eagles from atop their tree at the fish hatchery in Decorah, Iowa.



Awesome video stream of an eagle nest and some new hatchlings. Can you hear her babies tweet-tweeting?

Excitement is Building for Investigations in the Classroom Training!

When I cracked open my oh-so-official "Host-Site Coordinators' Manual" for our Investigations in the Classroom Workshop, I became giddy! Check this out:

You will receive shipments, via FedEx, that include, depending on the size of the workshop, three to eight trunks and 15 to 40 boxes. Each trunk weighs approximately 150 lbs. and contains the materials that the leaders will use in their sessions.

150 lbs.??? Let me do some math... ok..... 8 x (100 + 50)... so thats 800 plus half of 800... thats 1,200 lbs!!! 1200 lbs. of potential "stuff!" Of course, since TERC is located in Massachusetts and all - I'm hoping that at least one of those 8 trunks will be filled with lobster.

We already have 60 folks signed up, so it should be a FANTASTIC week! Woo!

Here's the Workshop Flyer. We still have plenty of room for more educators interested in delivering top-notch mathematics instruction!

An Illuminating Experience for He Dog 4th Graders!

Students at He Dog see the light as they work with arrays, factors, and multiples.

Ms. Rozier has a fantastic - REALLY - blog set up for her 4th grade students at He Dog.

Skedaddle on over there and say hello!

So, What's a Nuclear Fuel Rod, Anyway?

This video should be required viewing for anyone interested in what Japan is currently dealing with (at least the nuclear aspect... Japan is dealing with a LOT right now)

"I think it is, frankly, less upsetting to actually understand what is going on than it is to not understand." Rachel Maddow.

By the numbers: A single fuel rod weighs over 700 pounds! A single uranium fuel pellet the size of a fingertip contains as much energy as 17,000 cubic feet of natural gas, 1,780 pounds of coal or 149 gallons of oil.

Visit msnbc.com for breaking news, world news, and news about the economy

Overwhelming

How do humans cope with this level of catastrophe?


Text "RedCross" to 90999. Please. Japan has always been a good friend in our times of need (re: Katrina). It is time we return the favor.

Other ways to help.

How to Draw 3d Cube Designs

Isometric grid paper is AWESOME stuff!!! If you want your work to stand head-and-shoulders above the rest at the math competition, learn how to use this stuff!!!

Here is where you can download the paper. It is much easier (in my opinion) to use the paper if you lay it down landscape style. If you are interested in printing your own variety of grid paper, use this fabulous website: Incompetech.

Watch this yourself and teach your kids, or give them some paper, and let them have at it as they watch the video themselves. Have fun!

How to Use Isometric Grid Paper from (Chris) on Vimeo.

March 15 DtM Participant Link

Here is the LINK!

4th - 5th Grade Challenge Example

Hope this helps, kids! Go math!


4-5th Grade Notebook Entry from (Chris) on Vimeo.

Related Literacy skills:

4.W.2 - Write informative/explanatory texts to examine a topic and convey ideas and information clearly.  
a.  Introduce a topic clearly and group related information in paragraphs and sections, including formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.  
b.  Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.  
c.  Link ideas within categories of information using words and phrases (e.g., another, for example, also, because).  
d.  Use precise language and domain-specific vocabulary to inform about or explain the topic.  
e.  Provide a concluding statement or section related to the information or explanation presented.

6-7-8th Grade Challenge Example

Have at it, teams! We're expecting accuracy, creativity, thoroughness, and FUN!!!

8th Grade Notebook Entry from (Chris) on Vimeo.

Related Literacy Objectives:

6.W.L.2: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization and analysis of relevant content.

7.W.L.1: Write arguments to suppose claims with clear reasons and relevant evidence

8.W L.1: Write arguments to suppose claims with clear reasons and relevant evidence

Lakeview Students CRUSH Dividing with Fractions!

So there we were in Ms. Roshone's class - working with Trystan (who sends a shout-out to his former teacher Ms. Reevas!) and Travis (24! winner from the inaugural Pi Day Competition!) on some way-complicated problems involving division by fractions. I mean, this stuff is so complicated that only a rocket scientist can figure it out. Amirite????

Well.... a rocket scientist or a SIXTH GRADER!!!

These guys - along with Devan, Jessie, Kyle, Marky and Donetta absolutely crushed division with fractions.

Here was the situation - Ananda was working on an order for bows, and was like TOTALLY freaking out... She knew she'd need 2/3 yard of ribbon to make a bow. But she had NO CLUE how many bows she could make with 4/5 of a yard of ribbon!!! I mean, this situation was CRITICAL, yo!

Anyway, Trystan and Travis got down to it. They knew they were taking 4/5 of a yard of ribbon and dividing it into groups of 2/3.  They made diagrams to clear everything up. They knew Ananda had 4/5 of a yard of ribbon, so they divided their diagram into 5 equal parts. Because the last fifth wasn't really available, Travis X'd it out.

Trystan knew she needed 2/3 of a yard to make a bow, so they also divided this whole into thirds!

This suddenly made total sense! "15 is a common denominator of 1/5s and 1/3s," said Trystan.

"Yeah, and 2/3 of 15 is 10," said Travis as he colored in 10 parts. "So she can make ONE whole bow. And she'll have these 2 parts left." Oh noes!!! What do we do with those two parts?!?!?! Are they 2 parts out of 15??? 2 parts out of 10??? Snap out of it, pal.

"Those are two parts for her next bow." Who said that??? It was Devan, throwing down some input. Travis had it now - "So she'll be able to make 1 and 2/10 bows, right?"

CRUSHED!!!

But the best part was yet to come...

"Ya know if you multiply that 4 by the 3 you get those 12 pieces. And if you multiply that 5 by the 2 you get the 10 he colored in... That's 12/10." Devan - you rock!!!

At that point.... there was nothing left but the high-fiving. Gratz, Ms. Roshone! Who says kids can't figure things out on their own??? 

3rd Grade Challenge Example

Many students are wondering what will be expected of their competition entries on March 25. We will be expecting quality work! Also, the students will be working independently - a coach may be on hand, but can only offer advice in the form of a question. A question like, "Where have you seen a problem like this before? What helped you then?"

I put together an example of a possible solution to one of the challenge problems. Of course, we will expect the writing to be on par with 3rd grade expectations. Nevertheless, all 4 parts of the solution are required.


3rd Grade Notebook Entry from (Chris) on Vimeo.

Finally, I have attached a sentence frame you may want to encourage students to use in math class.

Sentence Frame Excel format  (you can edit this one)
Sentence Frame PDF format  (you just have to print this one)

3rd grade writing standard:

"3.W.2 - Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

a.  Introduce a topic and group related information together; include illustrations when useful to aiding comprehension

b. Develop the topic with facts, definitions, and details.

c.   Use linking words and phrases (e.g., also, another, and, more, but) to connect ideas within categories of information.

d.  Provide a concluding statement or section.

3.W.4 - With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose.  (Grade-specific expectations for writing types are defined in standards 1-2 above.)"

Creating Polygons with Logopaths Can Be Tricky

When creating polygons with specific angle measures in Logopaths, students often become confused. Confusion isn't a bad thing - of course - but when using software, there is a tendency to think, "Oh, this program doesn't work correctly" rather than realize that you have a deeper issue on your hands.

So when a student wants to create an equilateral triangle, for example, they may know they need a 60 degree angle, so they program, "rt 60" and are very surprised when they don't end up with what they thought they were going to end up with!

In this video, I try to clear up some of the confusion


Timmy Turns Polygons from (Chris) on Vimeo.

Pi Day: Circle Hunt!

Just in time for your Pi Day celebration! I put the beginning of this activity together with a younger audience in mind (Grades 1-3) but also included some spreadsheet love for 4th and 5th graders.

When I last did this activity (in a joint operation with Lacosta way back when) it was Anthony Bizardie who made "the discovery" about the magical 3.14.

Who will your Master Conjecturer be???


Pi Day: Circle Hunt! from (Chris) on Vimeo.

Logopaths: Feed the Turtle

Years ago, my students absolutely LOVED Geo-Logo. I'll never forget the amazing and complex creations of a kid named Derek Red Feather. (Derek - where are you???)

Unfortunately, Geo-Logo was gimped in the Investigations 2nd Edition. Doug Clements (the creator of Geo-Logo AND Building Blocks) and myself had quite a session lamenting this fact at the last NCTM Conference.

Nevertheless, the Logopaths software will still provide plenty of learning opportunities for your students. Hopefully, they've already experienced this in Unit 3. If not... there's no time like the present to add this to your workshop! You can find the software on your Investigations disk, assumed to still be in your binder.


Logopaths: Feeding the Turtle from (Chris) on Vimeo.

Why Pi?

I recently attended an excellent Webinar, Slices of Pi, with Key Curriculum Press. In one of the activities, we investigated Pi in a rather unusual way: by looking at the ratio 22/7.

In honor of the upcoming Pi Day celebrations, I thought I'd share this with you and your students. Very interesting!

Pi Flower from (Chris) on Vimeo.

Walking With Henri and Emile!

Walking With Henri and Emile Sketchpad tutorial.

One of the learning goals for Unit 5 (Moving Straight Ahead) is "I can construct tables, graphs, and symbolic equations that express linear relationships."

I've put together a Sketchpad tutorial to show you (or your students) how the investigation with Henri and Emile can be represented using dynamic software. You may want to use this tutorial to teach yourself how to construct the representation and then lead your students through it, or set it up as an independent activity.

Have fun!

Got Legs?

Then you've got no excuses! Get out there and do something challenging.

Today!



Aaron 'Wheelz' Fotheringham - Wheelchair Action Sports from Unit Clothing on Vimeo.

Representing Stories Graphically

The Geometer's Sketchpad can do so much more than build polygons! Use this sketch to help your 7th graders build their connections between graphic representations and real-world situations.

This sketch, while excellent for demonstration purposes, is ideally put into the hands of students so they can manipulate the variables and see how their actions impact the graph and the action.

Download the sketch!

"You better lose yourself in the digits of pi, it’s a high"

What the heck.... it's fun. /grin Are you ready for Pi Day??? Maybe this will help get your class in the mood!



Mathmaticious is still the king, imho. 2,398,000 views! Superstar!

57 Degrees and Climbing

It's my blog and I'll ride if I want to!

Absolutely spectacular day here in the Sandhills. After only 35 kicks or so (and no hyper-extended knee this time, whew!) I was able to take the Pi Project around the block. This meant, of course, slipping in and out of the ice floes and ponds still found on most streets and every intersection.

But hey - it was a ride!

After rebuilding the engine last Fall, I'm still anxious to get it out on the highway and open it up.

Looking at the Skills of Speaking and Listening In First Grade

Some years ago, Ms. Ogonoski's first graders were struggling with the skills of listening to and speaking with one another. Ms. Ogonoski devised a rather clever lesson in which she and her class negotiated a rubric, practiced it, and then used it to assess their listening and speaking skills throughout the day.

Despite this being an experience set in a first grade classroom, I can think of no reason that this wouldn't be an important process at any grade level.

We made this video to document their experience with a very real and practical performance assessment. I hope you enjoy this one from the vault!


Listening and Speaking: Grade One from (Chris) on Vimeo.

Even Old Geezers Can Learn a New Trick

What have each of us learned lately? Was it easy? Should we expect learning to be easy for our students?

Using Language to Explain Our Thinking: Grade One

The North 1st Grade CWG has set the following Smart Goal: By May, 2011 80% of the North Elementary First grade students will offer a proficient explanation of their work as measured by the Rubric for Assessing Language. 
Here is the rubric we are currently using to assess students' explanations. 
I've also created a couple of "models" that the teachers can use to explain the rubric to students and talk about what they will be looking for. Here is a second example. And a third.

Untitled from (Chris) on Vimeo.

Just Plug It in

Just Plug It In from (Chris) on Vimeo.

TKE and The Ladies get plugged in (and give Mrs. Linster the bidness)

/grins and giggles - thanks for being such a good sport Mrs. Linster!!!

Kathy Richardson Piloted in North Carolina

These teachers seem pretty pumped to be using Kathy Richardson's assessments! (Hope they synchronize those Palms! /shudder)

Bobbie, Meredith and I attended a workshop with Kathy last Spring. We spent part of the week (mainly the parts related to eating large Texas hamburgers) with 2 representatives from The North Carolina Department of Education. It is good to see that their planned implementation is receiving a lot of buy-in from teachers, administrators, and local TV stations.

Comparing Fractions, with Reason

Students in Mrs. Knox's classroom have been comparing fractions, decimals, and percents by reasoning about the relative size of their pieces. In this video - a follow-up to the previous day's lesson - students explain their conjectures about why 7/8 is larger than 5/6.

Grappling with Fractions from (Chris) on Vimeo.

In fact, they said their conjecture would work for any fraction that was 1/nth less than the whole! Students tested these conjectures by creating additional fractions to compare. In the process, students also began noticing equivalent fractions. It was exciting to hear students talk about their understandings! One of their next steps will be to master the mathematical language and clearly articulate their understandings and discoveries.

Are other 5th grade classrooms making similar conjectures? We'd love to hear about them here at TCSD Math!

Angle Sums Round Two

Angle Sums Round Two from (Chris) on Vimeo.

Okay, Springcreek - ready for round two? Download the Angles and Sums sketch right here.

Angle Sums of Any Polygon

I've created a couple of very short tutorials to assist students in using Sketchpad to investigate lesson 3.2 from Stretching and Shrinking. Here is the sketch to go along with them: Download Sketch



Angle Sums - Tia's Method from (Chris) on Vimeo.



Angle Sums - Cody's Method from (Chris) on Vimeo.

Trapped!

Finland's Education Success

Parents + Teamwork + Trust

 

It is interesting that in the developed world, Finnish children spend the least number of hours in school per day, yet produce the best results.

Looking at Letters

Most of us know that reading aloud to our children is critical in laying a strong foundation for success and enjoyment in reading. Do we provide the same experiences in mathematics?

Practice being a keen observer with children whenever possible. Notice patterns on clothing, details in pictures, plants, and in the street you live on. Talk with your children and really listen to what they are saying. Don't think you have to know an answer to every problem or question! That is one of the best examples we can set for our kids: teach them that asking questions can be more important than answering them!

I've been enjoying many of the activities in Family Math for Young Children by Coates and Stenmark. One of our favorite activities is called, Looking at Letters. It is a simple, yet powerful activity about observation. I think this is a worthwhile activity for Pre K and Kindergarten classrooms where children are beginning to master their letters, and are ready for a more challenging way of looking at them. We use an old coffee bag to keep our letters in.

On a recent snow day, we had some fun with letters.

Looking at Letters from (Chris) on Vimeo.

Symmetry

Symmetry is beautiful. And sometimes, just a little frightening.

Pi Day is Just aROUND the Corner!

Catch the web presentation, Slices of Pi, by Andres Marti. Slices of Pi provides you an opportunity to engage in Sketchpad activities that explore circles and use dynamic approaches to reveal the value of pi. In this webinar, you will:

• plot geometric measurements to derive the circumference-to-diameter ratio, then slice up a circle to derive the area formula

• explore simple animations that unexpectedly reveal pi

• investigate inscribed polygons, equations of circles, and the relationship between circles and ellipses.

Choose one of two offerings:

Tuesday, February 15, 2011 4:00 PM - 5:00 PM EST  
Wednesday, February 16, 2011 7:00 PM - 8:00 PM EST

Zingo! A Duncan-Approved Learning Game

I'm a hardcore gamer. Board games... card games... video games, you name it and I'll play it! Heck, I can't even walk across a playground without asking the double-dutchers if I can get in on a round!

Games help to develop all kinds of skills - especially the ones I care about the most: creativity, flexibility, and good 'ole strategic thinking. Naturally, I've wanted to get my own kids established in one of my favorite pastimes. We started things off with Cariboo, a fabulously fun game in which kids learn while matching letters, numbers, shapes and colors AND practice sharing and turn-taking.

Cariboo! from (Chris) on Vimeo.

Cariboo! was great fun for our 2 year old, but not so much for the little guy. When Finley turned 4 we gave her Zingo! and Wow - it was a hit from day one for both Finley and her 2 year old brother. 

Zingo is a fast-paced, energetic variation of Bingo. Kids get a kick out of pulling the Zinger forward to reveal two mystery tiles and attempting to be the first to call out the tiles that match the images on their cards. The first player to fill his or her card wins! 

Beyond just plain fun, kids have the opportunity to learn to read short words, to think quickly, and to keep images and associations stored in their memory. Oh, and an opportunity to beat dad is always a huge draw!

If I were teaching Pre-K or Kindergarten, I would definitely want a copy of Zingo! (I bet even first graders would love the game, although there might not be as much to learn) Kids quickly learn to manage the game for themselves, and play over and over again. There is even a new version, Zingo! 1-2-3, that requires children to match numerals with quantities. Heck yeah! Duncan's birthday is coming up!

Zingo! from (Chris) on Vimeo.

Valentine's Day Quilt

Put a little heart into your lessons this Valentine's Day! There is a fun quilting activity over at the Mathwire.

The Locket

Miss Haswell noticed a lovely locket 'round the neck of a 2nd grader, Leiloni.

"Oh! I just love that heart necklace!" said Miss Haswell.

"It's a heart and key," corrected Leiloni. "The key is for my locked notebook - where I keep all my equations."

How precious!

A Math Notebook is a Terrible Thing to Waste!  ;-)

Algebra Tiles Redux

Had some teachers asking about the algebra tiles video... so here it is!

Introduction to Algebra Tiles from (Chris) on Vimeo.

Is It Really Either/Or?

Of course, not all valuable learning is constructivist. Other types of learning, such as rote memorization, have an important role, too - as, for example, in learning foreign language vocabulary words. The instructional challenge for a teacher is in knowing when to use which approach.  - Charlotte Danielson

In her excellent Enhancing Professional Practice, Charlotte Danielson identified one of the most problematic decision points for today's teacher. Essentially, it boils down to this: When do I tell and when do I ask? Recent Core Reading sessions have reminded me that, because of curricular expectations, Todd County teachers struggle with this question more so than teachers from other districts.

Hopefully, we will come to realize that you can do both! Distinguished teachers avoid throwing constructivist strategies up against the left wall, explicit instruction up against the right, and then stubbornly adhering to one or the other. Distinguished teachers make judicious use of both practices.

Now, having identified a need for both approaches, I don't want to imply that there is some sort of perfect PC balance between the two - at least not in mathematics.

Questioning is a far more difficult form of pedagogy for teachers than are coaching and telling, because it is the least predictable.  - Ted Sizer, Horace's Compromise

The new Common Core Standards identify 8 "Standards for Mathematical Practice" describing the variety of expertise that mathematics educators at all levels should seek to develop in their students. The strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: 

• adaptive reasoning, 
• strategic competence, 
• conceptual understanding (comprehension of mathematical concepts, operations and relations), 
• procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and
• productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy)

Given this list of proficiencies, a math teacher would be most likely to use more explicit forms of teaching in helping students reach procedural fluency. Again, this isn't to say that the other proficiencies lend themselves exclusively to constructivism. But constructivist learning theories will certainly inform the majority of an accomplished math teacher's repertoire. Assuming, of course, that reasoning and sense-making are high on their list of objectives.

Infinity Elephants