Wednesday, January 25, 2012

A Peek Inside a 3rd Grade Classroom

It's always fun to peek inside other classsrooms and see how students and teachers are doing their thing.  With that in mind, I loved this look at a 3rd grade classroom and how active and engaging mathematics instruction is.  The use of "wait time" and the opportunities to practice mental math as a routine stood out to me.  I also thought that the way she had all student taulk about their thinking was a great way to encourage discourse.  What can we learn from Jen Saul's classroom?  How can we too encourage our students to "work hard every day"? 

Tuesday, December 13, 2011

Estimation- In the News

Time Magazine has a great article on the importance of estimation, and how to encourage young students to develop this skill, titled "Why Guessing is Undervalued."  Author Annie Murphy Paul explains: "Estimation, this research shows, is not an act of wild speculation but a highly sophisticated and valuable skill that, some experts say, is often given short shrift in the curriculum."  She goes on to show that even as babies, we posses some ability to estimate.  As time goes on, strong estimation skills are connected to mathematic proficiency. 

How do students develop and refine their estimation skills?  Paul explains that it begins with children having a "clear mental number line- one in which numbers are evenly spaced."  The best ways to help students develop this understanding?  Playing board games.  That's right, she talks about playing games such as Chutes and Ladders as great ways to develop an understanding of numbers.  Each time a child spins a spinner or rolls the dice and counts of spaces on a game board, they are reinforcing their ability to manipulate numbers in their heads.  There's more great stuff in this article, so do check it out.  But remember when doing your Christmas shopping this year- board games may be secret mathematic weapons!!

Thursday, November 10, 2011

Math Apps (and they're free!)

by Tara Swinehart

In my last NCTM newsletter they mentioned that they now have some free Apps which can be played on the iPad or on the computer:

Okta's Rescue-  Students can either count (but they won't get far) or they can start to group and use subitizing- fun to teach because it's fun to say :)

Concentration-  Has many different levels from shapes to whole numbers to basic multiplication (it has students match 2 numbers in different forms).

While downloading those to see what they were like, I came across a few others:

Motion Math Zoom-  A number line game
Pizza Fractions-  A really basic introduction to parts of a whole
My Math App-  Another form of flash cards for the 4 operations.

Check them out- pass them on!!

Kindergarten Estimation

Mrs. Houseman wanted to get her kindergarten students introduced to the concept of estimation.  So, she created a lesson that incorporated a fun estimation song and some hands-on activities.  To see what they did, check out the video below that Mrs. Houseman created.  One of the things that I really enjoy was hearing the students compare their estimates to the actual number, and then explain their mathematical reasoning orally: 


Thanks Danielle for sharing!  

Thursday, November 3, 2011

Round Up- Math Applications Around the District

Mrs. Hamman's class explored the wonderful world of triangles, and how they are EVERYWHERE.  They learned about geodesic structures, built from triangles.  Check out what they learned about triangles on their class blog, and see how they created their own geodesic structures.

In Mrs. Lebtich's class they dove into estimation in a literal, and pretty messy, way.  During their exploration of pumpkins, they compared their estimates to their actual findings:

Question                                                                  Estimate                                          Actual

How many cups of "goop" are there                  _____ cups                               _____ cups
in your pumpkin?

How much does your "goop" weigh?                 ______ grams                           _____ grams

How many seeds are there in your pumpkin?     ______ seeds                           ______ seeds

Students were then asked to evaluate their estimates.  They were asked:  how did you reach your estimate?  How close were you to your actual findings?

Monday, October 31, 2011

Happy Halloween- Estimation Style!

Over the past few months, we've talked a lot about the mathematical reasoning involved when students are estimating.  We've seen a wide variety of estimation jars and heard a great variety of questions to get students thinking about numbers, quantities, and how to justify their answers.  Check out what Robin Oswald's class did to practice their estimation skills while also decorating their door for Halloween:

How horrifyingly awesome!  Can you imagine the gruesome math conversations that students could have with these prompts?

Monday, October 24, 2011

Effective Math Practice

Bike Ride
"Bike Ride" by Courosa on Flickr
We all know that effective practice is the key to learning something first to mastery, and then to automaticity.  Reaching automaticity means that one can do something naturally and fluently, in an automatic way.  When students reach automaticity in single digit addition, for example, they can quickly answer that 4+3 is 7.  Students can reach automaticity through repeated practice, but it must be high quality practice.  What are the hallmarks of high quality practice?
  1. Clear expectations- students should see the skill modeled and know clearly what skill they are developing.
  2. Supported practice- Think about when learning to ride a bike.  Usually there is an adult's hand stabilizing the bike, or training wheels to keep every wobble from ending in scraped knees.  In learning, this is often the "We Do" in a skills' development.  This can be with the teacher and then with a partner or small group.
  3. Purposeful Feedback- When students begin to practice the skills for themselves, it is essential that they receive immediate feedback.  This feedback should tell them what they are doing right, and what they need to correct.  Think of a basketball coach teaching a player to shoot a free throw.  Basketball coaches often give pointed feedback that is different for each player, depending on what they see-  "follow through by snapping your wrist," "place your left hand here," "bend your knees," etc.
  4. Upward Basketball 
    Credit: Jason Tromm on Flickr
  5. Assess progress- Keep a clear eye on where students are in their skill development.  Be prepared to move some along as they master this particular skill, and offer more time for practice for those who still don't perform the skill naturally.  With the right amount of high quality practice (with specific and immediate feedback), they'll get there!

What does all this have to do with math?  Well, this process repeats itself over and over with each new skill or concept.  Technology gives us one way to give students immediate feedback on whether they're on the right track, or whether they need to refine their process, by telling students if they have the correct answer or not after every problem.  Here are some sites to check out that may be useful to you in providing students with practice and immediate responses:

FactMonster Flashcards
Calculation Nation (use Guest Pass)
Khan Academy (also on this website, explanatory videos for concepts)
AAA Math
Free Rice (choose Math- multiplication or basic math)
Education City (go to student webpage to choose your school: )

What other ways do you have to help students get the practice they need?