Tuesday, September 18, 2012

Math Anxiety

Imagine that you are in a restaurant, seated with many people at a large table. In the course of conversation the person sitting next to you laughingly remarks, “I’ve never been good at reading. Can you read the menu for me?” 

What would you say? Would you laugh along and confess that you never really learned to read either? What would others say at the table?
Now imagine the same scene, only this time the person next to you says, “How much do I owe? Can you add it up for me?  I’ve never been good at math.” 

What happens this time? You can expect other people at the table to chime in cheerfully, "I've never been good at math either."

When did it become socially acceptable to say, "I've never been good at math?"

Math anxiety or the fear of math is not uncommon. This emotional reaction to mathematics is based on an unpleasant experience from the past which harms future learning. 

OUCH: Those past learning experiences could be from my math class!!!

So how do I avoid creating math anxiety in my students? 

1. Be aware of your own attitude towards math. 
Students pick up on your math passion or lack of it. Avoid saying, "I wasn't good at math." Positive attitudes comes from quality teaching for understanding. 

2. Ditch the idea that "some" people are just good at math. 
Anyone can be good at anything when they have perseverance. 

3. Give help early. 
When you see a student struggling take action immediately! Work for understanding, and skip the "tricks." Understanding the math is what it is all about.

4. Help your students learn how to "shake off" mistakes. 

Develop a classroom environment where students can take risks, share their thinking, and celebrate mistakes! Everyone can learn from mistakes. Why do you think pencils have erasers?

5. Make math engaging and relevant. 
Look at all of the work you are giving your students. From warm-up to independent practice, is it engaging? Is it relevant? Does it have just the right amount of challenge? Would you want to do it? If not, fix it!

6. Dispel the myth that there is only one answer or one way to get the answer. 
There are a variety of ways and tools to solve problems. Allow the students to create their own strategies that build upon their own understanding. Don't make them solve it "your" way! 

Let's do our part to put an end to Math Anxiety!

Wednesday, September 12, 2012

Math Work Stations

It is not uncommon for elementary teachers to feel more comfortable in teaching language arts. Think about how you could build upon those strengths in your math instruction. There are several parallels among language arts and math. I discover more and more every single day as I work with coaches, teachers and leaders who have a passion and love for language arts. How can you relate math fact fluency to spelling words and/or reading, writer's workshop to problem solving and literacy work stations to math work stations?

So, what is a work station?
"Math work stations are a time for children to practice problem solving while reasoning, representing, communicating, and making connections among mathematical topics as the teacher observes and interacts with individuals at work or meets with a small group for differentiated math instruction." Math Work Stations: Independent Learning You Can Count On, by Debbie Diller.

These differ from traditional learning "centers" where all students do the same exact activity, many times without even experiencing it in class first. These were almost extra things to do when you "finished your work".

Work stations are REAL work. Materials are differentiated based on student level of math understanding. All students should work on something that brings them to the edge of their understanding, even if they work on the same concept for a few weeks. This might mean that you have students working on lots of different things!

What does the teacher do during this time?
The teacher role is usually one of two things; observing children at work or meeting with a small group.
Lots of beneficial information can be gathered by observing what children are doing. Take anecdotal notes! What choices do they make? How are they counting? How are they reasoning? Are they making conjectures? Are they ready for the next step? Do they know if they are ready for the next step? Use this valuable information to structure your small groups and future work stations. 

How are these related to literacy work stations?
Many of the same ways you structure your literacy work stations by using some type of gradual release model can be used in setting up your math work station system. Lindsay Starkjohann, a 3rd grade teacher at Bagdad Elementary, is an expert at using the Daily Five and CAFE for her language arts block. She is planning on using her expertise in this area to set up her work stations in math. I'm proud of her for taking on this challenge to differentiate for her students!

Do you have examples of teachers doing math work stations?
Yes! I would like to feature a math teacher leader, Heidi Dominguez, who teaches first grade at Westside Elementary. She allowed me to take some great pictures of her work stations. Thank you Heidi for giving us permission to learn from you!

Here is her work station board. On the left side, she has literacy work stations. On the right side, she has math work stations.

Students are paired up (white cards on left) and the math work stations have numbers (blue cards on right). The numbers are the corresponding tubs that the students grab.

Here is where she keeps the tubs.

COOL TIP!!! Every math tub has a shelf liner about 14' x 14' square inches. These define the student's work area! She said that they keep things organized and a little bit quieter when students are using the manipulatives!
Students grab their tub and work under the number that corresponds with the tub. So, if you have tub 6 and 7, then you would have a designated spot to do your math work.

I have a work station system started, but what are some other easy ideas for work stations?
This is a quick brainstorm, but check back as I know we will probably elaborate on these ideas!
  • Counting Collections-and then record how you counted!
  • "I can" charts that you can add on to and stick in the tub
  • Working on problem solving
  • Writing about math (problem-solving communication, glue a math artifacts in your journal and write about it, wonderings, etc.)
  • Math Games to conceptualize math facts
  • Vocabulary practice

For more information on Math Work Stations, this book provides color photos and practical ideas. It is written for K-2, but if you teach upper grades you will be inspired by just looking at the photos!

Tuesday, September 11, 2012

The Math Classroom Challenge

Close your eyes and try to picture the perfect math classroom. Walk in the room. What does it look like? What does it sound like? What does it feel like?

Now, take a look at these two classrooms. After a quick glance at the two, is there a classroom you would prefer to learn in?

Did you know that classroom environment does affect instruction?

This summer, I recently presented a mini-conference called, 'Rate My Space.' In this half day session, we explored many necessities that every math class should include. Over the next few weeks, I will be blogging about these different elements of the math classroom. Let's call it the 'Math Classroom Challenge!' I encourage you to take the "Challenge" and try to rev up your classroom environment for this new school year! On the right-hand side of this blog, I made a button that you could grab and post on your blog. :)

By thinking about how space is used in our classrooms, we have to think about instructional priorities. Ask yourself, "What type of teaching am I going to do this year and what kind of space am I going to need to meet my instructional priorities?"

Here are the beginning topics and classroom spaces that I will discuss because I believe they should be instructional priorities in the math classroom:

1. Math Vocabulary: Math Word Wall
2. Problem-Solving: Math Manipulative Storage
3. Problem-Solving Sharing: Whole Group Area
4. Small Group Instruction: Small Group Area
5. Math Work Stations: System for Work Stations
6. Transforming Math Homework
7. Number Talks

In following posts, I am going to elaborate on each item and give some helpful tips in how to implement them into your own classroom. Real classroom pictures and examples will be included. There is no reason to reinvent the wheel when so many teachers are doing amazing things!

My hope would be for you to consider these areas in your own classroom. Would they work? Why or why not? 

Let's change the space in our rooms to create a structure of teaching that can open up opportunities to involve students in the learning. As Debbie Diller says, "when we model for students on how to create organized spaces, we will help them as learners over the years, too!" Please join me in taking the math classroom challenge!

LISD Elementary Math

Don't forget to grab a button for your blog!

Monday, September 10, 2012

What is a Rekenrek?

Directly translated, rekenrek means calculating frame, or arithmetic rack. Adrian Treffers, a mathematics curriculum researcher at the Freudenthal Institute in Holland, designed it to support the natural mathematical development of children and to help them generate a variety of addition and subtraction strategies. 

Students can use the rekenrek to develop computation skills or solve contextual problems. Once children understand the operations of addition and subtraction, and can model various situations, it is important that they automatize the basic facts by finding and using patterns and relationships. 

Unlike drill and practice worksheets and flashcards, the rekenrek supports even the youngest learners with the visual models they need to discover number relationships and develop automaticity.

The rekenrek looks like an abacus, but it is not based on place value columns or used like an abacus. Instead, it features two rows of 10 beads, each broken into two sets of five, much like the ten frames.

How to Make a Class Rekenrek

First get a sturdy board. I used a large foam board (20"by 30") that I purchased from Hobby Lobby for $1.99. The clerk was nice enough to cut it in half for me so I can make two!

Next, I drilled two holes on each of the short ends. The holes are 4 inches in and 2 inches from the ends.
Gather scissors, 20 unifix cubes (10 blue and 10 red and free from your math manipulatives), and string. I used S'getti Strings that came on spool of 50 yards for just $1.99.

Then string them up! 

And tie them in the back! 

Now you have a classroom rekenrek (priceless!)

You can also download a free app called Number Rack. 

Your students each need one too! Use poster board, mat board or any stiff cardboard you can get your hands on. I cut my boards into 8 inches by 4 inches pieces but you can do whatever size works for you. Use red and white beads and the S'getti string just like your classroom board. Now you are ready to go!

Here is a confession from a 2nd grade teacher:

Give it a try and let me know how it works. 

Friday, September 7, 2012

Understanding Place Value

One of the most common concerns I hear from teachers at every grade level is that their students don't understand place value. So every teacher begins the school year with  place value instruction.

Most place value instruction seems to be revolved around the place value model. 

We relate place value to money.

We ask the students to:
  • read, write and compare the numbers 
  • identify the digit in the _____ place 
  • describe the  value of the ____ in this number  
So I ask, if every year students' math instruction starts with place value why don't they get it? 

I wonder, isn't understanding place value more than just knowing the hundreds, tens and ones? 

Yes, place value is so much more. Students need to understand "sets of ten" can be perceived as single entities. Ten "ones" become one "ten." Ten "tens" become one "hundred." The pattern continues forever! 

Isn't it mind blowing that these 10 digits create infinite  quantities?                                                                                          

It's the position of the digit in a number that determines what they represent! 
Large Quantities Build Place Value Understanding:
If we want our students to understand place value shouldn't we get them to work beyond these models?  "Really big" numbers are best understood in real-life situations. It is difficult to conceptualize quantities as large as 1000 or more. However, the number of people that fill a football stadium has a meaningful concept for those who have experienced that crowd! 

Below is a video that helps students explore large quantities. Have the students watch, ask questions, and find the answers!

Here are some other ideas to get them working with large quantities. Remember for larger computations students can use calculators!
Ask how many:
–Counting collections of all sizes

–Candy bars would cover the floor of your classroom

–Steps an ant would take to walk around the school building 

–Grains of rice would fill a cup or gallon jug

–Quarters could be stacked in one stack floor to ceiling

–Pennies can be laid side by side down the entire block

–Pieces of notebook paper would cover the gym floor

–Seconds you have lived 

I love how these ideas relate to measurement.

Building Understanding of Place Value by Exploring Large Numbers.... What a great idea!

Wednesday, September 5, 2012

Is It All About The Answer?

SLOW DOWN and enjoy the math!  
The first goal in math should be the mathematics learned.  So let’s slow down, because it's NOT all about the answer.  

What can we do as educators to make it more about the process, the reasoning, the thinking, and the common sense of math? 

Your students will take your lead! 

Make it your mission to give your students the opportunity to talk, process with each other and share different strategies. 

There is much to be learned from the “wrong answer”.  Are we taking advantage of those “just in time” teaching moments? 

Here in Leander ISD, we believe in the fail forward philosophy.  Let’s live that philosophy in our math classrooms and let the children experience learning from analyzing their work and growing mathematically from the mistakes that occur.   

Take a look at how one teacher is capitalizing on this very idea . . .

This idea could also be used as an exit ticket . . . really the possibilities are endless!