Common Core Standards for Mathematical Practice

Guest Blog Post by Kitty Rutherford

The Standards for Mathematical Practice impact all math teaching and learning. They focus on what it means for students to be mathematically proficient.  I have heard many say the Standards for Mathematical Practice are the heart and soul of the Common Core State Standards. These standards describe student behaviors, ensure an understanding of math, focus on the development of reasoning, and building mathematical communication.  Each standard has a unique focus, but each standard is also interwoven with the others as we put them into practice. These practices empower students to use math and to think mathematically. Our job as a teacher is to help students develop these practices to become effective mathematicians.

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are 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).

The Standards for Mathematical Practice are a significant focus of Common Core State Standards. These eight practices describe the thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics.

One way to build a deep understanding of the Standards for Mathematical Practice is to read one practice at a time and reflect on the following questions:

1. Why is this practice important?
2. What does this practice look like when students are doing it?
3. How can a teacher model this practice?
4. What could a teacher do within a lesson to encourage students in this practice?
5. How can you assess proficiency in this practice?

Before Common Core State Standards were implemented, I visited a few fourth grade mathematics classrooms.  I provided a high-leverage math task, students worked collaboratively together to solve.  I then introduced the Standards for Mathematical Practice by explaining to the students that these standards were practices that mathematicians do to help them excel in mathematical thinking. I asked them to think about the task they just solved, if they were to explain to someone what that practice meant or looked like how would they do it.

After some discussion, students created posters to represent their thinking about the Mathematical Practices. In this task students explored prime or composite by building possible rectangular arrays for numbers 1-25.

These are some of the posters students created after the task and much discussion.

Which products are composite and which are prime? I’ll think of products that have one factor pair and which have more than one factor pair.

This number is prime so it only has 1 array for the number.  

This number has 2 arrays so it must be composite.

Using correct math language to explain your thinking is important

In another fourth grade classroom students were given the task of finding the perimeter of a figure. These were the posters of the Standards for Mathematical Practice they created.

Make sense of problems and 

persevere in solving them.

Yes

Cha-Ching

 Model with Mathematics.

If I’m going to tile the perimeter, how many pieces of tile will I need?

Do these side lengths make sense?

Model with Mathematics.

These color tiles help me to find the missing sides so I can write an equation to find the perimeter.

I noticed a blond-hair, blue eyed, little boy working diligently by himself, as I advanced towards him, I noticed his simplistic drawing (see below).  As I approached, he looked up and in a sincere heart-felt tone he informed me that this was a picture of his friend persevering not only in math but in his everyday life. Pointing to the empty desk next to his, he whispered, “My friend has cancer. He is not in school because he just received a cancer treatment a few days ago.” His comments shook me to the very core. “Many of these Practices we do every day, not just in Mathematics!"

What do I need to know to solve?

This will be easy!

 
Kitty Rutherford serves as the North Carolina Elementary Mathematics Consultant for the Department of Public Instruction in Raleigh. She is an experienced leader, collaborator and licensed educator with a Master’s Degree in Elementary Education. She has received many honors such as the Presidential Award for Excellence in Mathematics and Science Teaching and the NCCTM Outstanding Elementary Mathematics Teacher. She is a member of the NCAEE Board and will be presenting two sessions at that Elementary School Conference. For more resources for implementing Common Core Standards, visit the Mathematics Wiki hosted by the NC DPI. 

Bouncy Bands Help Students Stay on Task

 Guest blog post by Scott Ertl

As an elementary school counselor, I work with teachers and parents to help students most effectively learn, behave and cope with problems. There are many different products available to help students stay on task in school, from yoga balls to wiggle cushions. They are all helpful, but they are often expensive when trying to accommodate a whole class.

Bouncy Bands are a perfect DIY project that can cost under $20 for a class of 26 students. They are recycled bicycle inner tubes tied across the front legs of a student’s desk for them to rest and bounce their feet while they work. Bungee cords, rope, and garden hose can also be used. Initially, the inner tubes kept sliding down to the floor, so I added 9” pieces of PVC pipe to keep the Bouncy Band at the optimum height.

Even though much research shows the importance of kinesthetic learning and incorporating movement for students to better learn, most teachers after first grade continue to spend the overwhelming majority of time expecting students to stay in their seat throughout the day while learning. And since many students struggle to sit still for so long, they do not learn to their best ability. Instead, they rush through their work, give up, or make careless errors. I found that Bouncy Bands help many students when they have a way to release their extra energy when they work. Students with learning disabilities and/or hyperactivity need appropriate ways for them to release their anxiety and energy without overwhelming them, where they shut down or simply tune out. One student describes Bouncy Bands as a way for his feet to play while he works. Here are a few benefits I've found to using Bouncy Bands:

• Students can stay on task longer.
• Students can release their anxiety and extra energy.
• The bands are quiet and don’t make any noise.
• They recycle used bicycle inner tubes and last all year!

Classroom Management Ideas for Bouncy Bands
However, like most things, there can be problems using Bouncy Bands in class. The biggest complaint is, “It’s not fair that so-and-so gets a Bouncy Band. I want one.” Giving students a way to earn their own can be a great incentive. I had a classroom last year and I added Bouncy Bands to all of the desks. When teachers would bring their classes to my room for Guidance, I expected only 5 or 6 students to actively use the Bouncy Bands during my lessons. However, every single student would use their Bouncy Band at one point or another during the lesson. They quickly became the ultimate reward for students to earn at my school. By the end of the year, many students had earned their own Bouncy Bands for good behavior, completing their work, or achieving other goals.

Students in two different classes got in trouble using their Bouncy Bands as sling shots. It was interesting how the teachers decided to handle the situations. One teacher immediately removed the student’s Bouncy Band and he had silent lunch for the day. The other teacher decided to seize the moment to teach how it could be dangerous and the class even had fun taking turns measuring the different distances when launching paper balls versus tennis balls. (He was given a warning, but he didn’t lose his Bouncy Band.)

Tips for Making and Using Your Own Bouncy Bands:

• Ask your local bike shop owner to donate their used bicycle inner tubes. Most I approached were extremely happy and willing to assist with this project. Most shop owners wished that they had Bouncy Bands when they were in school, since they struggled to sit still for such extended periods of time.
• Students enjoy being able to customize the PVC pipes with markers, stickers, contact paper, colored tape and ribbon. They like personalizing their desk station without marking up the desk.
• You can use regular scissors to cut the bicycle inner tubes; however, be sure to check for holes and use a 34-36” piece that is free of any holes, rips or tears. Also, be sure to cut off the nozzle.
• Be cautious when cutting the inner tubes to make sure there isn’t any gooey substance inside the inner tube. Some cyclists inject a “fix-a-flat” substance when they are on the road to help them finish their trip and you don’t want to have to clean that from your carpet or clothes.
• When getting the PVC pipe, first contact your local plumbing supply store to ask if they would be willing to donate four ten-foot long (1.5” diameter) pieces of PVC pipe. Each ten-foot piece can produce thirteen nine-inch pieces of PVC. Give the manager a written request on your school letterhead and they will likely oblige your request. You might decide to start by simply asking for 2 pieces of scrap pipe to see how your students respond to the Bouncy Bands before equipping your whole class. If you are unable to get your plumbing supply store to donate the pipes, it will only cost you about $20 for four pipes (26 sets) when you purchase the PVC pipe from your local Lowe’s or Home Depot. Perhaps your school PTA or parents would contribute towards making and/or collecting resources for this project.

Bouncy Bands are a great DIY project that can help students in your class stay on task and learn more effectively. They are an inexpensive way to help students get their wiggles out!

Scott Ertl is a school counselor at Ward Elementary School in Winston-Salem, NC. For more information, videos, and tips about making and using Bouncy Bands, feel free to visit his website,  BouncyBands.com. Scott will be presenting a session at the Elementary School Conference called "Fun Ways To Use Data To Help Students Track Their Progress With Specific Goals." 

Partnering with Parents

Guest blog post by Kelly Bergman

Research about the connection between parent involvement and student achievement is undeniable.  As I’ve been consulting in schools, I see a lack of parent involvement and it makes me wonder how we can do a better job of getting parents into our schools and classrooms.

My first thought is that we need to expand our definition of “parent involvement”.  There may have been a time when that meant volunteering in the classroom.  That may still work in some schools, but I’d like to think about “involvement” in three different ways: homework, parent education, and volunteering.

Homework

As a parent of upcoming third and fifth graders, I can tell you that I have a whole new perspective about homework.  As an educator, I was shocked in May when I was more excited about the end of the homework routine than my girls were.  It makes me think about parents who don’t have experience with certain math or reading strategies and it’s no wonder the homework isn’t getting done.  Sometimes the homework is so difficult for parents to understand that they cannot help their students get it done.  Here are a couple thoughts to ponder:

• Think about your community and choose your battles carefully.  If you teach in a community where homework is not traditionally done, consider assigning a minimal amount of homework and make it something easy to accomplish.  This might be two or three simple math problems or studying a couple spelling words a night.  These tasks are easy for parents to understand and can be done in a very short period of time.
• Make sure the homework truly is practice work.  Consider doing the first few problems or activities together in class in the hope that students will be able to do it independently at home.  We need to make sure that students understand the homework well enough to do it without parent support.

Family Activities

Here are a couple thoughts about activities that you might host for your families:

• One of my favorite activities to do with parents was Family Math Night.  Once a month (scheduled at the beginning of the year) I held Family Math Night in my classroom.  This event was for my students and their parents and was really a lot of fun for all of us.  I used the book shown here which made it really simple.  I didn’t have to do a lot of searching for activities.  All of the activities in this book are high-interest, fun games for parents and students to do together.  While we were having fun playing games, we were also doing some parent education because I could model different questions and strategies that parents might use with their students at home.  In the section on volunteering, I’ve suggested a way for you to have these games made for you.
• If math is not your favorite subject, consider hosting a Family Reading Night each month.  You might begin the evening with a read-aloud so you can model this for parents.  After that, you might let students and parents read together.  I think about the families who don’t have books at home and know that this would be at least one opportunity for families to enjoy this activity together.
• As we all know, food makes everything better.  Consider providing a few snacks to help warm the environment.
• One other fun element is to give away door prizes at these events.  The prizes could be as simple as one of the games you’ve had made for Family Math Night or books that you purchase with your book club points.  You might also ask your PTA and/or local businesses to donate door prizes.

Volunteering

What kinds of volunteer work can be done, regardless of a language barrier?  Here are a couple of ideas:

• Practicing Math Facts – one teacher I know asks for volunteers each day during math to help students practice math facts.  She sets it up at the beginning of the year, trains parents the first time they come in, and then it flows very smoothly for the rest of the year.  Basically, parents go in , get the Volunteer Basket (with class list, timer, pencil, and flash cards), and then they call each student out for one minute to see how many facts they can get done.  She gives math facts quizzes each week so, once the students pass the addition quiz, she makes note on the recording sheet so the parent volunteer will help that student with subtraction.  Students love it and parents truly feel like it’s a good use of their time.  There is no language barrier with math facts.
• Preparing Materials – teachers need many materials and games prepared and we don’t need to spend our time doing it.  Whether parents come in or can make materials at home, regardless of their native language, we can have them make games for us.  I can make one example of the game, gather the materials, and the parent can copy what has been done.  Parents love to help prepare tools for the classroom.
• Are you still searching for a great way to schedule parent volunteers?  One teacher I knew did her scheduling by having you sign up on the calendar outside of her room.  This wasn’t very convenient, especially if a parent had a last minute opening and could drop in to volunteer.  Instead, consider using an online tool like www.signupgenius.com.  This fabulous, free tool is easy to use, allows parents to check the volunteer schedule any time, and even sends them a reminder.  Making it easy to sign up and sending a reminder will increase the number of volunteers you have in your classroom.

Wouldn’t it be great if you could get each one of your classroom parents involved in one way or another?  I challenge you to set this as a goal for yourself for the upcoming school year.  Your students will certainly reap the benefits!

Kelly Bergman is a master of classroom management.  In her 22 years as an educator, she has become known as a person who can help educators simplify the teaching process in order to meet high accountability standards and still enjoy this incredible profession.  Kelly is also the author of professional resources for educators including Quick Tips: Making the First Six Weeks a Success and a video and guide on 4 Keys to Successful Classroom Management. She will be presenting the keynote address entitled “Joyful Teaching Through Changes and Challenges” at this year's annual NCAEE conference in October.  Kelly is being sponsored by Scholastic.