All posts by Nancy Belkov

Celebrate Kids’ Math Conversations! E-books & New Scripts for Upper Elementary

Do you see math students struggling to engage in math practices?

–       Unwilling to share their thinking with others?

–       Giving up easily rather than persevering to solve problems?

–       Unsure of how they can work together to learn?

Read Use Your Math Power ebooks to  students.  Project the ebooks for all to observe the characters persevere to understand unfamiliar problems and reconsider misconceptions.  Your students will discover how they can discuss math problems just like the children in the books! Now available on Teachers Pay Teachers.  Here are links for the ebooks:

https://www.teacherspayteachers.com/Product/Monkeys-for-the-Zoo-4109222

https://www.teacherspayteachers.com/Product/Hatching-Butterflies-4110841

https://www.teacherspayteachers.com/Product/Penguins-on-Parade-4110849

In addition,  three Use Your Math Power Readers’ Theater Scripts focusing on fractions and division with remainders as well as the Common Core Math Practices are now available on Teachers Pay Teachers.

Animal Race               

https://www.teacherspayteachers.com/Product/Penguins-on-Parade-4110849

The Cupcake Bakers

https://www.teacherspayteachers.com/Product/The-Cupcake-Bakers-Math-Readers-Theater-4060504

What’s the Problem?

https://www.teacherspayteachers.com/Product/Whats-the-Problem-Math-Readers-Theater-4060559

Each script is $1.50.  A set of the three scripts is $3.00.

In the scripts, Mr. Trotter’s students work to make sense of fractions and division with remainders. Here are descriptions of the scripts.

Animal Race
In Animal Race, students see children learn to help each other ask questions and work through confusions in math together as they strengthen their growth mindset.  As your students take on the roles in this script, they will see strategies they can use to compare fractions such as model drawing, drawing number lines and using their understanding of numerators and denominators.

The Cupcake Bakers

In The Cupcake Bakers, students see children learning to work together more cooperatively, giving everyone a chance to share their thinking so they all see themselves growing in math.  As your students take on the roles in this script, they see strategies they can use to find equivalent fractions.  They explore ways to use number lines, paper folding and knowledge about unit fractions to find equivalent fractions.

What’s the Problem?

In What’s the Problem Readers’ Theater students see how children learn to work more cooperatively by sharing their understanding more completely and learning from each others’ ideas.  As your students take on the roles in this script, they see ways to create different types of division story problems, use the relationship between multiplication and division, and interpret remainders.

UYMP Books Deepen Teachers’ Understanding of Practices

An instructor at the University of Arizona Center for Retention-Recruitment for Math Teachers just ordered a second set of Use Your Math Power books. This instructor and her students loved the first set of books she’d ordered.  I thought you might be interested in how she used the books to help teachers deepen their understanding of teaching and learning guided by the Common Core Math Standards.

This instructor used the books in workshops to help teachers tease out what the Standards for Mathematical Practice really MEAN and how they might look.  They first discussed examples of a practice in action within K-5 content clusters.  Then they read a Use Your Math Power book that exemplified the practice, discussed the attributes exemplified in the book and examples of other math practices within the story.  They also looked at key representations in the book, the reasoning for using those representations, and significant benefits of the representations.  Finally, they focused on the messaging in the book and how it fits with the 4 academic mindsets they discuss.

This instructor has also used the Use Your Math Power books in methods courses with secondary students as a way to look at diversity in terms of gender, culture, and race representation in mathematics literature.  In an institute this summer, she plans to focus on content and learning trajectories with the sets she just purchased. Teachers will examine important questions. Where is the child in the book along the trajectory, and what might be next for him/her?

I know that many math educators have used the Use Your Math Power books to help teachers explore the Standards for Mathematical Practice.  They provide a unique opportunity to examine children learning to engage in the practices.  I hope you will appreciate hearing these ideas from the University of Arizona.

  

Students Learning about Growth Mindset

I’m so delighted by letters from Newton, Massachusetts 2nd graders about my Use Your Math Power books!  A pair of students wrote,

“You did a really good job teaching kids to use their math power and never give up even if you do not understand the problem.”

Another pair wrote: “Monkeys for the Zoo….made our synapses fire!’

The class linked using your math power with their class conversations about Growth Mindset.  It’s so wonderful to read that the books reinforce the importance of a growth mindset for these students!  I hope the books help your students learn about engaging in math as thinkers and learners this coming school year.

One of these second graders wrote to me saying:

“In my opinion, Penguins on Parade is great because it teaches kids about tens frames and to use their growth mindset (Math Power). And you make the problems fun with monkeys or butterflies not with dots or stripes. You make it fun with the different characters. You do a great job! Please make more books!”

Two other students wrote about how they like the problems in the books and the way students work together to solve a problem in Monkeys for the Zoo.

Review of Use Your Math Power books from Valley View Schools

I hope you will enjoy this teacher review of Use Your Math Power books from  the Valley View School District.  Primary teachers in this Illinois district recently received copies of the Use Your Math Power picture books. The Director of Pre K – 5 Math and Science shared the books with her teachers.  Now teachers are sharing the books  and activities with their students to support their work solving math problems.

“The story math books are an excellent resource to encourage inquiry based learning.  The stories are engaging and hold the students’ attention.  The books have problems at the end of the story that naturally lead to students working collaboratively or independently.  The book we read today, “Penguins on Parade”, had an open ended question at the end that students performed at different levels.  For example, some students went above 300, some above 200, and all students at least met the success criteria of at least 100.  I would encourage every teacher to use these books as part of intervention time, or as an extension of daily math lessons.  I would say the only con for me was it took about an hour to complete the entire activity, but teachers can split it up.”        -Saeed Ghafoor (1st grade teacher, Valley View 365U)

Here is some information about the district (from their website): Valley View School District 365U is located about 35 miles southwest of downtown Chicago, where Interstates 55 & 355 intersect. Our district comprises most of the thriving communities of Bolingbrook, Romeoville and portions of Plainfield, Lockport, and Downers Grove in Illinois. Formed in 1972, the district now serves the educational needs of approximately 18,000 students in 22 educational facilities. Valley View School District 365U is one of Will County’s largest employers, with more than 2000 full time employees.

Our district enjoys a diverse community, providing many settings for learning, sharing, and celebrating. The Board of Education works in partnership with the community to provide engaged learning opportunities and a safe environment that result in continuous learning for all students.

Learning from Mistakes!

Like many teachers and math coaches, I have often thought about missed opportunities for learning when I see mistakes in students’ work, and I long for ways to have students engage with misconceptions and errors. For as Jo Boaler explains about why mistakes cause your brain to grow: 

When teachers ask me how this can be possible, I tell them that the best thinking we have on this now is that the brain sparks and grows when we make a mistake, even if we are not aware of it, because it is a time of struggle; the brain is challenged and the challenge results in growth.

I am excited about Nancy Anderson’s new book, What’s Right About Wrong Answers: Learning from Math Mistakes, Grades 4-5. She provides twenty-two error analysis tasks for students that focus on common misconceptions. Each task, presented on a handout, is part of an activity including independent work, partner work, group discussion tasks and extension problems. The handouts are presented in 3 different engaging formats, comic strips, letters, and sample student work. Teacher notes for using the activities are clear and easy to follow. The combination of discussing the misconceptions of fictionalized students and working on similar problems, invites students to talk about mistakes and reflect on their own misconceptions.

In her introduction, Nancy personalizes the importance of students reflecting on their own errors. Reflecting on her own experiences in math, she writes, “I didn’t need explanations that focused on correct solution strategies but help in finding the flaw in my approach… to identify and unravel my misconceptions and use my mistakes to find correct solutions.” Isn’t that what we want for our students?

Reading the book led me to search for other resources focusing on math mistakes. The format for error-analysis activities in What’s Right About Wrong Answers seems to be unique. But there are many other wonderful resources with insights about students’ mistakes and misconceptions. I found the following books and websites:

Books:

Common Mistakes in Teaching Elementary Math- And How to Avoid Them by Fuchang Liu; 2017 

Smarter Than We Think by Cathy Seeley: 2014; specifically Chapter 8 Oops! The Value of Mistakes, Failures, and Wrong Turns

 

 

#1 hint: Model how to deal with mistakes

 

 

 

 

Math Misconceptions, PreK-Grade 5: From Misunderstanding to Deep Understanding by Bamberger and Oberdorf; 2010

Activities to Undo Math Misconceptions, PreK-Grade 2 by Bamberger and Schultz-Ferrell; 2010

Mathematical Misconceptions: A Guide for Primary Teachers edited by Cockburn and Littler; November 2008

Websites:

http://mathsolutions.com/uncategorized/teaching-students-to-learn-from-their-mistakes/ Tips for helping students learn from mistakes:

Examples:

  • Make them commonplace topics for discussion
  • Give problems with challenges that will be likely to bring up some misconceptions

http://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Linda-M_-Gojak/The-Power-of-a-Good-Mistake/

By NCTM President Linda M. Gojak
NCTM Summing Up, January 8, 2013

Linda quotes Norman Juster’s wonderful book The Phantom Tollbooth. I fondly remember reading this to my third and fourth grade students and discussing the role of making mistakes in learning

“It has been a long trip,” said Milo, climbing onto the couch where the princesses sat; “but we would have been here much sooner if I hadn’t made so many mistakes. I’m afraid it’s all my fault.”

“You must never feel badly about making mistakes,” explained Reason quietly, “as long as you take the trouble to learn from them. For you often learn more by being wrong for the right reasons than you do by being right for the wrong reasons.” 
―  Norton Juster,  The Phantom Tollbooth

Let’s keep helping our students engage in learning from mistakes!

 

Engage Students as Accountable Listeners!

Wondering about steps to help engage all students in meaningful math discussions? I believe that telling “students what to listen for” helps students learn to engage fully in discussions. Damon Bahr and Kim Bahr describe four steps that enhance listening  in their February 2017 TCM article Engaging All Students in Mathematical Discussions.

By telling students what to listen for, more students think about how what they hear connects to a purpose or idea. They can be held accountable for this listening. You can even call on students at random, as the authors suggest, increasing participation. We can model and teach listening and then use routines to get all students engaged.

You can model students working to listen with purpose by reading and discussing my Use Your Math Power picture books. Your students can analyze what the books’ characters are being asked to listen for and how they follow through. Teachers looking for instructional moves to enhance discussions can analyze how Ms. Green, the teacher, helps her students listen more effectively.

In Monkeys for the Zoo, Ms. Green reads a problem twice and tells her students, “Now talk about this problem with your partner. Get ready to tell us what you think this problem is about.” After partners have shared, she says “Carlos, tell us what you and your partner think. Then we can act it out.” With these instructions she gives students a specific purpose by telling them how they will use what they hear.

Later she asks, “What is Ellie’s idea? Will it work?” By telling students to focus on whether the idea will work, she lets them know she will hold them accountable for thinking about their classmates’ explanations.

 

There are similar examples in Hatching Butterflies and Penguins on Parade. One of my favorites is in Hatching Butterflies when a pair of students is getting ready to share their problem solving strategy with the class. Ms. Green says, “Listen carefully, everyone. Then you’ll be able to explain what they did.”

Once the pair of students has finished sharing, Ms. Green calls on a student randomly to explain the strategy. Then she asks if there are any questions. Because the listeners were really thinking about the strategy, they raise questions about unclear parts of the explanation. This is the kind of listening and interaction that empowers students as thinkers and learners. Careful listening was key!

I highly recommend focusing on listening to help enhance math discourse in your classroom. I hope the article Engaging All Students in Mathematical Discussions and my Use Your Math Power books can help you in this endeavor.

“Engaging All Students in Mathematical Discussions”; Damon L. Bahr and Kim Bahr; Teaching Children Mathematics; February 2017, Vol. 23, Issue 6

Some Favorite Resources

I have enjoyed using these resources in helping teachers facilitate discussions and in providing rich activities that engage students in productive discourse!

Suggested resources to focus on student thinking, reasoning, and math discourse:

  • Classroom Discussions in Math: A Teacher’s Guide for using talk moves to support the Common Core and more by Suzanne Chapin et al. (with video).  For more information, click here.
  • Intentional Talk: How to Structure and Lead Productive Mathematical Discussions by Elham Kazemi & Allison Hintz.  For more about this resource, click here.
  • “Orchestrating Discussions” by Margaret S. Smith et al.  For a list of important steps, click here.
  • Developing Number Concepts (Books 1 – 3) by Kathy Richardson.  For more information, click here.
  • “Never Say Anything a Kid Can Say” by Steven C. Reinhart.  For a link to the article, click here.
  • Contexts for Learning Mathematics units by Cathy Fosnot et al.  For information about the materials click here.  For information about Cathy Fosnot, click here.
  • “Promoting Mathematical Argumentation” by Chapina Rumsey & Cynthia W. Langrall.  For a link to the article, click here.
  • Focus on math in picture books:                                                   http://www.the-best-childrens-books.org/math-for-kids.html     This website has categorized lists of picture books for many topics in elementary math.  Each book is summarized.  The lists are updated regularly.  A great resource.  Click here for a link to the site.

Can Picture Books Help Students Engage in Math Discourse?

“What are the Use Your Math Power  (UYMP) books,?” asked a teacher recently.  “Are they a resource?”  “What purpose would they serve in my classroom or school?”

Perhaps the request that led me to write these books helps with these questions.  A first grade teacher I was coaching asked, “Is there a picture book that shows students engaged in math discourse?  I am working to get my students to all engage thoughtfully in discussions, but some struggle.  I use picture books to give students models for other behaviors.  So why not for math discourse.”

I couldn’t find the books this teacher wanted, but I thank her for the idea for my UYMP books.  In each of these books Ms. Green engages her primary classroom in making sense of and solving an unfamiliar problem.  These children are learning to use the Standards for Mathematical Practice.  As in your classroom, children have struggles in the books, but your students can see how other children share ideas, take risks, ask questions, and learn to engage effectively.  I’ll give you a glimpse into each book.

I’ll start with the first pages of Hatching Butterflies.

As the story continues, Hannah asks Carlos what he didn’t understand. He eventually asks why she subtracted when the butterflies don’t fly away, and they need more butterflies.  With time and a number line, they are able to see a way to add up to find how many more they need.  When they share their strategy with the class, another pair says they got the same answer by subtracting.  In a turn and talk and a group discussion, we see the students use a number line to figure out why they can add up or subtract to find the solution.  And Carlos and Hannah have learned to work together.

Before I go on to the first pages of Monkeys for the Zoo, here’s a bit about the books as a resource.  With read alouds and discussions the books help students consider how they can participate in math class more effectively.  In addition, I know that teachers and other educators have used the books in professional development, goal setting, and a variety of activities to help them enhance student participation.  My other posts give more details about use of the books.

Now for Monkeys for the Zoo.

Well, another child does suggest a way, 3 Howlers and 10 Spiders. Gradually more ideas are suggested, and someone asks if there can be more than one right answer.  During the discussion, Mia overcomes her reticence to speak and shares her idea.  The story ends with Mia finding lots of ways as she helps Ben understand why they are finding so many answers.

And finally,  the beginning pages of Penguins on Parade.

Using the ten frames, Zoe helps Trevor see that they can figure out a strategy to get the numbers for the count, but they’re using ones.  Ms Green has them share their work with the class to help everyone.  Together the children find the pattern in the count, 8, 18, 28, 38, discuss the pattern and why it works when you count by tens from a non-zero number.  And Trevor develops some confidence about figuring out how to solve problems that he hasn’t been taught how to do.

I hope you will take a peek at my other posts that give more ideas about the books.  Enjoy!

Common Core Content & Practice Standards in UYMP Books

I have developed a chart to show the connection between the Use Your Math Power picture books and the math content standards and practice standards.  In each  UYMP book, students work on a problem that addresses two or more of the content standards at first and second grade and  engage in ways that model most of the practice standards.  One of the books addresses one of the content standards for kindergarten.

I hope this chart uymp-standards-match-document-11-10-16 will be helpful.  Two of the pages at the end of each book examine how the practice standards appear in that book.  They look like this:

screen-shot-2016-11-13-at-8-44-21-pm

Those are also attached here for your use!

Hatching Butterflies and the Standards of Mathematical Practice: butterflies-smps

Monkeys for the Zoo and the Standards of Mathematical Practice: uymp-monkeys_-smps

Penguins on Parade and the Standards of Mathematical Practice: penguins_-smps

 

UYMP Lessons Focusing on Perseverance & Communication

Here are links to  a new version of lessons and Reader’s Theater scripts I’ve written for using my Use Your Math Power books  to focus on the mathematical practices and growth mindsets.

uymp-guides-10-5

readers-theater-scripts-10-5uymp-guides-10-5

The lessons particularly focus on perseverance and communication.

tyler-noticing-2016-02-24-at-7-01-29-pm trvor-zoe-disc-2016-02-16-at-8-19-10-pm kayla-noticing2016-02-24-at-7-04-03-pm

This collection of lessons begins with suggestions for reading the books to students the first time.  There are two follow-up lesson ideas for each book, one engaging students in focusing on how they can communicate their thinking more effectively and one focusing on how they can work more effectively with classmates.  Two of the lessons  include a Reader’s Theater. All of the follow-up lessons include individual or group reflective activities

Again, here are links to the lessons and the Reader’s Theater scripts.

uymp-guides-10-5

readers-theater-scripts-10-5uymp-guides-10-5