Monthly Archives: March 2016

My Books

Supporting Student Participation with Use Your Math Power Books

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Educators have asked me a variety of questions about using the Use Your Math Power books.  I put together this set of ideas.  I’d love input from any of you, especially based on experiences with the books.  I’d like to make these ideas more accessible to users.  Here is what I have so far:

Suggestions for using the books with students:

  • To model student discourse and perseverance in solving cognitively demanding problems.
  • To model students using the Standards for Math Practice as they learn together.
  • To discuss how the characters in the books share their thinking about unfamiliar problems.
  • To reflect on use of the Standards for Math Practice in your classroom.

These books focus on the practices by showing students discussing a math problem. This table can help you coordinate each book with a time of year when students have had relevant experiences with the math content.

Monkeys for the Zoo Penguins on Parade Hatching Butterflies
K Mid – End of year: Extend & support thinking in K.OA2 & K.OA3; Supports strategies for sums thru 10 but uses sum of 13
1 Early – End of year;

Focus: 1.OA1 & 1.OA.3;

Once Ss are familiar with “Put Together Take Apart”* problems with “Total Unknown”* for sums over 10

 

 Mid – End of year;

Focus:1.NBT.2 & 1.NBT.4;

Once Ss are familiar with counting by tens, counting on, and seeing tens and ones in a teen number

 Mid – End of year;

Focus: 1.OA.1 & 1.OA.6;

Once Ss are familiar with “Add To”* problems with result unknown for sums over 10
2 & up Anytime in year;

Focus: 2.OA1 & 2.OA.2;

Reinforces work with “Put Together Take Apart”* problems with “Both Addends Unknown”* for sums over 10

 Anytime in year;

Focus:1.NBT.1 & 1.NBT.5;

Reinforces concepts about tens and ones in fluency adding one digit numbers to two digit numbers

 

 Anytime in year;

Focus: 2.OA.1 & 2.NBT.5;

Reinforces work with “Add To” problems with “Change Unknown” for sums over 20

First Reading:

Pre-read:

  • Have students think about a time when they worked on an unfamiliar math problem.
    • What was that like?
    • What helped you?
  • Optional: Do or think about the math problem in the book*

Read the story and discuss:

  • What was the story about? Any surprises?
  • What did the characters do? What were they feeling? Why?

Subsequent Readings

Discuss how the characters engage in math class. Draw connections to your own class. Suggested questions:

  • What does Ms. Green mean when she tells her students to use their math power?
  • How do Ms. Green’s students use their math power?
  • Think about our class. How do we use our math power? How can we use our math power even more?

Support your students in discussing:

  • How the characters discuss what they notice and wonder about unfamiliar problems
  • How the characters use retelling, acting out, and visualizing to make sense of problems and find entry points for solving them
  • How the characters develop problem solving strategies using a variety of tools and modeling

Also reread portions of a book to focus on issues coming up in your class. For example:

  • What if your students are shy about explaining their ideas?
    • Monkeys for the Zoo focuses on Mia who works up her courage to share her ideas. In all of the books, we see the characters figuring out how to share their thinking.
  • What if your students are reticent to ask questions?
    • Hatching Butterflies focuses on Carlos and Hannah who figure out how to ask each other questions to help them work together. The characters model asking questions in the other books too.
  • What about students who have trouble working together?
    • Hatching Butterflies shows how Carlos and Hannah learn to share their thinking in ways that helps both of them learn. Penguins on Parade shows how Zoe helps Trevor see that they can work together to figure out how to do a problem.
  • What if your students have trouble persevering to figure out how to work with a problem?
    • Penguins on Parade shows how Trevor learns that he can figure out strategies to solve problems without a teacher showing him a strategy.

This chart shows the  practices appearing in each book.  It may help you focus on particular practices.  Pages 30 and 31 in each book give more details.

Standards of Mathematical Practice Monkeys for the Zoo Penguins on Parade Hatching Butterflies
1. “make sense of problems and persevere in solving them” yes yes yes
2. “reason abstractly and quantitatively” yes yes
3. “construct viable arguments and critique the reasoning of others” yes yes yes
4. “model with mathematics” yes yes
5. “uses appropriate tools strategically” yes yes yes
6. “attend to precision” yes yes yes
7. “look for and make use of structure” yes yes
8.   “look for repeated reasoning” yes yes
My Books, Teaching Tips

Powerful Partner Discourse

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In a math talk community students learn together and help each other. Partners share responsibility for understanding problems they solve.

she went so fast 2016-03-21 at 10.05.08 AMWhat if partners aren’t sharing the responsibility for their work? Sometimes one person’s ideas dominate and the talk becomes a monologue with little opportunity for learning together.

Just copied yours 2016-03-21 at 10.04.30 AM

Can we help students learn to work well with a variety of people?

In a recent Teaching Children Mathematics article, a fourth grade teacher explains how she has encouraged more productive math talk in her class.  (Click here for article.)  She lists 5 steps that helped her.

5 stps more meaningful discoursse 2016-03-21 at 10.22.17 AM

The author explains how her class explicitly discussed the importance of math discourse throughout the year and how they gradually learned the skills of active listening, revoicing, responding, and justifying ideas.

Ms G Use mP to discuss

When students see that discussing ideas helps them all learn, they engage in more productive discussions in large groups, small groups, and in pairs.  Just as the article’s author reminds her students more and more frequently to use active listening and revoicing, we need to regularly remind students of our math talk expectations.

Need to add some 2016-03-21 at 10.52.46 AMThen surprising things can happen!  Here’s an example from  Use Your Math Power: Hatching Butterflies.  In the beginning of the story, Carlos does not ask his partner Hannah questions about her strategy, even though he doesn’t understand it.   He just copies her work.  Once their teacher reminds them to discuss their ideas, Carlos gets Hannah to think about a different strategy.  

Wh + & -2016-03-21 at 10.53.16 AM

This led to  the students reasoning about why they could use addition or subtraction to solve the problem.  As a math specialist recently observed after reading Hatching Butterflies, “they both grew. Hannah couldn’t even describe why she did take away. Carlos knew where he wanted to go with his method, and he forgot to add up the jumps. He grew in his understanding as he shared in front of the class.”

When students share ideas, they often get to think about refining their ideas and connections between different strategies, deepening their math understanding.  This is the richness of math discourse and the power of paired work!

 

 

My Books, Teaching Tips

Puzzling about Problems in the Curriculum

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In my last post, I talked about giving students the opportunity to puzzle about unfamiliar problems in the curriculum.  I offered the table of Common Addition and Subtraction Situations  as a source for problems.  In my book,  Use Your Math Power: Monkeys for the Zoo,  the teacher, Ms. Green, asks her students to think about one of these types of problems          Ms G %22Now talk about%22

 

As her students talk about the problem in pairs, their questions and misunderstandings suggest that this is an unfamiliar problem for them.  Here is part of one of the conversations about the problem.  Screen Shot 2016-03-13 at 1.45.54 PM

 

After their “Turn & Talk”, Ms. Green has the class come together to share some of their ideas.

Screen Shot 2016-03-13 at 1.47.11 PM

Screen Shot 2016-03-13 at 1.47.48 PM

Once Carlos has retold part of the problem, one student asks a question about how they can begin to solve it.Screen Shot 2016-03-13 at 1.54.21 PM

 “Other kids might be wondering about that too,” Ms. Green replied.  “Can anyone help us find a way to start?”

This leads to Ellie’s idea of having 13 children stand up with 3 on one side to be howlers and 10 on the other side to be spider monkeys.  When Ms. Green asks her class if this will work, the discussion takes off.  Some think it should be solved another way.  This leads to a discussion about whether this problem has many possible solutions, which leads to them finding more combinations that work.

By discussing the meaning of the problem and how they might solve it, students develop problem solving strategies and make sense of important math ideas.  They use retelling and acting out to help them make sense of the problem.  Ms. Green’s questions and prompts move the discussion along  productively.

It is so powerful to help students use discussions, retelling, acting out, and visualizing to make sense of and solve problems.  I am wondering about your students’ experiences using these strategies.  How can we help all of our students feel confident about using strategies like these to persevere to make sense of a problem instead of wanting to be told which procedure to use?

Teaching Tips

More Puzzling and Wondering: In the Curriculum

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In my last post I wrote about some materials we can use to engage students in puzzling through problems, the Contexts for Learning Mathematics units.  These materials present a wonderful model for giving students the opportunity to think through the meaning of a problem.  Then they engage students in applying their prior knowledge to find a variety of solution paths.

We can really help our students grow as mathematicians if we provide similar opportunities throughout the curriculum.  By presenting students with scenarios, problems, or puzzles that are unfamiliar, but for which they have sufficient prior knowledge to figure out a solution path, we give them the opportunity to think mathematically in constructing their understanding.  By engaging students in discussions about these scenarios, problems, or puzzles, we encourage them to think together about what makes sense and how they can apply what they know.  We are asking them to do math rather than just follow a procedure that has been explained to them.

So how do we do this?  Here are examples using the variety of types of problems in the table of common addition and subtraction situations (click here) and the table of common multiplication and division situations (click here).   At some point in the year, primary students might be comfortable with “add to” and “take from” situations where the result is unknown, but unfamiliar with “take from” situations where the change or start is unknown, or “put together” situations where one addend or both addends are unknown.  We can engage students in making sense of these unfamiliar situations by asking them what they notice about the new situations and what they wonder.  Rather then showing them what procedure to use, we can empower them to think mathematically by asking them to discuss the situation.  We can help them learn to use strategies that help all of us make sense of problems and situations: retelling, acting out (physically, with manipulatives, or with pictures), and visualizing.

Similarly, in the middle grades, when students are comfortable with “unknown product” situations with equal groups, we can have them discuss and apply sense making strategies to figure out “unknown product” situations where we are comparing (ex. “A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost?”).  Rather than showing them what procedure to use, by discussing, acting out, and visualizing comparison situations,  students can work together to think about the meaning of these unfamiliar situations.  That will help them apply their knowledge about multiplication and make sense of the connections between these types of problems.

Talking about what they are doing and thinking, helps students learn to use  sense making strategies.  As they agree and disagree with each other, they learn to think through what makes sense and try out different ideas on a regular basis.  This helps them develop a “growth mindset”.

We need to provide regular opportunities for students to puzzle through math problems and ideas.  These ideas are right there in our curriculum.  When we work on new content standards, we can provide problems or situations for which students  have prior applicable knowledge.  We can use questions and prompts that engage them in modeling ideas and thinking about relevant concepts and skills.   Then our students can do the thinking and talking that will help them figure out how to apply that prior knowledge.  Let’s engage our students in puzzling and wondering throughout the content standards!