Do your learners have a mathematical mindset?

This year my district is embarking on an exciting venture.  We are actively working to build a math community!  Our work started last year when we analyzed and piloted several math programs.  When one program surfaced to the top, we started to learn about teaching with a mathematical mindset.  I was already very familiar with growth mindset.  This was something different - focusing on math.

Since that time many educators in our district have started to delve into Jo Boaler's Mathematical Mindset.  What an amazing resource!  Our district is embracing this thinking.  Our goal is to create critical problem solvers that have a love of math, starting in the primary grades.

Within the first few days of this new school year, I stopped into a couple second grade classrooms to see the beginning stages of this mathematical mindset in action.  Teachers had already introduced some powerful vocabulary to their learners: perseverance, flexibility, optimism, empathy, and resilience. The goal of the lesson I observed was for these little mathematicians to show what a mathematical mindset looks like.

They had seven big ideas to illustrate:

• Isn't to heart warming to see how this learner is celebrating math?

  

  
  

• Don't you just love the "oopps" for a mistake?
  

• The perplexed face on this sketch really speaks to confusion and the power of asking questions.

• It's so exciting for a second grader to articulate many ways to solve a problem.  Remember this is just the first few days of school.

• Math learning is social.  We learn by talking about the math and sharing our ideas with each other.

• This mathematician paints a perfect picture that faster is not better.  Many times faster results in careless errors.  Furthermore. students need to hear the message that processing time is needed for deeper learning and making connections in math.

• This sketch captures the importance of learning over time.  

These little people were spot on!  I am giddy with excitement as I think of how strong their mathematical mindset will be as they continue to grow and learn.

Making this mindset work explicit for students is the first step.  Next we will need to keep these big ideas living and breathing during math learning each and every day.  Celebrate asking questions and learning from mistakes!

What are you doing to build a positive math culture?  Share your ideas.  We all learn from each other.

Fun Fluency Frenzy

Who doesn't like an addicting, fast-paced game?  Put it in the form of a puzzle, add points to earn medals, and presto...kids are hooked!

Here are two interactive games that can be put on the top of the list of ways to support addition and multiplication fluency:  Fluency Games.  They can be played on both the computer and tablets.

These games are perfect for those students well on their way to knowing their basic facts and ready for a new challenge.  Each game is a puzzle of blocks.  Both the addition and the multiplication versions include options to vary the speed and difficulty.  The best part is that they are truly addictive! (Yes, I even got hooked.)

Once children know their basic addition facts to ten, they are ready for Addition Blocks .  The object of the game is to destroy the target sum block falling from the right side of the screen.  You must connect digit blocks to equal the target sum.

 As the level moves up, the sums become slightly larger (12, 15, and 20).  This promotes opportunities to add three or more digits to create the targeted sum, which earns even more points. Additionally, as the player knocks out all of the blocks in the puzzle, the game moves to another level.

Multiplication Blocks  is perfect for those that know their multiplication facts and are ready for the challenge of fast-paced puzzle action.  The object of the game is to destroy the target product falling on the right side of the screen.  Like the addition game, the blocks must be connected to equal the targeted product.

 As the levels move up, more challenging facts are woven into the game and more point are earns for finding three or more digits that can be multiplied together to equal the targeted product.

So if you have some kiddos that want to have fun keeping their facts fresh and automatic, check out these games.  And for those that like the addition game, stay tuned because the subtraction version is in the works.

What are some of your fun-favorite ways to promote math fact fluency?  Share your ideas.  We all learn from each other.

Family Math is Fun!

In my school district, we are all about reading.  Now, don't get me wrong.  I, too, truly value reading and have always loved reading to my kids.  However, in my last few years as a math coach, I find myself constantly thinking, "What about math?"  So one of my goals this year is to foster making math more visible in our schools and in our community.

My colleagues and I brainstormed ways to reach out to our parent community.  Research shows that if we want our children to grow a love of math, then we need to make math fun at home.  We decided to start by creating monthly math challenges for families to tackle together.

We shared this PBS article - Instill a Love of Math - with parents.  Then we announced that each month we would offer some themed math questions for four grade bands:  Kindergarten, 1-2, 3-4, and 5-6.  We challenged families to do the math together and then double challenged them to notice math in a typical day and make it come alive for their children.

When brainstorming the first round of questions, sports instantly came to mind.  It was important that the questions be open ended with multiple solutions.  I found myself not only thinking hard about sports scenarios for each developmental level, but for the Grade 5-6 band I even did some research on current ticket prices to make this math truly real life.

Here are our sports related math challenges for families.

This is just one of our ideas to promote the love of math with families.  I am so excited to hear feedback from parents and students.  It's all about the little things we do to make a difference in our learners' lives.

What do you do to foster the love of math?  Share your ideas.  We all learn from each other.

The Power of Words - in Math

This post continues the series on building a math community.  I remember one of my first experiences with geometry as a child.  For weeks I felt like the teacher was talking in a foreign language.  Then finally I made a connection and thought, "Oh!  That's what a plane is."  Math vocabulary is an instrumental part of strengthening our math learning.

Our math students hear "math words" for maybe an hour each day, that isolated time of math instruction.  It's no secret that we need to hear a new word many times before we start to make it part of our own vocabulary.  So how can we help learners make meaning of these words and better yet, make these words become part of our learners' math discussions?  It's this natural use of math vocabulary that strengthens students' ability to communicate their thinking and speak with precision.

Ideas to build mathematicians' vocabulary:

• Model vocabulary and highlight it in your math anchor charts.  The anchor chart serves as a visual scaffold for learners.
  
• Math discussions -
• Model using math words that connect to the lesson.
• Pose questions using math vocabulary.
• When a learner shares an idea, ask, "Who can restate this idea using a math word?"
• Use multiple representations:  Frayer Models, word banks, or have students build models in their math notebooks.
• When students write about math, encourage them to revise adding math words.

Granite School District has created math vocabulary cards that offer a comprehensive way to foster the growth of math vocabulary. The cards are available Kindergarten through Grade 6 with an additional secondary section of word cards. Plus, there are sets in Spanish, French, and Chinese. They are perfect for a Math Word Wall.  Each card consists of three sections:

• Section 1 is only the word.
• Section 2 is the word with a visual representation.
• Section 3 is the word, the visual representation, and the definition.

Some other resources to support the development of math vocabulary include the following:

• Have a math dictionary available for learners.  Math Dictionary: Homework Help for Families is very user friendly for students with clear examples to connect to.
  

• An interactive math dictionary:   http://www.amathsdictionaryforkids.com/dictionary.html  This site not only models the math term, but also gives the user the opportunity to test out its meaning.

What are some strategies you use to promote the growth of your mathematicans' math vocabulary? Share your ideas.  We all learn from each other.

Talk with Your Hands

This post continues the series on building a math community.  As the saying goes, "Actions speak louder than words." Hand signals are powerful tools in the math classroom.  Students can all share their thinking at the same time without hearing a sound.  Amazing!  Learners are engaged and actively listening.  Lastly, these motions serve as real time formative assessment for the teacher. Such power!

Here are some favorites that I use.

• Thumb up right in front of your chest - This says, "I've had time to think and I have an idea."
• When students agree with the speaker, they hold up their thumb and pinky, folding down their three middle fingers, waving them to say, "I agree with you."  A student mathematican has a boost of confidence as peers make this motion, agreeing with the speaker's strategy or comment.
  
• After an idea has been shared, many times I ask students if they agree, disagree, or are still thinking, simply using their thumbs.  This same signal also works well when I ask student to self-assess their comfort level with a new strategy:  thumb up if they feel comfy; thumb down if they feel confused; and thumb sideways if they are starting to feel comfy.  It's a quick and effective way to take a pulse of the class.
  

  Agree	Disagree	Still thinking about it

Interested in how other teachers use hand signals.  Check out these Teaching Channel video clips: 

• https://www.teachingchannel.org/videos/student-silent-signals
• https://www.teachingchannel.org/videos/classroom-silent-communication-signals

As the school year starts, it's a perfect time to model hand signals and weave them into your math discussions.  They can actually be used throughout the day, too.  What are some ways you use hand signals to strengthen the math discussions in your classroom? Share your ideas.  We all learn from each other.

Supporting Students' Math Talk

This post continues the series centering on building a math community.  When starting a new school year with a new group of math students, as you start to have math discussions, it's the perfect time to introduce prompts to support student conversations.

In reading, students regularly turn and talk.  They learn to use sentence stems to grow a reading conversation.  Some favorites that I hear the students use include: "I can add on...", "This connects with...", "A different idea I have is...".  Why do we use these in reading?  They offer the students an entry point, a way to get started on their conversation.

This same structure is essential in math.  It's not easy for many young mathematicians to verbalize their thinking.  The use of prompts gives students a way to start or respond.

During the early days in math, introducing math talk prompts requires continuous modeling.  Then students need to practice using them.  It takes time, but it's time well spent.  As the prompts are introduced they can be displayed on a class chart and even taped onto students' math notebooks as tools for their conversations.  Like all new routines. with time the prompts become a natural part of the class' math conversations.  And the reward is deeper math discussions!

When students start to use the prompts freely, compliment them.  This will inspire others to use them more, too.  Some students may create their own sentence starters.  Add their ideas to the list.

What are some strategies you use to grow math conversations in your classroom?  Share your ideas.  We all learn from each other.

Hearing ALL Answers + ALL Voices

This post is part of a series centering on building a math community.  When starting the school year with a new group of students, it is key to grow a community where all answers are welcome and emphasize that it is essential to hear all voices.

It's math - why not focus on the answers that are accurate?  Honestly, some of the most powerful student-centered math discussions I've facilitated or observed stem from the idea of sharing all student answers.  When an answer is shared, many teacher ask for other solutions that students have come up with.  Another strategy I regularly use, is to circle around observing student work and noting all the possible answers and then post them for students to ponder. Sometimes I include an answer from a common misconception, even if I have not noticed it on the student work for that day. This fosters student reflection before the math discussion begins.

Having multiple answers centers the discussion on student reasoning and justification.  It aids in revealing both understanding and misunderstanding.  Further, through the discussion, students construct viable arguments and critique the reasoning of others - CCSS.MATH.PRACTICE.MP3.

Throughout math discussions, all voices need to be heard.  This is not only instrumental in building community, but it's a key part of student engagement.  Several classroom teachers I know employ the concept of no hand raising, unless you have a question. For more on this, check out my post:  Do NOT Raise Your Hand. Now as a learner, this idea can initially be a bit terrifying.  "What if I can't answer the question I'm asked?"  The structure of not hand raising includes options for the student - phone a friend, pass, or the student can answer with a question to help better understand.  All voices can also be heard by using turn and talk partner strategies.  It's less intimidating to share the ideas of your partnership.  You can even ask a more reserved student to share what his or her partner was thinking.

Another way to encourage all voices is to ask a question of one student and then ask another student what he or she thinks about the original student's response.  Dylan William's call it Pose, Pause, Bounce, Bounce!  He compares sharing student voices with the game of basketball, where a team of voices can be heard.  This counters the traditional questioning approach of teacher-student, teacher-student, which William's connects with the game of tennis.  

As the students start a new school year with a new teacher, taking the time to build the math community by emphasizing that all answers are welcome and all voices are important sends the message to students that their ideas are valued.  It is a foundational step in creating a risk-free environment, one where all children are open to learning and trying new things.

What are some of your strategies for sharing all answers and having all voices heard?  Share your ideas.  We all learn from each other.