Helping Your Child Understand Our World Through Math

One of the questions classroom teachers and I are asked on a regular basis by parents is, "How can I support my child's math learning at home?"  It is so wonderful when parents want to support their child's growth and understanding of how mathematics is relevant outside of school!  Plus, there is a significant body of research that shows how beneficial it is when parents support the learning efforts started at school.

While some people may think of activities like practicing math facts with flashcards or purchasing math workbooks, I would like to offer some alternatives that are arguably more meaningful since these ideas allow students to make sense of our world through the lens of math.  Through counting, comparing, and composing or decomposing numbers and/or shapes, children learn how to understand mathematical relationships in authentic contexts.  Here are some of the ideas I recently provided for parents of kindergarteners, though these ideas can certainly be adapted for a variety of age levels to include more complex math concepts like fractions, decimals, percentages, ratios, multiplication, and division.  

• Have your child make math stories from book illustrations when reading together by counting, comparing, or adding/subtracting.  

• Ask your child to count the number of coins or dollar bills in your wallet.  See if your child can skip count by 5s, 10s, or 20s if you have multiple of the same bills!

• Involve your child in cooking.  Measuring the number of Tbs, tsp, cups, etc. provides both measurement and counting practice.

• Ask your child questions related to comparisons of number and size using words like most, least, bigger, smaller, more, fewer.  For example, “Who has more broccoli on their dinner plate, you or your brother?”  Then see if your child can tell you how many more/less pieces each person has when compared to the other or how many pieces will be left if your child eats a certain number.

• Count the number of pages you read after you finish a book.  To take this to the next level, see if your child can find the total number of pages read if you read multiple books.

• When checking out at a store, ask your child to tell you how many people are in each line, and then determine the best line to stand in (and remember, it may not always be the line with the fewest people based on how many items each person purchases).

• When you are out shopping, use whole number costs to have your child tell you which item is the better deal/costs less.

• Build something together!  Using blocks or Legos are great opportunities for counting, measurement, and conversations about shapes and spatial awareness.

• If you are taking a family trip, use a map to show your child where you are going compared to where you live.  Compare the distances to other locations you have visited.  For example, “We live in Chicago, and here is New York City where we will go next week.  We visited your grandmother in Indianapolis last month, which is here.  Which city is farther away?”

• Try exercising together at home!  Have your child count the number of jumping jacks/sit-ups/squats, and you can make it more competitive by comparing the number each of you can do.

• Ask your child to help you put items into equal group items.  For example, if you are plating dinner, ask your child to put an equal number of carrot sticks on each plate.  Then have your child tell you how many total carrot sticks were used.

• Look for opportunities when you can ask your child how many are missing.  For example, how many eggs are missing from the carton or how many ice cubes have been taken from the tray.

• Patterns can be found in so many places, from clothing and jewelry to floor tiles and artwork.  Ask your child to look for patterns wherever you are, and then have your child explain why it is an example of a pattern and what the sequence of the pattern is.

• Do number or shape scavenger hunts around the house or out and about, and then use the opportunities to make mathematical comparisons between numbers or shapes.
• Whenever you play a game with moving a piece on a game board, have your child count the number of spaces to be moved for each player.  If scoring is involved, ask your child to use tally marks or addition/subtraction to be the game's official scorekeeper.

The websites Math Before Bed and Bedtime Math also provide prompts for families to use to facilitate math conversations at home, and Bedtime Math has developed two free apps as well, MiniMath (ages 3 - 5) and Bedtime Math (ages 3 - 9).  Games are another great way to engage the whole family in math-related activities and conversation, so stay tuned for a future blog post on that!  What are additional ideas you give to parents to help support their child's math development at home?

Creating a Community of Mathematicians through Number Talks

One of the primary goals of a math educator is to support the growth of mathematicians who are strong thinkers and problem solvers.  In order to do this, the math classroom needs to become a community of thinkers, where students feel safe and welcome sharing their ideas and different methods of problem-solving and where students regularly learn from each other.  A great way to build a culture of problem-solving in a classroom is through Number Talks (also called Math Talks).  I have been inspired by so many wonderful math talk scenarios that I have seen in the first few weeks at of school at GEMS World Academy Chicago, so I want to take some time to share some resources and best practices for number talks in the classroom.

What is a Number Talk?
A Number Talk is a brief (5-15 minute) discussions about a single, strategically chosen mental math problem or situation.

• Students are presented with the mental math problem and are provided adequate wait time to think to themselves about the math problem.  Giving a silent thumbs-up hand signal on their chests notifies the teacher when they are ready to share.  Placing the thumbs-up on the chest is more discrete rather than raising a hand so others are not made to feel self-conscious if they are taking longer to think.
• In a non-judgemental way, the teacher allows all willing members of the class to share their answers only. 
• The teacher then follows up by asking students to share their problem-solving strategies orally, which the teacher charts on the board to compile a visual representation of the various strategies the students share.  
• The teacher invites students to ask questions of each other and make connections between the various strategies.  The teacher may also ask strategic questions to prompt thinking and help students compare/contrast strategies.

Why use Number Talks?
Through independent thinking and then communicating and comparing/contrasting various strategies, Number Talks are one way teachers can engage students in the Five Strands of Mathematical Proficiency as explained in the National Research Council's book Adding It Up: Helping Children Learn Mathematics.

Image from Adding It Up: Helping Children Learn Mathematics

Jo Boaler, Standford Professor of Mathematics Education and faculty director of YouCubed, also argues that Number Talks are one of the best ways to build number sense.  The focus of a Number Talk is not necessarily on the answer, but on how you arrived at the answer since problems can be seen in many different ways.  When students verbally share their thinking, the role of the teacher is to visually model/record the multiple strategies with the purpose of making connections among the students' many different methods for thinking mathematically.  (You can hear from Boaler herself about how routines are established and what these number talks look and sound like in this 15-minute video, which is an excerpt from her Stanford online course.)

Where can I find ideas for Number Talk prompts?

• The book Good Questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom by Marian Small provides ideas for open questions that are accessible to a variety of learners and allow for mathematical debate and conversation.
• Fractiontalks.com provide images that can be great prompts for fraction-related number talks.
• VisualPatterns.org provides images that can be used as prompts for number talks.
• MathTalks.net provides math talk prompts used with 6-8th grade students.
• Which One Doesn't Belong? is a "website dedicated to providing thought-provoking puzzles" which allow for rich mathematical conversation. You can also follow the #WoDB hashtag on Twitter for more ideas.
• Use any mathematical problem that allows for multiple ways of thinking!  This graphic organizer from SFUSD may be helpful to use as you start to plan your own.

What if I want to read more about Number Talks?
Check out the following resources for more information about how to implement number talks in your classroom with students!

• The article Number Talks: Building Numerical Reasoning from NCTM's Teaching Children Mathematic's provides a wonderfully detailed overview of a Number Talk's key components. "The heart of number talks is classroom conversations focused on making sense of mathematics."
• Inside Mathematics, an education non-profit focused on supporting high-quality math education, has a series of number talk video clips which allow you to see number talks in action in a variety of classrooms with a debrief afterward.
• Number Talks: Whole Number Computation Grades K - 5 is a fabulous (but pricey) resource that details how to start doing number talks, ask strategic questions to follow and prompt students' thinking, and advice for developing grade-specific number talk prompts.
• The Teaching Channel (Tch) also has created a page called "Dig Into Math Talks" with links to many additional resources.

Spread the Number Talk Love!
What are some of your favorite resources for number talks?  What have been some of your most successful number talk prompts?  Do you have any advice for someone new to doing number talks?

Thank you for growing our community of learners by sharing in the comments section!

Building a Classroom Community Through Math

I know I will have a hard time sleeping tonight as I anticipate the students coming to school for the first day tomorrow, which will kick off my (lucky!) 13th year as an educator.  To me, there are few times as exciting as the night before the first day of school.  There are such great possibilities for new curiosities to be sparked, for new friendships to form, and for tremendous learning and growth.

One of the most important things teachers do at the beginning of each school year is create a warm, welcoming classroom community.  Educators know that students need to feel physically and emotionally secure before they can learn and take risks.

"Before the brain  can attend to cognitive learning, students must feel physically safe and emotionally secure...A positive learning environment increases endorphins in the bloodstream which generates a positive feeling and stimulates the brain’s frontal lobe to support memory of both the learning objective and the positive situation."                  Sousa &Tomlinson, 2017

As a former math teacher and current math specialist and curriculum coordinator, I love building a classroom community through math at the beginning of a new school year.  In addition, it is important to start the year by fostering positive attitudes towards math so students feel they have capacity for success.  Here are a few of my favorite mathematical ways to build a classroom community at the beginning of a new school year:

• Getting to Know You By the Numbers:  This can be adapted to any grade level and can be as open-ended or as structured as you would like.  Ask students to use numbers to describe themselves.  If you teach early elementary, students may simply use basic numerals, and if you teach upper elementary, students may create numeric expressions to describe themselves.  Upper middle/early high school students may write algebraic equations that, when solved, allow the class to learn more about them.  (This can also be used as a way for staff members to get to know each other.  Modeling ideas that can be implemented in the classroom is always helpful!)

• Math Read-Aloud: Doing a read-aloud from a picture book related to math is one of my favorite activities, not only to kick off the school year, but to start new units of study.  Read-alouds are great ways to help students recall prior knowledge, build connections, and appeal to diverse groups of learners.  I wrote a more detailed post on math read-alouds a few years ago, but one of my favorite read-alouds for the beginning of the school year is The Math Curse by Jon Scieszka.  After reading, students can write their own "math curse" story about how math has followed them around in their own lives.  This can be done in a variety of ways depending on how in-depth you want this to be (i.e. good old fashioned paper/pencil, in a blog post, or using an app like My Story or Book Creator).

• About Me Math Photo Stream:  A classroom is a diverse place, and it is important to share and appreciate what makes each member of the classroom community unique while also finding out what we have in common.  To start the school year, I have asked students to create an "About Me Math Photo Stream" by taking photos using 1:1 iPads (or personal smartphones) of at least 5 items that are meaningful/special to them.  The caveat is that the items must be related to math in some way.  Student creativity really shines through with this assignment, and we get to learn a lot about each other as we share our photos via a gallery walk or short presentations to the class.  Some students have shown photos of nutrition labels from favorite foods (Hot Cheetos and Takis!), photos of their street addresses on mailboxes, photos of their favorite sheet music to play on the piano, and photos showing athletic accomplishments like batting averages from their baseball seasons or swimming times from swim races.  Students can also use Clips or iMovie to add narration to their photos if they have iPads, which then allows these to be viewed outside the classroom as well since the narration is built into the student-created product.

What do you do to build your classroom community?  How do you make math approachable to your students at the beginning of the school year?  What a privilege it is to be a teacher, the one creating these circumstances for rich learning to occur!  Wishing everyone a fantastic start to a school year of full of wonder and growth!

Where Do You Do Your Best Work?

Where do you do your best work?  I pondered this question as I sat down to write this blog post.  For me, and I am sure for many of you as well, it depends on what type of "work" I need to do.  When I wrote my book, I was most productive and inspired when I was writing at various hole-in-the-wall neighborhood coffee shops.  I wanted the quiet solitude of the study rooms at my local library when I needed to study for a grad school exam.  A brightly lit group fitness studio with loud music is most energizing to me when I am working on my physical fitness.  I realize, however, that others may have totally different preferences when it comes to creating the ideal learning and working environment.

Trung Le talks to D107 staff
about learning spaces on 8/22/17.

As educators, we must acknowledge the need for flexibility in our learning spaces as well, which is why Building Learning Environments is one of our three goal areas on our District 107 Strategic Blueprint.  Building flexible learning spaces means providing environments that can easily transform and shift based on the needs of the learners and the type of work that needs to be done.  At our district's opening institute day, one of the speakers we were lucky to learn with was Trung Le of Wonder Design Studio.  One of the key takeaways from his presentation was "making sure there are choices, and new choices, in learning spaces."  I also wrote about this in a post last year when I compared the thought process for designing learning spaces in our schools to designing our daughter's nursery.  Our learning spaces need to allow for flexibility as our learners grow and their needs change.  Learners should have space to collaborate, to work independently, to listen, and to speak.  They should have space to work with their hands, to work with technology, to move, and to be still.

Mrs. Georganas's Classroom

We have a few teachers exploring this in their own classrooms already this year, providing a variety of seating options and tablespaces.  As a school, we are also investigating other options for maximizing the potential of our learning spaces.  One idea is to re-purpose our computer lab into a more flexible learning space for innovation.  Since students have one-to-one devices, they no longer need to come to the computer lab to access such tools.  Possible ideas for this space include having a portable green screen, space to work with our two programmable Raspberry Pis and our Sphero, and movable furniture options to allow for collaboration.  Similarly, we are planning to transform one of our small classroom spaces to meet the needs of some of our students who may need a distraction-free environment for productively working or, conversely, may need a space to develop their senses through physical activity, lighting, and/or sound.

We are looking forward to investigating the possibilities that lie within our learning spaces in more detail this year and welcome ideas from our community of learners as we strive to create optimal learning spaces for all!