Where’s The Math?

Math is a natural way of thinking and making sense of the world. Mathematical situations arise every day. You have to be ready to notice the math all around us and to engage children in doing and talking about math. Attribute is a mathematical idea that arises very early. Attributes are properties or qualities that allow us to describe & classify the world around us. We perceive attributes of the world around us through our senses. Attributes can be used to group. Attributes can be described with increasing precision.

What might you see or hear if children are thinking mathematically about attribute? They might be matching objects, describing objects or sorting objects. They might be paying attention to color or shape or size or texture.  If you notice children noticing and using attributes, you might ask them: Why do these go together? Why do these not go together?

When adults are comfortable talking about math, children will share ideas without prompting. Here’s an example from a preschool classroom:

Chris & Tracy approach their teacher with excitement: “Look, our shoes are the same so they are a group! There are 4 shoes, 1, 2, 3, 4 … It is a group of shoes with holes”


Teacher: “I see you have a group of 4 shoes with holes. My shoes have little holes on the strap where I buckle the shoes. Can my shoes be part of your group?”

Chris & Tracy: “No, teacher, you have to have big holes all over to be in our group”

Teacher: “I see … you have made a group of shoes with big holes all over. Does anyone else have shoes that belong to your group?”

In a kindergarten classroom, a child runs up to the teacher and says, “A triangle equals a square!” Some teachers might say, “What do you mean? Triangles have 3 sides, and squares have 4. They’re not the same.” However, this mathematically sensitive teacher says, “What do you mean?” The child answers, “Come see!” The child leads the teacher over to the block area, where there are a lot of unit blocks for the children to play with. (Do blocks give you an idea of what the child might be thinking?) This is what the child showed the teacher:


Two square blocks can be put together to make the same shape as one longer rectangle block.

Two long triangle blocks can also be put together to make the same size rectangle shape.

Therefore, one of the squares takes up the same space as one of the triangles. In other words, they are worth the same, or, as the child says, they are “equal.”

This child was thinking hard about both the attributes of these shapes and the relationships between them. One might even say that the child was doing algebra, because they were using equivalences:

2S = R   and   2T = R           Therefore, 2S = 2T               Therefore, S = T

In both of these scenarios, the teachers are building the children’s understanding of foundational mathematical ideas and their confidence in using math to make sense of their world.

I hope that you will be open to the joy of finding math any time, anywhere with the children in your life!

What Are They Thinking?

posted by Lisa Ginet

It is hard to know what is going on in anyone’s brain. Even when asked to explain ourselves, we cannot always express our ideas clearly. Young children, who are still developing both their communication and reasoning abilities, have an especially hard time explain their own thinking in words or “showing their work” when they are solving problems. Why does it matter to understand what children are thinking about? It helps us to respond to them in ways that nurture competence and confidence.

So, how do we figure out what’s happening in children’s minds? We need to watch what they are doing and listen to what they are saying for clues, then interact with them intentionally. Here is an example from a preschool classroom:

From nearby the teacher has been watching Jenny and Samantha work with the materials at the sorting station.














The teacher has noticed the children taking the straight items from the collection without talking and putting them on the black paper. The teacher also noticed that Samantha takes each item and rolls it with her hand before she places it on the paper. After the paper is almost full with items, the teacher decides to approach the children.

Teacher: Tell me about your group.

Jenny: Son Palitos (These are sticks)

Samantha: Uh… no..no

Teacher: Samantha you don’t seem to agree with Jenny. What is your group then?

Samantha: A group that rolls

Teacher: Are you saying that what makes this a group is that all the things in it roll?

Samantha: yes, see (Samantha shows how different items in her group roll)

Teacher: Could this be part of your group? (The teacher offers a circular wooden object)

Samantha: (Samantha takes the wooden objects and tests if it rolls) Well, it kind of rolls.

(Samantha then adds the object to her paper)

Teacher: What should we call the group then?

Jenny: Cosas que ruedan (things that roll)

Teacher: I can see why you are naming your group: “things that roll.” There are sticks, pens, brushes, markers, pencils, straws and round pieces of wood but they all roll.

This teacher is drawing from a repertoire of intentional responses that help to surface children’s thinking:

  • Stop & Look – Take the time to observe what a child is doing. Try to figure out what the child’s ideas or goals are.
  • Say what you see – Use precise, descriptive language to describe what you notice. Provide labels to actions or structures that are mathematical.
  • Re-voice what you hear – Use precise, descriptive language to echo and expand on what a child says.
  • Check with the child – Always ask child to confirm your understanding of their ideas and intentions.
  • Wait – Allow child the time to react or respond to an adult prompt
  • Use comments / questions to invite / provoke children’s thinking

We will never be able to be inside children’s brains, but we can closely attend to their actions and words, and then intentionally respond in ways that draw out their ideas. The more we understand about what children are thinking, the easier it will be to help them love, understand and use math.


Blogger of the Month- Sasha Fajerstein

Meet Sasha Fajerstein, our guest blogger for the month of October.  Sasha is a teacher of mathematics and an avid fan of all things “math.”  She is an innovative educator who makes math accessible for all students.  We are very excited to have Sasha share her knowledge about math education and how we can all benefit from understanding “new math” in order to support the children in our care.

Sasha Fajerstein currently teaches mathematics at New Trier High School in Winnetka, Illinois. She previously taught at Nichols Middle School in Evanston, Illinois. Sasha received her Bachelors of Science in Mathematics from the University of Illinois at Urbana Champaign. After graduating, she taught English in Costa Rica for a year before returning to the United States to teach math.


Sasha is passionate about trying new things in the classroom, and she works hard to integrate technology into her lessons. She recently piloted a new geometry textbook for High School students entirely on the iPad. She has presented at the Illinois Council of Teachers of Mathematics conference and the Metropolitan Mathematics Club of Chicago.

Introducing the Guest Blogger for the month of September – Stephanie Forsman

I am so pleased to introduce the Math at Home readers to our guest blogger of the month – Ms. Stephanie Forsman.  Stephanie is one of my oldest friends.  We met while serving in the US Peace Corps in West Africa in the early 90s and have remained close friends ever since.  We have followed the same career trajectory; education, teaching, and a focus on supporting children and families and have been working together on the Math at Home site (Stephanie wrote dozens and dozens of the Math Lesson Plans you can find on the site).

Last year, I spent a day in her 3rd grade classroom. Have you ever been a classroom where every corner and space is dedicated to supporting the children with careful and thoughtful planning, where the children come in and clearly understand that “this space is for them”, and where education works?  Well, that is Ms. Forsman’s classroom.  I wish you could all go and visit.

Since that isn’t possible, I urge you to read Stephanie’s posts this month as she is going to tell you about how she thinks about setting up her space to support early math in the early grades.  Enjoy!


Stephanie Forsman

Stephanie Forsman has been teaching in the NYC Independent School system for over 15 years. She received her B.A. in Art History and Fine Art from Trinity College in Washington DC, served as a Peace Corps Volunteer in Mali, West Africa and has a M.Ed in Elementary Education and Museum Education from Bank Street College in New York City.


Stephanie currently works at The Berkeley Carroll School in Brooklyn where she has taught 2nd and 3rd grades and is currently a 4th grade teacher. She has served as the Mathematics in the City school facilitator, presented workshops such as “Math Puzzles & Logic Games”, “Technology & Math”, “Napier’s Bones” at ATIS conferences and was the Math Subcomittee Chair for the 2013, ten-year NYSAIS school review. In addition, Stephanie wrote many of the math lessons found on the Math at Home website.


Introducing the Guest Blogger for August – Alison Balis Hirsch

Hello readers!  Today, I am pleased to introduce you to Alison Balis Hirsch: my friend and colleague.  Over the years, I have mentioned Alison in several of my own posts as I have always looked to her as a model for exceptional teaching and parenting.

This month, Alison is writing about setting up classroom systems that support early math competencies.  We thought August was a good month to consider these ideas as this is time of the year when we take a step back and consider our classroom environments and ideally make innovative changes. I hope you enjoy reading the blog this month and be sure to ask questions or leave comments at the bottom of the page.

Alison Balis Hirsch

Alison has been involved with early childhood education for over 20 years. She received her BS from the University of Massachusetts and her M.Ed. with a focus in Creative Arts in Learning from Lesley University. She began her career in Chicago, working in a kindergarten classroom and then in a pre-kindergarten classroom before becoming the head teacher and Executive Director of a non-profit preschool where she worked for 12 years. Alison’s focus is developing hands-on, creative activities that support educational standards and creating beautiful play-based environments that welcome, nurture and excite young children and their families.


In 2008, Alison and her husband relocated to San Francisco where they are raising their two children, ages 7 and 5. Currently, she volunteers in a variety of capacities at her children’s schools, collaborating with teachers within the classroom setting in addition to serving on a number of committees where she volunteers with other parents and early childhood professionals in areas such as inclusion, playground and building design, and classroom organization.


10 New Things To Be Thankful For This Thanksgiving – The Early Childhood Edition

Last year I posted a list of 10 Things to be Thankful for this Thanksgiving – the Early Childhood Edition so I challenged myself to think of 10 new things to be thankful for this year.  That makes 20 things to focus on as we move into this holiday season.

10.  Everyday small, chubby, soft hands reach for ours. 

9.  Nobody cares if we can’t carry a tune when we sing, and we get to sing everyday.

8.  At the end of the day when we empty our pockets, we often find crayon drawings created just for us. 

7.  Our work is never boring.

6. Nobody would notice if we wore our pajamas to work.

5.  When we put our music libraries on shuffle, an Ella Jenkins song might come on.

4.  Finger paint

3.  There is no such thing as “sitting all day.”

2.  The people we work with smell like fresh bread, talcum powder, and cinnamon sugar.

1.  Our work is monumentally rewarding.

Another Reminder – Child Care and Education Wages

This article reminds us all that the way we pay our child care workforce is shameful.  Read the first paragraph and pay attention to the way the author describes the teacher’s interactions with a young child in her care.  Her specialized training, experience, and dedication deserve a real living wage.  All parents want what is best for their children.  Well-paid teachers should be a given.

The Museum Of Childhood

Last week I visited the Victoria and Albert Museum of Childhood in London, England.  We were on vacation visiting my family in Jolly Olde England and I made it a point to get over to this museum since I knew it would provide inspiration for this blog and it would fill my heart with images of children at play and children throughout history.

Over the next few weeks, I am going to write about some of the areas of the museum, especially those connected to early math learning.

One of the first things I noticed was the sheer quantity of toys specifially designed for open-ended construction play.  Everything from Legos to large wooden blocks are placed strategically throughout the museum.  You can also see how these “types” of toys exist in other areas of the world.

IMG_1410These are very simple blocks with nongender specific figures that can be arranged and designed in an infinite array of scenes.  Here, the blocks are set up as a playground area, but they could depict anything a child’s imagination can create.IMG_1411These blocks are much older but you can see how they are not unlike the newer version.  I love the wooden carry box and the endless possibilities for open-ended play this set provided for children a century and a half ago.

The museum is very careful to remind guests that many of these toys were not available to most people.  Only people with disposable income might buy these toys for their children or a set, like the one above, might be a gift for a many children at Christmas time, for example.

Open-ended construction manipulatives are grounded in early math concepts.  As children manipulate these block sets, they consider their attributes (and therefore, their uses), the spatial requirements for placement and utility, the quantity of available pieces…. the list goes on.

Next week, I will share some photos of nesting blocks, Froebel’s gifts, and doll houses.




Chicago Little League and Why I Love Baseball

I have personnally watched almost one million hours of little league baseball over the past 16 years.  Every summer, I have sat and tried to feign interest in what may be the longest sports commitments of any childhood choice.  Some games went on for well over 2 hours, only to end in a 1-1 tie .  Those games were deadly for moms like me. There were more Sundays than I care to count, when I went from one game to another, from one field to another, from one exciting win to another devastating loss

The only thing worse than watching my own kids play baseball is watching other people’s kids play baseball and the only possible thing that could be worse than that, is to watch it on TV.

I would now like to recant all of the above. Boy,was I wrong.

This week I am singing a completely different tune.  This year’s Little League World Series has been one of the best sporting events I have ever watched and it has proven once again that even an old gal like me can change. I have loved watching other people’s kids, playing what was heretofore, the most boring game ever, on TV no less.

The Jackie Robinson West players have stolen my heart and changed my mind.  I have spent the better part of the past 2 weeks cheering for those south side darlings. I am shouting at the TV, jumping up and down, and silently wishing and praying for the wins.  I never once did that during my own children’s games.

Whether they win or lose the international game, these little boys are hometown heroes.  They are bringing attention to Chicago for something wonderful and positive. After a summer of negative news, this series has been so uplifting for so many.

Thank you Jackie Robinson West for reminding me why I should love baseball.

Greg Maddux, The Hall of Fame, and Why Math Language Matters

Greg_Maddux_promoIt was a big weekend for a couple of Chicago’s favorite ball players.  Frank Thomas, also known as the Big Hurt, and Greg Maddux received baseball’s highest honor when they were inducted into the Baseball Hall of Fame. If you’ve never been to Cooperstown, the Hall of Fame is actually a “hall” in a larger baseball museum where plaques hang commemorating baseball’s greats.

So what is the connection between Greg Maddux, the Hall of Fame, and Math Language?

Maddux’s plaque reads, “the only hurler with 300 wins, 3,000 strikeouts and less than 1,000 walks.”

Did you catch it? Did you see it?

Math language experts will tell you that the plaque should read:

…fewer than 1,000 walks.

“Fewer” is used when referring to things or items in the plural, i.e., walks, home runs, strikeouts, RBIs, and errors.  “Less than” is used when speaking about items that can’t be counted, i.e., sunshine, rain, and happiness.

The writers of the plaques would have benefitted from early math language exposure – used correctly.  A couple of lessons in comma usage might also be a good idea.