Our Montessori Bookshelf: Mathematical Thinking
Montessori Thrive • January 30, 2023

As humans, we are predisposed toward order, exactness, and precision. Wheaton Montessori teachers call this tendency to abstract and imagine our mathematical minds. Children, young and old alike, are drawn to numbers and mathematical ideas. 


For thousands of years, math has been a part of the human search for meaning. We have long tried to quantify our natural world. From carbon dating artifacts to analyzing voting trends in politics, from understanding traffic patterns to examining climate change, math continues to be an integral part of our search for understanding.


Learning to think in mathematical terms is an essential part of becoming a person adapted to our time and place. Math is such an integral part of our lives and we feel that it’s vital to ensure our children are not only in touch with mathematics but also captured by the beauty and wonder of math in our world. 


With this in mind, we pulled some of our favorite books that promote mathematical thinking for young children through early adolescence. 


Counting Is for the Birds

by Frank Mazzola Jr.

https://www.goodreads.com/book/show/2850143-counting-is-for-the-birds

Written in rhyme, this picture book can be used in different ways with young children. Some may just enjoy the story and illustrations, others can clue into the counting aspect of the book, and older children might explore the ornithological details provided on each page. This is the kind of book that you can revisit again and again with your children!


4,962,571

by Trevor Eissler, Ruth Chung, Bobby George, June George

https://www.goodreads.com/book/show/12054759-4-962-571

Written by a former Montessori parent, this picture book is a lovely introduction to and extension of the concept of place value. A young boy wants to see how high he can count, so he figures out ways to create groups of numbers so he can count to four million, nine hundred sixty-two thousand, five hundred seventy-one (and beyond!). Bonus: anyone who has been in Montessori will appreciate the color coding of the numbers in the title!


How Much, How Many, How Far, How Heavy, How Long, How Tall Is 1000?

by Helen Nolan, illustrated by Tracy Walker 

https://www.goodreads.com/en/book/show/1471736.How_Much_How_Many_How_Far_How_Heavy_How_Long_How_Tall_Is_1000_

Children at the end of their primary years with Ms. Chiste, Ms. Carrillo, Mrs. Rogers, or Mrs. Berdick and those who have recently transitioned into elementary with Mrs. Mayhugh and Mrs. Fortun will definitely appreciate this exploration of the quantity of 1,000. This picture book takes readers on a journey through how a 1,000 can be represented in so many different ways – and how that can change our impression of the size of the number. This book is full of thought-provoking questions.


One Grain of Rice: A Mathematical Folktale

by Demi

https://www.goodreads.com/book/show/417181.One_Grain_of_Rice

This stunningly illustrated picture book provides both a moral tale and an example of the exponential power of multiplying by two. After a raja in India has hoarded rice for his own benefit, a young girl returns some spilled rice to him and as a reward, requests only one grain of rice, as long as the raja doubles what he gave her the day before over the course of 30 days. By the end, she has more than enough rice to share with all the villagers who are food insecure, as well as, the goodwill to support the raja in continued kindness. 


Anno's Mysterious Multiplying Jar

by Masaichiro Anno, Mitsumasa Anno

https://www.goodreads.com/book/show/596697.Anno_s_Mysterious_Multiplying_Jar

For those who love Anno’s Journey, this is a must-read, but this time the illustrations and text take the reader on a mathematical journey through factorials. To show what happened mathematically, the Annos (father and son) illustrate the multiplication in a graphic way that fits so well with what children experience at Wheaton Montessori School. 


Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Volumes 1 & 2

by Luetta Reimer, Wilbert Reimer

https://www.goodreads.com/en/book/show/1629218.Mathematicians_Are_People_Too

https://www.goodreads.com/en/book/show/443990.Mathematicians_are_People_Too

This collection of short stories dramatizes conversations and lives of mathematicians throughout history and can easily capture the imagination of elementary-aged children who love the power of a good story. The stories can stand alone or be jumping-off points for further mathematical or historical investigations. We love the glossary at the end, the short biography at the start of every story, and the fact that female mathematicians are fairly well represented in these two volumes. 


The Number Devil: A Mathematical Adventure

by Hans Magnus Enzensberger, illustrated by Rotraut Susanne Berner, translated by Michael Henry Heim 

https://www.goodreads.com/book/show/91358.The_Number_Devil

This has been on Wheaton Montessori’s summer reading list for fifteen years and still holds up! This is the perfect book for older elementary-aged children who aren’t quite sure they want to still love math. A boy meets a number devil in his dreams who leads an exploration of all sorts of fascinating aspects of numbers. The wildly fun and irreverent approach (led by the devil) makes even complicated math feel accessible. The whimsical illustrations certainly help, too! And for those wanting to go back and reference helpful information, there is a “Seek-and-Ye-Shall-Find List” (aka index) at the end of the book. 


Doodle Yourself Smart . . . Math

by Helen Greaves, Simon Greaves

https://www.goodreads.com/en/book/show/13235749-doodle-yourself-smart-math

For elementary children and adolescents who like to play around with mathematical thinking, this is a fun activity-style book that appeals to mathematicians and artists alike. Each page offers beautiful space for playing around with the problems (and yes, there are answers in the back for those who just need to know if they got it right!).


The Man Who Counted: A Collection of Mathematical Adventures

by Malba Tahan

https://www.goodreads.com/book/show/1160800.The_Man_Who_Counted

Those who like a good mathematical challenge, combined with a taste of the adventure that comes with travel, will love this series of chapters that form a bit of a novel. Each chapter of this book can stand alone or work as a cohesive whole as the narrator and the “man who counted” move through the Middle East. They encounter a slew of social problems that are solved with a sophisticated level of number sense that feels both mystical and matter-of-fact. 



If the World Were a Village: A Book about the World's People

David J. Smith

https://www.goodreads.com/book/show/225679.If_the_World_Were_a_Village

This book takes real data and ask readers to image the whole world population as a village of 100. How many people would have enough food to eat? This neither pessimistic nor overly hopeful book provides a manageable way to consider the world’s population and human needs. While not strictly a math book, the statistics and imagery are great links with geography and world citizenship.


Click here for a downloadable PDF of this booklist! As always you are also welcome to come visit the school and see how we support mathematical thinking for all ages. 

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By Suzanna Mayhugh, Lower Elementary Teacher January 19, 2026
Montessori Mayhem? Pint-Sized Pandemonium? When I give tours of the Elementary classrooms or welcome new parents to the Elementary program at Wheaton Montessori School, some parents believe that students are allowed complete freedom, as if the classrooms are a beautiful den of chaos and anarchy. Indeed, this is one of the biggest misconceptions about Montessori education. (The biggest misconception being, in my experience, that Montessori isn’t “real world” education. But as we say in our lessons, “That’s a story for another day.”) While Montessori classrooms DO give children the freedoms they require and deserve, it’s not an unlimited free-for-all with an adult watching from an observation chair! Freedom is always balanced with responsibility, to oneself and to the community. These values, freedom and responsibility, are essential for creating a happy, busy, humming classroom where children thrive. What Does Freedom Mean in Our Classroom? “Freedom” in the classroom means that students are encouraged to make choices about their learning. Just as in our Primary classrooms at Wheaton Montessori School, students are free to choose their work, their seat, and their work partners. They are free to move about the classroom and do not need to raise their hands to visit the restroom, get a drink of water, or ask a question. Let’s look at a few of these freedoms more closely. Students are Free to Choose Their Work. For example, they may choose which book to read, choose a work partner to research a chosen topic, or practice a tricky bit of a lesson over and over. They are also able to choose how they will show their understanding. They might present their understanding through a poster, a diorama, a model, a handmade book, or an enormous amount of cardboard and hot glue. These choices empower students to take charge of their education and express themselves in ways that suit their interests and strengths, something a standardized test or a worksheet can never do. However, freedom in the classroom ALWAYS has limits. For example, students are free to choose their work, but choosing NOT to work is not an option. They are free to choose their work from the lessons that have been presented to them. While students may choose their reading material, it must be appropriate for their reading level and classroom guidelines. When students select a partner, they must do so respectfully and inclusively. When students create projects and work output, they must do so with care, make proper use of materials, and in a way that shows what they understand about their topic. Additionally, these choices should never disrupt their own learning and construction, or that of their peers. The Role of Responsibility In a true Montessori classroom, freedom comes with responsibility. And that responsibility can sometimes be uncomfortable at first. Students are expected to care for classroom materials, such as returning books and lesson materials to the shelf, taking part in classroom jobs, keeping a record of their work in their work journals, and handling art supplies properly. They are responsible for practicing their lessons and completing chosen follow-up work, listening attentively during lessons or when a classmate is sharing a presentation or thought, and helping classmates when needed and available. A student is not free to use materials in a way that damages or wastes the classroom supplies or puts anyone in harm’s way. Freedom within our classroom never allows for harming oneself, others, or the classroom materials. Healthy boundaries, limits, and structures are consistently communicated in advance with clarity and respect, ensuring practicality and alignment within the community. Classroom expectations and rules are collaboratively developed and agreed upon by the community. In order to foster a positive learning environment, both students and teachers are expected to adhere to the shared expectations and responsibilities. When necessary, the classroom adult will address students and reiterate expectations and boundaries in a firm yet considerate manner. This balanced approach is effective only when maintained consistently throughout each day. What Might it Look Like When the Balance Needs to Shift? The adults in the classroom are constantly observing the children to be sure that each child has as much freedom as they are ready for, providing them space, room, and opportunities to show their strengths, and make their own choices throughout the day. When that freedom is too much, a teacher might need to provide more lessons in how to use materials that have been damaged or used improperly, limit work partner choices, or have a student sit with the teacher while they practice lessons or work with precious art materials. The adults will be watching for the perfect moment to allow the child increased freedom within the classroom, and within the limits of the understood responsibilities. How Freedom and Responsibility Work Together Finding the right mix of freedom and responsibility is something we work on together every day in our classroom. Montessori teachers are specially trained to guide this balance, helping students practice important skills like making good choices, solving problems, and learning self-control. When children are trusted to make decisions, they also learn to take responsibility for those choices. Experiencing the natural consequences of their actions helps them become kind, thoughtful, and capable members of their community who understand how their choices affect others. What Does This Have to Do with Parents? Your support at home makes a big difference. By working together, we can help your child thrive both at school and at home. Encouraging your child to take responsibility for their actions and decisions reinforces what they learn in class. Yes, it can be uncomfortable, but it is necessary. It also becomes easier, more comfortable, and needs to be practiced less often when practiced consistently (like most things!). This supportive consistency across settings, at home and at school, helps children feel confident, cared for, and increasingly independent.