Introducing Little Kids to the Big Ideas of Mathematics: A Rad Makeover for Teaching Math

By Evelyn Raiken Lewis

We all expect children to learn their native language without lessons, worksheets, or tests. They are linguistic geniuses who can learn language by immersion. But this time of linguist genius is short-lived.
If we can leave the assumption aside that young children must spend years doing simplistic arithmetic and provide an early introduction to higher-level math vocabulary and concepts, children could learn math as easily as they learn their native language.

I explore the idea that the core reason children have difficulty with math is the lack of exposure to high-level math vocabulary and concepts in early childhood. Those children who hear mathematical terminology at the dinner table or in everyday conversations will become increasingly proficient. Children who spend their early years adding with pebbles and filling out rote worksheets are at a disadvantage. They are doing this busy work just when their brains are in high gear for learning language, including the language of math. They will be introduced to math terminology and concepts in later years when their brains actively blocking new language patterns. As a result, children who learned their native language without difficulty will think themselves too dumb to understand the relatively simple algorithms of math.

I ask us to consider whether shifting the emphasis in early math education from simplistic arithmetic to an exploration of mathematical ideas would give children an opportunity to excel in mathematical reasoning. I also briefly describe the national math programs that over the last 20+ years have cost over $80 billion with no discernable benefit to children.
Also included is a list of resources for teaching the vocabulary and concepts of math to young children.

• Language: English
• Publisher: Evelyn Raiken Lewis
• Release date: Sep 18, 2016
• ISBN: 9781370440023

Evelyn Raiken Lewis

Like many parents and social justice advocates, I have been distressed about the current state of our education system which has left so many children without basic skills for success, however they might define it.Through my work at the Human Subjects Division of the Office of Research at the University of Washington, I was introduced to current research in brain science and language acquisition. This research mapped the critical age to learn language and the decline in this ability after seven years of age. By applying this research to my experience as a parent and math tutor, I came to understand why so many children can't seem to learn math, even though they had no trouble learning their native language, whose rules, or algorithms, are much more complex. Additional research pointed to the same conclusion, that math vocabulary and concepts, similarly to all language, is most easily learned in early childhood.I advocate for teaching the language of math, the vocabulary and concepts of algebra, geometry, trig and calculus, to young children in a program of discovery and inquiry. This method of teaching math differs from the current methodology of assessment and accountability which focuses through high stakes testing of rote arithmetic.I ask readers to consider the hypothesis that it is the delay in learning math vocabulary and concepts that makes math difficult for children.

Book preview

Introducing Little Kids to the

Big Ideas of Mathematics

A Rad Makeover

for Teaching Math

Evelyn Raiken Lewis

Smashwords Edition

Copyright 2024 Evelyn Raiken Lewis

*Note that this strategy of teaching math as a language when learning language is easy is not an alternative for increased and equitable funding for schools. Nor is it a replacement for racial, economic, and social justice. It is intended to work in tandem with a more equitable distribution of wealth. Poverty will remain, this strategy notwithstanding, the biggest barrier to academic achievement.

Dedication

To my granddaughter and all the little ones

Math is a song that will help you find your peaceful center.

The hypothesis

In the currently accepted mythology of math education, young children must take small, measured steps in basic arithmetic before moving on to the conceptual ideas of algebra. Children start first grade at the approximate skill level of chimpanzees. They need their fingers, or pebbles, or pictures to add 4+5. The current focus on computational arithmetic might be inadvertently shaping our perception of young children’s ability in pursuing higher-level mathematics.

Alternatively, we could shape our perception by focusing on linguistic ability rather than computational skills. First graders who need their fingers, or pebbles, or pictures to add 4+5 understand about 20,000 words, 80% of their parents’ vocabulary. They have analyzed the expressions, grammar, and sentence structure of their native language(s). They are able to converse on many topics and even negotiate with adults. Never in their lives will they be able to learn a new language so easily and naturally. This includes, I will argue, the mathematical expressions and the scientific, financial, engineering and tech concepts that often form the context of math problems.

Using spoken language as a basis of comparison, I am asking us to consider that young children, who can learn any language effortlessly and automatically, could learn the vocabulary and concepts of algebra, geometry, trig, and calculus in a project-based program of discovery and inquiry.

As an example, when children are playing kickball, they do not have to be told that the ball will go faster and farther if it is kicked with more force. Children intuitively understand this relationship, but the vocabulary of this and other mathematical relationships must be learned. If they are repeatedly introduced to the math terminology of this mathematical relationship – force, mass, and acceleration as well as the algebraic expression – Force equals mass times acceleration (F=ma), the terms and algebraic expression will become part of their native language. They are less likely to be confused years later in math class when presented with a problem using these variables.

An early start is essential because the biology of the human brain makes it much more difficult for a teen to remember these terms and expressions, especially when hearing them for the first time in math class, and when there are dozens of other mathematical expressions or formulas to remember.

By introducing young children to the vocabulary and concepts of math, we could capitalize on their linguistic genius to provide a mathematical foundation for enhanced proficiency, more sophisticated analyses, and profound discoveries later in life.

Table of Contents

Chapter Zero: The Paradox of Super Smart Babies

Chapter 1: A New Model for Math Education

Chapter 2: Children are Natural Mathematicians

Chapter 3: The Systematic Decline

Chapter 4: Irreparable Harm

Chapter 5: Ideas for an Early Start

Conclusion

Recommended Links, Reading, and Resources

Acknowledgements

About the Author and Contact Information

Chapter Zero

The Paradox of Super Smart Babies

Cracking the speech code

Is China genetically engineering super-smart babies? How else can you explain that by the time they are three, they can all speak Chinese? – Stephen Colbert's 'Tinfoil Hat' Segment Explains GOP Conspiracy Theories: They ARE watching you. (Aug 25, 2016)

Babies can crack the speech code of any language they hear. If they hear French, they learn French. If they hear Swahili, they learn Swahili. If they hear two languages, they learn two languages. with no problem at all. (Keep this thought.)

This amazing linguistic feat is somewhat obscured by their seemingly endless years of physical dependency and emotional instability. Children can’t feed or clothe themselves for years and they melt down at the slightest inconvenience.

This leads us to assume that the first years of life are not the best time to introduce high-level math or rocket science. I will ask us to reconsider this assumption.

Babies and young children are working on overdrive to analyze the language(s) they hear. They are far more efficient at this than teens or adults. For this reason, I am proposing that the first years of life are the best time for an introduction to the vocabulary and concepts of algebra, geometry, trig, and calculus (as well as rocket science.)

While babies and young children learn language easily, anyone who has tried to learn a new language later in life knows it becomes increasingly difficult as years go by. Learning a new language after early childhood requires memorization of lists of words, practice of verb conjugations, conscious study of grammatical structures, and more.

Similarly, learning the language of math becomes more difficult as time goes by. The vocabulary and concepts of algebra and geometry are typically not introduced until the teen years and, thus, require memorization and conscious study. The additional effort required doesn’t seem worth the trouble for most high-school students.

Like Stephen Colbert, who asks if China is genetically engineering super-smart babies, I cannot imagine learning to speak Chinese or any other new language. Similarly, many American students cannot imagine being able to solve algebraic problems.

I will ask us to challenge the conventional belief that young children should spend years on a math curriculum of repetitive rote arithmetic. The ease at which young children can learn a new language suggests that children would benefit by an early introduction to the math vocabulary and concepts that they will encounter in high school and beyond.

Flipping the traditional early math model from rote arithmetic to a program of math vocabulary and concepts could have long-term benefits. This is because the ability to learn a new language easily and automatically starts to decline at seven years. Students who have been confined in early childhood to the traditional math curriculum of rote arithmetic typically find it difficult to transition to algebraic thinking as Bart Simpson notably encountered in his algebra class.

Bart Simpson in algebra class

The scene begins with a closeup of Bart in the classroom. He is holding his head in his hands looking down at his worksheet in despair. Then, after chewing up the end of his pencil, he starts reading the problem aloud:

At 7:30 AM, an express train traveling 60 miles per hour leaves Santa Fe bound for Phoenix, 520 miles away…

Shhh. Bart’s teacher interrupts, Visualize it, Bart.

Bart visualizes a train leaving the station. As he continues to read the problem, he sets off on a dystopian dream. He is inside a train car watching a steady stream of numbers and math symbols float in front of him. As passengers get on and off the train, his head swims with a concoction of algebraic problems.

The number of passengers equal to the number of minutes past the hour get off and three times as many plus six get on.

The train starts speeding out of control and crashes head-on with another train. Bart is bumped out of his dream state and wakes up on the floor of his classroom.

Like Bart, most American students respond to algebraic problems with futile behaviorisms and catastrophic thinking.

Rethinking the trainwreck of American math education

According to the prevailing wisdom, elementary-school math should start with counting in kindergarten, followed by adding single-digit numbers in the first grade, then subtracting single-digit numbers in the second. It is not until high school that most students are introduced to algebra and geometry, each having their own vocabulary and concepts.

Particularly important to rethink is the underlying assumption that students can easily transition from years of rote arithmetic to algebraic thinking once they become teens. Math often has a linguistic component. Algebra has its own vocabulary and expressions which, like all vocabulary and expressions, are easiest to learn in early childhood.

To give an example: Toddlers love to stomp in puddles. They spend considerable time trying to get the biggest splash and they watch as water enlarges the circumference of the puddle. That’s the fun of it. Adding vocabulary to their discoveries makes their discoveries even more interesting. Yet, our current educational model takes the approach that young children are not ready to learn the terminology for this fun activity. Schools wait until students are in high school and then introduce the concept of displacement of water in the context of a container ship. No wonder students find their social media accounts more interesting.

Parents and teachers might be resistant to teaching toddlers the concept of displacement of water. You might hear a response such as, Don’t trouble little kids with complicated ideas. Let children be children. This response suggests that math is a burden that children will eventually have to endure but should be postponed as long as possible.

However, learning new vocabulary is what toddlers are genetically programmed to do. That’s why we read to them. We don’t sermonize, Let them be children, they have plenty of time to listen to boring books. They can wait until they are older to learn about penguins in Antarctica, for example.

There is already a general understanding that there is power in giving children a broad base of ideas with which to express themselves. Children who have an early introduction to concepts that describe their activities, such as displacement of water, are not as likely to zone out later in high-school math classes when they encounter problems related to these concepts.

Then, as children grow into teens and adults, and and they become aware that the environmental clock is ticking, their collective ability to understand the effects of displacement of water caused by melting glaciers and fragmented ice sheets might be necessary to save penguins along with themselves and many of the species on our planet.

Math as a discovery of thoughts and ideas

The priority of young children is to acquire a greater range of knowledge from which to express themselves. They want to learn about their world. Learning language, including the language of math is a process of inquiry, a process of reaching deeper and deeper within. Given an early introduction, children automatically develop specificity in their communication and glean deeper meaning from conversations.

For this reason, it is flawed logic to delay the introduction of math vocabulary and concepts. Spending the early years on worksheets of rote arithmetic when language learning is automatic and organic, could be the reason that children struggle with math. Children have not been given a mathematical foundation to grow their knowledge in later years.

Typically, if students have not acquired a foundation in algebraic thinking before the teen years, they will fall behind. Once behind, it is hard to catch up.

Not good with numbers

With all their linguistic brilliance, young children are not good with numbers, far from it. The same five-year-olds who have a vocabulary of 10,000 words, need pebbles, or pictures, or their fingers to add 4 plus 6. It will be two more years before they can subtract 15 from 32. They have an inherent understanding of addition, but they generally do not remember the totals of any two numbers. They can fill out worksheet after worksheet of addition problems and still need their fingers or pebbles to fill out the next. Practice does not make them faster or more competent in any way.

It's not only young children who are not good with numbers, humans, in general, are numbers-challenged. I will get back to our numbers-challenged brains, but for now, I will switch focus to the shortcomings of our education strategy which confines young children to computational arithmetic, the area of learning where they are least capable, at an age when they are at the height of their linguistic genius.

Children’s intuitive understanding of math concepts

Getting back to Bart and his train wreck, the advice of Bart’s teacher, Visualize it, Bart, doesn’t help. Bart can visualize a train leaving the station, but he cannot visualize the train problem as a mathematical expression. He is blindsided even though he intuitively understands the relationships between distance, rate, and time, like all children and animated characters.

These relationships between distance, rate, and time are hardwired into most animal species. Babies crawl faster to meet Mom at the door. Toddlers race to the corner to beat Dad. Children run if they are late. Even insects and fish intuitively understand these relationships as they attack prey or flee from predators.

Bart gets into many scrapes where his intuitive understanding of the relationships between distance, rate, and time are of critical value. It’s baked into the hardware, as they say in the tech industry.

But while children intuitively understand the relationships between distance, rate, and time, the ability to solve algebraic problems based on these relationships must be learned. Unfortunately, practice in rote arithmetic does not prepare students to apply their intuitive knowledge of algebraic relationships to solving algebraic problems.

Many algebraic problems, such as those to determine the whereabouts of trains, have a linguistic aspect. So, it follows that like all linguistic endeavors, the vocabulary and concepts of math would be easiest to learn in early childhood.

If these terms and mathematical relationships are introduced early, they would become part of a child’s native language. With this early foundation, students are not as likely to catastrophize when they see a problem that starts A train leaves the station…

Many children do not have the opportunity to integrate math terms into their vocabulary at this optimal time. This could be the reason that they find math difficult in later years. They are trying to learn new vocabulary and concepts when they are past the optimal time to learn a new language.

The backstory

I became aware of alternate education models when I enrolled my son in a Montessori preschool. In his class there were many projects that build an intuitive understanding of math concepts. It was a significantly different approach than what I remember of elementary school.

One of these projects was a board where children place a given number of tokens in columns and rows. Then they add up the tokens giving them a visual, tactile, and conceptual introduction to multiplication. By contrast, in public schools, children in second or third grade are expected to memorize multiplication tables and fill out worksheets of multiplication problems.

Another Montessori project is a