Place value is fundamental to understanding the base-ten number system. It helps children comprehend the relationship between digits in a number and their positional value, which is crucial for performing arithmetic operations accurately. However, many children struggle with grasping the concept of place value, particularly when they encounter multi-digit numbers. They may have difficulty understanding that the value of a digit depends on its position in the number.
While I enjoy teaching my math dance program to many schools and teachers internationally, I am the homeroom teacher for grade 2 at the European School in Costa Rica. My students are learning with me in English, although English is their second or third language. My classroom is a zero-technology environment, so a lot of learning happens within projects and tactile, interactive activities. They also write in cursive and are proficient note-takers. I teach them Language Arts, Math, Science, and Art. In math, we are learning to subtract with 3 and 4-digit numbers. Already, by grade 2, my group of 20 students have vastly different skills and abilities in regards to mathematics. While some have properly mastered the art of borrowing, many students need a foundational understanding of place value, and therefore borrowing is a confusing and foreign concept.
I've gone back to the basics and prefer to take them away from desks, paper, and pencils altogether! Sitting on the carpet with the Montessori Golden Beads (or a paper version available for Dance Equations subscribers) is proving to be far more useful. Those who are confused by arithmetic operations on paper are learning to physically subtract. I love the Montessori method of teaching addition, subtraction, multiplication, and division. Although I do not have a Montessori classroom, the Golden Beads are a useful tool that I very much appreciate and use often.
Without a solid understanding of place value, children may struggle with these operations as they progress through their math education. Children may develop misconceptions about place value, such as believing that the digit with the most value is always the largest in the number or misunderstanding the role of zero as a placeholder. Understanding has to be more important than mimicking operations so that it’s absorbed fully.
One of my Dance Equations place value exercises uses the Mayan base 20 system. When I introduce Mayan numbers to a class that’s already shown a good understanding of place value, it is with this activity that their understanding is ultimately challenged. Because the number 1,111 in Mayan numbers is valued as 8,421. Each “place” is a multiple of 20 with 20 initial digits 0-19.
Assessing children's understanding of place value is essential for identifying areas of weakness and providing targeted intervention. My Dancing Digits activity is another Dance Equations activity I use for teaching rapid calculations and requires a good understanding of place value. In Dancing Digits, the ones are danced in the feet, the tens in the arms, hundreds in the fingers, and thousands with the head. Although this is the method that I developed, turning the body into a calculator, the idea was inspired by the Indian Chisanbop method of rapid finger calculations. With Dancing Digits, I can see which students can group, borrow, and share over the borders of each category, and without the need to memorize a series of calculations, they can quickly calculate in groupings and multiples of 10.
Working away from the desk and moving one’s body is stimulating and provides a break in routine along with classroom expectations. Movement is a wonderful and simple addition to the classroom and fits well with the teaching philosophies outlined in Building Thinking Classrooms and along with the Rosenshine Principles.
In the video below, my daughter is calling out numbers for me to rapidly add together.
I am currently teaching Dancing Digits in small online groups. If you would like to learn my Dancing Digits codified dance method of rapid calculations, you can register via my event page. If the event times do not work well with your schedule, you may sign up and request another time.
I thoroughly enjoy teaching place value through movement activities. Having these various methods while working away from the desks has proven to be highly successful.