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Many ways to get to five

Deep counting, from the concrete to the abstract, in Kindergarten
Tuesday, September 19, 2017
 
The seventh and eighth grade dance elective was counting to four and counting to eight, in three groups of four and one group of two.


Kindergarten green group stopped to watch, and count along.

 



Then, the five- and six-year-olds hurried back to the classroom to continue thinking about counting.

 


For the next forty-five minutes, the teacher tugged and prodded them through a variety of ways to represent numbers.

 


The lesson felt free-flowing, but it moved tidily from “the concrete to the pictorial to the abstract”, a phrase familiar to anyone who has been trained in Math In Focus, the curriculum Gordon uses from Kindergarten to eighth grade.

 

It was the tenth day of school, a big day for tallying.

 


On that day, the nine popsicle sticks in the ones cup become one bundle in the tens cup.

 

 

As they talked this through, their teacher spoke of numbers as numerals, and numbers as popsicle sticks, switching repeatedly between the concrete and the abstract.

 

One advantage of using numerals? You have zero, the hero, to help you tell the difference between one and ten.

 

Zero popsicle sticks doesn’t look like anything.

 


The teacher earnestly asked the class to help her draw all of the many ways they represent numbers in Kindergarten.

 

She began with fingers. “I am not very good at drawing hands,” she confided. “Do you expect me to do my best? I will, but I need your help.”

 

The class helped her every step of the way.

 

They urged her along as she drew the numbers as fingers, she drew them as dice, she drew them as popsicle sticks, and she drew them as “ten-frames” with dots in them.

 

The teacher asked the students for their help continuously.

 


The students were invested in her success.

 



They held up their fingers for her to draw.

 

They counted with her as she checked her work.

 

They strained for the perfect word - sideways! slanty! diagonal! - to describe how to arrange three dots on a die.

 



With her questions, the teacher tugged at the corners of their understanding, and stretched their imaginations continually.

 

“With this ten-frame, there’s something missing! There are only eight boxes.”

 

“I need to draw one more line to make ten. Is it up and down, or horizontal?”

 



She even worked in some of yesterday’s Spanish lesson - “We counted four. How do we double-check? That’s right, en espanol…”

 

Finally, the class had completed a grid of hands, dice, tallies and boxes, up to five.

 



Only then did their teacher make a last leap into abstraction and ask for their help writing one to five as numerals.

 



Fingers in the air, they triumphantly drew each line and curve along with her.

 



When they broke for snack, two students lept up to run their hands across the grid, whispering numbers.

 



This one was eager to move beyond five. Her friend, after all, had just turned six today.

 
 
The seventh and eighth grade dance instructor, yon Tande of Denizen Arts, and the percussionist Jesus Andujar, come to Gordon through the support of last May's Gordon Groove fundraising event.

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