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If I’m Ever a Kindergarten Math Teacher

During my ten-year teaching career, I worked primarily with upper elementary and middle school students.  Therefore, I faced steep challenges when I transitioned from the classroom to math coaching, and tried demonstrating lower grade lessons.  The younger the students, the less comfortable I felt, and I found myself petrified whenever I was asked to teach kindergarteners.  Although I felt like I knew the content well, I couldn’t communicate effectively with five and six year-olds in a whole-group setting.  I lacked the skill to both stimulate their thinking and check for understanding.

Nine years and hundreds of demonstration lessons later, I feel as comfortable instructing kindergarteners as I do any other age group.  Still, I find that the balance between educational success and failure is more fragile at this age than any other, because students’ academic readiness is still developing.  If I’m ever hired to be a full-time kindergarten math teacher, I will begin the school year by training students to:

  1. Wait for signals to respond.

  2. Constructively converse with a partner.

  3. Use whiteboards and dry-erase markers as learning tools.

When kindergarteners master these basic classroom social skills, the ceiling on what they can learn is significantly raised.

1.  Wait for Signals to respond.

 

Raising a hand to speak is often the first school procedure that children learn.  It creates a system of fairness and although the rule helps teachers maintain order in any subject, it holds a deeper purpose for mathematics.  Five and six year-olds arrive in kindergarten with drastically different skill and processing levels.  Because of this, the most confident and precocious students have a tendency to take away think time from their slower processing classmates.

For the picture on the right, consider the mathematical consequences of a child calling out answers to any of the following questions:

 
  • How many horses are in the barnyard?

  • How many baby chicks are in the barnyard?

  • Are there more horses or baby chicks?

  • How many more baby chicks than horses are there?

If given a short time to think and count, 95% of kindergarteners could correctly answer three or four of the questions.  However, if children spontaneously call out, the slower processing students are robbed of think time and counting practice.  As a result, they quickly lose interest in the lesson, because they know someone will always call out the answer before they have a chance to finish thinking.

 

The dynamic shifts when teachers rephrase questions into imperative statements and signal for a choral response:

  • Raise your hand if you know how many horses are in the barnyard. (Waits several seconds.)  Ready…(signal)

  • Raise your hand if you know how many baby chicks are in the barnyard. (Waits several seconds.)  Ready…(signal)

  • Are there more horses or baby chicks?  (Waits several seconds.) Ready…(signal)

  • Raise your hand if you know how many more baby chicks than horses there are?  (Waits several seconds.)  Ready…(signal)

 

All students are given think time and everyone who wants to answer has the opportunity to do so.  Basic counting practice is embedded in the lesson and - knowing that they’ll always have the opportunity to respond - students stay engaged. 

This call-response teaching style has an especially powerful role in lower elementary grades (1).  By nature, kindergarteners want to participate in lessons and show off what they know.  Choral responses allow them to do both, but the technique is only effective if all students exercise enough self-regulation to wait before responding.

2.  Constructively converse with a partner.

 

Like choral responses, the turn and talk strategy complements math lessons by channeling kindergarteners’ natural inclinations. On the very first day of school, I would pair students and teach them the social skill of talking with a partner.  Students would practice eye contact, voice modulation, and listening, while discussing simple questions such as:

  • What did you eat for breakfast?

  • What is your favorite movie?

  • Why is it your favorite movie?

Functionally conversing about simple topics such as these prepares students to productively discuss mathematical concepts later in the school year, e.g.

  • What do you think will come next in the pattern?

  • How many small triangles do you see in the big triangle?

  • How could we find out which string is longer?

When students have opportunities to share their thoughts and listen to their classmates’ ideas, they become better mathematical thinkers and reasoners.  However, when they talk over each other and/or don’t listen to what their partners say, they stunt their own learning.

  • 3.  Use whiteboards and dry-erase markers as learning tools.

 

Through choral responses and partner discussions, I would want my students talking almost constantly during math class.  Still, neither strategy is effective for individual, high stakes informal assessment.  To teach any grade level well, it’s vital for instructors to know what students do and do not understand, so that they can provide appropriate remediation or extension.  An efficient way of doing this is through whiteboard exchanges.

On the first day of school, I would provide students with dry-erase markers and sheet protectors, with a piece of white and colored cardstock inserted inside.  They would be expected to:

  • Keep their markers capped except when they’re directed to show their thinking.

  • Always write on the white side unless they’re told otherwise.

  • Pinch the open end of the whiteboard, so the cardstock doesn’t fall out.

Sheet protectors possess most advantages of traditional whiteboards, with the added benefit of holding graphic organizer inserts. Five and six year-old brains process information significantly faster than their hand can write, because their written dexterity is still developing.  A good graphic insert allows students to express their thinking, while keeping handwriting to a minimum.  Using the number path insert to the right, teachers could efficiently assess individual student understanding for any of the barnyard questions, e.g. Circle the number of horses you see., Circle the number of baby chicks you see., etc.

See other examples below:

 

(T holds up 3 fingers.)  Draw an X for each finger I’m raising. Then, circle the number of Xs you drew.

5 frame.png
 

Circle 4 dots, Then, write the parts of 5 in your number bond.

Number Bond.png
 

When students treat whiteboards and markers as academic tools, they can more actively participate in lessons, providing their teachers with insight into what they do and do not understand.  However, when children treat the marker and whiteboard as a paintbrush and canvas, lessons become dysfunctional. Teachers find themselves constantly redirecting individual students, and lose everyone’s focus in the process.

***

I don’t know if I’ll ever have the pleasure of being a kindergarten math teacher, and can’t be sure that I could train a group of five and six year-olds to wait patiently for signals, hold meaningful math discussions, and exercise self-regulation when using whiteboards and markers. I do know, however, that I would devote incredible time and energy into developing these three academic socialization skills. This is because young brains are mossy for learning and internalizing math concepts, but they’re also vulnerable to distractibility and disorganization. Minimizing the latter is vital to maximizing the former.

1 To the best of my knowledge, Dr. Yoram Sagher, professor of mathematics at Florida Atlantic University, invented (or at the very least refined) this type of call-response delivery.