Subitize
- Merriam and Webster don’t know this word, but if you’re an early-grade math
teacher, you do. Subitizing is the rapid, accurate, and confident discernment
of numbers without counting. The word subitize is derived from the Latin
adjective subitus, meaning sudden.
Teachers,
of course, make many sudden decisions every day. There are curveballs in even
the best-planned lessons; “monitor and adjust” is the mantra of teaching. During
a lesson, teachers become immediately aware of problems and opportunities. These
subitizing moments are supported by preparation. Going in with a plan allows us
to be responsive in the moment. I had that conversation yesterday with Haylee,
a third-grade teacher.
The
lesson I’d observed in Haylee’s room went well, and I knew how carefully she’d
thought through that lesson in advance. She had shared her lesson plan with me,
and it included a checklist for evaluation, notes about transitions, and
thoughtful questions. The lesson had lots of moving parts as students individually
chose how they would demonstrate their knowledge at the end of a unit on sea
animals. But instruction had a settled feeling because of Haylee’s careful plan,
even though there were “subitizing moments” where she had to recognize relationships
and think on her feet.
In
math, we are immediately aware of what is being displayed if it’s within the
subitizing range. In Haylee’s lesson, she was immediately aware of opportunities
to extend understanding because of her careful preparation.
Later,
as Haylee reflected on the lesson, she talked about the value of her careful
plan and admitted that, when such plans weren’t in place, things didn’t go as well.
At such times, she overlooked teachable moments because she had to be thinking
about the lesson’s next steps. She couldn’t see patterns in student thinking as
easily. She wasn’t able to make rapid, confident decisions in the moment.
It’s
interesting that, mathematically, the number of objects that can be subitized (enumerated
without counting) increases when we see a familiar pattern. With careful
noticing and experience, recognition becomes automatic. Helping teachers
recognize patterns is an important role of coaching.
My
thoughts about subitizing were sparked by a first-grade math lesson I observed
yesterday in Ms. Rivera’s class. The objective of the lesson was for students to
identify the number of things in a set by quickly looking at them. But a pattern
I’d noticed with Gabbi (Ms. Rivera) was the lack of a through line connecting
all of a lesson’s activities to the objective. The subitizing lesson started out
with a clear connection: Gabbi flashed different sets of dots on the screen and
students responded with both the quantity they saw and the subitized groups
they used to get to their answer. The lesson’s culminating activity was Bingo,
which thrilled the students. The Bingo cards had counting dots in each square, and
when Gabbi called out the number for students to cover, she showed the numeral
on the SmartBoard. I noticed students counting the dots on their cards before
covering them. They weren’t subitizing, so the activity wasn’t reinforcing the
lesson’s objective.
Reflecting
on the pattern I’d seen when working with Gabbi (lesson activities not clearly
connected to objective), I had time to plan how to draw attention to this
important need during our follow-up conversation. I even planned the exact
wording I wanted to use for a question: “How could the Bingo activity be
changed to make it more about subitizing?”
When
I met with Gabbi at the end of the day, I asked her what stood out for her from
the math lesson. We celebrated successes, then she brought up a concern about
how students had been distracted while one of their friends came to the board
and shared her thinking. She wondered how she could keep the other students focused
on their friend’s demonstration. Her focus was all on those non-presenting
students. But this was a situation she couldn’t subitize. She needed to shift her
attention.
In
mathematics, when the number of objects exceeds the subitizing range,
mathematicians shift their viewpoint around the display until all of the
elements represented have been counted; they shift their zone of attention.
I
mentioned that I’d noticed students’ distraction, too. Having shifted my
attention across Gabbi, the presenting students, and the listeners, I felt students’
distraction may have been due to the repetitious description the girl at the
board was providing. If Gabbi’s prompts and questions for the presenter could lead
to quicker descriptions, listeners could maintain attention. Gabbi felt this
was worth working on.
So
far, Gabbi hadn’t brought up any concerns about the Bingo activity, but I still
felt we needed to go there. I posed my planned question and paused, but even
with what seemed like a lot of think time, Gabbi didn’t respond. Knowing my own
coaching patterns (too ready with a recommendation!), I reminded myself that Gabbi
was gaining experience and had a growing teaching repertoire. I felt she had it
in her to come up with answers to the question. I made a few “filler” comments
(about focusing on the lesson objective, about subitizing), giving her more
time to think. In the middle of one of my sentences, I saw that hoped-for
light-bulb moment spread over Gabbi’s face.
“What
if I put the numerals on the Bingo card and flashed the dots on the screen?” she
said. “Is that what you were thinking?” I affirmed that it was, but that there were
likely other ways to tweak the game to emphasize the lesson’s objective. I hadn’t
been fishing for that specific answer.
Like
object counting and teaching, coaching is enhanced when we recognize familiar
patterns – in both the teachers we are working with and ourselves. Like object
counting and teaching, coaching, too, includes rapid and accurate decisions
made in the midst of a conversation. As we develop our abilities to both recognize
patterns and “subitize,” making quick and targeted decisions, the effectiveness
of our coaching will increase.
*from
Wikipedia, Subitizing.
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Hooray!!!
My new book, Differentiated Mentoring &
Coaching in Education: From Preservice Teacher to Expert Practitioner is a fall release from
Teachers College Press! I’m so excited
to share it with you! During October, you can use the code: OCT2022 for
15% off plus FREE SHIPPING.
Click here and I’ll email you the free
Book Group Study Guide that
includes questions, prompts, and activities you can use as you share the
book with colleagues. I hope you’ll love
this book as much as I loved making it for you!
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week, you might want to take a look at:
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