Meet the Children Where They Are: Episode 4

Narrator:  “Although this series makes this interaction seem like a long period of time, it was actually only about 3 minutes…well, maybe 5!  Time flies when you’re having fun, okay?  Anyway, can Bob count two hidden piles of rocks?  Let’s get back to the action.”

(Math research associate narrates…)

RA:  So it was the bottom of the 9th in the World Series…or…overtime in the Super Bowl.  I was under pressure knowing that 5-year-olds have shorter attention spans than goldfish.

(Video: goldfish in a goldfish bowl — alive, preferably)

RA:  And I… now, what was I saying?  Oh, yes.  I was running out of time and still hadn’t found the extent of Bob’s counting abilities.  So, I had him count 9 rocks and I covered them.

(Video: counting 9 rocks, heartbeat for each count; scary music)

RA:  I then had him count 6 rocks into another pile.  As he did, instead of starting with 1, he said, “10, 11, 12, …”  I said, “Whoa, horsey!”

(Video of the Lone Ranger bringing Silver to a stop… horse whinnies, record screeches to a stop.)

(Video: math research associate kneeling in mud with child — slowly zoom in.)

RA:  Suddenly, I’m perplexed.  Is this kid cheating?  He’s supposed to find out how many rocks with BOTH piles being hidden, not just count more.  So what to do?  I grabbed 4 rocks without him seeing.  I told him there were now 11 under my first hand and 4 under my other hand. I asked him, “How many all together?”

(Dramatic music and still frame of Bob and RA…)

RA:  After 7-10 seconds, Bob said, “12, 13, 14, 15,” with an emphasis on the 15.

I said, “I heard you count 12, 13, 14, 15.  How did you know to stop at 15?”

Bob replied, “Because 12 is 1, 13 is 2, 14 is 3, and 15 is 4.”

(Slow-motion video of RA jumping up and down with arms raised…)

(Zoom out as RA walks toward camera — reminiscent of a political spot.)

RA:  At this point, there was smoke coming out of Bob’s ears.  His difficulty solving the double-hidden problem and his body language screamed, “I’m done!!!”  I told him, “Thanks, Bob, for doing math with me.”  And just like that, he was off like a shot, climbing on splintery boards and stepping on rusty nails again.

(Still shot of RA… anti-climactic music.)

RA:  There I was, a weary, muddy, yet elated man.  A kindergartner that can “count his counts”?  Wow!  What an exciting world it is when young children have such mathematical potential (given the right opportunities).  I was mentally exhausted, but I had a better idea of “where he was”.  

RA:  What we do is not for the faint of heart.  Neither is it for those afraid of dirty hands.  Educators, meet the children where they are.  It’s not a job, it’s a way of life.  Out.

(Dramatic orchestra music… fade to credit roll and outtakes.)

A Heart for Professional Learning

Who do you rely on professionally? I could name a long list of people, places, journals, periodicals, podcasts, and websites, but most recently I listened to my colleague Chris Brownell’s recent podcast with Director of Special Education Studies at Fresno Pacific University, Megan Chaney. Megan is doing her doctoral research on teachers dispositions and she… Continue Reading

“Play is the Answer to how Anything New Comes About” – Piaget

As the early math team moves forward on the work we are doing, the concept of practicality is an issue we are addressing. One-on-one interviews with the children have taught us a wealth of information about young children’s mathematics, but it is not a realistic structure that early childhood teachers have time to do in… Continue Reading

Which is Bigger?

Which is bigger 5/6 or 7/8? If the answer isn’t popping into your head in seconds, you are not alone. Fractions are one of the most misunderstood concepts among both young and old in mathematics.  They don’t seem to follow the same rules as whole numbers.  Many of us purposely never work with fractions at… Continue Reading

Episode 27 | Professional Noticing Part 3: Deciding

In the studio with David Pearce and Wilma Hashimoto two of the AIMS Center’s Research Associates, and we discuss the third aspect of Professional Noticing: Deciding. We discuss how this aspect takes place in the midst of classroom activity, and how it is dependent upon the two prior aspects of: Attend and Interpret. We end up discussing how this supports the goal of creating a student centered classroom, one in which the learner’s thinking and conceptualization is valued as the starting place for academic learning.

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Change Unknown

Recently, while working with students, we offered up a situation where nineteen counters were placed under a cloth.  Seven of the counters were pulled out and the students were asked how many remained under the cloth. One child extended ten fingers, pulled them back, and then re-extended nine. He pulled back seven fingers, one by… Continue Reading

Intensive Quantity and Extensive Quantity

In discussing coordinating units as a way to understand multiplicative reasoning, it is not always evident that there are differences in multiplicative and additive reasoning. What I want to do is give some examples to help clarify the differences. Multiplication is often presented to children as repeated addition. But there is more. In math classes,… Continue Reading