What I Learned In Kindergarten, Part 1: On Pattern Blocks

     8 schools.  24 classrooms.  30 teachers.  Over 500 kids.  I spent a lot of time this year in kindergarten.  Armed with Amy Noelle Parks's Exploring Mathematics Through Play in the Early Childhood Classroom and Julie Sarama and Douglas Clements's Early Childhood Mathematics Education Research, I watched, listened, and learned from some incredibly talented and thoughtful kindergarten teachers and their incredibly talented and thoughtful students.  What should a kindergarten math classroom look like?  What kinds of activities should students be engaged in?  What's the appropriate balance between free exploration and direct teacher instruction?  How are students held accountable for their work and learning?  This first in series of posts will attempt to illustrate how we tried to answer those questions.

   Here are two students working with large, foam pattern blocks.  What are they learning?

pattern blocks free play from Joe Schwartz on Vimeo.

   
     So much about what these kindergarteners were doing fascinated me.  The quiet way they worked together.  The symmetry.  The way they thought about the negative space.  The trial and error.  The teacher, who you can hear in the background running a guided math group, put no constraints on the activity, and she trusted the the students would work cooperatively and use the pattern blocks in an appropriate way.  That doesn't happen by chance; the teacher made sure that her students knew just how to act in this independent center using these specific materials.

A different classroom.  Again, no teacher direction.  This took four students close to 20 minutes to create.

     Play settings like this, Parks writes,
   
     Often provide children with far more genuine opportunities to engage in mathematical practices than in formal lessons.  Because in lessons, teachers have clear goals about what they want students to do and understand, and they are able to nudge students in subtle and obvious ways to complete the task.  ("Ivan why don't you see if you can make the smaller rectangle fit?")  In providing these hints, teachers often take over a good deal of the mathematical reasoning, while also cutting down on children's opportunities to persevere on their own.  pgs. 9-10

     As I read, watched, listened, and learned, I began to encourage teachers to explore the many different ways their students could interact with pattern blocks in independent, non-teacher directed centers:

Colored and outlined, I thought of these as "entry level" pattern block puzzles.

No color, just outlines.  The prompt in the top left corner provides a nice way to combine this geometry activity with counting.  I stood by and watched as a student worked for over 10 minutes trying to complete a similar puzzle.  His perseverance was astonishing.

These puzzles are more challenging because all the pattern block outlines are missing.  It was interesting to watch the students work on these.  They struggled at times, like the student in the video below.  Watch how she fills the missing triangular space with a triangle...that doesn't fit in the outline.

pattern block puzzle from Joe Schwartz on Vimeo.

      Some teachers asked their students to create their own pattern block puzzles...

Trace and color.

Matching shapes.

     One teacher I've relied on heavily to help me navigate my way though the world of kindergarten math is Cristina Arena.  She deserves a follow, people!!  She took this idea to another level:

Ss create their own pattern block puzzles then their classmates recreate it! #mathchat #Kindergarten @JSchwartz10a pic.twitter.com/Yn3JsykzfK

— Cristina Arena (@arenaABC) April 24, 2018

     Her students took pictures of their creations (one way to hold students accountable for their work) and posted them in their Seesaw journals.  Later, she printed them.

     Other teachers combined pattern blocks with playdough.  Another way to help those fine motor skills develop:

Copy a shape.

Do your own thing.

    Navigating their way through Sarama and Clements's progressions for the composition of 2-D shapes, from piece assembler to picture maker, to shape composer and decomposer to everything between and beyond, these students were engaged in valuable learning experiences.  Parks calls them play based contexts (47), and some teachers expressed concern that, should an administrator walk in and see their students playing around with pattern blocks, they might be called to task.  Not to worry, however.  According to Sarama and Clements,
     
     For early childhood, the area of geometry is the second most important area of mathematics learning.  One could argue that this area--including spatial thinking--is as important as number.  (160)

The kids agree.