Spatial Relations

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Inservice: Going Deeper with Spatial Relations

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Often in professional development settings it is productive to anchor the content of the day around one activity designed for children.  Within the context of the activity, we can engage participants as learners themselves, explore ideas of children's mathematical thinking within specific content areas, and discuss how the activity can be used in classrooms.  This one-day session for practicing teachers explores spatial relations through the activity Describe, Draw, Describe

Professional Development: 2-3 Hours

This plan can be used in one session with practicing teachers or spread out over a multi-day workshop on early mathematics.



  • Do the activity Describe, Draw, Describe (DDD) with a group of young children. Start with a children’s literature book (tip: choose a short one with engaging illustrations) and read to the children, pausing at a few pages to ask them to describe what they notice. At the end of the story, return to a strategically-chosen page and ask them to “draw what they see”. Collect their drawings.
  • Review What Children Know and Need to Learn About Shape and Space, focusing in particular on the ideas of space.
  • Review the TE Activity we designed for DDD as this session draws from its components.


During the PD

Initiate an opening conversation about spatial relations and young children with the following quote, asking participants to consider how young children engage with spatial relations on a daily basis (lining up to go outside, playing on the playground, building with blocks, setting the table, etc.):

Geometry is grasping space. And since it is about the education of children, it is grasping that space in which the child lives, breathes, and moves. The space that the child must learn to know, explore, and conquer, in order to live, breathe, and move better in. (Freudenthal, 1973)

Experiencing the Activity: Describe

  • Engage the whole group in Describe, Draw, Describe, enacting the activity just as you did with children. Often teachers only get to see video snapshots of an activity; we want them to experience the whole activity just as children would. Let them know that it’s storytime!
  • After the story reading, ask them to share (first in small groups, then as a whole group) about the following:
    • What kinds of spatial ideas were worked on during the activity?  
    • How did the teacher (TE) support the participants to describe spatial ideas?  What questions did the teacher ask?  Be specific.
  • Chart the ideas shared, making one list of the mathematical ideas and one of the pedagogical moves.  Sort the spatial ideas, as described in the activity chart.


Role-Playing the Activity: Describe

  • In small groups, ask participants to choose a children’s book and try the activity with each other. (Note: You could ask them ahead of time to bring their own favorite literature). Circulate among groups and support participants to be specific about what children might notice and what the teacher might do to facilitate conversation.
  • Ask participants to read DLLs: Assessing Geometry and Spatial Relations, then reflect in small groups about supporting mathematical language (which is important for both children who are and are not dual language learners).  Invite the group to reflect upon what happened during the activity in relation to this article, specifically highlighting the use of gesture and connecting informal language to formal spatial terminology.


Experiencing the Activity: Draw

  • Now return to your strategically-chosen page of your book and ask participants to draw what they see. Remind them it doesn’t have to look perfect. Circulate during this and ask participants about their drawings (what did you draw first?  what did you choose next?  how did you choose where to begin your drawing? what was tricky about how to draw ___?) Take the participants’ lead in what they describe and ask follow-up questions.  
  • Ask participants to reflect upon their experience drawing with the whole group. Then show a range of children’s drawings, asking participants to discuss what they notice.  



  • Either in a written reflection or in partners, ask participants to reflect on the following questions:
    • Why are spatial relations important for young children?
    • What role did drawing/representation play in this mathematical work?  
    • What ideas do you plan to bring back to your classrooms?  How will you implement these ideas?
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