Building Number Sense Through Quick Draw Explorations

quick drawThis school year I have embarked on a new career experience and am teaching 1st-4th grade students with moderate to severe learning disabilities.  Almost all of my students are with me all day except for when they go to specials with a general education class.

I am a firm believer in discourse rich, inquiry based learning and am committed to bringing this experience to my students.  This poses a unique challenge as my students are a  very diverse group of learners.  I have tried a few estimation stations with them and have facilitated some sessions of, “The Answer is ____.  What Could the Question Be?”  These have proven to be too challenging for most of my kiddos  as they struggle with subitizing and basic number sense.   With this in mind I have established the routine of  using Quick Draws and Quick Looks.

Prior to launching a Quick Draw I choose an image and think of all of the possible questions I can ask, and the possible challenges students will have when deciphering an image.  I try to think of follow up questions that will facilitate deeper conceptual understanding.  I also try to see the image in as many different ways as I can as well.  Almost all of the images can be seen in 2-D or 3-D, and these present different questions and explorations.


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Two of the Quick Draws we explored this week are above.  I have told my students that it is not important that they are able to draw the images exactly as they see them.  This is necessary as I have discovered that my students who receive Occupational and Physical Therapy get very discouraged and upset by their inability to draw what they perceive.   We use the quote in our room, “If you can’t make a mistake, you can’t make anything.”  I assure my students that what is important is their ability to communicate to one another what they see and how they see it.  This has freed their anxiety and everyone is eager and willing to participate.

We begin the activity in listening, learning position and I make sure all eyes are on the board before I reveal an image.  Many of my students also have Attention Deficit Disorder and if they miss an image because they have been distracted they become very upset.  My students are wonderful and cheer each other to success and encourage each other to pay attention.  I also assure them that we will take quick looks, draw, and discuss until they are comfortable with their drawings and ideas.  Once we have taken our first look and students are drawing I walk around observing.  I ask students what they are thinking and this allows me to scaffold the discussion.  I always allow my students to give a thumbs up if they wish to share and allow them to opt out if they choose not to share their ideas.  I do ask the ones who opt out to restate what others have said to promote good communication and listening skills as well as to allow productive discourse to take place.  I usually start by calling on the student who only has a vague idea of what was displayed and once we discuss and validate the piece that they bring to the discussion I ask who would like to add on.  As we go along I draw exactly what the students are explaining and I encourage them to correct me if I make a mistake.  If they are not using mathematical vocabulary I will restate what they are saying with the desired vocabulary.  As I do this students are picking up the vocabulary and utilizing it in their descriptions as well.  On Friday one of the students said that there was a diamond in the middle of the square and another student kindly reminded her that mathematicians use the word rhombus, and that Naegele Navigators are Mathematicians.

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My drawings as the students share their perceptions.

 I have noticed that as we progress in our year students are quickly picking up mathematical language.  I routinely hear them use correct terminology such as rhombus, vertical, horizontal, triangle, vertices.  They notice that others are drawing the same thing as they are but  the image may be rotated or with different dimensions.  We are comparing and contrasting shapes and wondering what would happen if we removed pieces of the drawings and put the remaining pieces together.  On Friday we actually created a square piece of paper and cut out the middle triangle.  I asked the students to conjecture what shape would be created with the remaining pieces.  Half of the students said we would have a square and the other half said we would have a rhombus.  We then discussed if we should just move the pieces together to check our conjectures or if we should rotate a piece to join them.  Unanimously we agreed to do both!  The students were thrilled to discover a kite, “that is almost like a rhombus,” and a rectangle that is similar to a square.  When we first began these explorations several of my students would get upset if they didn’t get the “right” answer, but I am finding that they are more likely to take risks and make conjectures and are learning from mistakes rather than being disappointed! As the teacher of these amazing mathematicians I notice that my students who struggle the most with fine motor skills and drawing the images are the ones who can communicate what they observe the best.  I find myself wondering if continued experiences with these Quick Draws will enhance spatial awareness and if this awareness will lead to better number sense skills.

I find the use of Quick Draws to be a dynamic mathematical experience for my students.  They feel proud and accomplished and through these experiences are gaining confidence in their mathematical thinking and are considering themselves to be mathematicians.  We are exploring and being introduced to a plethora of geometric concepts while developing spatial awareness and it is my hope that as spatial sense develops so too will number sense.

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