Inviting Students to Explore Mathematics
Jill Britton
Grades 3 Teacher
W. F. Ready School
Regina Saskatchewan

   I arrived at school this morning with a greeting from Darcy, one of my year two students. "Can I build another one?" "Another what?", I asked. "Another cube!" Darcy's eyes are dancing as she pleads with me to continue an activity we had begun last night at our Family Math Night. I am so pleased to watch the enthusiasm in my students over mathematical activities in our classroom. This particular activity was the closing event from the previous evening.
  This activity comes from Interactions, a program I was piloting the year I began having Math nights. My students were using miniature marshmallows and toothpicks to construct cubes. I was hoping my children would be able to discern the differences between a cube and a square shape. I was both pleased and surprised with their responses! Parents too, exhibited a great deal of interest; many were interested in making and recording their own work!
  It has been several years since I implemented an interactive Math Night for my students and their families. As I reflect back on these past evenings, I appreciate the successes as well as the less-than-perfect experiences. Foremost in my mind however is the reason I began these evenings.
  In an effort to inform and to educate my students' parents, I decided to invite families in to participate in the activities my students and I experience in our day-to-day Math. I was hoping to give parents an understanding of both the Math Curriculum used in our province as well as the teaching and learning methods employed to introduce these concepts to their children. A bonus was and is the delight and interest students have in sharing their learning with the families!
  While I have made changes to the outline of this activity-packed evening, there are some experiences that have remained constant each year. The closing activity working with geometry is one. I enjoy watching the families work together on this task. The insights parents glean regarding their child is remarkable. I too, learn much about the family dynamics of my students, the rapport between parent and child, the support for new understandings, and the pleasure parents have in observing their child actively involved in new learning.
  The activity begins by reviewing the attributes of a square. At this point, I presented a cube for the students to view. I asked them to suggest attributes for a cube. Students were told they would use marshmallows and toothpicks to construct their own three-dimensional cube. We estimated the number of marshmallows and toothpicks we would need to construct a cube. I noticed the enthusiasm with which students began to build their cubes. They were very animated as they discussed with their parents what was required and how to go about completing the project! I was also encouraged by the responses in their math logs. The students recorded both the estimates and the actual number of materials required, along with a diagram of the completed cube. I was astonished by the number of diagrams which were drawn by adults rather than 7 and 8 year olds. Evidently, parents were either keen to have their child's diagram correct, and/or these same adults did not trust that their child would and could illustrate what they saw as necessary for a complete recording of a three-dimensional figure.
  To build on last night's learning, our class discussed all the attributes that could be built into a three dimensional shape. We discussed a variety of shapes, and even invented some new ones!
  I provided pipe cleaners and straws as construction materials this time. I have the year 7/8 teacher on our staff to thank for this idea. He had done a similar activity designing buildings with his students. The pipe cleaners were used for the corners. The straws were cut into various lengths and used as the sides.
  My students explored the attributes necessary for three dimensional objects. They designed their own shapes, recording the materials used, the corners and sides built, and whether their shape was free standing or not.
  We then worked in groups. Each group was asked to build the same three-dimensional figure. All students were told the number of corners and sides required. The ensuing activity captured the interest of every student. The children worked the entire afternoon, building and reconstructing various shapes. They shared ideas, successes and failures. The learning was phenomenal. The completed math logs were amazing to read! "My shape ended up with more sides that I thought!" "I thought my shape would be able to stand up my itself but I had to add a few more sides to it." "My partner's shape was different than mine. I don't think he had all the corners he was supposed to!" "This was fun! Can we make buildings like this?" Clearly, an introductory geometry lesson had generated learnings I had not anticipated. Another time, I would utilize the children's year 7/8 school buddies and have the students design and construct more complex structures together.
  I know students of all ages and abilities can and will explore mathematical concepts together, particularly if the experience is exciting and invites students to support one another's learning by working together.

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