Geometric Habits Of Mind

Since the beginning of our time together as a class, we have held many late night discussions on what geometry instruction may look like at the elementary level. I have learned about the Geometric Habits of Mind that should be present in our classrooms as we engage our students in geometric thinking. I have also had demonstrated for me what it looks like for a teacher to help his/her students move forward to higher Van Hiele levels of thought. These two systems of thinking, along with the readings and class activities, have helped to structure the discussions we have had as a class and the vision I have for my future classroom.
The five phases of learning, as discussed by Howse and Howse in Linking the Van Hiele Theory to Instruction, should …show more content…
The Clements and Sarama article gave examples of activities with puzzles, images, maps, and acting with our bodies. We have also looked at examples of play that involved forming figures or investing figures with ropes, straws, attribute blocks, tangrams, interlocking shapes, and cutouts of shapes. These activities encouraged us, and would encourage our students as well, to discover the properties of shapes and relationships between shapes. They have helped me to begin to understand how future students are going to learn while they are at school. These activities solidified for me the idea that we, as the teachers, hold immense power when it comes to what messages students will pick up about learning while they are at school, along with the depth of understanding that accompanies that learning. Children are able to naturally learn as they play. Such learning can support positive feelings about learning. They are actively engaged in play as they learn, and as such are not bogged down with rote tasks. I believe that these positive experiences and feelings can aid students in feeling successful at math. Teachers should assist their students in realizing that there are not categories of those with math brains and those without math brains. Such categories could place students into a grouping that tells them that they are just not good at math. These messages can be …show more content…
Visualization is the first level of Van Hiele thought. At the elementary level, spatial visualization is a component of geometry that we must labor in helping our students to uncover. It can be tricky to get students to have mental representations of objects in their minds. However, these representations give students the ability to alter geometric figures and gain perspective with their minds as the main tool. We have spent time as a class discussing how we can go about developing this spatial visualization in our students. Many times, we even initially went back to this level of thought when participating in activities to help us think about this development. I think the best way to go about this task is to provide students with repeated exposure and chances to explore. One of the last activities we did as a class at the elementary level was to be shown an image for a split second and then be required to reproduce that image to the best of our ability by drawing it. This activity expected us to sustain a representation of that image in our minds with the aid of our knowledge of shapes and their properties, as well as our perception of location. We have had repeated exposure to shapes and distances throughout our lives, and were accordingly able to complete the activity with a high level of accuracy. Repeated exposure for my future students may look like