A calling ...

"We are called to be architects of the future, not its victims."

"Make the world work for 100% of humanity in the shortest possible time through spontaneous cooperation without ecological offense or the disadvantage of anyone."

- Buckminster Fuller

Saturday, February 23, 2013

Is measurement instruction measuring up?


When students are introduced to measurement in elementary school, I have too often observed teachers not intentionally linking to prior knowledge, i.e., their life experiences with how and why we measure things. Or, too often, I have observed teachers fail to offer a preview of how students will be using measurements as students and in their daily lives, i.e., why we measure things. Thus, opportunities to introduce students to a critical life skill in a connected way are frequently wasted, through rote, unconnected activities.

That was, partially, not the case with a 1st grade class, in which the teacher tasked me with reading aloud a selection from Measuring Penny before I sent students off to their math centers. In the case of the 1st grade class, unfortunately, I did not see any measurement activities connected with the story in any of her centers, despite the evidence of her excellence as a teacher, reflected in the problem solving proclivities of her 1st graders. Thus, an opportunity to reinforce important concepts modeled in this classic math children's book, such as various ways we can use standard and non standard measurements, was lost for this particular group of 1st graders.

Dr. Usha Rajdev, my math methods professor at Marymount University, would have applauded the use of a story. In addition to the story, however, Dr. Rajdev would have insisted upon a historical connection, a kit of activities that incorporated manipulatives, procedures that prompted meaningful responses, sometimes including Math Raps, always including pictorial representations, and a bulleted list of resources, as well as a rubric for assessing student understanding.

Recently, I did a body measurement lesson with a 3rd grade GT (advanced academic program) class. Somewhat surprisingly, although I had no idea that this was an advanced class until the end of the day, after I met with the teacher, this particular advanced class had a handful of students who were not quite feral, but chronic offenders, third graders who lacked body control, a filter for their comments, and the habit of maintaining respectful attitudes, three essential factors for promoting a healthy learning environment. After I learned from the Instructional Assistant (IA) assigned to some of these students that the measurement lesson from the previous day with their teacher had devolved into utter chaos, my jaw squared, my eyes squinted, and I channeled Clint Eastwood. Before sending students off to do their measurements, I sat the students at the carpet to engage them in a brief conversation about expectations of how mathematicians and scientists do their work.

To set up the students for a success, I stressed emphatically to students that they would be working with math tools, not toys. Students were asked to share ways measurement tools might be used inappropriately. Students were easily able to come up with a number of problems that might occur, including safety concerns and off task behaviors. Also, I modeled a 2' voice, instructing students that if I could hear them, they were too loud. In general, students had no trouble explaining the difference between productive math talk and its opposite, although I was sensing troubling behavior occurring below the radar, and had to redirect the group more frequently than I would normally would have to do.

Those who I noticed demonstrating self control at the carpet picked first from the partner picker bag (a nice innovation of their teacher which I had never seen before). Despite our conversation, during which, I elicited meaningful contributions from many of the students about reasons why we needed to behave like mathematicians and scientists while collecting our measurement data, and why we should not see anybody playing around, one student, Louis, a chronic disrupter, was unable to handle normal transitions, such as choosing a partner, in a calm, businesslike manner, and was unable to refrain from disrupting other students in the classroom as we transitioned. After two quick warnings about voice and body control, on the third strike I sent Louis to another classroom so that others could learn.

During the lesson, the class continued to need frequent reminders about voice levels, but most seemed to be using their math tools appropriately. Throughout the activity phase of the lesson, as I engaged with students throughout the room, I would stop the entire class to focus on a measurement procedure, and with a second teacher in the room, the class was able to collect the needed data efficiently.

During our introductory math talk, a few students had shouted out that one of the girls had been reading a book on Ancient Rome after I raised the question about how measurement might have been used by the ancient civilizations. The connection to ancient civilizations seemed particularly relevant considering that students were being tasked with first collecting body measurement data, then reflecting on proportional relationships which could be found in the data afterwards. Instead of criticizing the highly engaged little girl, I asked for permission to use her book in our discussion. I held up pictures of statues and architecture from her book as I repeated the question about some of the ways measurement might have been used by ancient civilizations, which generated a marked increase in the volume of student responses.

After 20 minutes of data collection, when it came time to reflect about proportional relationships in the data that students could discover in the data, for example, that the diameter of the neck is about 2 x the diameter of the wrist, I referred back to the pictures of statues and explained that the Ancient Greeks had discovered relationships in body measurements, and that we could discover them too. I modeled how, in several cases, the we might discover the generalization that diameter of the neck is about 2 x the diameter of the wrist. Unfortunately, our reflection procedures had not been well thought out. Difficulties students might encounter in discovering relationships in the data had not been properly anticipated.

Unfortunately, our method of sharing measurement data lacked an obvious and consistent way for students to discover these amazing relationships. Thus, an opportunity was lost to awaken a deep passion for mathematics and scientists that might lead children from an early age, on the path to becoming doctors, and engineers, chemists, or neuroscientists, as it was awakened in Dr. V.S. Ramachandran, from a very early age. Instead, a number of the students, who as 3rd graders might not be developmentally ready for algebraic thinking, were left confused when unable to process how and why we make data comparisons and feel the thrill of gestalt, the flash of insight, when we discover patterns in the data.

Later, during the read aloud of "Davy Crocket," from American Tall Tales, by Mary Pope Osborne, which I used to launch independent reading, I asked them to compare Davy Crocket's supposed weight at 8 years old, 200 pounds, with their weight as 3rd graders. One of these days, I am going to have to start recording read alouds, because my manner of expression, the way I channeled the boastful character's expression as he told tales, had the majority of the children hanging on my every word. Before sending the children off to independent reading, I stopped just before the climax, to leave the students wanting more. The class was as quiet as church mice afterwards. I was able to continue my reading of Kurzweill, generally undisturbed.

Late at night, after my 2 hour workout at the Audrey Moore Recreation Center, upon further reflection, I began exploring the possibility of using Google Forms as a way for a class, using a Smartboard as a central data display site, might collect measurement data collaboratively, in a manner that would have enabled the class to discover averages, and relationships between body measurements which had so fascinated mathematicians of the ancient world.



In that search, I stumbled upon Moodle, a site dedicated to sharing open source educational resources. Perhaps, when I am done, I will be able to share my Google Form on Moodle, to offer a more guided procedure for the reflection phase of the body measurement lesson.