A Next Step

On Monday, I will take over some 6th grade math classes in a middle school, some advanced, and some regular. From a professional standpoint, the ability to focus on one curricular area is highly appealing.

One of my great frustrations about typical elementary classrooms has been the pressure of being held accountable for test scores in four subject areas, Language Arts, Mathematics, Science, and Social Studies, when so many factors have been outside of my control. Many students of low socio-economic status, a population segment that has seemed to expand dramatically over the past 10 years, have shaky foundations in Language and Mathematics, rooted in impoverished language opportunities. Try asking a student to write about her weekend when nobody in the family ate dinner at the same time, when all were watching television in different rooms.

Student deficits with decoding and number sense, e.g., reading to learn and applying decimal place value skills, might account for "Swiss Cheese" understandings of Science Experiments, or more broadly, what Jim Cummins described as deficits in "Cognitive Academic Language Proficiency" or CALP, which Cummins found in second language learners. How can the ability to construct abstract thoughts, i.e., the ability to generalize, develop at an appropriate rate when everyday cognitive inputs are choppy, with everyday direct instruction processed as a Cloze Exercise, which one of my former co-teachers, Sonja, demonstrated to me one day by speaking Japanese:

何が問題だ、あなたは私が言っているか理解していない？

The research is fairly conclusive that developmental differences in vocabulary exposure lead to exponentially different outcomes. On one end of the spectrum, we have students exposed to nuances such as Smoked Spanish Paprika. On the other hand of the language exposure spectrum, we have those whose experiences have been limited to Kraft Mac and Cheese. If Johnny has a limited vocabulary and cannot decode, how can Johnny comprehend a science experiment? If Jane has not been conditioned to recognize sequence in the early primary grades, how can Jane understand history in middle school? Linear experiences correspond to linear understandings, which does not translate to advanced pattern recognition, something which computers are being programmed and are programming themselves do at an accelerating rate.  According to V.S. Ramachandran, the ability to automatically recognize patterns is, perhaps, the key differentiator between homo sapiens and other primates.

A key thrust in Mathematics instruction has been the push for increased rigor, particularly algebraic thinking, or what Van de Walle described as "relational understandings." Multisensory approaches to teaching Mathematics, which are critical for preparing students for relational understandings, require knowledge of and access to resource kits aligned to instructional objectives, with clear procedures, with activities that include manipulatives, visual components, historical connections, and an evaluative rubric. Dr. Rajdev, who teaches math and science teaching methods at Marymount University, prepares her students with a system for purposively constructing their own math kits, since these kits are typically not already awaiting new teachers.

To begin preparing a few kits, I pulled out my copy of Helping Children Learn Mathematics, and have been focusing on the chapters on Geometry and Data. Time to get busy.