Introduction
Teaching the dailies, in November
Back in October, I began teaching short lessons called the “dailies.” These workbooks, published by Evan-Moor, contain short warm-up exercises covering a range of grade-level content. Each day, we complete the lesson in each of the four books: Daily Language Practice, Daily Paragraph, Daily Math Practice, and Daily Word Problem. Leading the dailies became my first ongoing responsibility as a student teacher in my sixth grade classroom. It was also my first experience with whole-class instruction, and the fact that I continued to lead these lessons over several months means that I have had significant opportunity to reflect upon – and experiment with – my teaching using them as a baseline. I begin my portfolio here, then, because the dailies are, in a way, the ground from which grew my inquiry question. They also play prominently in some of the conclusions (although that might be too strong a word) at which I have arrived through my inquiry. Within these fifteen or twenty minutes of instruction every day, I recognize the limitations and the possibilities before me as I enter teaching at a time when the external pressure on teachers is often at odds with the type of planning and instruction that is best for their students.
For the purpose of focus, I am going to frame my inquiry around mathematics, although this inquiry has implications for every content area. Here's the story of how I arrived at my question: Our cohort was in the midst of methods courses when I inherited the dailies in October. Professor Caroline Ebby set the tone for Math Methods on the first day, titling that class "What does it mean to learn mathematics?" and providing readings that depicted, essentially, two different outcomes from math instruction. These outcomes can be described in various terms, but here I will borrow from Skemp (who himself is borrowing from Mellin-Olson) and call them "relational understanding and instrumental understanding" (1976). To quickly summarize, Skemp (1976) defines relational understanding as "both knowing what to do and why" while the latter is simply "rules without reasons" (p. 21) [emphasis mine]. Though it may be obvious, it should be noted that the author strongly advocated for relational understanding as the desired goal of math instruction. In a complimentary reading, Kohn (2011) took this dichotomy a step further by adding a socio-political dimension. He described a "pedagogy of poverty" in which mechanized, skill-and-drill-based lessons are the norm in schools serving low-income students of color, standing in contrast to the critical thinking and inquiry fostered in schools that primarily serve a white, middle- or upper-class demographic (Kohn, 2011). A synthesis: we are emphasizing instrumental understanding for some and relational understanding for others, with the split occurring largely along racial and socioeconomic lines.
It follows, then, that we spent much of our time in Math Methods looking at pedagogical strategies that can foster relational understanding in students, strategies like number talks and purposeful discourse. In short time, it occurred to me that I was not seeing many of these techniques being implemented in my student teaching classroom. Rather, these students (low-income and of color) were receiving a type of instruction not too dissimilar from Kohn's "pedagogy of poverty" (2011). Armed with perhaps an inflated sense of influence and backed by recent research, I immediately began an attempt to implement some of these techniques into my Daily Math Practice and Daily Word Problem lessons. As I wrote in the first paragraph, these attempts exemplify the limitations as well as the possibilities for teaching toward deep, relational understanding within an educational climate that appears to discourage such understanding for particular students.
My grappling with these limitations and possibilities form the response to my inquiry question: what impact did high-stakes testing have on my math planning and instruction, and what are the implications for my future practice? Until this point, I had not directly mentioned high-stakes testing, but I contend that a major influence on the emphasis toward instrumental understanding is the looming spectre of the Pennsylvania System of School Assessment (PSSA). I know from personal conversations that my Classroom Mentor has adjusted her teaching in ways that she laments, but that she feels are necessary for dealing with the reality of this high-stakes test (personal correspondence, 2012; see Appendix, Artifact A). As the year progressed, I found myself adjusting my own teaching to this reality, too. In the first part of this portfolio, I will present the context for this inquiry by describing the PSSA-based pressure in our class. Although this context is not immediately about my own teaching, I firmly believe it is a necessary component to this portfolio. From there, I will move on to a deeper look at how I attempted to find a balance between accommodating the reality of the high-stakes test and implementing some of the techniques learned in my Math Methods course. In the final part, I will look toward the future and consider how my experience as a student teacher this year might inform my future practice.
Continue to Part I: Within the Context of High-Stakes Testing.
(References are cited here.)
It follows, then, that we spent much of our time in Math Methods looking at pedagogical strategies that can foster relational understanding in students, strategies like number talks and purposeful discourse. In short time, it occurred to me that I was not seeing many of these techniques being implemented in my student teaching classroom. Rather, these students (low-income and of color) were receiving a type of instruction not too dissimilar from Kohn's "pedagogy of poverty" (2011). Armed with perhaps an inflated sense of influence and backed by recent research, I immediately began an attempt to implement some of these techniques into my Daily Math Practice and Daily Word Problem lessons. As I wrote in the first paragraph, these attempts exemplify the limitations as well as the possibilities for teaching toward deep, relational understanding within an educational climate that appears to discourage such understanding for particular students.
My grappling with these limitations and possibilities form the response to my inquiry question: what impact did high-stakes testing have on my math planning and instruction, and what are the implications for my future practice? Until this point, I had not directly mentioned high-stakes testing, but I contend that a major influence on the emphasis toward instrumental understanding is the looming spectre of the Pennsylvania System of School Assessment (PSSA). I know from personal conversations that my Classroom Mentor has adjusted her teaching in ways that she laments, but that she feels are necessary for dealing with the reality of this high-stakes test (personal correspondence, 2012; see Appendix, Artifact A). As the year progressed, I found myself adjusting my own teaching to this reality, too. In the first part of this portfolio, I will present the context for this inquiry by describing the PSSA-based pressure in our class. Although this context is not immediately about my own teaching, I firmly believe it is a necessary component to this portfolio. From there, I will move on to a deeper look at how I attempted to find a balance between accommodating the reality of the high-stakes test and implementing some of the techniques learned in my Math Methods course. In the final part, I will look toward the future and consider how my experience as a student teacher this year might inform my future practice.
Continue to Part I: Within the Context of High-Stakes Testing.
(References are cited here.)