Teaching Problems: Teaching the Nature of Accomplishment

This is one of a series of posts on Teaching Problems and the Problems of Teaching, by Magdalene Lampert. In each chapter, Lampert examines the one challenge of teaching in the context of her fifth grade math classroom, and I try to learn some things from her.

Students cannot be said to make progress in learning unless they acquire some knowledge or a degree of skill that they did not already have (329).

This chapter of Lampert’s book focuses on the challenge of ascertaining what students have learned, and communicating that back to students in a way that is meaningful and productive for future learning. in short, assessment and feedback. I’d like to draw a contrast here.

My thinking about the goals of assessment before reading this chapter were informed by a number of sources, in particular this post by Michael. I divided assessment into three goals:

  • Evaluation. Assessment tells various stakeholders what students know, and what they do not know.
  • Feedback. Assessment provides feedback that moves learning forward by creating opportunities for more student thinking.
  • Incentives. Assessment provides incentives for certain behaviors, and disincentives for others.

Lampert uses a different framework. She presents four problems in assessment:

  • Demonstrating knowledge and skill. Students show progress by demonstrating what they know.
  • Multiple dimensions of competence. Learning does not consists of giant leaps, but fits and starts that are multifaceted and complex.
  • Different starting points. Every student does not start in the same place, and these differences should be honored and valued.
  • Public progress. Differences in learning lead to differences in status in the classroom, and this status affects future learning.

It seems like an interesting exercise to evaluate my current assessment system with respect to each set of criteria. I wrote about my current system of standards-based grading here. In short — 75% skills assessments, which isolate individual standards. Students can retake for full credit, with review assessments as the course goes on. 20% synthesis tasks that students have a week to work on and involve multiple standards and sustained reasoning.

My Original Approach
I like the way my system evaluates students, and I think it provides actionable information about what students know and don’t know and what they might do about it. I think it falls short in giving feedback that regularly provides students an opportunity to do more mathematical thinking — retakes are optional, and often pretty far removed (read: right before grades are due). I do like the incentives, as they line up with what I care about, and avoid the negative consequences of trying to incentivize everyday classwork.

Lampert’s Approach
I like the way my system allows students to demonstrate knowledge and skill and creates opportunities for students at different starting points. I need to think more about how it frames progress publicly, I’m not sure I’m addressing that area in a positive or negative way. I think I have a great deal of room to grow in multiple dimensions of competence — standards-based grading tends to place a great deal of value on performing individual skills in isolation, which does not value this area.

Both of these frameworks point to overhauling my synthesis tasks, with an emphasis on multiple dimensions of competence and giving useful feedback that moves learning forward. I’m not sure what this looks like, but it provides useful food for thought.

More importantly, I think that the challenges of building an assessment system that works for all students, and works for me, is an ongoing challenge, and I like adding a new tool to evaluate where I can improve and find new areas for growth.

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