The following are my thoughts on the article, Selecting and Creating Mathematical Tasks: From Research to Practice (see below).
Although this article was written fifteen years ago, its ideas are very relevant to math education today. There is a very close correlation between the Levels of Demand described by Smith and Stein and Webb's Depth of Knowledge, which is widely being used in schools today. Moving from low- to high-level in Levels of Demand/Webb's Depth of Knowledge, we have: memorization/recall, procedures without connections/skill concept, procedures with connections/strategic thinking, and doing mathematics/extended thinking. It is interesting to read that teachers had some significant discrepancies in their classification of certain mathematical tasks. Often times teachers feel that tasks are more demanding than they actually are. Developing accurate labels for various tasks is vitally important in the preparation of our students for standardized tests (i.e. SBAC). Additionally, we must ensure that we are challenging students with higher-level tasks, as Smith and Stein point out that through these tasks students have higher engagement resulting in higher levels of learning.
In my classroom, here are a couple examples of different levels of demand:
1) Higher-Demand: Geometric Proof Group Activity (There is not a set procedure as to proving any given statement. Students must have a good understanding of definitions, theorems, etc. and be able to apply them. The unpredictable nature causes anxiety in some students.)
2) Lower-Demand: Practice with Area and Perimeter (Students must practice determining area, perimeter, side length, etc of regular geometric objects with some given information. This is very procedural and students can memorize the formulas in order to solve the problems.)
Source:
Smith, M. S., & Stein, M. K. (1998, February). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3, 344-350.
Although this article was written fifteen years ago, its ideas are very relevant to math education today. There is a very close correlation between the Levels of Demand described by Smith and Stein and Webb's Depth of Knowledge, which is widely being used in schools today. Moving from low- to high-level in Levels of Demand/Webb's Depth of Knowledge, we have: memorization/recall, procedures without connections/skill concept, procedures with connections/strategic thinking, and doing mathematics/extended thinking. It is interesting to read that teachers had some significant discrepancies in their classification of certain mathematical tasks. Often times teachers feel that tasks are more demanding than they actually are. Developing accurate labels for various tasks is vitally important in the preparation of our students for standardized tests (i.e. SBAC). Additionally, we must ensure that we are challenging students with higher-level tasks, as Smith and Stein point out that through these tasks students have higher engagement resulting in higher levels of learning.
In my classroom, here are a couple examples of different levels of demand:
1) Higher-Demand: Geometric Proof Group Activity (There is not a set procedure as to proving any given statement. Students must have a good understanding of definitions, theorems, etc. and be able to apply them. The unpredictable nature causes anxiety in some students.)
2) Lower-Demand: Practice with Area and Perimeter (Students must practice determining area, perimeter, side length, etc of regular geometric objects with some given information. This is very procedural and students can memorize the formulas in order to solve the problems.)
Source:
Smith, M. S., & Stein, M. K. (1998, February). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3, 344-350.
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