The Standards: A Series

This is the second in a series of posts about learning standards.  We recognize we must go beyond the state standards in order to support teaching and learning to the highest possibilities for our PK-12 students in Texas.  We read in the high level alignment indicators of the Visioning Document Implementation Matrix:

Students learning is based on challenging, meaningful content standards that have been articulated, specified, and described PK-12. Learning standards in all content areas extend beyond the state curriculum including such things as: Ÿ

  • clarification/enhancement of the cognitive demand of the standards Ÿ
  • supports for ensuring that students have access to the full content of the discipline Ÿ
  • identification/clustering of “power” standards to ensure depth over breadth Ÿ
  • communicating linkages across disciplines.

The first post in this series mentioned the importance of awareness and regular access to the state standards in order to ground ourselves in the practice of standards-focused or standards-driven instruction.  This post describes the clarification/enhancement of the cognitive demand of the standards.


We may gain insight into the standards by looking through a lens of content, context, and cognitive level.

Content

The content includes the knowledge and skills articulated within the standard.  What are the students expected to know and be able to do?

Context

The context includes the relative circumstances under which the content will be demonstrated.  What specifically is expected of the students in this grade level, within this course?  This may shed light on the development sequence/progression of learning of this course content.

Cognitive Level

The cognitive level is the level of thinking required to meet the standard.  A significant number of educators have utilized Bloom’s Taxonomy to classify learning objectives; however, careful consideration should be afforded to this process as the verb alone may not be sufficient to accurately identify the level of thinking required to demonstrate mastery of the standard.  Another set of criteria to consider when determining the cognitive level of standards is Webb’s Depth of Knowledge.


Example use of Content, Context, and Cognitive Level analysis of a standard:

In grade 5 mathematics,

(3)  Number and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy. The student is expected to:

(B)  multiply with fluency a three-digit number by a two-digit number using the standard algorithm.

Content

The student will know that:

  • the standard algorithm is used to multiply positive rational numbers efficiently and accurately; and
  • multiplication using the standard algorithm is used when finding the total number of objects in equal groups or area of a given space when provided the length and width, for example.

The student will be skilled at:

  • using the standard algorithm to multiply a three-digit number by a two-digit number;
  • apply multiplication with the standard algorithm to solve problems arising in everyday life, society, and the workplace;
  • use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy (including the standard algorithm for multiplication), determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution; and
  • select tools and techniques, including use of the standard algorithm for multiplication to solve problems.

Context

Students are expected to multiply with fluency a three-digit number by a two-digit number using the standard algorithm within given problem situations.

Pre-requisite skills for this standard include using strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. (4.4D)

Following this standard, in grade 6, student is expected to multiply and divide positive rational numbers fluently. (6.3E)

Cognitive Level

The Depth of Knowledge required of this standard, including the context of a problem situation, is Level 2: Working with Skills and Concepts/Basic Reasoning, as long as the given task requires the student to using reasoning to conclude multiplication is the most appropriate strategy to use to solve the problem.

If the student is provided a three-digit number and a two-digit number and instructed to use the standard algorithm to multiply, this is considered Depth of Knowledge Level 1: Recall and Reproduction, as reasoning is not necessary to solve.  The inclusion of estimation (prior to solving) and justification (following solving) would raise the Depth of Knowledge to Level 2.

 

Note: Identifying the Cognitive Level of the standards is the first step, as raising the level of cognitive demand of the “low rigor” is needed in order to prepare our students for the life and work competencies essential to thriving in our global society.


The next post in this series will include supports for ensuring that students have access to the full content of the discipline.

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