April 2014
High School Mathematics Newsletter
DEPTH OF KNOWLEDGE
Common Core State Standards in Mathematics (CCSSM) and the Partnership for Assessment of Readiness for College
and Careers (PARCC) require deeper levels of understanding than the Arkansas State Frameworks. According to
Herman and Linn (2013), the PARCC assessment will “assess every student on a full range of Depth of Knowledge or
cognitive complexity to encourage schools to provide opportunities for deeper learning for all students” (p. 6). Norman
Webb’s Depth of Knowledge (DOK) is a key instrument in analyzing the cognitive demand intended by the CCSSM and
PARCC assessments. Webb identified four DOK levels
Level
Summary
Description
DOK 1
Recall &
Reproduction
working with facts, terms, calculations,
properties, and formulas
summarize, estimate, organize, classify, extend,
and make inference
DOK 2
Skills & Concepts
DOK 3
Strategic Thinking
& Reasoning
analyze, evaluate, solve real-world problems
DOK 4
Extended Thinking
investigations to solve real-world problems,
produce product
When standards and items are assigned a DOK level, the level should reflect the complexity of cognitive processes
demanded by the standard or item, rather than the difficulty. The DOK level should describe the depth of
understanding required and level of work students are required to perform. In a recent RAND study of state released
items from 17 different states, the majority of the selected response items were at or below DOK 2 with the majority
at DOK 1. The released open response items had about 88% at DOK 1 and DOK 2 and 11% at DOK 3 (Herman and Linn,
2013, p. 17).
The study indicated that state released items were insufficient in meeting the cognitive demands students will need
for college and career success. PARCC has indicated that the items and tasks on the assessments will be at or above
DOK 2. DOK 3 and DOK 4 will be assessed by analyzing information in a variety of forms and synthesizing it into new
forms.
Students need to be prepared for the future rigor required by CCSSM and PARCC. Teachers need to assist students in
1) becoming independent critical thinkers in problem solving,
2) communicating their reasoning process and possible solution(s), and
3) collaborating with others during the analysis and evaluation process to determine validity of their solution(s).
In preparing for what to do differently next year, look for materials that promote real-life application skills of reasoning,
inquiry, and evaluation. As teachers make a shift to instruction focused on deeper knowledge and real-life application,
students will begin to perform at a higher level.
Herman, J.L. & Linn, R.L. (2013). On the road to assessing deeper learning: The status of Smarter Balanced and PARCC assessment consortia.
(CRESST Report 823). Los Angeles, CA: University of California, National Center for Research on Evaluation, Standards, and Student Testing
(CRESST).
April 2014
High School Mathematics Newsletter
MASTERING THE COMMON CORE STATE STANDARDS AND MATHEMATICAL PRACTICES
Mastering the Common Core State Standards in Mathematics (CCSSM) and the Standards for Mathematical Practice
(MP) will not happen in a single year. After a year of implementation, many have struggled with the rigor of the new
standards and assessment items. Many teachers felt overwhelmed preparing students for the Arkansas Benchmark
and EOC exams. Some teachers continued to use the same lessons that were stored in the file cabinets and hoped
to include some glimpse of CCSSM. Some tried new textbooks but found that they were inadequate for the depth of
learning required. After reflecting on how they taught CCSSM this year, teachers feel the need to improve instruction
in 2014-15.
Next year CCSSM and MP will be the primary focus. Students
will need to be given problems that require them to use the
Standards for Mathematical Practices and allow discourse and
risk-taking in the classroom. Teachers will need to focus on
modifying 1) instructional strategies and materials that connect
content, practices, conceptual understanding and application,
2) classroom assessments that measure mathematical
practices, concepts, and computational skills, and 3) feedback
that focuses on mathematical reasoning and modeling, and not
just the correct answer.
Instructional Strategies
and Materials
Classroom Assessments
Feedback
There are many resources available to help with making these
changes. Consider reading some of these books in preparation for next year:

5 Practices for Orchestrating Productive Mathematics Discussions
Smith, Margaret Schwan., and Mary Kay. Stein. 5 Practices for Orchestrating Productive Mathematics Discussions.
Reston, VA: National Council of Teachers of Mathematics, 2011. Print.

Implementing the Common Core State Standards through Mathematical Problem Solving
Gurl, Theresa J., Alice F. Artzt, Alan Sultan, and Frances R. Curcio. Implementing the Common Core State Standards
through Mathematical Problem Solving: High School. Reston, VA: National Council of Teachers of Mathematics, 2012.
Print.

Focus in High School Mathematics: Fostering Reasoning and Sense Making for All Students
Strutchens, Marilyn E., and Judith Reed. Quander. Focus in High School Mathematics: Fostering Reasoning and Sense
Making for All Students. Reston, VA: National Council of Teachers of Mathematics, 2011. Print.

More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction
Small, Marian, and Amy Lin. More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction.
New York: Teachers College, 2010. Print.
Previous High School Newsletters
may be viewed in the Secondary Math Curriculum section of the TLI Portal.