Rigor: Illustrations of Conceptual Understanding, Fluency, and Application

1
Rigor Illustrations of Conceptual Understanding,
Fluency, and Application

• Here rigor does not mean hard problems.
• Its a balance of three fundamental components
  that result in deep mathematical understanding.
• There must be variety in what students are asked
  to produce.

2
Frequently Asked Questions

• How can we assess fluency other than giving a
  timed test?
• Is it really possible to assess conceptual
  understanding? What does it look like?
• Arent the Common Core State Standards for Math
  all about application and meaningful tasks?

3
Rigor

• Conceptual Understanding
• 3.NF.1 Understand a fraction 1/b as the
  quantity formed by 1 part when a whole is
  partitioned into b equal parts understand a
  fraction a/b as the quantity formed by a parts of
  size 1/b.
• Sample Video
• Procedural Skill and Fluency
• 5.NBT.5 Fluently multiply multi-digit whole
  numbers using the standard algorithm.
• Sample Video
• Application
• 7.NS.3 Solve real-world and mathematical
  problems involving the four operations with
  rational numbers.
• Sample Video 1 Sample Video 2

4
Sample Problems

• Read through a few problems from each aspect of
  rigor.
• What does it look like when we are asking
  students to work on procedural skill and fluency,
  conceptual understanding, or application?
• Are we seeing a balance of these three
  fundamental components in our EnvisionMATH
  program?

5
Task

• Use the Tri-State Quality Review Rubric to
  evaluate an upcoming topic from the EnvisionMATH
  program.
• Closely examine the unit through the lens of
  each criterion in each of the four dimensions
• If clear and substantial evidence is found,
  place a check by the criterion on the rubric if
  not, use the comments column to provide input on
  specific improvements
• Examine the pattern of checks in the column to
  determine which of the descriptors (3-2-1-0) best
  characterizes the current alignment of the unit
• Use the criteria to make observations and
  recommendations about this unit