Standards Based Grading in an
AP Calculus AB Classroom
Taylor Gibson - gibson@ncssm.edu
North Carolina School of Science and Mathematics
Presentation Overview
 Overview of Standards Based Grading
 What we’re doing at NCSSM
 Questions
Standard Based Grading:
An Overview
The Case Against Percentage Grades
A Story: Part I
1912: Starch and Elliot
147 English Teachers grade two English papers
Paper 1: Scores range from 64 to 98
Paper 2: Scores range from 50 to 97, 15% failing, 12% “A”
Starch, D., & Elliott, E. C. (1912). Reliability of the grading of high school work in English.
School Review, 20,442–457
A Story: Part II
1913: Starch and Elliot
128 Math Teachers grade Geometry papers
Scores range from 28 to 95
Starch, D., & Elliott, E. C. (1913). Reliability of the grading of high school work in mathematics.
School Review, 21,254–259
A Story: Part III
2012: Hunter Brimi
73 High School Teachers grade the same student paper
20 hours of training in writing assessment
Scores ranged from 50 to 96
Brimi, H. M. (2011). Reliability of grading high school work in English.
Practical Assessment, Research and Evaluation, 16(17), 1–12.
A Story: Part IV
1918: Johnson and Rugg
Move towards scales with few categories
Excellent, Average, and Poor
Excellent, Good, Average, Poor and Failing (A, B, C, D, F)
Johnson, R. H. (1918). Educational research and statistics: The coefficient marking system.
School and Society, 7(181), 714–716
Rugg, H. O. (1918). Teachers’ marks and the reconstruction of the marking system.
Elementary School Journal, 18(9), 701–719.
Tenets of Standards Based Grading
Tenets 1&2 of Standards Based Grading
Grades represent only student achievement on
learning standards
Percentage based grading and averaging are
poor measurement tools to describe student
learning
Tenets 1&2 of Standards Based Grading
The Goal of Grading
To communicate, to all stakeholders,
student achievement towards a set of
learning goals at a certain point in time
Tenets 1&2 of Standards Based Grading
What Does Not Go into a Grade
 Student Behavior
Late work penalties
Cheating
Attendance
 Bonus Points
 Relative Grading
 Zeros for missing assignments
Tenets 3&4 of Standards Based Grading
No (or less focus on) summative or omnibus grades
Grades should engage students in the learning
process
Sample Mathematics Report Card (Middle School)
Marzano, Robert J, and Tammy Heflebower, Grades That Show What Students Know, Educational Leadership 69-3 (2011)
Tenets 5&6 of Standards Based Grading
A students grade can change on a standard
through reassessment
The most recent evidence of learning counts the
most when determining mastery on a standard
Standards Based Grading at NCSSM
AP Calculus AB
The Standards
AP Calculus AB
First Trimester
Wrote our own standards
Grouped learning objectives into 3 major types:
 C-level: Skills based standards
 B-level: Content specific conceptual understanding
 A-level: Overarching Mathematical Skills
First Trimester
Struggled with:
How many standards?
How to word learning objectives?
How to align assessments with these objectives?
AP Calculus Curriculum Framework
https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap-calculus-curriculum-framework.pdf
Our Updated Standards
Limits
Students will understand that:
 The concept of a limit can be used to understand the behavior of
functions
 Continuity is a key property of functions that is defined using limits
Derivatives
Students will understand that:
 The derivative of a function is defined as the limit of a difference
quotient and can be determined using a variety of strategies.
 A function’s derivative, which is itself a function, can be used to
understand the behavior of the function.
 The derivative has multiple representations and applications
including those that involve instantaneous rates of change.
Integrals and the FTC
Students will understand that:
 Antidifferentiation is the inverse process of differentiation.
 The definite integral of a function over an interval is the limit of a Riemann sum over that
interval and can be calculated using a variety of strategies.
 The Fundamental Theorem of Calculus, which has two distinct formulations, connects
differentiation and integration.
 The definite integral of a function over an interval is a mathematical tool with many
interpretations and applications involving accumulation.
 Antidifferentation is an underlying concept involved in solving separable differential
equations. Solving separable differential equations involves determine a function or
relation given its rate of change.
Derivatives: C-level
Deriv.C.3 Calculate explicit derivatives
LO2.1C
Students will know that…
 Direct application of the definition of the derivative can be used to
find the derivative for selected functions, including polynomial, power,
sine, cosine, exponential, and logarithmic functions.
 Specific rules can be used to calculate derivatives for classes of
functions, including polynomial, rational, power, exponential,
logarithmic, trigonometric, and inverse trigonometric.
 Sums differences products, and quotients of functions can be
differentiated using derivative rules.
 The chain rule provides a way to differentiate composite functions
Limits: B-level
Lim.B.1
Analyze functions for intervals of continuity or points of discontinuity
LO1.2A
Students will know that…
 A function 𝑓 is continuous at 𝑥 = 𝑐 provided that 𝑓 𝑐 exists, lim 𝑓 𝑥
exists, and 𝑓 𝑐 = lim 𝑓 𝑥 .
𝑥→𝑐
𝑥→𝑐
 Polynomial, rational, power, exponential, logarithmic, and trigonometric
functions are continuous at all points in their domains.
 Types of discontinuities include removable discontinuities, jump
discontinuities, and discontinuities due to vertical asymptotes.
Integrals: C-level
Int.C.#
Approximate a definite integral
LO3.2B
Students will know that…
 Definite integrals can be approximated for functions that are
represented graphically, numerically, algebraically, and verbally.
 Definite integrals can be approximated using a left Riemann sum, a
right Riemann sum, a midpoint Riemann sum, or a trapezoidal sum;
approximations can be computed using either uniform or nonuniform
partitions.
Assessing the Standards
Proficiency Scale
0: No Evidence of Learning
1: Beginning
2: Developing
3: Proficient
4: Advanced
Adapted from Frank Noschese
Sample Question #1
Deriv.B.1
Use derivatives to
analyze properties
of a function
Sample Question #2
The number of jobs in North Carolina, in thousands, is
modeled by the function 𝐸 𝑡 , where 𝑡 is the number
of months that have passed in the year 2014.
Interpret the following mathematical statements in
context using correct units.
a) 𝐸 3 = 4373 and 𝐸 ′ 3 = 14.4
b) 𝐸 ′′ 3 = −4
Deriv.B.3
Interpret the meaning of a derivative within a problem
Reassessment
Reassessment
Students may be reassessed on previous content
Teacher or Student Initiated
If student initiated, must demonstrate improvement
before reassessment
Most recent assessment counts 60% of score
Reporting Grades
Reporting the Standards
Reporting the Standards
ActiveGrade
Converting to a Course Grade
C-
C: 2.4 B: 2
A: 1.5
C C: 2.6 B: 2.3
A: 1.75
C+
C: 2.8 B: 2.5
A: 2
B-
C: 3
A: 2.25
B
A: 2.5
B+
C: 3.4 B: 3.1
A: 2.75
A-
C: 3.6 B: 3.3
A: 3
A C: 3.8 B: 3.5
A: 3.25
A+
C: 3.8 B: 3.7
A: 3.5
B: 2.7
C: 3.2 B: 2.9
Student Reactions
Questions