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 Elliot147 English Teachers grade two English papersPaper 1: Scores range from 64 to 98Paper 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 Elliot128 Math Teachers grade Geometry papersScores 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 Brimi73 High School Teachers grade the same student paper20 hours of training in writing assessmentScores 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 RuggMove towards scales with few categoriesExcellent, Average, and PoorExcellent, 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 GradingThe 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 GradingWhat 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 standardsGrouped 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 is continuous at provided that exists, exists, and 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 , where is the number of months that have passed in the year 2014. Interpret the following mathematical statements in context using correct units.

a) and

b)

Deriv.B.3 Interpret the meaning of a derivative within a problem

Reassessment

Reassessment

Students may be reassessed on previous content

Teacher or Student InitiatedIf 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: 2A: 1.5

C C: 2.6 B: 2.3 A: 1.75

C+ C: 2.8 B: 2.5 A: 2

B- C: 3 B: 2.7 A: 2.25B C: 3.2 B: 2.9 A: 2.5

B+ C: 3.4 B: 3.1 A: 2.75

A- C: 3.6 B: 3.3 A: 3A C: 3.8 B: 3.5 A: 3.25

A+ C: 3.8 B: 3.7 A: 3.5

Student Reactions

Questions