Presentation on theme: "Standards Based Grading in an AP Calculus AB Classroom"— Presentation transcript:
1 Standards Based Grading in an AP Calculus AB Classroom Taylor Gibson -North Carolina School of Science and Mathematics
2 Presentation Overview Overview of Standards Based GradingWhat we’re doing at NCSSMQuestions
3 Standard Based Grading: An Overview The Case Against Percentage Grades
4 A Story: Part I 1912: Starch and Elliot 147 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
5 A Story: Part II 1913: Starch and Elliot 128 Math Teachers grade Geometry papersScores range from 28 to 95Starch, D., & Elliott, E. C. (1913). Reliability of the grading of high school work in mathematics. School Review, 21,254–259
6 A Story: Part III 2012: Hunter Brimi 73 High School Teachers grade the same student paper20 hours of training in writing assessmentScores ranged from 50 to 96Brimi, H. M. (2011). Reliability of grading high school work in English. Practical Assessment, Research and Evaluation, 16(17), 1–12.
7 A Story: Part IV 1918: Johnson and Rugg Move 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), 714–716Rugg, H. O. (1918). Teachers’ marks and the reconstruction of the marking system. Elementary School Journal, 18(9), 701–719.
19 First Trimester Wrote our own standards Grouped learning objectives into 3 major types:C-level: Skills based standardsB-level: Content specific conceptual understandingA-level: Overarching Mathematical Skills
20 First Trimester Struggled with: How many standards? How to word learning objectives?How to align assessments with these objectives?
23 Limits Students will understand that: The concept of a limit can be used to understand the behavior of functionsContinuity is a key property of functions that is defined using limits
24 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.
25 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.
26 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
27 Limits: B-levelLim.B.1Analyze functions for intervals of continuity or points of discontinuityLO1.2AStudents will know that…A function 𝑓 is continuous at 𝑥=𝑐 provided that 𝑓 𝑐 exists, lim 𝑥→𝑐 𝑓 𝑥 exists, and 𝑓 𝑐 = lim 𝑥→𝑐 𝑓 𝑥 .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.
28 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.
30 Proficiency Scale0: No Evidence of Learning 1: Beginning 2: Developing 3: Proficient 4: AdvancedAdapted from Frank Noschese
31 Sample Question #1 Deriv.B.1 Use derivatives to analyze properties of a function
32 Sample Question #2The 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 Interpret the following mathematical statements in context using correct units.𝐸 3 =4373 and 𝐸 ′ 3 =14.4𝐸 ′′ 3 =−4Deriv.B.3Interpret the meaning of a derivative within a problem
34 Reassessment Students may be reassessed on previous content Teacher or Student InitiatedIf student initiated, must demonstrate improvement before reassessmentMost recent assessment counts 60% of score