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Standards Based Grading in an AP Calculus AB Classroom Taylor Gibson - North Carolina School of Science and Mathematics Taylor Gibson.

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Presentation on theme: "Standards Based Grading in an AP Calculus AB Classroom Taylor Gibson - North Carolina School of Science and Mathematics Taylor Gibson."— Presentation transcript:

1 Standards Based Grading in an AP Calculus AB Classroom Taylor Gibson - North Carolina School of Science and Mathematics Taylor Gibson - North Carolina School of Science and Mathematics

2 Presentation Overview  Overview of Standards Based Grading  What we’re doing at NCSSM  Questions  Overview of Standards Based Grading  What we’re doing at NCSSM  Questions

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 papers  Paper 1: Scores range from 64 to 98  Paper 2: Scores range from 50 to 97, 15% failing, 12% “A” 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

5 A Story: Part II 1913:Starch and Elliot  128 Math Teachers grade Geometry papers  Scores range from 28 to :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

6 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 :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.

7 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) 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.

8 Tenets of Standards Based Grading

9 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  Grades represent only student achievement on learning standards  Percentage based grading and averaging are poor measurement tools to describe student learning

10 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

11 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  Student Behavior  Late work penalties  Cheating  Attendance  Bonus Points  Relative Grading  Zeros for missing assignments

12 Tenets 3&4 of Standards Based Grading  No (or less focus on) summative or omnibus grades  Grades should engage students in the learning process  No (or less focus on) summative or omnibus grades  Grades should engage students in the learning process

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14 Sample Mathematics Report Card (Middle School) Marzano, Robert J, and Tammy Heflebower, Grades That Show What Students Know, Educational Leadership 69-3 (2011)

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16 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  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

17 Standards Based Grading at NCSSM AP Calculus AB

18 The Standards AP Calculus AB

19 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  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

20 First Trimester  Struggled with:  How many standards?  How to word learning objectives?  How to align assessments with these objectives?  Struggled with:  How many standards?  How to word learning objectives?  How to align assessments with these objectives?

21 AP Calculus Curriculum Framework https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap-calculus-curriculum-framework.pdf

22 Our Updated Standards

23 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 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

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. 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. 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.3Calculate 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-level Lim.B.1Analyze functions for intervals of continuity or points of discontinuity LO1.2A Students will know that…

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.

29 Assessing the Standards

30 Proficiency Scale 0: No Evidence of Learning 1: Beginning 2: Developing 3: Proficient 4: Advanced 0: No Evidence of Learning 1: Beginning 2: Developing 3: Proficient 4: Advanced Adapted from Frank Noschese

31 Sample Question #1 Deriv.B.1Use derivatives to analyze properties of a function

32 Sample Question #2 Deriv.B.3Interpret the meaning of a derivative within a problem

33 Reassessment

34  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  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

35 Reporting Grades

36 Reporting the Standards

37 ActiveGrade

38 Converting to a Course Grade C- C: 2.4B: 2A: 1.5 C C: 2.6B: 2.3A: 1.75 C+ C: 2.8B: 2.5A: 2 B- C: 3B: 2.7A: 2.25 B C: 3.2B: 2.9A: 2.5 B+ C: 3.4B: 3.1A: 2.75 A- C: 3.6B: 3.3A: 3 A C: 3.8B: 3.5A: 3.25 A+ C: 3.8B: 3.7A: 3.5

39 Student Reactions

40 Questions


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