Course Syllabus

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Why Calculus?

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty-a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." Bertrand Russell, Mysticism and Logic (1918)

The beauty of calculus is primarily one of ideas. The idea behind the derivative is beautiful, the idea captured by an envelop of tangents is gorgeous, and the relationship between derivatives and integrals is stunning.  

How will you learn Calculus?

  • You will have multiple opportunities to problem pose, interpret, problem solve, communicate your mathematical thinking and self-monitor your progress.
  • You will have multiple opportunities to interpret multiple representations, solve novel problems & compare to model solution pathways, and personalize your notes by summarizing.
  • You will have weekly opportunities to be learning resources for one another and make choices with different challenge levels to clear up misconceptions and extend reasoning.
  • You will have weekly opportunities to interpret evidence and adapt your next action steps.
  • You will have opportunities to seek and embrace brilliant failure.
  • You will have weekly opportunities to goal set and reflect on progress.
  • You will have weekly opportunities to compare your work to success criteria to reflect on past actions and adapt future actions based on progress.
  • You will have at least two weeks to deepen your knowledge and thinking around multiple concepts, procedures and solve complex problems across concept categories between a Practice Final and Final Exam where no new material is introduced.
  • You will demonstrate final mastery at the end of each semester in two different ways (final and oral defense).
  • You will create a personalized action plan that maximizes how you learn Calculus.
  • You will get to apply your knowledge of Calculus toward personalized projects in Project Leo

 

What Calculus will we be learning together?

  • Big Ideas:  Limits, Derivatives, Integrals, and Applied Integrals
  • Topics:  Evaluating Limits, Asymptotes & Continuity, Concept of a Derivative, Rates of Change & Curve Sketching, Derivative Rules, Optimization & Related Rates, Concept of an Integral & The Fundamental Theorem of Calculus, Calculating Integrals & Areas, Differential Equations, Volumes & Rates of Change, Mean Value Theorems & Average Rates of Change (Learning Targets with specific details can be found on Canvas and Project Leo)
  • AP College Board Exam Outline: AP Calculus AB Course and Exam Description, Effective Fall 2020 (collegeboard.org)

 

What Materials do you need to support your learning?

Graphing Calculator:  TI-84-Plus

Standard size Spiral for notes (need to purchase)

Office hours: 10:40-11:35 am on Mondays, after school on Wednesdays, and by appointment 

 

Grading scale  

A

A-

B+

B

B-

C+

C

C-

D+

D

D-

100-93

92-90

89-87

86-83

82-80

79-77

76-73

72-70

69-67

66-63

62-60

(Decimals greater than or equal to .51 are rounded up)

 

Grading System: An interesting synthesis of research on feedback from Guskey (2008), Assessment Reform      Group(2002), Dweck (2001), Black and Wiliam (1998), Butler (1998), and Sadler (1989)

It’s the quality of feedback rather than its existence or absence that determines its power.  Specifically, what makes the difference is the use of descriptive, criterion-based feedback as opposed to numerical scoring or letter grades.  Feedback emphasizing that it’s the learning that’s important leads to greater learning than feedback implying that what is important is looking good or how you compare to others. 

Assessments that communicate where you are in your Calculus learning progression: There are 3 types of assessments that provide you with feedback on (1) where you are in your learning: product (2) how you are learning: process, and (3) what next steps will get you to your learning goal progress. 

Product: communicates current level of mastery 

    • First Semester:  #1-Limit Exam, Sept. 30 (Learning Targets 1A-1F & 2E, #2-Limit & Derivative Exam, Nov. 20 (LT 1A-F, 2A-G, 3A,B), #3-Practice Final Exam, Dec. 6 (LT 1all, 2A-G, 3all, 4A-C), #4-Final Exam, Dec 18 on Limits & Derivatives (same LT as #3 exam).  Second Semester:  #5-Limits & Derivatives, Feb. 10 (LT 1all, 2all, 3all, 4all, 5A-C), #6-Integrals, Derivatives, Limits, March 10 (LT 1all,2all,3all,4all,5all,6A-C, 7A-C), #7- Practice Final Exam on Limits, Derivatives, Integrals, Applied Integrals, April 4 (all LTs 1-10), #8-Final Exam on Limits, Derivatives, Integrals, Applied Integrals (same LT as #8 exam)
    • Each test replaces the previous exam score in the appropriate category within each semester
    • Oral Defense Opportunity at the end of each semester for students who have demonstrated growth over time (progress), but feel the final exam is not a true reflection of current mastery
  • Graded:  Most recent demonstration of mastery is graded, there is no averaging over time. Evidence communicated in Project Leo and Canvas

Process: communicates how you are learning 

    • Pop Quizzes: On topics aligned to Learning Targets within Limits, Derivatives, Integrals, & Applied Integrals.  Student analysis of evidence collected on new and old learning targets. 
    • Not Graded: Criterion referenced scale used that provides feedback on retention & progress in learning new material.  Scale: 
      • No Evidence Yet: N =in progress (note, no evidence does not mean “blank”, means learning is still in progress).  Indicates initial learning and also no change over time
      • Some Evidence: S = can do the problem(s) or reason through problem (s), but not both yet
      • Good Evidence: G = can do & reason, 
      • Su =evidence moving upward from an N
      • S- =evidence moving downward from a G
  • Evidence communicated in Canvas:  criterion indicators are replaced frequently to provide feedback on current level of retention and how learning is progressing/retaining over time.
  • 2 week in-class study time between practice final and final exam: provides cumulative evidence of current level of mastery and feedback for prioritizing topics of study and informs needed adaptations to personalized action plan.

Progress: communicates how much you are gaining from your Calculus learning experiences

  • Personalized Learning Structure: The personalized learning structure we will co-create together emphasizes what you do with the feedback from formative assessments to attain the following outcomes: (1) improve your work on novel tasks, (2) activate yourself as a learning resources for your peers, (3) activate yourself as an owner of your own learning, and (4) lead your learning through mathematical thinking, problem solving, and self-regulation. 
  • Not Graded.  Direct Guidance from Eno during class on what action steps you should take to move your learning forward & how to adapt your personalized learning structure to be more effective in attaining outcomes
  • Evidence is tracked in Project Leo where responses to feedback during class learning activities are analyzed to inform goal setting, prioritizing actions, and adapting your learning structure in response to evidence. Sample actions: Targeted Practice, Self-test questions, Summarizing, and Peer collaboration (Action Plan)

Where does Homework fit?: An interesting finding by Kitsantas, A., Cheema, J., Ware, H. (2011). Mathematics Achievement:  The Role of Homework and Self-Efficacy Beliefs Journal of Advanced Academics, Vol 22, Number 2, pp 310-339:

Third, our findings show that increasing the amount of time spent on mathematics homework does not lead to higher mathematics achievement scores. 

Purpose of homework in Calculus:  An opportunity to independently “self-test” and gather more evidence to inform next steps in action plan=> Personalized Learning Structure

  • Homework and example problems in the textbook and class notes should always be treated as an opportunity to test yourself. 
  • Homework should not be done by looking at example problems in the textbook or in class notes and trying to copy the steps laid out there in order to arrive at the correct answer. 
  • Select two or three problems at a time, treating each problem like a quiz or test question, looking at answers or worked-out solutions only after having made your best attempt to solve the selected set of problems.
  • Before looking at the homework questions or problems, actively read the relevant part of the textbook or any class notes. As you come across an example problem in notes or the book, work the problems without referring to the given solutions. If you get stuck and don’t know the next step, do your very best to power through and arrive at an answer. Then check only the final answer and not the entire solution. If answer is incorrect, reread the text or class notes to investigate why and where you made mistakes. When you arrive at the correct answer, compare your approach to the textbook’s or instructor’s. If the approaches are different, ask yourself whether both approaches are valid. Why or why not? If they are both valid, do you prefer your approach or the alternative approach? Why? This method provides many opportunities for reflection, metacognition, and deep learning. 
  • Not Graded:  The efficacy of homework & effort in class can be seen in powerschool within the Learning Target Categories by the “u” (improvement-up), “-“ (decrease-down), just the letter N, S, G (no change). 
  • Reflections are tracked in Project Leo: Write your questions and summarize your learning, then get answers in class from peers and Eno as well as critique of summary of learning and your application of Calculus to your personalized Projects.

Research that informs my grading system: 

  • Wiliam, Dylan (2014), Formative assessment and contingency in the regulation of learning processes

  • O'Connor, K. (2009). How to grade for learning, K–12 (3rd ed.). Thousand Oaks, CA: Corwin. 

  • Scriffiny, P. L. (2008). Seven reasons for standards-based grading. Educational Leadership, 66(2), 70–74. 

  • Wormeli, R. (2006). Fair isn't always equal. Portland, OR: Stenhouse. 

  • Earl, L. M. (2003). Assessment as learning: Using classroom assessment to maximize student learning. Thousand Oaks, CA: Corwin. 

  • Guskey, T. R., & Bailey, J. M. (2001). Developing grading and reporting systems for student learning. Thousand Oaks, CA: Corwin. 

  • Marzano, R. J. (2000). Transforming classroom grading. Alexandria, VA: ASCD.

I look forward to having a wonderful year with you, and I encourage you to ask questions, seek to fail hard and fast to inform actions needed for success, to seek my coaching the moment you begin to feel behind, and to NEVER doubt your ability to succeed.  HARD WORK and a willingness to seek and embrace brilliant failure will lead to success!  

 

Students can reach me through my cell phone:  310-766-0791 & email: seno@pacificachristian.org

Parents can reach me through Email:  seno@pacificachristian.org

 

We are in this together and together we will succeed

 

Course Summary:

Date Details Due