writing prompts for calculus -...
TRANSCRIPT
Writing Prompts for Calculus
Murphy Waggoner Simpson College Indianola, Iowa
Why write in Calculus? The writing must help the students learn
the mathematics Make strong connections between the
verbal, analytical, graphical and numerical representations of calculus
Student writing is the best formative assessment of teaching and learning
Students become better verbal communicators
How did I plan to use writing? Assignments once or twice a week Hand-written responses,
approximately one page Group writing in class Essay questions as part of the exam Use in Calc I, II and III
Barriers and solutions Mark papers quickly and effectively
Solution: Develop general rubric Access to a large number of prompts
Solution: Gather and write 750 prompts
Teach how to write mathematics Solution: Early, frequent and effective feedback
Value of a General Rubric
Do not need to invent a new rubric for each essay
Students understand expectations when they are consistent throughout the semester
Writing Rubric - 4 points Is the response well written, clear? Is the mathematics used and
represented correctly? Does the response address the
question? Supporting data included (graphs,
diagrams, tables, examples, etc.)?
Question Sources/Inspirations
Author’s notes Margin notes Student misconceptions Common and not-so-common
mistakes in student work Classroom questions
Types of questions Concept Maps: Create a concept
map of the convergence/divergence tests we know that will help you understand when and in what order to apply these tests.
Types of questions Review another’s work: A friend
of yours has done this work. Gently and kindly help your friend understand the mistake that was made and explain how to do the problem correctly.
0 0
sin 3 sin 3 sin 3lim lim 0.07062 2 2x x
x xx x→ →
= = ≈
Types of questions
Look-alike Integrals: Compare and contrast the evaluation of the integrals and . 21
dx
x−∫21
x dx
x−∫
Types of questions Explain a Procedure True or False with Justification Compare and Contrast Explain to a Friend Form Evaluation Use Tables to Validate Analysis Annotate an Example Write Review Questions
Student Comments A typical response: love-hate
relationship “Writing assignments really stink sometimes but were really helpful in forcing me to really understand what we were working on.”
Student Comments 10% of calculus students chose
writing as most effective part of the course: “The writing assignments were the most helpful part of the class...because they gave you practice translating math formulas/ideas into words.”
The future I will continue to use writing in all
my classes with more group writing. Please, use these questions but note
the authors, especially when the question came from a text.
Please, share new questions with me (but only if you want me to share it with the world).
Thank you. simpson.edu/author/mwaggoner/ [email protected]
Early and Regular Feedback A brief written guideline with short
examples Worked, graded examples on the board Copies of good and bad responses, graded Specific comments on papers The writing helped me understand the
concepts.
Types of questions Procedures: You have just come
across an integral involving rational functions. Make a list of the techniques you know for doing these types of integrals and explain how to decide which approach to use.
True or false with justification: Always true, sometimes true or always false: If {an} is bounded, then {an} converges.
Types of questions Compare and contrast: Compare and
contrast the derivatives of e x sin x, e x sin x and x e sin x.
Explain to a friend: A friend of yours missed the day we talked about related rates problems and wants to know what we did so in order to do the homework. Rewrite and improve Example 1 from the text to help your friend understand.
Types of questions Form Evaluation: We have seen 3 ways to
represent a curve in the plane: y = f(x), r = r(θ), and {x = x(t), y = y(t)}. What are the advantages and disadvantages of each representation? List an application for which you would prefer each representation and explain your choices.
Checking Numerically: Consider this limit: . Using a table, investigate whether this work is correct.
1lim ln 0 01x
xxx→∞
− = ∞ ⋅ = +
Types of questions • Investigations: Investigate
the validity of this statement: If x is close to zero, then so is x–3.
Types of questions Create Review Questions: Write
up to 5 distinct questions from the material in this chapter that might be on an exam using the data (1, 2) and (–3, 5).
Types of questions Annotated Examples: Give an
annotated example to show how to use L’Hospital’s Rule.
Writing Assignment Assessment 5-point Likert Scale
1 = strongly disagree 5 = strongly agree
Intermediate Algebra (1 question/class day)
Calculus I (1 question/every 2nd class day) Calculus III (1 question/every 4th class
day)
Survey Statements I understood the purpose of the writing. The writing was more difficult than the
homework. I put an honest effort into the writing. The number of assignments was
appropriate.
Writing Assignment Assessment
1
2
3
4
5
UnderstandConcepts
Purpose More Difficult Honest Effort AppropriateNumber
Algebra
Calc I
Calc III
Student Comments Writing assignments should be worth
more points. There should be fewer writing
assignments. Writing...on the exam pressured the
students into finishing the exam at a faster pace. Shorten the exams or eliminate the writing on the exam.