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/ Murphy.waggoner@simpson.edu

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.