Projector: Prove differentiation formulas for \(e^x\), \(e^{kx}\), \(b^x\), \(\ln x\), and \(\log_b x\)

Tables and boards: Differentiate some functions

// After class

Complete the Homework for Section 5.3, be ready for the 5.3 Mastery Quiz on Monday.

Start preparing for the next Retake opportunity, which will be in one week. Choose whichever section you want to try again to master, and start studying!

Mon Feb 5 – 5.2 Exp/Log Limits

// During class

Mastery Quiz

Hand back Retake quizzes (great job!!)

Take 5.1 Mastery Quiz

Section 5.2

Table discussion – basic exp/log limits

pp.353-355 – High-level overview of the reading

Projector and WolframAlpha – Definition of \(e\)

Projector and WolframAlpha – Limit with substitution

Group work at boards – Calculate various limits

// After class

Complete the Homework for Section 5.2, be ready for the 5.2 Mastery Quiz on Wednesday.

Wed Jan 31 – 5.1 Exp & Log Functions

// During class

Mastery Quiz

Hand back 4.4 Mastery Quiz

At the same time, select a Mastery Quiz Retake (keep it face down please)

Please be sure to put your old 4.4 Mastery Quiz away in your bag before starting the new quiz

Section 5.1

p.342, 343 – Definition of exponential function, natural exponential function

Table discussion – growth/decay constants and graphs

p.343, 344 – Exponential functions are invertible, and their inverses are logarithmic functions

Projector page – Algebraic rules for exponents and logarithms

Group problems at tables and whiteboards

// After class

Complete the homework for Section 5.1, and make use of study groups, the SMLC, and Slack to help you master the material and be ready for the 5.1 Mastery Quiz on Monday.

Mon Jan 29 – Questions Day

// During class

Still needs to complete Policy Check: Kashetta, Welsh

Still not on Slack: Carew, Cro, Crow, Hakki, LaTourette, Marshall, Mattson, McIntosh, Wilkerson

Mastery Quiz

Hand back 4.3 Mastery Quizzes

Take 4.4 Mastery Quiz

Questions?

What do you want to discuss from Sections 4.2, 4.3, 4.4?

Class discussion, table problems, board work depending on questions asked

// After class

On Wednesday you’ll have a Retake opportunity, so get prepared! You can choose to be re-evaluated for mastery on any one of the previous sections (4.2, 4.3, 4.4, or even the 231 Review).

Reminders/advice: The Retakes are randomly generated multiple-choice questions based on the homework assignments for each section, so be sure to work for mastery on the entire assignment, not just on a previous quiz. Your grade for the semester will be determined by your highest demonstrated mastery on each of the 18 Mastery Quizzes. See the Homework Calendar, Mastery Quizzes FAQ, and Grades FAQ for more information.

Wed Jan 24 – 4.4 Rational Functions

// During class

Still needs to complete Policy Check: Crow, Roseberry. Last reminder!

Mastery Quiz

Hand back 4.2 Mastery Quizzes

Take 4.3 Mastery Quiz

Section 4.4

Reading/discussion

Big graphing problem on the boards

// After class

We won’t be covering the slant/curve asymptotes part of this section, so you can ignore anything in the reading or exercises that asks about those types of asymptotes.

Don’t forget your resources: working with other students, asking questions in Slack, and visiting the SMLC.

Remember also to use the long break between Wednesday and Monday to start preparing for your next chosen Retake quiz; you will have a Retake opportunity next week on Wednesday.

Mon Jan 22 – 4.3 Polynomial Functions

// During class

Still need to complete Policy Check: Crow, Curran, Hakki, Holford, Long, Marshall, Roseberry, Seiber, Yasa, Young. This will likely be your last reminder, so please take care of this today. Non-Mastery-Quiz assignments such as this one can help push borderline grades.

Mastery Quiz

Take 4.2 Mastery Quiz

Hand back 231 Review Mastery Quizzes

Reminder of Retake opportunities

Section 4.3

Reading/discussion

Some group problems

// After class

Synthetic division is used in Example 3 of the 4.3 reading, and you’ll need to know how to use it for some of the homework problems. If you don’t know or can’t remember how to use synthetic division, see Section 4.1 or watch this Khan Academy video: Synthetic Division.

Pro tip: You’ll have a much easier time with the homework if you first work through all the examples in the reading and make sure that you can answer the “Test Your Understanding” questions at the end of the reading.

If you didn’t do as well as you wanted on the 231 Review Mastery Quiz and/or the 4.2 Mastery Quiz, then schedule some time this week to master that material. Don’t wait until just before the retake opportunity next week.

The homework for Section 4.3 is listed in the Homework Calendar. This is the hard part of the week: you only have a couple of days to master this material and be ready for the 4.3 Mastery Quiz on Wednesday.

Don’t forget your resources: working with other students, asking questions in Slack, and visiting the SMLC.

Wed Jan 17 – 4.2 Power Functions

// During class

Anyone new? Talk to me after class please…

Mastery Quiz

Choose any retake (231 Review quiz)

Hand back “practice” Mastery Quiz (not graded b/c calculators were used)

Q&A about Mastery Quizzes and “why now” – MW, code, readalong

Complete the Policy Check with 100% mastery right away, if you have not done so already

Over the next five days, complete the Section 4.2 Homework (see the Homework Calendar), work with others, ask questions in Slack, and/or visit the SMLC as much as needed to be ready for Monday’s 4.2 Mastery Quiz.

Questions and discussion about other Math 231 review problems

// After class

Next Monday is Martin Luther King, Jr. day and there are no classes at JMU.

Next Wednesday you will have a Retake opportunity for the Mastery Quiz you just took. Please remember that the Retake is based on the entire review assignment from the homework, not on the three questions that happened to be on today’s quiz. You have one week to master the material so that you can raise your performance on this Mastery Quiz.

When we return on Wednesday the class will pick up pace significantly, typically covering one section of material a day, and with new Mastery Quizzes each class period. You won’t have a lot of time to review 231 material after this week, and mastery of that material is really important for your success in this class, so please use your time wisely 🙂

Mon Jan 8 – Growth and Mastery

Hello and welcome to MATH 232. Each day of class I’ll post a blog entry like this one on the class Timeline, to outline what we’ll be doing during class, and what you should remember to do after class. Today’s is a little long, because we have a lot to discuss…

// During Class

Roll call and names/nametags

Let’s talk about MATH 231. How did it go? What was hard/easy about it? How are you feeling about your mastery of the masterial from that course? How do you feel about your ability to do mathematics in general, and how have you dealt with failures and setbacks in math classes in the past?

Who has heard about “Growth Mindset” already? What do you know? We will watch this 10-minute video together as a class:

Take a few minutes to talk to the people at your table and reflect on the video you just watched. Did anything in the video have relevance to you personally? Do you think you currently have a fixed mindset or a growth mindset regarding your abilities in matheamatics? Is there anything from this video that you think you could use to help you succeed in MATH 232?

To encourage a positive growth mindset in this math class, we’re going to try something that is new to me, and possibly new to you as well: Mastery-Based Grading. Basically, we’re going to move away from the typical calculus-class model in which there are a few high-stakes, do-or-die exams. We are going to try a new system where there is a continuous stream of lower-stakes Mastery Quiz evaluations, each of which has opportunities for being taken over again and improved upon. Let’s discuss what I’m planning for these Mastery Quizzes (see the “What to Expect” post below), what you all think about it, and what you think the pitfalls, problems, and benefits might be.

Finally, your success in MATH 232 will be highly dependent on your ability to recall and build from the material you learned in MATH 231. In particular, if you earned less than a “C-” in MATH 232 then I strenuously encourage you to retake MATH 231 instead of taking this course. To help you brush up your MATH 231 skills, your first homework assignment is a set of review problems, and Wednesday’s Mastery Quiz will be a three-question multiple choice question based on those review problems.

// After Class

Sign up for the class Slack group and leave a post saying hello and introducing yourself.

Make sure you have the textbook. If for some reason you do not, then find someone who is willing to share with you for a while by asking around or posting in the Slack group.

Take the online 232 Policy Check survey, and retake it as necessary until you have acheived 100% mastery on all questions. You may freely look up anything you like on the class website during the survey.

According to the Homework Calendar, your homework after this class is to complete the 231 Review Problems. Take this assignment seriously; in order to succeed in MATH 232 you will have to have mastered this MATH 231 material.

There will be a 231 Review Mastery Quiz at the start of class on Wednesday. Get ready for this quiz by working on the problems in the review assignment until you feel you have mastery of the basic skills and concepts from MATH 231.

What to expect in this class

All sections of MATH 232 use the same textbook, but each instructor implements their own style and philosophy of teaching. Here’s what it will be like day-to-day in my sections of MATH 232 this semester:

// During class

2:30-2:45: Distribute and take Mastery Quizzes or Retakes, according to the schedule on the Homework Calendar;

2:45-3:00: Short lecture/presentation on the reading for the day’s new section in the textbook;

3:00-3:45: Students work in groups at the whiteboards on various problems and activities.

// After class

Read the section and complete as many problems from the current homework assignment as needed to acheive mastery of the material.