[SBG] More, Shorter Tests; Less Textbook

More, Shorter Tests
Before the recent spate of blog posts on SBG, I had already switched partway to something similar. I gave mastery tests on teh most important concepts, along with my regular tests (two chapters at a time). This semester I decided to switch over to mastery tests almost completely (plus a final exam).

This past summer I looked over the official syllabus for our beginning algebra course (at a community college), and decided what I thought was most important.  (The official syllabus seems to just follow the chapters of the texts we use, instead of laying out what's really important.) Then I thought about how it fit together. I think the long lists of standards some algebra classes have to cover are a problem. I wanted something shorter; I wanted to be able to easily describe what we do in the course. I decided that, like a play, the course has two main acts, along with prologue, intermission, and epilogue:

• Prologue. Pre-Algebra Toughies. Fractions, Integers, Distributing, Order of Operations. (Chapter 1 in most texts.)
• Act I. Linear. Solving Equations, Graphing, Systems of Equations. (Chapters 2 to 4 in many texts.)
• Intermission. Exponents and Scientific Notation.
• Act II. Quadratic. Multiplying and Factoring Polynomials. Solving (Quadratic) Equations. Graphing Parabolas. (With a side trip to Roots. Chapters 5, 6, 8 and 9 in our text.)
• Epilogue. Everything else there's time for. Inequalities, Rational Expressions (chapter 7), Proportions. (I think I can have more fun with these when they're frills at the end.)

Then I decided on the mastery tests:

1. Multiplication Facts
2. Pre-Algebra Toughies
3. Solving Equations
4. Graphing Basics
5. Graphing Applications
6. Systems of Equations
7. Scientific Notation
8. Factoring Quadratics (and solving)
9. Solving and Graphing Quadratics

It looked good on paper, but what I found out after I started was that I did want to break it down more. Now I'm thinking of most of the mastery tests as collections of subtests. Students can retake any subtest, and I'm keeping scores for each of those in my gradebook (an Excel spreadsheet). For example, the graphing test has 3 parts: Equations to Graphs, Points to Equations, and Visual (estimate the slope of a line without identifying points). The first two parts each have two problems with two or three parts. This is the longest test I've given so far. The only tests that aren't broken into subtests are Multiplication Facts and Graphing Applications (identify rate of change and y-intercept with units, and explain their meaning in a sentence).

Many of my students say they aren't able to come to my office hours, so I'm ending class twenty minutes early each Thursday to make time for retests. I make a new version of each test each week. I think next year I'll limit retests to two or three days a week so there's less time between the first person seeing a test and the last person taking it (my attempt to limit the cheating). If you'd like to see my tests, let me know. If it's one or two people I can email you. If it's lots, I can post them.

On the graphing test, I made up problems for one person who had gotten everything but y-intercept questions right. I gave her an equation in slope-intercept form, an equation in standard form, and a problem with two points. In all 3 she just had to tell me the y-intercept. Otherwise, people just take the standard retest.

I used to spend a lot of time figuring out the partial credit. Now I don't give much partial credit. Small mistakes lose some points. Bigger mistakes just make the problem wrong. The time I've gained in grading I spend making new versions of the tests. I also like that we seldom use up a whole class period for testing.

I don't really have a sense yet of whether students are doing better with this system. I think there are students who would have had to drop who are sticking with it. That seems to be the biggest improvement.


Less Textbook
The required textbook costs about $140. It's the 5th edition, and there are very minor changes from the 4th edition. On my syllabus I told students they could get the required book, or they could get any Beginning Algebra textbook. Few opted to get a book by a different author, and I realized I like having them all getting their homework from basically the same book. I have sheets with suggested homework problems for both 4th and 5th editions of our text. It turns out, there are plenty of used copies of the 4th edition, for 3 or 4 dollars each! So next semester I'm going to require our official text, 4th or 5th edition. (This semester there were a bunch of people who never got a text, and I eventually bought 8 copies of the 4th edition and sold them to students. One of them said he felt like he was at a chop shop.)

I like them having the book for the homework. It's easier to remind them what they ought to do. (And students in a class like this need some help getting themselves on track.) But I'm having fun avoiding the book in my decisions about what to do with our classtime. After 20 years of teaching this course, I would have thought I knew it pretty well. But it was only this term, because of avoiding using the book, that I noticed that I don't like the organization of the chapter on polynomials.

• 5.1 Exponents
• 5.2 Adding and Subtracting Polynomials (does not need a section, I knew that already)
• 5.3 Multiplying Polynomials
• 5.4 Special Factors (using FOIL, and multiplying (a+b)(a-b)...)
• 5.5 Negative Exponents and Scientific Notation (should be two sections)
• 5.6 Dividing Polynomials (I've always skipped dividing by a binomial - they aren't ready for it, and dividing by a monomial is like work we've done earlier, so it's quick)

I think the negative exponents belong after 5.1, and scientific notation can easily follow that. The adding, subtracting, and dividing are just footnotes for the next main topic, which is multiplying polynomials. I keep reminding them that we're doing this in preparation for factoring, which will help us solve problems having to do with gravity (for example).

I don't know if this is helpful for anyone else, but I think I'll be happy later that I wrote this now. After I've gotten used to this new system, I'll start trying to do something about video lectures, so we can invert the class. (Lecture as homework, problem-solving in class.) That might take me another year...