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Math 20: welcome • calendar • responsibilities • resources • unit 1 • unit 2 • unit 3 • unit 4 Other: Math 25 packet • for Math 25 instructors • factoring • my next textbook? |
Most of Math 25's pedagogy involves building and managing student morale.
The most delicate time is at the term's start. During the first two weeks you should emphasize how the class builds on Math 20 sufficiently to scare away unprepared students but without alienating students who are prepared without having taken Math 20 at LCC. Make a big deal about not falling behind, which is an especially sticky trap for students with math anxiety.
Student appreciate an accessible instructor. Promptly replying to e-mail and phone messages is really appreciated. A "welcome" e-mail before the term begins is also appreciated.
I use the Starboard software to record all of my lecture notes, and post them online. Many students find this helpful. During tests I allow printed copies of my lecture notes as valid open-book reference material, the same as I allow students to reference what I write when I help them during office hours. (Supposedly the Math 20 content includes being taught how to take math notes, but this is almost never evident and there simply is not time during Math 25 to teach this important topic. This results in a tricky balance: a Math 25 instructor should stress the importance of organized and complete notes while realizing this may be an impossible and potentially demoralizing goal for many students.)
I have found most LCC students appreciate being recognized and known by name. I sort my class list by first name, and during class call on students by first name. When a student who normally has regular attendance is absent twice consecutively without communicating why, I often use e-mail or phone to "check in" and ask if they need help understanding the online class notes, arranging a classmate study partner if needed to catch up, etc.
Be prepared to spend a surprising amount of time teaching "calculator wrangling". Typically half the students have never used their exponent key (and do not know how it differs from the Scientific Notation key), and almost none have used the previous-answer key or memory keys. They also will need explanation about how parenthesis are all the same on the calculator even if an outer pair is often written as brackets when typed or in larger font when written by hand.
Also be prepared to teach students how to "decipher" word problems, identifying which values are meaningful and how they pertain to the problem, as opposed to extraneous information.
The latter half of the Activities have no official example problems. But they do contain many unofficial example problems! Pick some of these to do (with changed numbers) on the board before group work begins. How many depends upon your students: their math background and how well they have learned to work in groups during the first half of the class.
Consider multiple-choice problems for tests, except for the "challenge problems". The math topics are simple enough that you can easily create incorrect answers corresponding to the common student mistakes. Students with low confidence appreciate multiple-choice problems even though these are often actually more difficult because the common incorrect answers look so inviting.
Students in Math 25 are much more distressed by test taking than students in higher math classes. I always offer to show students my answer key after they have turned in their test. (Usually I post it outside the classroom door fifteen minutes before the test time is complete, to minimize noise inside the classroom without conflicting with earlier restroom trips.)
I devote six class days to the two midterms! Each midterm has not only a review day before it, but a "corrections day" after it. Students receive half-credit for problems they fix. These "correction days" are often the best learning experiences for students, as well as being foundational for building morale. When necessary I combine review days with portfolio presentation or Activity 13 rather than schedule anything else on the "correction days".
Moodle is a mixed blessing. Students like having infinite attempts at homework problems with immediate feedback, which is a genuine aid to learning. But Moodle also insists on numbering questions a second time incorrectly, and it is unavoidable that some multiple-part questions must be worded differently in Moodle than in the homework. If the class size is 15 or less I allow students the option of turning in homework normally rather than by Moodle, but then they must wait for feedback and are not allowed any chances to fix their work for credit.
Math 25 is really a problem solving class thinly disguised as a math class. Devote as much class time as possible to group work (this becomes easier during the latter activities, which use less time for example problems.)
Good luck finding a way to encourage group work... each term I have a few "lone ranger" students who insist on working alone. Most of these succeed, but a few really need the group work yet will not participate.
During a few terms I have tried to schedule weekly study sesions. Despite student promises, these never had enough attendance to be worthwhile.
Think carefully about posting Moodle problems before their respective class day. Doing so pleases the students with a strong math background who like to do work early. But it also allows these students to pay less attention during class, which often decreases their effectiveness in group participation. I usually post Moodle problems early only if the class size is small, for then I can allocate more of my own time to each group.
Use a "syllabus quiz" to encourage students to read the syllabus carefully, so that you do not need to devote too much time on the first day to syllabus content.
Problem 1-3 will need explanation. I am not sure how to word it more clearly.
Problem 1-4 should be discussed after most groups have attempted it.
If the students do not have time to attempt problems 1-9 and 1-10 during class (which is likely) use these as warm-up problems the second class day.
Remind students that if they really want enough room under each problem to do all their work then they can download, edit, and print those pages from the website. But a better habit is to do work on separate paper.
Emphasize (page 2) listing variables first, before writing the equation.
Example problems 5 and 6 are a bit odd in this context. But they provide an appreciate for the compound interest formula the next class day, and are needed to look back on during Activity 10's problems about charge options.
Example problems 6 through 10 can be skipped if time is precious. Time for group work is more valuable.
Emphasize that men and women use different formulas for BMR and DCI (page 1). Do not worry about students understanding how the BMR formulas are buried within the DCI formulas: some students will not grasp this until they have completed a few homework problems.
Make sure students notice the calories per gram information (page 2). This is easy to overlook but is used in the homework.
Example problems 1 through 7 help avoid confusions. They are more important than they appear.
Point out that the homework still has numbered problems! Otherwise some students will try to cram all their work in the grey boxes and ignore the provided guidance.
Notice the homework problems about expected value form a progression. Problem 6-4 needs only addition. Problem 6-8 also needs products calculated. Problem 6-9 needs the entire table. Problem 6-10 asks the students to work backwords.
For problem 6-5 wait until some groups have finished and then show the "trick" to fill in the table quickly by changing the first letter while otherwise duplicating the "block" that fills one-third of the table.
Emphasize the bottom of page 1, about "squared feet" verses "square feet".
I provide an additional example problem for this activity. I measure the width of the front wall of the classroom, then ask a student to walk backwards heel-toe that distance while everyone watches the clock to time him or her. Then I demonstrate converting yards per second into miles per hour.
At the end of the previous class day, point out that the derivation of the Sum of Annuity Due formula is only for their information. There is no need for students to be able to follow that discussion.
Be sure to write out the "calculator key version" of solving the equation the first few times you solve a problem for the class.
This Activity is about misleading statements, so it is potentially confusing even though the math is not difficult. Thus the entire Activity is done together as a class. Let student groups attempt a few problems, then you do the work for the class, etc.
This entire Activity can be skipped if holidays or snow days are stealing away class days. In the past business programs required Math 25, but not currently.