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MATH 365.502 – Fall 2009
Structure of Mathematics, I

Below you will find information for Math 365, Section 502. I will attempt to keep this webpage updated. If I'm getting too far behind, you can encourage me to catch up.


Course Information
Office Hours
Monday 10:30–11:30 a.m., Blocker Room 641G
Tuesday 4:00–5:00 p.m., Blocker Room 641G
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Class Times & Location
Monday/Wednesday/Friday 1:50--2:40 p.m., CVLB Room 419
Syllabus, Resources, Etc.
In the syllabus (“first day handout”) you will find our class contract: what the goal of the course is; what I plan to cover; suggested homework problems; how I plan to assign grades; etc. version)
The webpages of Drost and Scarborough provide two very good resources.
A word on academic honesty: if you are having trouble in this course, you are encouraged to come to office hours, or to work in groups. You are not encouraged to copy. The prudent student will take the time to learn the difference.
Announcements
(11/21/09)  Exam #3 grades: They were a little bit lower than I expected. Check the assignments section below for how we're going to deal with it.
(11/17/09)  Exam #3 practice solutions: Here are some solutions, as promised, to the practice problems below, for your Wednesday exam (11/18). Rest assured that the calculations on the test will not be so lengthy. Note, also, that it's perfectly acceptable to leave your answers in factored form (as I did here) unless I explicitly ask to see a numeral.
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(11/15/09)  Exam #3 practice: Here are some practice problems, as promised, for your Wednesday exam (11/18).
(11/11/09)  Exam #3: Your third midterm exam is one week from today. We will have the usual-style review session on Monday. Practice problems will be posted on-line Sunday evening. Homework on Section 6-3 will also be due on Wednesday.
(11/06/09)  One of your next reading assignments will be to pick your favorite article from the 31 that your fellow students picked. You may want to get started browsing through them.
(11/06/09)  Upcoming Events. Back to normal office hours (Monday morning and Tuesday afternoon. Our next in-class activity is Wednesday. Homework will be due on Wednesday (below). The in-class and supplemental reading (below) will be due on Friday.

Remember, I am moving your next scheduled exam from the Nov.13 to Nov. 18.
(10/31/09)  Upcoming Events. I am moving your next scheduled exam from the Nov.13 to Nov. 18. We may or may not have an activity day on the 11th, but we will definitely have one on the 16th (in the form of an exam review).

Also, homework for next week will be due on Friday, not the usual Wednesday. (See table below.)
(10/31/09)  Temporary OFFICE HOUR change. Next week, there will be no office hours on Monday and Tuesday (since homework is due on Friday). Instead, they will take place at 10:30 a.m. on Wednesday and Friday, as well as 4:00 p.m. on Thursday.
(10/23/09)  Heads-Up. I have finally posted your upcoming assignments. Sorry for the delay.

Conni Liaw (your Monday teacher) has agreed to let you attend her office hours on Monday (Milner Hall, Rm. 331, 3:50--4:40).

I am arriving back in town around 10AM, Wednesday. I will be available for office hours at 10:30AM.
(10/23/09)  Due date change. As mentioned on the cover of the in-class assignment, it is due on Wednesday. (That makes three different assignments due on Wednesday. Please budget your time accordingly.
(10/11/09)  Some solutions to the practice problems. (Watch the typos!)
(10/11/09)  Exam #2. Your second exam is this Friday, October 16th. It will cover Sections 3-1 through 3-5, plus 4-1 and 4-2. (The last sentence has no typos in it.) Here are some practice problems.
(10/11/09)  Looking through some back issues of an NCTM publication, I found this article about injecting some student exploration into the classroom. (Lockhart would be heartened.)
(10/05/09)  Heads-Up. I modified the homework assignment that is due on Wednesday.
(09/28/09)  Exam#1 Patch. IF: you pick a problem from {2,3,5,6,8,9} that you did poorly on, and you make up a similar problem of your own, and you solve it and submit it to me by Wednesday,
THEN: you may replace your score X by the new score (X/90)^(.52),
ELSE: your grade stays the same.
RESOURCES: you may consult me and your textbook for guidance, but the problem you solve must be original to you. It must not come from anything or anybody else (this includes friends as well as other professors).
Please submit separate from your homework, with a title indicating the problem number you are replacing.
(09/28/09)  I have prepared solutions to your first midterm exam.
(09/28/09)  NEW OFFICE HOURS: see above.
(09/22/09)  You have your FIRST EXAM!! this Friday. Here are some example test questions. We will work on these in class on Wednesday. (I will bring spare copies, but please feel free to start early.)
(09/18/09)  Found some nice Virtual Manipulatives today.
(09/11/09)  Your next reading quiz is due Monday. You can find the quiz under the Classroom Materials link below, and also in the Assignments table.
Monday is also our 2nd in-class activity. It would be nice if you could all bring the following:
  * 5 coins of one denomination (pennies, dimes, etc.)
  * 5 coins of another denomination

We won't be working base-5, on Monday, but we will be on Wednesday, so you may want to have some base-5 manipulatives handy. I have made some monopoly-style money that you can print off and cut out. (See 09/09/09 announcement.) Consider bringing it for Wednesday.
(09/09/09)  I made some base-5 money. You should print it out, cut it up, and have it handy for classroom exercises. If you have any suggestions for how to make the bills look better or convey more meaning for you, please let me know.
(09/02/09)  Added a link to Classroom Materials under “Assignments” below.
(08/31/09)  Your first reading assignment ( S.I ) is ready. See the assignments section below for details. There will be a quiz on it at the beginning of class on Friday.
(08/25/09)  This page is under construction. Check back later.
Assignments
List of Errata Classroom Materials Suggested Problems
Due Material
Nov 23 Exam#3 Boost: Look over the third exam, focus on problems {2,5,7,8,9}. Pick the one you feel you did worst on, make up and solve a similar problem, and submit it Monday to give your Exam#3 score a booster-shot... X → (X/97)0.76

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Nov 20 S.VI: Read all of these articles collected by your peers, pick the five you like the best, and give a sentence or two about why you like them.

Nov 18 6-3 A: 1, 6(c,d), 8, 11, 12, 18, 25, 28, 29;   6-3 B: 1, 2(b,c), 4(a,b), 9, 19(a,c,e), 20(a,b), 21*, 27(b,c,d), 29;   6-3 Conn: 1, 4, 6, 9, 10, 16, 22, 25;  
* := Watch out!! a and b are rational numbers.

Nov 13 S.V: Read chapter 3 of Liping Ma's book. Topic: dividing by fractions and submit this quiz on Friday.

Nov 11 6-1 A: 2(b), 4, 9, 20(a);   6-1 B: 4, 5, 7, 9;   6-1 Conn: 2, 3, 6, 16, 24;  
6-2 A: 1(a,b,c,d), 2, 14;   6-2 B: 1(e), 3, 10, 19, 20;   6-2 Conn: 2*, 12, 16, 17;  
* := See Problem 1.

Nov 06* 5-2 A: 13(a,d,g), 21(a,c,e,g,h);   5-2 B: 8(a), 14(a), 24(a), 31;   5-2 Conn: 6, 15, 17**, 19;
5-3 A: 5, 6;   5-3 B: 3, 11, 15(b,c);   5-3 Conn: 4, 19, 21;
5-4 A: 2(b,c,e,g);   5-4 B: 2(b,c), 7, 17, 18(a,c);   5-4 Conn: 2, 17;
5-5 A: 12;   5-5 B: 2, 3, 5, 9;   5-5 Conn: 4, 17, 19***
* := Don't worry about proper exposition on this assignment. This is a long assignment, and I don't need you fretting about the right way to present arithmetic. Just get 'em done.
** := If true, explain why it follows from what you have already taught the student; if false, give a counter-example.
*** := Reread the justification/discussion for the Euclidean algorithm on page 319.

Oct 28 All of the in-class activities from Friday ( A.VI ).

Oct 28 4-3 A: 3*, 4, 11, 16, 17   4-3 B: 6, 11(c,d), 13(b,c), 17, 27;   4-3 Conn: 2, 6, 12, 16;
5-1 A: 4, 5, 7, 15;   5-1 B: 1(b,e,f), 2(a), 3(a,c), 6, 14(a), 15, 19(a,b,c), 25(a,b), 26(a,b), 27(a,c);   5-1 Conn: 2, 10(a,b), 16, 17
* := Use the counting principle.

Oct 28 S.IV: (postponed from Oct 23) find an interesting activity either in the series Mathematics teaching in the middle school (library call number QA13.M37) or in the series Teaching children mathematics (library call number AQ135.A6). For example, I found a nice article about the “nets” of a cube in the March 2009 issue of TCM. (Don't use that one.)
In place of a reading quiz, you should submit a photocopy of the article, together with a short discussion about why you picked it and how you might implement it.

Oct 23 S.IV: (postponed from Oct 23) find an interesting activity either in the series Mathematics teaching in the middle school (library call number QA13.M37) or in the series Teaching children mathematics (library call number AQ135.A6). For example, I found a nice article about the “nets” of a cube in the March 2009 issue of TCM. (Don't use that one.)
In place of a reading quiz, you should submit a photocopy of the article, together with a short discussion about why you picked it and how you might implement it.

Oct 21 no book exercises: work on your supplemental reading assignment instead.

Oct 14 3-5 B: 2, 4, 14, 15;   3-5 Conn: 1,3, 4, 8, 9;
4-1 A: 6, 8;   4-1 B: 4, 6(a,d,g), 9;   4-1 Conn: 1, 3, 7;
4-2 A: 3, 4, 6;   4-2 B: 1, 4;   4-2 Conn: 5

Oct 07 3-3 B: 12, 13, 20, 23;   3-3 Conn: 11*;
3-4 A: 7, 8, 15, 18, 22; 3-4 B: 4, 5, 6, 10, 17, 18, 20(c,d); 3-4 Conn: 1, 2(a), 4, 10, 13, 15(b);
* := all of you can stand to think up another explanation. Use one of the models for multiplication to help Sue out.

Oct 05 S.III: read chapter two of Liping Ma's Knowing and teaching elementary mathematics and answer these questions

Sep 30 2-3 A: 20, 23;   2-3 B: 1, 19, 22, 23;   2-3 Conn: 4, 6, 10, 16;
3-3 A: 9;   3-3 B: 4, 6, 10, 18;   3-3 Conn: 4, 8, 10, 11;

Sep 23 1-3 A: 7, 14;   1-3 B: 2, 4, 9, 12, 15, 16;   1-3 Conn: 7, 14, 15;
2-2 A: 13, 16;   2-2 B: 3, 5, 7;   2-2 Conn: 9, 10, 15;

Sep 16 1-1 A: 4, 11;   1-1 B: 7, 15;   1-1 Conn: 2, 10, 13;
1-2 B: 2, 4, 6, 17;   1-2 Conn: 3, 11, 13, 15;
3-2 B: 7, 9, 12(d,e), 14(a,c), 17;   3-2 Conn: 5, 6, 8

Sep 14 S.II: read pages 1–14 in Lockharts Lament, up to "The Mathematics Curriculum." (If you have never read one of Plato's dialogues, you might miss part of the running joke.) Then answer these questions.

Sep 9 3-1 A: 6, 10, 15;   3-1 B: 14;   3-1 Conn: 4;  
2-1 A: 3, 19, 21;   2-1 B: 1, 2, 3, 9, 17, 19, 21, 22, 25;   2-1 Conn: 4  

Sep 4 S.I: read the back cover and first chapter of Liping Ma's Knowing and teaching elementary mathematics.