Professor: Jeff Johannes Section 3 TR 11:00a-12:15p South 336

Office: South 326a

Telephone: 5403 (245-5403)

Office Hours: Monday 5-6p in South 309, Tuesday 1-2p in South 309. Wednesday 12:30-1:20p in South 309, Thursday 8-9p in South

Email Address: Johannes@Geneseo.edu

Web-page: http://www.geneseo.edu/~johannes

Optional: A Problem Solving Approach To Mathematics For Elementary School Teachers by Rick Billstein, Shlomo Libeskind, Johnny W. Lott.

Occasional additional activities provided here

Knowing mathematics means being able to use it in purposeful ways. To learn mathematics, students must be engaged in exploring, conjecturing, and thinking rather than only rote learning of rules and procedures. Mathematics learning is not a spectator sport. When students construct knowledge derived from meaningful experiences, they are much more likely to retain and use what they have learned. This fact underlies the teacher's new role in providing experiences that help students make sense of mathematics, to view and use it as a tool for reasoning and problem solving.If you feel a need to review elementary school mathematics, this is your responsibility. For this purpose, I recommend reading our textbook and consulting with me outside of class. For a reference on the content of elementary school mathematics, here is the New York State Standards for Mathematics.

It is also the purpose of this course to improve your ability to engage in mathematical thinking and reasoning, to increase your ability to use mathematical knowledge to solve problems, and to learn mathematics through problem solving. The emphasis in this course is on learning numerical mathematical concepts through solving problems. You will often work with other students for the following reasons: Group problem solving is often broader, more creative, and more insightful than individual effort. While working on problems with others, students practice putting their mathematical ideas and reasoning into words. This ability to explain mathematics is clearly essential for future teachers. While working in groups, students learn to depend on themselves and each other (rather than the instructor) for problem solutions. In groups, students can motivate each other to excel and accept more challenging problems. Motivation to persevere with a difficult problem may be increased. Socialization skills are developed and practiced. Students are exposed to a variety of thinking and problem-solving styles different from their own. Interaction with others may stimulate additional insights and discoveries. Conceptual understanding is deeper and longer-lasting when ideas are shared and discussed.

- Solve open-ended elementary school problems in areas such as patterns, algebra, ratios, and percents,
- Justify the use of our numeration system by comparing it to historical alternatives and other bases, and describe the development of the system and its properties as it expands from the set of natural numbers to the set of real numbers,
- Demonstrate the use of mathematical reasoning by justifying and generalizing patterns and relationships,
- Display mastery of basic computational skills and recognize the appropriate use of technology to enhance those skills,
- Demonstrate and justify standard and alternative algorithms for addition, subtraction, multiplication and division of whole numbers, integers, fractions, and decimals,
- Identify, explain, and evaluate the use of elementary classroom manipulatives to model sets, operations, and algorithms, and
- Use number-theory arguments to justify relationships involving divisors, multiples and factoring.

10% - Participation

10% - Weekly Questions

20% - Each of two In-Class Exams

15% - Final Project

25% - Comprehensive Final Exam

In addition, you must pass several Basic Skills Checks throughout the semester or your course grade will be lowered by a half letter for each incomplete check. Further details are available below.

These questions and papers will be graded on the following scale

Question (out of 2)

0 – missing question

1 – question attempted, but incomplete work

2 – question addressed seriously and in depth

In order to provide you with extensive comments, there may be delays in returning these papers.

In-class exams will have two parts - the first part is devoted to a group exam, in which your group will complete an activity much like those done in-class. You will submit one well-written presentation of your findings from each group.

Individual exams will contain six questions: four of the questions will be direct problems. Two of the questions will be more open ended and ask you to explain key concepts from class. The exams will be graded as follows: you will receive 40 points for attempting the exam. You may earn up to 10 points on each of the questions.

Make-ups for exams will be given only in extreme cases with arrangements made with the instructor prior to the exam or if there is a verifiable medical excuse or permission from the Dean of Students. If you miss an exam and we have not made arrangements prior to the missed exam, you must contact me before the next class.

We will be undertaking a great amount of interactive group work in this course. You may view these as games. If you come in eager to play, then you will be more likely to be successful and perhaps occasionally enjoy the games. If you come in saying "I don't want to play this stupid game," we will all be annoyed and frustrated, and the course as a whole will be less successful. Please play nicely.

Out of necessity, I am more formal in class and more personal out of class. If you ever want additional help, please come to see me either during my office hours, at an appointed time, or by just stopping by (I am frequently in my office aside from the times that I will certainly be there). It is important that you seek help when you start needing it, rather than when you have reached desperation. Please be responsible.

Teaching is one profession where you have direct impact on hundreds of lives. It is truly an incredible responsibility. It is vitally important that teachers set high expectations for themselves and their students. Daily preparation of interesting, instructive lessons for twenty-five or more active children of varying aptitudes is extremely challenging. I am dedicated to helping you prepare for this exciting career, and will try to help you reach your full potential. Best wishes for a challenging and fulfilling semester.

August 29 Introduction, curiosity, sale activity

31 1.3 discussion, video #42

September 5 History of number systems - research to present: Tally, Egyptian, Greek, Roman, Babylonian, Mayan, Hindu-Arabic, Chinese numbers

7 Basic Skills Check I discussion of other bases; 2.1, 2.7, 2.8

12 2.2, 2.9

14 alternatives, 2.11 3.678

19 b 3.12 standard multiplication, b 3.13 lattice multiplication

21 2.12m, 2.13m

26 b 3.15, 2.4, 2.12d, 2.13d

28 Basic Skills Check II b 3.19 , b 3.20 Weekly Questions due

October 3 First Exam

5 3.6, 2.15 + checking mod 9

12 3.5, 3.3

17 NT3, NT4

19 3.8, 3.9

24 NT5, NT6

26 4.1

31 Basic Skills Check III 4.3 Weekly Questions due

November 2 4.5, 4.7

7 Second Exam

9 4.9

14 b 5.13, b 5.14

16 4.11

21 Further activities and discussions with decimals (RN9)

28 Relations between decimals and fractions (RN10)

30 4.13 Weekly Questions due

December 5 4.14, 4.15

7 Review

11 Final Project due by 6p

Monday, December 18 8:00-11:00a final exam