Required Materials: textbooks, scientific calculator (or graphing calculator), metric and standard ruler, scissor, pencil, notebook paper, graph paper, access to supplemental readings/websites (student membership to NCTM recommended)

Course Goals

Teaching is a melding of various skills. Effective teaching requires an ability to represent and formulate a subject to make it comprehensible to others. This means understanding what makes the learning of a concept easy or difficult, which requires an ability to synthesize knowledge about content with students’ interests, needs, and cultural influences.

This course investigates elementary mathematics at a conceptual level to provide a foundation for effective mathematics instruction. Within the context of this course, teaching methods are modeled and made explicit to introduce the complexity of teaching for understanding. You will develop a deeper understanding of the mathematics concepts that you will be expected to teach, and enhance your communication and self-assessment skills.

You will:

(a) gain knowledge of the underlying concepts related to numbers, operations, and problem solving

(b) use a quantitative approach to learning algebra and graphing

(d) increase your confidence and enthusiasm for teaching mathematics

(e) examine and use the local and national standards for teaching mathematics

(f) discuss how the teaching methods modeled in the course can be used at K-8 level

(g) enhance your communication and self-assessment skills

(h) understand the interdisciplinary nature of mathematics

Course Objectives

Listed here are the skills you should be able to demonstrate upon completion of this course:

1. Use problem-solving models and apply them to concepts introduced in the course

2. Understand the structure of the real number system and describe how it relates to learning mathematics

3. Use various algorithms, mental computations, manipulatives, and calculators for solving problems dealing with whole numbers, fractions, decimals, percentages, integers, patterns, functions and graphs

4. Critique strategies for helping K-8 students to learn mathematical concepts

5. Apply mathematics across another discipline (art, music, motion, culture, or literature)

Course Expectations

You are expected to attend all class sessions, to arrive on-time and be prepared for the daily lesson. Being prepared means that homework assignments are complete, and that you have all the necessary supplies for full participation in the daily coursework. You will:

1. Work individually and collaboratively in small and large groups to accomplish the course goals and objectives

2. Actively engage in mathematical manipulation and representation through the course activities.

3. Articulate your understanding of mathematical concepts and procedures through involvement in course activities and reflective observations in a mathematics journal.

4. Critique your own and others procedures and thinking about math for the purpose of deepening your understanding of how people come to learn and understand mathematics. Self evaluation and peer evaluation will be integrated throughout the course.

Assessment

In-Class: Partnership/Small Group/Whole Class Activities

Activities and discussions are conducted in small groups. The group members report their findings to class with emphasis on the important concepts, connecting unconventional procedures with standard algorithms. You will be actively involved during the class time, either working on mathematics problems, presenting your solution processes, evaluating peer presentations, or reflecting on your understanding of the mathematics.

Communication is an important aspect of this class, therefore you are responsible for providing evidence that you understand the material presented. One way to do this is by fully participating in partnership, small group, and whole class activities. The partnership and small group formats provide support to: (a) ease math anxiety, (b) learn to work collaboratively, (c) develop problem solving and critical thinking skills, and (d) clearly communicate solution processes to convince others that the answer is correct. Also, you are expected to summarize and communicate your group’s findings to the whole class.

You will work in the small groups to do class work and take tests; therefore it is important that you contribute your thinking, questions, and insights to make this a collective process. As a productive group member it is your responsibility to listen carefully, provide positive feedback, ask clarifying questions rather than depend upon assumptions, and share your thinking, concerns, and critique of solution processes with one another.

Homework

The daily Math Problems deepen your understanding of the mathematical concepts you learned in previous classes by explicitly connecting the standard algorithm with the underlying mathematical concept. Homework is listed in the Course Calendar on the day it is due. Please do all homework assignments on regular notebook paper (no spiral bound or scrap pieces of paper), or if you are word processing your work, then use regular printer paper. Try to keep the homework as neat as possible. If you are absent, bring in your missed work on the day of your return. Completing and handing in homework on time is essential as it prepares you to be a full participant in the class activities.

Tests, Midterm Essay, and Project

Much of the learning in this class is done through group work, therefore group tests are used to assess your understanding. This does NOT mean that you get a group grade. Test problems are complex and require an explanation of the reasoning used to solve the problem. The testing format provides an opportunity to discuss the solution process with group members prior to writing solutions in your own words. A correct answer to a problem is sufficient for a passing grade (which is a 75% or a 2.0); however, if you wish to earn a higher grade, you must clearly communicate your thinking and demonstrate your solution process. The group work is designed to hone your communication skills (this is a course objective). The individual write-up is how you provide evidence of your understanding for a formal assessment grade. This process will be explained in more depth and your questions will be answered prior to the first formal test.

No make-up tests will be given, however, you can replace a test grade with the grade you get on the final exam.

The mid term essay is worth 100 pts. I strongly recommend you read the entire book, Esquith, Rafe, (2003) There Are No Shortcuts, Anchor Books, NY. However only Chapter 10: ”When Numbers Get Serious” is required. This is a two page essay. The first paragraph you should provide a brief synopsis of the chapter (explain the premise of the chapter in your own words—do analyze, merely describe.) The rest of the essay, please discuss your impression of how Rafe incorporates math into his classroom norms. What do you see as the strengths and weaknesses of this approach? What concerns do you have? What do you feel you could use or might feel uncomfortable using and explain your reasoning. The essay should be double spaced, 12pt Times Roman font. Please submit by email as a Word attachment.

The Quarter Project is an individual project; however, you will have opportunities in class to work with others who have chosen a similar project. This small group will help you with planning, editing, and revising. The project is explained in detail on the Project Protocol page. The project will have due dates for different aspects of the project, with the final project write-up due the day of the final exam.

Grading policy, criteria and scales

The proposed grade distribution is: 40% class participation and homework, 40% tests and final exam, and 20% quarter project.

· Participation: You will receive 10 points for each day that you attend class. Points are deducted if you arrive late or leave early, are not able to attend a session, and for disruptive and disrespectful behavior.

· Homework: Math Problems—10 points.

· Tests & Essay are each 100 pts. The Final Exam is 100 points (the final exam grade can replace lowest test grade.)

· Quarter Project is 100 points. Please see the Project Protocol page for details.

100 > 94% = 4.0 > 3.9 = A

93 > 90% = 3.8 > 3.5 = A-

89 > 87% = 3.4 > 3.2 = B+

86 > 84% = 3.1 > 2.9 = B

83 > 80% = 2.8 > 2.5 = B-

79 > 77% = 2.4 > 2.2 = C+

76 > 74% = 2.1 > 1.9 = C

73 > 70% = 1.8 > 1.5 = C-

69 > 67% = 1.4 > 1.2 = D+

66 > 64% = 1.1 > 0.9 = D

63 > 60% = 0.8 > 0.7 = D-

60% > = 0.7 > = E

If you feel that the grade distribution does not adequately reflect your understanding of the mathematics in this course, then I encourage you to make an appointment to discuss it with me. This must be done sometime before the last month of the quarter.

“NC” (No Credit) grades are NOT given under any circumstances. If you want to withdraw from the course, request a “W” grade before the published deadline. “I” (Incomplete) grades are only given in strict conformity with the college catalog. Specifically, a student must be in “good standing” to request an Incomplete. For this course, “good standing” will mean, at a minimum, a current grade of at least 2.0. “I” grades can only be requested in situations and circumstances that are out of the control of the student…please read the catalog for details. I reserve all rights about when and if an “Incomplete” will be issued. It is your responsibility to request and submit the signatures and paperwork required for “W” and “I” grades by the deadlines established by the college.

Tutorial Assistance

I am available to help clarify or provide tutorial assistance. However, (since I have approximately 100 students each quarter) please discuss the problem with your group members first. Make an appointment to speak with me if your group members are unable to help you. I am also available to work with the whole group.

If you need tutoring assistance on a fairly regular basis, please use the math lab in SAM106.

For help with dealing with math phobia or test anxiety, please make an appointment to talk with me. We can discuss your particular issues and devise a plan to help you be successful.

Students with Disabilities Statement

Students with documented disabilities, who need course accommodations, have emergency medical information or require special arrangements for building evacuation should contact me within the first week of class.

The instructor reserves the right to reasonably adjust this syllabus if deemed necessary and will make available written changes for students to add to this document.

Project Protocol

Submitting Project

Use the Project Template to submit your reports. The sections of the Template align with the reports listed here. You will update the template and resubmit by the due dates. Use proper grammar and spelling. Electronic copy submission for grading is required. Student work should be scanned submitted as a separate attachment. I recommend that you use this project as part of your electronic portfolio.

Save the Project Template onto your desktop, and then open it using Word. When you have completed the appropriate sections on the template, save it as a Word document and send it to me by email. Student work, work sheets, etc. should be scanned and sent as an attachment also (if you are unable to scan, hard copies should be submitted.)

Project Declaration: First box on Template

Identify the Project Theme, grade level, and Mathematical Concept for your project

Project Themes

Mathematizing Literature

Math and Art

Math and Music

Math and Motion

Math and World Cultures

Grade Levels

Pre-K

K-2

2-4

4-6

6-8

Mathematical Concepts

Quantitative Analysis

Place Value

Bases other than Ten

Working with Whole Numbers

Estimation

Working with Fractions

Multiplicative reasoning

Ratios and proportions

Working with Signed Numbers

Number Theory

Algebra—Time, Distance, and Rate

Algebra—Symbolic Representation

Algebra—Patterns and Functions

Project Overview – First section of the Project Template

1. Identify the Project Theme, Grade Level, and Mathematical Concept for your project.

2. Identify a couple of EALRs/GLEs and NCTM Standards that relate to your project, indicating the primary and supplementary standards. Make sure to have at least one for each discipline.

3. Make a record/bibliography of literature, websites, and information sources (i.e., elementary school teachers, after school programs) that you are using to research your project.

4. Identify and contact students (younger sibling, niece or nephew, your child, neighbor or friend’s child, etc.) who might be willing to work with you on this project. Make sure to assign a pseudonym for each student.

5. Determine the time frame and location for conducting an activity

If you are doing this project in combination with service credits, then you will work with your cooperating teacher to establish your project parameters.

Activity Description: Second section of the Project Template

1) Choose and describe an appropriate activity that fits your project parameters and the ability/interest level of the child/children who will be working with you.

a) Explain where you found the activity (full citation).

b) Identify the main goal of the activity, keep this simple. (i.e., to determine what 3^rd graders know about adding fractions with different denominators)

c) Record any adjustments you made to the activity to fit your parameters, time constraints, student interest/abilities, EALRs/GLEs and/or NCTM Standards.

d) Explain how you assessed the child’s/children’s ability/interest level before developing the activity.

2) Prepare the activity and record the following:

a) Supplies needed

b) Do the activity yourself (or with a peer) and record appropriate changes

c) Make arrangements for conducting the activity (time, place, etc.)

3) Write out how you will explain the activity to the child/children (mini script)

4) Do the activity with the child/children who have agreed to work with you

a) Record the time, place, who attended, etc.

b) Collect student work, and/or record notes on student outcomes

c) Write down what happened during the activity

Activity Analysis – Last section of the Project Template

1) Explain what you hoped to accomplish with the activity. Do you feel it was successful? Why, why not?

2) Explain the specific mathematics expectations you had for this activity (make sure to site the EALRs and NCTM Standards.) Was this a good activity for meeting those expectations? Why/why not?

3) Explain how the children responded to the activity. How do you know if they enjoyed it? How do you know whether they recognized that they were learning something mathematical?

4) Are there things you would do differently if you were to use the activity again for this age group? What changes would you recommend to use this as a whole class activity? Would you use it for another age group, and if so, how would you change the activity?

5) Has this project changed how you think about teaching mathematics? If yes, explain. If no, how has it reinforced or validated your beliefs?

Project Assessment

This project is worth 100 points. Assessment is described using the following rubric.

	poss. points	100%-90% Meets All Expectations	89%-80% Meets Most Expectations	79%-70% Meets Some Expectations
Project Overview	20	All Project Parameters are completely identified, clearly recorded, and submitted on time or early.	All Project Parameters are identified (may be missing some small details), neatly recorded, and submitted on time	Most Project Parameters are identified (may be missing some small details), recorded, and submitted.
Activity	30	All record keeping items collected, well organized, and explained clearly. Submitted on time or early.	All record keeping items collected, somewhat organized, and explained. Some small details may be missing. Submitted on time.	Most record keeping items collected and explained. Some small details may be missing. Submitted.
Activity Analysis	50	All Project Analysis Questions are clearly written with thorough responses. Submitted on time or early	All Project Analysis Questions are neatly written with responses. Submitted on time	Most Project Analysis Questions have responses and submitted on time.

Course Calendar

Bring appropriate textbook section from Modules 1& 2 (Student Edition available at the Professional Copy & Print at Broadway and John), scientific calculator, metric and standard ruler, scissor, pencil, notebook paper, and graph paper to class daily.

Although tests and math problems are used as evidence of your understanding and to assign a formal grade, they also provide a means by which I can determine the mathematical ideas that you and your classmates need to have further explained or emphasized. For this reason, the Course Calendar is not fixed, but rather is a working document which may change as we progress through the material. I will inform you of any changes to the calendar as they arise.

As you read through the book sections, it is important that you become familiar with the activities which we will be working on in class together. The math problems and reading response questions are due the day they are listed.

Week 1	Class Session Schedule	Assignment The homework is listed on the day it is due.
Weds. Sep.30	Ch.1 Reasoning about Quantities Introductions and admin. Stuff 1.1 What is Quantity? 1.2 Quantitative Analysis 1.3 Values of Quantities 1.4 Using quantitative reasoning to make sense of situations	Make a photocopy of Appendix B to keep with your module and then cut out the cardstock base blocks and store in a Ziploc bag. Use them to help you with the work in chapter 2. *Link to Ch1*
Week 2	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Oct. 5	Ch.2 Numeration Systems 2.1 Ways of Expressing Values of Quantities 2.2 Place Value 2.3 Bases other than Ten	1.1 Discussion 2: p.5 #2 1.2 pp.9-12 #1a,d; 2b; 3, 6, 8 1.3 pp.16-17 #1, 2c,d,e; 3, 4
Mon. Oct. 5	Explain Project and Service Learning Credits
Weds. Oct.7	2.4 Operations in Different Bases 2.5 Issues for Learning: Understand place value	Link to Ch2 2.1 pp.27-28 #1, 4, 5, 7 2.2 p.31 #1c,g,h, j, k; 6; 8 2.3 pp.38-39 #5, 11, 13, 14, 18a,c
Weds. Oct.7		Project Declaration due Email
Week 3	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Oct.12	Chapters 1 and 2 review	2.4 p.44 #2a,c; 4 a, c; 5 a, b; 7 a, b
Mon. Oct.12	CH. 1 & 2 TEST	2.4 p.44 #2a,c; 4 a, c; 5 a, b; 7 a, b
Weds. Oct.14	Ch.3 Understanding Whole Number Operations 3.1 Additive combinations and comparisons 3.2 Ways of thinking about add. and sub. 3.3 Children’s ways of adding and subtracting 3.4 Ways of thinking about multiplication 3.5 … about division 3.6 Children find products and quotients 3.7 Developing number sense	Video Clip 1: First graders add and subtract. Video Clip 2: Javier uses mental strategies to multiply.
Weds. Oct.14	Form Project Groups
Week 4	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Oct.19	Ch.4 Some Conventional Ways of Computing 4.1 Operating on whole numbers and decimal numbers 4.2 Issues of learning: The role of algorithms	3.1 p.53-54 #2, 3, 4, 6, 8, 10 3.2 pp.59-61 #1, 7, 8 3.3 pp.65-67 #2 Cases: B & C; 4, 5a,b 3.4 pp.73-75 #1, 5, 6d,e; 7, 10c; 12 3.5 pp.79-81 #2, 3a,d; 4, 8a,b 3.6 p. 83 #5 explained 3.7 pp.85-86 #1a,c,d; 2, 5
Weds. Oct.21	Ch.5 Using Numbers in Sensible Ways 5.1 Mental computation 5.2 Computational estimation 5.3 Estimating values of quantities 5.4 Using scientific notation 5.5 Estimating fractional values 5.6 Issues of learning: Mental computation	4.1 pp.93-94 #1b; 2a,b; 5
Weds. Oct.21	Group: Edit/Revise Essays	Bring in the rough draft of your essay. Link to rubric
Week 5	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Oct.26	Chapters 3, 4, & 5 review	5.1 pp.100 #1a,c; 2c,e; 3c,e; 4d 5.2 p.105 #1, 2, 7b,c,d; 8b,d,f 5.3 p.108 #2, 4 5.4 pp.110-111 #1a, 4, 8, 10
Mon. Oct.26	CH. 3, 4, & 5 TEST
Weds. Oct.28	Ch.6 Meanings for Fractions 6.1 Understanding the meaning of a/b 6.2 Equivalent (equal) fractions 6.3 Relating fractions and decimals 6.4 Estimating fractional values 6.5 Issues of learning: Understanding fractions and decimals	Midterm Essay Due
Weds. Oct.28		Video Clip 3: Rachel explains how to change a mixed number into an improper fraction. Video Clip 4: Ally is asked to compare pairs of fractions and change a mixed number to an improper fraction and an improper fraction into a mixed number. Video Clip 5: Felisha explores basic fraction concepts.
Week 6	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Nov.2	Ch.7 Computing with Fractions 7.1 Adding and subtracting fractions 7.2 Multiplying by a fraction 7.3 Dividing by a fraction 7.4 Issues of Learning: Notes on teaching calculations of fractions	6.1 pp.117-122 #2a,b,c; 4, 6a,b; 8b,c; 13, 20, 21 6.2 pp.125-126 #1; 2b; 5, 6, 7a,c; 10a 6.3 pp.131-132 #1b,d; 2b,d,f; 3, 4b,c; 5, 9 6.4 pp.137-138 #6, 8, 10, 12a,e,h; 13, 17a,c,e Video Clip 6: Elliot shows how to divide fractions.
Weds. Nov.4	Ch.8 Multiplicative Comparisons Reasoning 8.1 Quantitative analysis of multiplicative situations 8.2 Fractions in multiplicative comparisons 8.3 Issues of learning	7.1 pp.144-145 #1, 3a,c; 8, 9, 10 7.2 pp.149-153 #1, 3, 6, 12a,c; 16, 17 7.3 pp.158-161 #1, 2, 3a,c,e; 7, 13, 14b,d,f 7.4 pp.163-164 #2, 6, 8
Weds. Nov.4		Project Overview due Email
Week 7	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Nov.9	Chapters 6, 7, & 8 Review	8.1 p.169 #1a,c; 3; 8.2 pp.173-174 #1, 3, 6 8.3 Read through this section and jot down some of your thinking, questions, and concerns to share in class.
Mon. Nov.9	CH. 6, 7, & 8 TEST
Weds. Nov.11	No School	Veterans’ Day
Week 8	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Nov.16	Ch.9 Ratio, Rates, Proportions 9.1 Ratio as a measure 9.2 Using proportions to compare ratios and solve for missing values 9.3 Percents in comparisons and changes 9.4 Practicing multiplicative reasoning 9.5 Issues of learning: Developing proportional reasoning
Mon. Nov.16	Project group work
Weds. Nov.18	Ch.10 Expanding Our Number System 10.1 Adding and Subtracting Signed Numbers 10.2 Another Way to Think about Addition and Subtraction 10.3 Multiplying and Dividing Signed Numbers	9.1 p.181 #3e,f,h; 5 9.2 pp.188-191 #2, 5, 7, 18, 20 9.3 pp.196-198 #6, 7, 8, 9, 15, 17, 18, 20a,c,e,g,i; 21a,c,e,g,i 9.4 pp.198-199 Using the criteria listed, explain why/why not you consider yourself to be a proportional thinker
Week 9	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Nov.23	Ch.12 Quantitative Approach to Algebra and Graphing 12.1 Quantities and their Relationships 12.2 Using Graphs and Algebraic symbols to show quantitative relationships 12.3 Understanding Slope: Making connections across quantitative situations, graphs, and algebraic equations 12.4 Issues for learning: Algebra in the elementary grades	10.1 pp.205-207 #1,4, 6, 10 10.2 p. 215 #3 10.3 pp.222-223 #3, 4, 7a,c,e,g,i; 8 10.4 p.227 #3
Weds. Nov.25	Chapters 9, 10, & 12 Review	12.1 p.266 #3 12.2 pp.271-272 #3, 5 12.3 pp.275-278 #1, 4, 5
Weds. Nov.25	CH. 9, 10, & 12 TEST	Activity Description due Email
Week 10	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Nov.30	Ch.13 Understanding Change: Relationships among time, distance, and rate 13.1 Distance-Time and Position-Time graphs 13.2 Using Motion Detectors 13.3 Graphs of Speed against Time 13.4 Interpreting Graphs 13.5 Issues for Learning: Common Graphing Errors	[need motion detector] Over & Back Applet
Mon. Nov.30	Project group work	[need motion detector] Over & Back Applet
Weds. Dec.2	Ch.14 Algebra as a Language and as Generalized Arithmetic 14.1 Using Algebraic symbols to represent relationships 14.2 Using algebra to solve problems	13.1 p.287 #6, 7 13.2 p.290 #1, 2 13.3 pp.293-296 #1, 3, 5, 8, 9 13.4 pp.298-303 #1, 3, 5, 7
Week 11	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Dec.7	14.3 Average speed and weighted averages 14.4 Algebra as generalized arithmetic 14.5 Issues for Learning: Topics in Algebra	14.1 pp.312-315 #1, 5, 8, 10 , 13 14.2 pp.321-322 #1, 4, 5, 8, 10
Mon. Dec.7		Project Consent Form and Activity Analysis due Email
Weds. Dec.9	Ch. 13 &14 Review	14.3 pp.326-327 #1, 3, 6, 9 14.4 pp.332-333 #2a,b; 3a,c; 4a,b,d,f; 5a,d 14.5 p.337 #2, 3a,d; 4c,f; 6
Weds. Dec.9	Ch. 13 & 14 Test
Finals Week	Class Session Schedule	Assignment The homework is listed on the day it is due.
Mon. Dec.14	Course Evaluation Final Review	Project Presentations
Weds. Dec.16	FINAL EXAM	Same time and location

Text and Course Materials

Course Goals

Course Objectives

Course Expectations

Assessment

In-Class: Partnership/Small Group/Whole Class Activities

Homework

Tests, Midterm Essay, and Project

Grading policy, criteria and scales

Tutorial Assistance

Students with Disabilities Statement

Project Protocol

Submitting Project

Project Declaration: First box on Template

Project Overview – First section of the Project Template

Activity Description: Second section of the Project Template

Activity Analysis – Last section of the Project Template

Project Assessment

Course Calendar

Week 1

Week 2

Week 3

Week 4

Week 5

Week 6

Week 7

Week 8

Week 9

Week 10

Week 11

Mon. Dec.7

Weds. Dec.9

Finals Week