Sowder, J., Sowder, L., Nickerson, S., (2008), Reconceptualizing Mathematics Parts 1 & 2, W.H. Freeman & Co., NY, ISBN #1429215054 (Available at the SCCC Bookstore)

and

Esquith, Rafe, (2003) There Are No Shortcuts, Anchor Books, NY.

Supplementary Readings/Website Access:

OSPI: Washington Assessment of Student Learning (WASL) http://www.k12.wa.us/assessment/WASL/overview.aspx

Essential Academic Learning Requirements (EALRs) http://www.k12.wa.us/CurriculumInstruct/EALR_GLE.aspx

NCTM: Principles and Standards for Science and Mathematics http://standards.nctm.org/document/appendix/numb.htm

Teaching Children Mathematics Magazine (optional) http://my.nctm.org/eresources/journal_home.asp?journal_id=4

National Association for the Education of Young Children (NAEYC)

Standard 2: Curriculum Content Area for Cognitive Development - Early Mathematics

Washington State Early Learning and Development Benchmarks

A Guide to Young Children’s Learning and Development: From Birth to Kindergarten Entry

http://www.k12.wa.us/EarlyLearning/pubdocs/EarlyLearningBenchmarks.pdf

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 to three 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 not 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 as a hard copy (or 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 reports will be made on the project template. You will fill in sections of the template throughout the quarter. The final completed project template is due the day of the final exam.

Grading policy, criteria and scales

The proposed grade distribution is: 40% class participation and homework, 50% tests and final exam, and 10% 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.

Course Calendar Bring textbook, 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.
Week 1	Class Session Schedule	The homework is listed on the day it is due.
Mon. Jan.4	Ch.1 Reasoning about Quantities Introductions and admin. Stuff 1.1 What is Quantity? 1.2 Quantitative Analysis	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.
Tues. Jan.5	1.3 Values of Quantities 1.4 Using quantitative reasoning to make sense of situations	1.1 Discussion 2: p.5 #2 1.2 #1a,d; 2b; 3, 6, 8

Weds. Jan.6	Ch.2 Numeration Systems 2.1 Ways of Expressing Values of Quantities 2.2 Place Value	1.3 #1, 2c,d,e; 3, 4 1.4 #4
	Explain Service Learning Credits: locations & reflection paper
Thurs. Jan.7	2.3 Bases other than Ten Explain Project	2.1 #1, 4, 5, 7 2.2 #1c,g,h, j, k; 6a,c,e; 8
Fri. Jan.8	2.4 Operations in Different Bases 2.5 Issues for Learning: Understand place value	2.3 #5, 11, 13, 14, 18a,c
Week 2	Class Session Schedule	The homework is listed on the day it is due.
Mon. Jan.11	Chapters 1 and 2 review	2.4 #2a,c; 4 a, c; 5 a, b; 7 a, b
		Project Declaration due: hard copy or Email
Tues. Jan.12	CH. 1 & 2 TEST
Weds. Jan.13	Go over CH1-2 test	No hmwk
	Ch.3 Understanding Whole Number Operations 3.1 Additive combinations and comparisons
Thurs. Jan.14	3.2 Ways of thinking about add. and sub. 3.3 Children’s ways of adding and subtracting Video Clip 1: First graders add and subtract.	3.1 #2, 3, 4, 6, 8, 10
Fri. Jan.15	3.4 Ways of thinking about multiplication Video Clip 2: Javier uses mental strategies to multiply.	3.2 #1, 7, 8 3.3 #2 Cases: B & C; 4 (for cases B&C), 5a,b
Week 3	Class Session Schedule	The homework is listed on the day it is due.
Mon. Jan. 18	Martin Luther King’s Birthday	No School
Tues. Jan.19	3.5 Ways of thinking about division 3.6 Children find products and quotients 3.7 Developing number sense	3.4 #1, 5, 6d,e; 7, 10c; 12
Weds. Jan.20	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	3.5 #2, 3a,b; 4, 8a,b 3.6 #5 explained 3.7 #1a,c,d; 2, 5
Thurs. Jan 21	Ch.5 Using Numbers in Sensible Ways 5.1 Mental computation	4.1 #1b; 2a,b; 5
Fri. Jan.22	5.2 Computational estimation 5.3 Estimating values of quantities	5.1 #1a,c; 2c,e; 3c,e; 4d
	Introduce EALRs & GLEs
Week 4	Class Session Schedule Log into student computers	The homework is listed on the day it is due.
Mon. Jan.25	5.4 Using scientific notation 5.5 Estimating fractional values 5.6 Issues of learning: Mental computation	5.2 #1, 2, 7b,c,d; 8b,d,f 5.3 #2, 4
Tues. Jan.26	Chapters 3, 4, & 5 review	5.4 #1a, 4, 8, 10
Weds. Jan.27	CH. 3, 4, & 5 TEST
Thurs. Jan.28	NO CLASS
Fri. Jan.29
Week 5	Class Session Schedule	The homework is listed on the day it is due.
Mon. Feb.1	Go over CH3-5 test	Esquith, Rafe, (2003) Chapter 10: ”When Numbers Get Serious” Bring in the rough draft of your essay. Link to rubric
	Ch.6 Meanings for Fractions 6.1 Understanding the meaning of a/b 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.
	Edit/Revise Essays
Tues. Feb.2	6.2 Equivalent (equal) fractions Video Clip 3: Rachel explains how to change a mixed number into an improper fraction.	6.1 #2a,b,c; 4, 6a,b; 8b,c; 13, 20, 21
Weds. Feb.3	6.3 Relating fractions and decimals	6.2 #1; 2b; 5, 6, 7a,c; 10a
Thurs. Feb.4	6.4 Estimating fractional values 6.5 Issues of learning: Understanding fractions and decimals	6.3 #1b,d; 2b,d,f; 3, 4b,c; 5, 9
Fri. Feb.5	Ch.7 Computing with Fractions 7.1 Adding and subtracting fraction 7.2 Multiplying by a fraction Video Clip 5: Felisha explores basic fraction concepts.	Midterm Essay Due
		6.4 #6, 8, 10, 12a,e,h; 13, 17a,c,e
Week 6	Class Session Schedule	The homework is listed on the day it is due.
Mon. Feb.8	7.3 Dividing by a fraction Video Clip 6: Elliot shows how to divide fractions.	7.1 #1, 3a,c; 8, 9, 10 7.2 #1, 3, 6, 12a,c; 16, 17
Tues. Feb.9	Winter Quarter In-Service	No Classes
Weds. Feb.10	7.4 Issues of Learning: Notes on teaching calculations of fractions	7.3 #1, 2, 3a,c,e; 7, 13, 14b,d,f
Thurs. Feb.11	Ch.8 Multiplicative Comparisons Reasoning 8.1 Quantitative analysis of multiplicative situations	7.4 #2, 6, 8
Fri. Feb.12	8.2 Fractions in multiplicative comparisons 8.3 Issues of learning	8.1 #1a,c; 3
		Project Overview due Email You have 3 weeks to complete activity with students
Week 7	Class Session Schedule	The homework is listed on the day it is due.
Mon. Feb.15	President’s Day	No School
Tues. Feb.16	Chapters 6, 7, & 8 Review	8.2 #1, 3, 6
Weds. Feb.17	CH. 6, 7, & 8 TEST
Thurs. Feb.18	Go over CH6-8 test	No hmwk
	Ch.9 Ratio, Rates, Proportions 9.1 Ratio as a measure 9.2 Using proportions to compare ratios and solve for missing values
Fri. Feb.19	9.3 Percents in comparisons and changes 9.4 Issues of learning: Developing proportional reasoning 9.5 Check Your Reasoning	9.1 #3e,f,h; 5 9.2 #2, 5, 7, 18, 20
Week 8	Class Session Schedule	The homework is listed on the day it is due.
Mon. Feb.22	Ch.10 Expanding Our Number System 10.1 Adding and Subtracting Signed Numbers 10.2 Another Way to Think about Addition and Subtraction	9.3 #6, 7, 8, 9, 15, 17, 18, 20a,c,e,g,i; 21a,c,e,g,i
Tues. Feb.23	10.3 Multiplying and Dividing Signed Numbers	10.1 #1,4, 6, 10 10.2 #3
Weds. Feb.24	12.5 Algebraic Reasoning about Quantities 13.1 Using Graphs and Algebraic to show quantitative relationships	10.3 #3, 4, 7a,c,e,g,i; 8
Thurs. Feb.25	13.2 Understanding Slope: Making connections across quantitative situations, graphs, and algebraic equations 13.5 Issues for learning: Algebra in the elementary grades	12.5 #3 13.1 #3, 5
Fri. Feb.26	Chapters 9, 10, 12.5, 13.1, & 13.2 Review	13.2 #1, 4, 5
Week 9	Class Session Schedule	The homework is listed on the day it is due.
Mon. Mar. 1	CH 9, 10, 12.5, 13.1, & 13.2 TEST
Tues. Mar.2	Ch.14 Understanding Change: Relationships among time, distance, and rate 14.1 (13.1) Distance-Time and Position-Time graphs	No hmwk Please note section number in italics is the corresponding section in the old edition.
	Go over Ch 9, 10, 12.5, 13.1, & 13.2 Test
Weds. Mar.3	14.2 (13.2) Using Motion Detectors [need motion detector]	14.1 (13.1) #6, 8 bring in graph paper and ruler Over & Back Applet
Thurs. Mar.4	14.3 (13.3) Graphs of Speed against Time 14.4 (13.4) Interpreting Graphs 14.5 (13.5) Issues for Learning: Common Graphing Errors	14.2 (13.2) #1, 2
		Activity with students should be completed
Fri. Mar.5	Project Group Work - we will be working on the Activity Description and Analysis in class today.	Bring in your Project (thumb drive). Your activity should be completed.
		Service Learning supervisor’s evaluation due
Week 10	Class Session Schedule	The homework is listed on the day it is due.
Mon. Mar.8	Ch.12 What isAlgebra 12.1 (14.1) Algebra as Symbolic language	Activity Description due Email
		14.3 (13.3) #1, 3, 5, 8, 9 14.4 (13.4) #1,2, 5
Tues. Mar.9	12.2 (14.4) Algebra as generalized arithmetic	12.1 (14.1) #1, 5, 8, 10 , 14 a, d
Weds. Mar.10	15.3 (14.2) Different Approaches to Problems	12.2 (14.4) #2a,b; 3; 4; 5, 11
Thurs. Mar.11	15.4 (14.3) Average speed and weighted averages	15.3 (14.2) #4, 5, 8
Fri. Mar.12	15.6 (14.5) Issues for Learning: Topics in Algebra	15.4 (14.3) #1, 3, 6, 8
Week 11	Class Session Schedule	The homework is listed on the day it is due.
Mon. Mar.15	Ch. 12.1, 12.2, ch14, 15.3-15.6 Review	15.6 (14.5) #2, 3a,d; 4c,f; 6
Tues. Mar.16	CH. 12.1, 12.2, ch14, 15.3-15.6 Test	Service Learning Reflection Paper Due and timesheet
Weds. Mar.17	Finish test	Activity Analysis Complete template publication ready due Email
	Project Group Work
	Course Evaluation
Thurs. Mar.18	Go over Ch 12.1, 12.2, ch14, 15.3-15.6 Test	Project Consent Form Copies of student work
	Project Presentations
Fri. Mar.19	Final Review
Finals Week	Class Session Schedule	The homework is listed on the day it is due.
Tues. Mar.23	FINAL EXAM	8-10am

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

Course Calendar

Week 1

Thurs. Jan.7

Fri. Jan.8

Week 2

Week 3

Week 4

Week 5

Weds. Feb.3

Fri. Feb.5

Week 8

Week 9

Mon. Mar.15

Tues. Mar.16

Weds. Mar.17

Fri. Mar.19

Finals Week