MAT 171
Mathematics for
Elementary School Teachers II
Geometry, Measurement,
Chance and Data
Winter 2008 Syllabus
Room SAM 301; Mon. & Weds. Professor: Andrea Levy, Ed.D. Office: SAM214 Box: SAM110 Office Phone: 206-587-4082 Email: alevy@sccd.ctc.edu Website: http://seattlecentral.edu/faculty/alevy Office Drop-in Hours: daily
11:00-11:50am or by appointment. Sowder, J., Sowder,
L., Nickerson, S., (2006-Pilot edition), Reconceptualizing
Mathematics for Elementary and Middle School Teachers: Module #3 Reasoning about Numbers and Quantities and Module #4 Reasoning about Chance and
Data, San Diego State University, National Science Foundation Grant No. ESI
9354104, W.H. Freeman & Co., NY (Available at the SCCC bookstore) Required Materials: Textbook
Modules 3 & 4, three-ring binder, scientific calculator, metric and
standard ruler, pencil, notebook paper, graph paper, compass, ruler,
protractor, scissors, transparent tape. From the Text: Make
the kit from the nets found in the first chapter (store in shoe box). Use the
square dot paper and the isometric dot paper in your materials as masters and
make several copies of each. Optional Materials: Set of 100
interlocking snap cubes, student membership to NCTM Supplementary
Readings/Website Access: OSPI:
Essential Academic Learning Requirements (EALRs) http://www.k12.wa.us/CurriculumInstruct/default.aspx
NCTM: Principles and Standards for Science and
Mathematics http://www.nctm.org/standards/ Teaching Children Mathematics
Magazine (optional) http://my.nctm.org/eresources/journal_home.asp?journal_id=4 This course delves deeply into the mathematics elementary teachers are responsible for teaching at the K-8 levels. The mathematics examined in this course covers polyhedra, polygons, symmetry, tessellations, size changes, curves and curved surfaces, transformations, length, angles, area and surface area, volume, measure formulas, reasoning, chance, probability and data analysis. You will gain knowledge of the underlying concepts
related to exploring
geometric and measurement concepts that you already know from a new
perspective, exploring some concepts that are new to you, and developing your
visualization skills. The course is
designed to improve your basic content knowledge, model methods of teaching
mathematics to K-8 students, engage you in activities that increase
confidence and enthusiasm for the subject area, and familiarize you with
local and national standards for teaching mathematics. 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. One major goal of this
course is that pre-service and current elementary school teachers develop a
deep understanding of the geometric and measurement concepts. A second major
goal is to help students develop a deep sensitivity to sense-making, with an
emphasis on explanation and justification.
The key ideas presented in this course are as follows, although not
necessarily in this order: 3-D and 2-D Shapes - Construct polyhedra and
develop workable vocabulary for describing and distinguishing 3-D shapes. - Explore geometric solids
and their properties. - Explore and review
polygons with an emphasis on the relationship between sides and angles. - Planar symmetry developed
using tessellations. - Issues of similarity with
emphasis on multiplicative relationships (ratio/proportionality). - Multiplicative comparisons
of surface area and volume (squaring and cubing). - Planar curves with an
emphasis on mastering circle vocabulary. - Curved surfaces with a
cross-cultural (cross-disciplinary) element. - Transformation geometry
with emphasis on rigid motion/isometry. Measurement - Key ideas of measurement
with a focus on understanding standard units and the metric system. - Cross-cultural aspects of
measurement systems. - Explore how approximation
relates to measurement. - Area, perimeter, length,
and surface area are explored and calculated - Explore volume to
understand it conceptually. - The history of Pythagorean
Theorem, introducing a Chinese proof, and recognizing Pythagorean triples - Measuring temperature:
Fahrenheit, Celsius, Kelvin - Measuring volume: tbsp,
tsp, cups, pints, gallons, etc. - Development of area
formulas: relationship to area of a rectangle - Development of volume
formulas: layering and relation to area of a rectangular prism - Conservation of volume Data
Analysis and Probability - Reasoning About Chance - Chance Events - Methods of Assigning Probabilities -
Simulating
Probabilistic Situations - Tree Diagrams and Lists for Multistep Experiments - Probability of One Event OR Another
Event - Probability of One Event AND
Another Event - Conditional Probability - Sampling: The Why and the How - Simulating Random Sampling - Types of Data - Conducting a Survey - Representing Categorical Data with
Bar and Circle Graphs - Representing and Interpreting
Measurement Data - Examining the “Spread-outness” of Data - Measures of Central Tendency and
Spread - Examining Distributions - Issues for Learning: Understanding
the Mean - Comparing Data Sets -
Lines
of Best Fit and Correlation - Having Confidence in a Sample
Statistic - Confidence Intervals You are expected to attend all
class sessions, arrive in class on-time and be prepared for the daily lesson.
Being prepared means that homework assignments are complete, and 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. 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 assignments 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. No
late work will be accepted; therefore, if you know you will be absent,
email your work before the day it is due. Completing and handing in
homework on time is essential as it prepares you to be a full participant in
the class activities. Tests 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 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. If you decide to sign-up for the full three-course math
series, you can apply your project to the two service credits you will
receive. 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: 20% class participation, 20% homework – Math
Problems; 40% tests and final exam, and 20% quarter project. o
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. o
Homework: Math Problems—10 points. Homework is due at the start
of each class session, and are listed on the day
they are due on the Course Calendar. No late work will be accepted; however
you may submit them early by email or in class if you know you will be
absent. o
Tests are 100 pts. Since tests are designed for working in groups, it
is important that you make every effort to attend, arriving on-time, and
prepared so that you can support one another. The Final Exam is 100 points
(the final exam grade can replace lowest test grade.) o
Quarter Project is 100 points. Please see the Project Protocol
page for details. 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 visit the math lab in SAM 106, Mon-Thurs
9AM—6PM, Fri 9AM—4PM. 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. |
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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, 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 Overview – 1st
section of template
1.
Identify the Project Theme, Grade Level, and Mathematical Concept for
your project. 2.
Identify the EALRs and NCTM Standards that relate to your
project, indicating the primary and supplementary standards. 3. Make a record/bibliography of literature,
websites, and information sources (i.e., elementary school teachers, after
school programs) that relate to 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. 5. Determine the time frame and
location for conducting an activity If you are doing
this project in combination with service-learning credits, then you will work
with your cooperating teacher to establish your project parameters. http://seattlecentral.edu/faculty/alevy/service_credits.htm
Activity Description – 2nd
section of 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. c) Record any adjustments you made to
the activity to fit your parameters, time constraints, student interest/abilities,
EALRs
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 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)
Explain how you could integrate this activity into a regular
elementary school curriculum. 6)
Has this project changed how you think about 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.
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