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Augusta State University

Department of Mathematics and Computer Science

MATH 6243 * Understanding Algebra

Fall 2009 *Allgood Hall E260

 

 

           

Instructor

Linda Crawford, Ph.D.

Allgood Hall N322

(706) 667-4477

lcrawfor@aug.edu  (observe:  it is lcrawfor-----there is no “d”!!)

Office Hours

·            Monday & Wednesday, 2:30-3:45

·            Tuesday & Thursday, 11:30-12:30

·            Other times by appointment

 

 

Course Description

This course focuses on developing a deep understanding of the concepts and techniques related to algebraic thinking.  Collaboration, critical thinking, hands-on explorations using manipulatives, problem-based inquiry, and technological tools will be used to enrich understanding of how to develop algebraic thinking in students at the P-5 level.

Prerequisite:  Permission of Instructor

 

Purpose of the Course

This course focuses on preparing P-5 mathematics specialist candidates to:

 

Course Objectives

All students will be able to:

·         Express, extend, and generalize numerical and algebraic patterns and sequences.

·         Understand equality and equations as balance between quantities.

·         Recognize and create representations of quantitative relationships, including tables, graphs, algebraic symbols, verbal descriptions, manipulatives, and geometric figures, and translate flexibly among such representations.

·         Understand and use letters to represent numbers or quantities (variables, unknowns, and parameters).

·         Explore mathematical problems in mathematical and real-world contexts and interpret results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations.

·         Recognize and use the commutative, associative, distributive, additive and multiplicative identity, and additive and multiplicative inverse properties.

·         Recognize contexts in which proportional reasoning is appropriate and distinguish them from additive contexts.

·         Understand proportional relationships as multiplicative, where comparisons are relative and involve division, as opposed to additive contexts, where comparisons are absolute and involve subtraction.

·         Recognize proportional relationships in tables, symbols, diagrams, and words.

o   Understand that in a proportional relationship, one variable is a constant multiple of another.

o   Understand that the graph of a proportional relationship passes through the origin.

o   Understand that a proportional relationship can be represented symbolically as y = kx.

o   Understand that in a table, the ratio of y/x is constant.

·         Understand and apply properties of exponents, including zero, rational, and negative exponents, as well as scientific notation.

·         Understand and use absolute value as distance on a number line.

·         Evaluate numerical and algebraic expressions.

·         Add, subtract, multiply, factor, and divide algebraic expressions concretely, such as with length and area models, and abstractly.

·         Discover, recognize, and use patterns and special products in polynomials.

·         Solve equations and inequalities in one variable, using graphical, numerical, and symbolic methods, as well as informal reasoning, such as “backtracking” and the “cover-up” method.

·         Apply properties of equality to solve for a given variable in a formula.

·         Understand and apply the geometric meanings of the midpoint formula and the distance formula (i.e., the Pythagorean Theorem).

·         Understand and use the notion of function to express relationships between quantities.

·         Interpret and create function graphs, formulas (closed and recursive), and tables.

·         Determine whether a quantitative relationship given graphically, numerically, or symbolically is a function.

·         Investigate characteristics of particular classes of functions, especially linear, quadratic, and exponential functions, with some attention to absolute value, greatest integer, and piecewise-defined linear functions.

·         Recognize linear, quadratic, and exponential functions from graphs, tables, symbols, and contexts.

·         Identify and interpret the domain, range, intercepts, and zeros of functions, using various representations.

·         Recognize and interpret rate of change in contexts, tables, and symbols and as slope in graphs and via a definition.

·         Recognize and interpret y-intercept in graphs, contexts, tables, and symbols.

·         Using graphs, tables, and symbolic methods, determine extreme values as well as intervals over which a function is increasing or decreasing.

·         Determine the equation of a line in slope-intercept, point-slope, or standard form, including vertical and horizontal lines, given information such as points on the line, the slope, or the equation of a parallel or perpendicular line.

·         Apply symbolic, graphical, and other methods to solve systems of equations and inequalities.

·         Use the language of mathematics to formulate accurate, precise, and pedagogically appropriate definitions of terms related to algebra.

·         Reason from definitions to determine examples and nonexamples of mathematical ideas and to show that two definitions are or are not equivalent.

 

Pedagogy and Professional Development Objectives

 

Learning Outcomes 

All students will learn to:

1)    Understand patterns, relations, and functions.

2)   Represent and analyze mathematical situations and structures using algebraic symbols.

3)   Use mathematical models to represent and understand quantitative relationships.

4)   Analyze change in various contexts.

5)   Demonstrate a deep understanding of how P-5 students learn mathematics and of the pedagogical content knowledge appropriate to

P-5 mathematics teaching. 

 

Supplies

 

Some of the assignments will be in PDF form so you will need Adobe Reader software—this can be downloaded free from http://www.adobe.com/products/acrobat/readstep2.html

 

I often use Windows Journal to grade assignments you submit electronically. You may need the computer program Windows Journal Viewer to open the returned assignment. You can download it free by clicking on Windows Journal Viewer.

 

Some assignments will be submitted through GeorgiaVIEW Vista (WebCT Vista).  You can also access Vista through the My Courses tab on Pipeline.  If you need help with Vista, visit the online support center.

 

If you need help with technology, check with the Information Technology Student Help Desk--either in person or by phone.  The number is 706-737-1676.  Information about the Help Desk can be found at http://www.aug.edu/its/Welcome.html.

 

If you have a disability and wish to receive accommodations in class, please apply with the Office of Disability Services.

 

Assignments to be turned in are due at the beginning of the class period.  Put the assignment on my desk when you arrive for class.  Even if you are absent, your assignment is still due at the beginning of class.  If you will not be in class on a day that an assignment is due, you may email it to me or place it in my mailbox before class starts or send it with another student.  A late assignment will be accepted only in extreme and documented situations.

 

If You Have to Miss a Class…

MATH 6243 class sessions are interactive, providing many opportunities for you to express your own ideas and to listen to the ideas of your fellow classmates.  Much of what you learn in the course takes place by participating, sharing, and interacting with others through small-group and whole-group discussions.  This kind of learning cannot take place if you are absent so regular attendance and punctuality are required. 

 

Frequently, ideas that we introduce in one session are expanded upon and developed more fully in later sessions.  Thus, every class session is important.  However, if you find that you are unable to attend a particular class session or might miss a part of a session (by coming late or leaving early), please contact me as soon as possible.  Make arrangements to turn in assignments if you are going to be absent—even if you are absent you are expected to turn the work in when it is due.  You should ask a classmate to obtain any handouts given out during the class you will miss—do not ask me for handouts that you miss.  You are also responsible for any announcements made during the class.  Remember, you are going to be a teacher—you must take care of your obligations!

 

Prior to returning after a missed class you are responsible for meeting with a classmate(s) to discuss the class session you missed.  After this meeting you must write a 300-500 word “ Missed Class Paper” (typed) which includes the names of your classmates with whom you met, a description of the activities of the class you missed and how you engaged in these activities with your classmates, any research you might have done (use your book and the web as resources), an explanation of your understanding of the mathematical ideas investigated in class, any insights you gained, and any questions you have about these mathematical ideas.  The paper is not to be merely a list of what was done in class but instead shows your effort at making sense of these ideas and what learning you have gained.  This paper as well as any accompanying work from the missed class is to be handed in at the beginning of the next day’s class.  Two points are deducted from your participation grade for each absence; one point will be returned if your “Missed Class Paper” meets the criteria outlined above.

 

Roll will be taken; any student who is absent more than 10% of the class time may be dropped with a WF.  Excused absences count toward the 10%. 

 

The percentages to determine your course grade: 

           

·         Midterm exam—Wed, Oct. 7

25%

 

·         Other written or presented assignments—for ex, homework, quizzes, solutions of problems, reviews of websites or journal articles

 

15%

 

·         Ongoing assignments—for ex,  reflections & projects

20%

·         Participation—click here for more information

 

10%

 

·         Comprehensive final exam-- Mon, Dec 7, 6:00-8:00 PM 

30%

           

Other Written or Presented Assignments

The written or presented assignments may include quizzes, homework, in-class presentations, out-of-of class projects, reflective writings, reactions to readings, analyses of student work, analyses of mathematics lessons, solutions of problems, etc.

 

Homework

You will be assigned reading, writing, questions, and problems to be completed for homework.  All in-class activities will be based on the assumption that the required homework assignments and readings have been completed. This does not mean that all of your answers have to be perfectly correct. It does mean that you should have thought hard about each problem, made several attempts at solving it, and developed questions and conclusions about your solution strategies.  Not every homework assignment will be collected and graded.  Most homework assignments are listed on the assignment page; however, you are responsible for any assignment announced in class and not listed on this page.

 

Class Participation and In-Class Activities
     Much of the success of this course depends on your level of interaction and participation throughout the semester. As you will soon discover, we will spend most of our class time sharing ideas, solution strategies, insights, and questions. During class sessions, I will assess both your preparation for class (e.g. whether you completed readings and assignments) and the quality of your participation in course activities by observing and interacting with you. I will be paying particular attention to your willingness to listen, to discuss, and to contribute to whole-class and group activities.  Clearly, successful participation in this sort of class depends upon regular attendance.

Each class period will generally include a discussion of the homework and a review of the activities from the previous class.  Although the discussion will take different forms on different occasions, it will always be the case that your ideas, strategies, and questions will guide the discussion.  Sometimes, you will be asked to present a problem to the class. Other times, you may be asked to share your work in a small group. Other times, you and a small group of your classmates may work on a new problem related to your homework.  While I promise to support you in finding answers to your questions, please be warned that my support will NOT consist of simply explaining solutions of problems to you. My job is to help you develop meaningful understandings for yourself, with the help of your classmates. Because this is a student-centered class, it is of utmost importance that you attempt all of the homework problems before class and do the assigned readings so that you can participate in the discussion.  Satisfactory participation in this part of class means that you are willing to share your thought processes, questions, and solutions with the class (even when you don't think you have "the right answer") and that you also support your classmates as they participate.

During each class you will generally engage in some form of investigation of a mathematical topic. Typically, you will work cooperatively with 3 or 4 of your classmates, using various curriculum materials to guide your work.  This in-class work will provide a conceptual basis for your understanding of the course material.  Because your subsequent readings and homework assignments will build on these investigations, they require your careful attention. On occasion, without announcement, your in-class investigations may be collected. Also, you should be prepared to provide a written reflection on the in-class work.  Some class time will be spent discussing questions and ideas that arise from the group investigations.  It is imperative that you spend time outside of class reflecting on the group activities so that you fully understand the concepts.  Merely hearing another’s explanation is no guarantee that you understand. 

Your participation grade is determined using the Rubric for Participation.  Two points will be subtracted for any absence (you may receive a refund of 1 point—see the section “If you Have to Miss a Class”).

 

Course Notebook and Reflections

You should organize all materials (handouts, class notes, homework, readings, writings, tests) in a 3-ring binder.  This notebook will be a record of your work in the course and will also serve as a tool for reflection.  It will also be a valuable resource to you when you begin teaching. 

 

To assess your own growth as a mathematics educator you may be asked to  reflect on your progress in developing a deeper understanding of algebra and algebraic thinking.   Because your notebook chronicles your progress in the course, it is your primary resource for writing your reflections.  You should record those important moments when you experience a break-through in your understanding. 

 

Projects

·         Analysis of a Mathematics Video Lesson--To demonstrate your understanding of how to support students’ development of a mathematical concept in algebra, you will watch a videotaped mathematics lesson and reflect on your observations.

·    Analysis of an Algebra Instructional Unit—You will select and analyze an Algebra unit from the Mathematics Frameworks site of the Georgia Performance Standards.  

 

Professional Organizations

You are encouraged to join the following professional organizations:

 

Classroom Policies

·         It is a policy of Allgood Hall that food and drink are not allowed in the classrooms so cups, bottles, etc. should be capped and stored in your bag.  Furthermore, food and drink interfere with group activities and the use of manipulatives.

·         It is distracting to me and disruptive to the class activities if you leave the classroom during the class period.  Thus, I ask you to refrain from "taking a break" except for an emergency.

·         Visitors, including children, are not permitted without my prior permission.

·         You are expected to check your campus email regularly.

 

Academic honesty

Cheating will not be tolerated.  This pertains not only to in-class work but to outside assignments as well-any assignment that you submit as your own should be a report of YOUR thinking.  Any student who is caught cheating will face serious consequences.  You should read ASU's statement on academic honesty in the catalog.

 

Dates to Remember        

Mon-Tues, Sept 7-8

Wed-Fri, Nov 25-27

Holidays

Mon, Oct 12

Midterm date (if you plan to withdraw, do so no later than this date)      

Thurs, Dec 3

Fall semester classes end   

Mon, Dec 7, 6:00-8:00 PM 

Final exam

October 14-16 (Wed-Fri)

GCTM Conference at Rock Eagle—a limited number of rooms available for preservice teachers at $5.00 per night (GCTM membership required for this rate)

November 18-20 (Wed-Fri)

NCTM Regional Conference in Nashville

March 5-7 (Fri-Sun)

Teachers Teaching with Technology (T3) International Conference in Atlanta –Registration ($145) is complimentary for preservice teachers—register by January 22.