Mathematics

Accelerated Algebra Syllabus

Purpose of Course

The accelerated algebra course was specifically designed for motivated students to progress towards their mathematics or statistics course required by their major in one less semester. The purpose of all of the developmental mathematics courses is to support student success academically and beyond by advancing critical thinking and reasoning skills. Students, as a team, will examine final answers in terms of reasonableness to the given problem and to determine if the answer addresses the original problem (Polya step 4). In addition, students will explore the power of estimation as a tool to determine accuracy of solutions to numeric and or real world problems. A theme throughout the semester is to examine statements to determine if each is sometimes true or always true. Students will then justify each claim with examples if sometimes true or give a complete justification if always true.

TEACHING TEAM

Dr. Kirsty J Eisenhart (administrative)
Mrs. Thayma Lutz (content)

Instructors

See the program schedule or course times, rooms, office hours and final exam dates.

OVERVIEW

This accelerated algebra course was designed to incorporate pre-algebra number sense topics while covering Algebra I topics such as linear verses exponential functions. Students will be asked and encouraged to find patterns, make conjectures, and judge the validity of given conjectures. The students will test their conjectures and eventually provide counter examples to disprove invalid conjectures or give justifications for conjectures they determine are valid.

Accelerated Math 1100 enhances students’ basic math skills through the study of key skill strands that are explored across different types of numbers, including whole numbers, fractions, signed numbers, mixed numbers, and decimals. The skill strands covered in this course include estimation, numeric operations, properties of numbers, comparing numbers, converting numbers, proportional reasoning, interpreting mathematical notation, simplifying expressions, evaluating expressions, solving equations creating model for real world problems, and providing practical meaning of solutions or parts of a model in terms of the real world context provided.

Learning Objectives

By the end of this course, students will be able to

Analyze, model and solve real world problems
Consider the real-world context to determine the practical meaning of answers or components of a model
Justify conjectures and/or answers with written explanations and diagrams or computations as appropriate
Calculate efficiently by using the properties of numbers and operations and simplify answers as appropriate
Use estimation and/or the context of a problem to determine if final answers are reasonable
Determine if a given statement is sometimes true or always true and justify with examples if sometimes true or give a complete justification if always true

Number sense
Equivalent expressions
Contradictions, conditional equations or identities
Analyze work containing mathematical misconceptions and develop an argument, usually containing a counter example, to convince a peer that the solution is flawed

Given a function in either verbal, numeric (table of values), or symbolic form, determine if the function is linear, exponential or neither and provide a complete justification to support the claim
Use valid strategies in terms of number and variable properties to evaluate expressions, simplify expressions and solve equations

Learning Goals

Throughout the course, students will

Enhance mathematical skills and competencies fundamental to success in academic and professional contexts by developing and applying critical thinking skills
Establishing patterns of behavior that lead to academic and personal success

Observe how group problem solving enhances the learning of mathematics
Explore ways to organize class materials in a way that enhances learning
Discover how pre-reading and post class notes free up class time for deeper thoughts and discussions
Examine different ways to organize one’s time to be able to budget time

Use properties of numbers motivate common “rules” in mathematics. For example, understand how collecting like terms is the result of the distributive property of multiplication over addition
Observe how common misconceptions are made when using the properties of numbers and develop ways of deconstructing these misconceptions, like testing values
Discover how some algebraic misconceptions are due to a misuse or generalization of mathematical terms. For example, truncating the distributive property of multiplication over addition down to just the distributive property might lead peers to think all operators distribute over all other operators.
Re-read directions to make sure final answers address the given question and address the questions completely

Required course materials

Course Pack: The course pack contains some of the worksheets for the course and the writing assignments. Your instructor will inform you about how to obtain a course pack.
Three-ring notebook
graphing calculator

COURSE FORMAT AND PARTICIPATION

This is a laboratory-oriented course in which you will often investigate mathematics collectively (with a partner, in small groups, or whole class). Whole class discussions of different solutions to a problem and the mathematics underlying these solutions will play a central role in this course. Though these discussions will take different forms on different occasions, it will always be the case that your ideas, strategies and questions will guide the discussion. Thus, as a class, we will examine each other’s thinking and come to a better understanding of the mathematics by doing so.

Given the student-centered nature of this course, attendance and participation is of the utmost importance. Satisfactory participation means that you are willing to share your thought process, questions and solutions with the class (even when you don’t think you have the right answer), that you support your classmates by listening and thoughtfully reacting to their ideas, and that you attempt all of the homework before class so that you can actively participate in our discussions. Consistent and productive participation in class will be considered in determining final grades (see participation rubric below).

GRADING POLICY

If all course requirements have been met, grades will be assigned according to the scale.

A: 90-100 percent
BA: 85-90 percent
B: 80-85 percent
CB: 75-80 percent
C: 70-75 percent
DC: 65-70 percent
D: 60-65 percent
E: Below 60 percent

You must attain at least a "C" in this course in order to take the next mathematics course which satisfies Proficiency 3 of your general education requirements or quantitative literacy for essential studies.

COURSE REQUIREMENTS

The following is a tentative outline of the required graded assignments and their weights:

Exams: 38.5 percent of final grade
Comprehensive final exam: 25 percent of final grade
E-Learning on-line homework: 15 percent of final grade
Writing assignments: 10.5 percent of final grade
Class participation notebook checks and other assignments: 11 percent of final grade

Attendance policy

Each class utilizes tools and concepts learned from previous classes, so to optimize your understanding be sure to arrive on time and stay until you are dismissed. Excessive absences, tardiness, and early departure suggests a lack of professionalism and commitment, and will result in missing material and the objectives of this course. To reward you for your professionalism, class participation is a portion of your final letter grade (see participation rubric below).

Course notebook

Being able to find your past assignments and class notes will reduce the time spent studying. If you have a method to organize your materials, continue to use this method. If not, we suggest you organize your work for this course in a notebook ( (e.g. one-inch three-ring binder) that includes the following sections:

Activities with in-class notes. Use this section to organize your completed work from each activity along with the notes you took during class. You are expected to finish any activity not completed in class.
Post-class notes. It is often the case that you may have difficulty taking notes on the discussions that occur during class. For this reason we require that you take at least 10 minutes after each class to capture important mathematical ideas that have been discussed during class. This will help to solidify your understanding, and highlight areas/issues around which you still have questions. Post-class notes will save you valuable time when studying for an exam. Along with providing the main ideas of the activity, the post class notes could also contain "aha" moments (a defining moment in which you gained real wisdom or insight), a list of questions you still have about the material in the activity, and a "cheat sheet" like list (things you would need to know for an exam: definitions, formulas, important examples, calculator key strokes, etc).
Scratch work. Use this section to organize scratch work from E-Learning quizzes. Most of the problems on this online homework will require paper and pencil calculations. You will not want to complete the assignment in your head or with a calculator since portions of your exams will not permit calculators. You will want to keep all of your work, correct and incorrect calculations. We highly recommend crossing out incorrect work rather than erasing it and then write yourself some notes as to why your first methods were invalid. This will help you learn from your past errors rather than repeat them.
Assignments and exams. This section will contain all of your exams and assignments. You will want to keep both the graded and not graded assignments in this section as well as all of your drafts of each assignment so that you can reflect on all before tutor sessions, group homework sessions, or an exam.

The goal is to make your notebook into something that will serve as a resource for you over time. This will also serve as your main resource when studying for each exam. Items within your notebook will be assessed through various means. Therefore, it is critical to always bring your notebook to class with you, and to keep up on your daily work and seek help when you don’t understand an assignment. If you have a more efficient way of organizing your notebook, discuss your plan with your instructor. Otherwise, your note book should contain four sections as described above.

Collaboration

Your instructor might allow/encourage students to work together on assignments. What this means is that students can share strategies. You cannot share final versions of assignments. The final polished version of the assignment must be your own work. Similar problems may appear on an exam, so you will want to be sure that you can complete each problem on your own after working with peers.

Assignments

In order to succeed in any class, it is critical that you stay on top of your assignments. Be sure to start your homework early and utilize your instructor and the tutor lab when needed. Also to keep you on schedule, late homework will not be accepted. In the event that you must be absent from class, have your homework delivered to your class. If allowed by your instructor, you may either send an e-mail scanned copy of your homework before class or have your homework delivered to the Math Department mail room before class. Each instructor has a mailbox in the Math Department office on the 3rd floor of Everett Tower. Be sure to attach a cover sheet to your homework that contains your name, class time, and instructor's name.

E-Learning

We use E-Learning as an online interactive tool that can provide immediate feedback. All quizzes can be attempted infinitely many times, so start early and retake the quiz until you earn a 90 percent or higher. We will be utilizing this tool to help strengthen your mathematical skills and help you to become more efficient. Efficiency will be vital for your success in both this mathematics course and the next. After completing an activity in your text, go to E-Learning and take the corresponding quiz. Note that most quizzes will be due shortly after you finish the corresponding activity in class. Be sure to visit E-Learning a few times throughout the week so that you do not miss a due date. If you miss a quiz due date, you can take the quiz with penalty. You can earn at most a 75 percent on the penalty quiz, but this is much better than a zero.

Exams

There will be five unit tests worth a total of 38.5 percent of your final grade: three 25 minute exams worth 5.5 percent each and two 50 minutes exams worth 11 percent each. Most of the problems on the unit tests will be similar to, or elaborations of, homework and group work. Each exam will contain at least one problem very similar to the writing assignment problems. Note that the sections in your text entitle "What Have I Learned?" are like our writing assignment problems, so these would be good practice problems prior to an exam. Other questions may test definitions, example problems, and/or class work. Note that answers to selected section problems are in the back of your text. You may wish to use these as practice problems. The final will be a comprehensive test worth 25 percent of your grade. If you are unable to attend class on any exam day you must notify Dr. Eisenhart (269) 387-4117 or (269) 873-8194 before the exam or a make-up may be denied. All APPROVED make-up exams will be given on the mass final exam date: Thursday, Dec, 12 some time in the evening.

Accommodations

Any student with a documented disability (e.g., physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable accommodations must contact their instructor and the appropriate disability services office at the beginning of the semester. If you believe you need some type of accommodation due to a disability and haven’t yet talked with the Disabled Services for Students office, do so immediately.

Policy on incompletes

According to University policy, incompletes are given only in those rare instances when extenuating circumstances have prevented a student from completing a small segment of the course. An incomplete is never given as a substitute for a failing grade and the Chair of the Department of Mathematics must approve all incomplete grades. The last day a student can officially withdrawal from a class to avoid a failing grade is Monday, October 28 for fall 2019.

Student conduct

Please familiarize yourself with the student code of conduct and the definition of plagiarism. The use of cell phones is strictly prohibited during class, unless it’s a life-and-death emergency. Silence your phones, tablets, iPods, etc., at the entrance of the classroom and store them. If seen using one of these devices, you will be asked to leave since this is disruptive not only to the class but also the instructor. If there is an emergency situation, place your devise on vibrate, sit close to the door and leave the classroom as inconspicuous as possible. For a complete copy of the student conduct code go to the office of student conduct.

Academic integrity

Students are responsible for making themselves aware of and understanding the University policies and procedures that pertain to Academic Honesty. These policies include cheating, fabrication, falsification and forgery, multiple submission, plagiarism, complicity and computer misuse. The academic policies addressing Student Rights and Responsibilities can be found in the Undergraduate Catalog.If there is reason to believe you have been involved in academic dishonesty, you will be referred to the Office of Student Conduct. You will be given the opportunity to review the charge(s) and if you believe you are not responsible, you will have the opportunity for a hearing. You should consult with your instructor if you are uncertain about an issue of academic honesty prior to the submission of an assignment or test.

Professionalism and Mutual Respect

Students and instructors are responsible for making themselves aware of and abiding by the “Western Michigan University Sexual and Gender-Based Harassment and Violence, Intimate Partner Violence, and Stalking Policy and Procedures” related to prohibited sexual misconduct under Title IX, the Clery Act and the Violence Against Women Act (VAWA)and Campus Safe. Under this policy, responsible employees (including instructors) are required to report claims of sexual misconduct to the Title IX Coordinator or designee (located in the Office of Institutional Equity). Responsible employees are not confidential resources. For a complete list of resources and more information about the policy see www.wmich.edu/sexualmisconduct

In addition, students are encouraged to access the Code of Conduct, as well as resources and general academic policies on such issues as diversity, religious observance, and student disabilities:

Class participation rubric

Class participation will be informally assessed on a continuing basis. Class participation grades will be based on participation in both small group and whole group settings.

A: Contributing to others' learning

This is the goal of the class. This does not mean telling or showing someone else how to do something. Sometimes it means sharing your thoughts about the mathematics so that others can analyze and learn from it. Always it means listening carefully to what others are saying, connecting what you hear to your own thinking and asking questions that will help everyone involved better understand the mathematics. The expectations for receiving this grade will increase as the semester goes on. That is, it is assumed that these are skills that you are learning so in the beginning attempts at doing this will be sufficient to earn the grade. As you develop these skills, it will require competence in them to earn the "A".

B: Contributing to one’s own learning

Here you are clearly engaged in learning the mathematics, but haven’t moved outside yourself to interact well with others. It generally means doing quality work, but not being willing to share your thinking with others or not showing interest in making sense of their thinking. In the context of whole class discussion, it would mean listening and learning, but not sharing your ideas or observations with the class.

C: Getting by

This involves showing up, minding your own business and doing what you are told.

D: Interfering with learning of self or others

There are various ways one can do this; the most obvious are distracting group members from the task at hand or being belligerent about what one is asked to do. More subtle ways include implying someone is stupid because they don’t understand a problem or telling someone how to do a problem and thus undercutting their opportunity to figure it out for themselves.

F: Not there

This includes not being there physically and/or mentally. Note that whenever you are absent, it is your responsibility to make up the work, preferably before the next class so that you are able to participate in class.