Outline:
1. Overview:
A. Time to glance through the packet of stuff. (10 mins)
B. How I got to this point. (Intro to me, Reasons for portf. – 10 mins)
C. Summary of packet contents. (5 mins)
D. Examination of packet, taking notes (5 min)
E. Discussion (10 min)
F. Develop own portfolios (10+ mins)
2. Intro to me (origins of my interest)
A. Interplay of math & language, esp. role of language in communicating math
B. As a grad student @ UW
1) Steve Monk – Vygotskian, hence social constructivist; opened my eyes to the role of metaphors in math learning
2) Caspar Curjel – “out of the closet” rhetorician, introduced me to the analysis of a rhetorical context, prompted my collaboration with others (highly recommended!)
C. As an instructor
1) Futility of searching for profound relevance
2) Desire to develop a learning community, hence the need for honest dialogue.
3. Reasons for turning to portfolios.
A. I feel that students truly reveal their understanding of concepts when forced to explain them in words. The attempt to do so also stimulates additional learning and provides some motivation for knowing an idea.
My initial attempts were to introduce more writing into my classes:
A) “How To” manuals for working with fractions
B) Math 95 – Student papers making arguments supported with data & graphs
C) Learning journals (not so good)
B. Writing department already uses as exit criteria: Idea of requiring students to own their knowledge and explain to me what they know was appealing.
C. More holistic assessment of student learning.
D. Encourages reflection on learning habits.
E. Accommodates multiple learning styles.
F. Mike Kenyon provided a helpful packet and model, much like I hope to do today.
4. In the packet:
A. Notes sheet
B. Contents page
C. Words of advice
1) Make explicit your reasons for using a portfolio
2) Clearly describe the learning objectives and measurable behaviors that will show achievement of the objectives
3) Have others check that your descriptions indeed describe what you say they do
4) Don’t assign too many points to any one criterion – it just makes judgment calls harder and slows your grading
5) Spend a class day building a sample assessment letter with your class (have a student take notes), type up the notes, and give that back as a template to follow.
D. One intact course: Precalculus
1) Syllabus
2) Some of the “weekly course objectives”
3) A quiz
4) Exams
5) Portfolio assignment
6) Scoring rubrics
7) Sample self-assessment letter
E. Math & Study skills portfolio (Arithmetic)
1) Assignment
2) Rubric
F. Streamlined portfolio (Algebra & beyond)
1) Assignment
2) Rubric
3) 81 exam
G. Samples of student work
5. Give them 10 minutes to examine the packet, ask them to make notes about things that sparked interest or a question.
6. General Q & A.
7. Developing own portfolios.
A. Pick a topic that is rich enough to contain at least one big idea and a number of techniques.
B. Describe the key ideas in your topic
C. Describe at least three key skills
D. Describe two to three ways your students could demonstrate sufficient understanding of one idea and one skill.
8. Discussion & Refinement
CONTENTS:
(Note: The packet starts on page 3 since my presentation notes occupied pages 1 & 2. So, no, you’re not missing any pages.)
Questions to consider before constructing a portfolio assessment tool
A Precalculus course
pp. 4 – 7 / Syllabuspp. 8 – 9 / Some of the “weekly course objectives”
p. 10 / Knowledge Inventory
pp. 11 – 12 / Portfolio assignment
p. 13 / Sample self-assessment letter
p. 14 / A quiz
pp. 15 – 21 / Exams
p. 22 / Scoring rubrics
A Portfolio for a Math & Study skills course
pp. 23 – 25 / Portfolio assignmentp. 26 / Scoring rubric
A streamlined portfolio that is applicable to most courses
pp. 27 – 28 / Portfolio assignmentp. 29 / Scoring rubric
pp. 30 – 32 / First exam for a Prealgebra course
Samples of student work
(Included at the end of the packet)
Words of advice for constructing your own portfolios
· Make explicit your reasons for using a portfolio
· Clearly describe the learning objectives and measurable behaviors that will show achievement of the objectives
· Have others check that your descriptions indeed describe what you say they do
· Don’t assign too many points to any one criterion – it just makes judgment calls harder and slows your grading
· Spend a class day building a sample assessment letter with your class (have a student take notes), type up the notes, and give that back as a template to follow.
Welcome to Math 115: Precalculus I!
The packet you have before you contains some of the most important information you’ll receive from me. The cover letter you are now reading will (hopefully!) give you the big picture for the class. It describes what you are expected to learn as well as my teaching philosophy. The rest of this packet is the formal syllabus for the course – all the details on how to reach me, the materials you need, my class policies, my grading system, and a daily schedule for the quarter. Read this entire packet carefully – it is a CONTRACT between you and I, and you have already agreed to it by signing up for my class.
So, what is the goal of this class? In a nutshell, it gives you an introduction to the basic properties and types of functions. Functions are the mathematical objects that allow us to convert one number to another in a predictable way; for example, the instruction “When a number is provided, multiply it by seven.” describes a function. Functions allow people to describe how things change with time, something algebraic equations cannot do. So even though most of your prior math training focused on equations, much of your future math coursework will revolve around functions.
The list below describes all of the skills the college and state expect you to have at the conclusion of Math 115. You should be able to
· understand the concept and notation of functions, as well as be able to graph them and identify a specific function’s domain, range, and inverse,
· recognize and graph polynomial functions, as well as be able to find or approximate the zeros of polynomials (especially using synthetic division),
· recognize and graph rational functions,
· recognize and graph absolute value functions,
· recognize and graph exponential functions,
· recognize and graph logarithmic functions,
· apply the above knowledge to verbal problems,
· compose proofs by mathematical induction,
· understand the basic topics relating to sequences and series,
· and use a graphing calculator to help you accomplish the above tasks.
You can see from this list that I wasn't kidding about this course focusing on functions. I also need to call attention to a particular entry in the above list – “compose proofs by mathematical induction.” This course objective should be viewed as a serious wake-up call! It signals the fact that Math 115 emphasizes mathematical THEORY, and NOT just mechanical techniques. This will be hard for many students in the class because it means a person can't just learn these ideas by simply following examples, which is exactly how most people have learned math up until now.
To help you learn in this new way, I will do a number of things. First, I will set aside class time to help you learn to read and understand the way math books present theoretical ideas. I will expect you to regularly ask questions about the descriptions (NOT the examples or homework) in the textbook as part of class discussions. Second, I will try to clearly indicate when you should be focusing on a skill and when you should focus on an overall concept. It will help me remember if you ask when you are not sure. Third, I will require you to participate in an online discussion group (like a chat room) as a way to help questions get answered and ideas get clarified outside of the limited time we have in class. Fourth and finally, I will evaluate you using a “portfolio” approach that provides an opportunity for revision.
Again, welcome to my class, and I look forward to working with you.
-Erik
Instructor: Erik Scott
Office: Building 18, Office 109
Office Ph#: (206) 878-3710, ext. 3113; FAX: (206) 870-4850
Email:
Web Page: http://flightline.highline.edu/escott
Office Hours: 11:00 – 11:50 M – F in my office, and by appointment
Class Time and Location: 1:10 – 2:13 M – Th in Bldg. 17, Rm. 103
Text: Precalculus: Functions and Graphs, 5th ed., by Barnett, Ziegler, and Byleen ($104.75 new/$78.50 used at the bookstore in Building 6)
Other Required Materials/Fees: A graphing calculator (TI-83 Plus preferred, TI-86 okay), which may be rented from the mathematics department for $20 per quarter. (The TI-83 Plus costs about $100.)
Prerequisite: Completion of Math 97 with at least a 2.0, COMPASS Algebra score above 70, or an approved equivalent course.
Course Overview
Math 115 is intended to expand your vocabulary of mathematical functions. Just as equations have been the central object of study in your previous math classes, functions will be at the center of much of your remaining mathematical training. This course will help you become skilled at using function notation and creating new functions using algebraic operations. You will also learn how to identify where functions are valid (domains and ranges) as well as key features (zeros and asymptotes). Finally, you will be introduced to methods for deriving formulas and working with infinity through your exploration of sequences and series.
Class Policies (subject to revision as needed)
· Class Participation – As you probably know, learning math is a lot like learning a foreign language – you learn and understand it best by trying to use it. I will therefore have you spend a lot of class time working on problems and activities. At different times you will work on your own, with your neighbors, or in preassigned groups.
· Attendance – I do not include attendance in my grading scheme. However, missing opportunities to discuss the ideas with others will make it very difficult to understand some concepts. It is not my (or your classmates’) responsibility to teach you the material you missed! Furthermore, you can only earn credit for in-class activities by actually being in class. (Amazing how that works, huh?)
· Late Arrival/Early Departure – All of us have reasons to arrive late or leave early once in a while. If you must do so, please respect your fellow students and me by moving yourself and your belongings quietly and generally not being a distraction.
· Cell Phones/Pagers – Allowing your cell phone or pager to ring in class is disrespectful to your classmates and the instructor, and it interferes with people's ability to learn. DO NOT answer a phone call in the classroom. Turn your phones and pagers off or to silent mode when you come to class. Please tell me before class if you expect an important call. If this becomes a problem, I may reduce the grade of those students whose phones or pagers interrupt class.
· Cheating – In this class, there are times when you will work with others, and times when you will work alone. When I am trying to determine what you understand, I cannot allow copying of other students’ work. If you are caught doing so, you will receive a zero on that evaluation. I encourage you to work with others on homework assignments, though each person must turn in his or her own solutions. If you are unsure about whether you must work alone, please ask me or work by yourself.
Grading (percent of total grade is given in parentheses)
· Homework (20%) – Homework will generally be assigned and due twice a week. The purpose of homework is to provide you with a chance to practice both skills and concepts. The absence of a short time limit and your ability to have questions answered should make this the least stressful of your evaluations. Note that the speed at which we cover material limits the number of problems I can assign in each section. I will almost always assign fewer problems than you need in order to fully understand the ideas – it's up to you to do extra problems until you have mastered the skills. This part of your grade also includes all other evaluations not specified below.
· Quizzes (15%) – Quizzes provide a way for me to measure how well each individual student understands the skills we cover. You will take a 10 to 15-minute quiz almost every week. You will only be allowed to make up a quiz if I am notified in advance, and the absence is for a significant (documentable) reason, such as a family member in the hospital.
· Discussion Web Participation (5%) – This is my crafty way of encouraging you to discover how much you can learn by conversing with your peers. You can access it through the course page at http://flightline.highline.edu/escott/Courses/115webf02/115mat.html and will find details about acceptable postings provided on the discussion web itself. To earn full credit, you will need to make an acceptable posting to the discussion web once per week.