Algebra, like grammar, has very little pizzazz. A few hardy souls find
grammar interesting, but for most people it is dull and cannot be made
otherwise. And so it is with algebra. Even though there are teachers and
students who do find grammar interesting, and it can be expected that
algebra will likewise have its small band of enthusiasts, I make no effort
here to con the student into believing that algebra is useful or exciting
for everyone in everyday life.
– George F. Simmons, Precalculus Mathematics in a Nutshell
Welcome to Students
- What does this math course have to offer?
- Studying algebra is the first step in a progression that builds fluency in thinking abstractly about quantities and how they relate. Prior to learning algebra, you might already have a solid grasp of addition and multiplication facts, but they don't come alive to create new meanings until you appreciate the concept of a variable. This course develops from such small beginnings to explore four specific types of relations: linear, quadratic, polynomial, and exponential/logarithmic. Modeling applications are used throughout to ground our explorations in the world we inhabit.
- What are some skills that I can take from this class?
- Improved reading comprehension emerges as you work through word problems that require you to identify the unknowns, recognize what is relevant, and affix proper labels to the quantities given.
- Expanded mathematical vocabulary will allow you to express yourself clearly when talking about numerical observations in your everyday life. No more will you casually toss around the descriptor "exponential" as a catch-all term for any rapidly growing quantity.
- Better computational skills follow from a deepened understanding of the analogy between polynomials and our place-value system of representing whole numbers. The distributive law and the division algorithm give you new insight into the arithmetic procedures you learned in elementary school.
- What do I need to succeed in this class?
- Just as you would for any class you take in college, be sure to read the assigned text before each lecture. Make sure you read actively, with pen or pencil in hand and a dedicated math notebook ready for jotting down the key ideas. Adopt a skeptical attitude toward the expositions provided, coming up with questions that force the words on the page to reveal meanings and connections buried under the surface. Play with math as if you were a toddler trying a new toy, looking for all the ways it can be broken or repurposed. After you think you understand a new concept from all possible angles, attempt to solve the end-of-section exercises without referring to the example problems in the text.
Notes for Teachers
- Which innovations in your course or lesson planning have been most beneficial to student success?
- The send-a-problem method of groupwork has received good student feedback, for offering them the chance to practice communicating mathematics and critiquing their peers' solution write-ups.
- The use of test-taking teams helps reduce anxiety around assessment days by letting students earn points on both the group effort and the individual effort.
- Graphical information organizing tools, such as word webs and sequence chains, usually improves students' skills at note-taking and studying.
- Which innovations in your course or lesson planning have met with disappointment or frustration?
- I can't rule out the possibility that my students enjoyed significant learning gains from the writing assignments I gave in my first semester teaching intermediate algebra, but my hunch is that my writing prompts encouraged frivolous rambling rather than deeper reflection on the course content. Although playing around with words in poetry and drama has some indirect benefit on student cognition, the use of these items in determining part of a math student's grade raises serious implementation concerns.