We are the solution
4 years ago
Before you even start factoring, make sure students have a reason to use it, that they understand WHY they're factoring. Have them graph a simple polynomial equation, like the square of (x+3), using a T-chart for values, and find the zeroes.
I think it is extremely important for the students to understand factoring in polynomials is the same in factoring, say, 96.
They need to know that polynomials are the result of multiplication, so a good way to start is to have them multiply simple things, like the results of the graph they did and other squares, and then, for example, the sum and difference of 2 terms, to see if they discover the pattern, then give them the same problem, plus some similar ones, to factor. Then move on to things like (x+1)(x+3), saving ones with a coefficient other than one for later.Using Algebra tiles is another way to visualize what's happening, and using the "box" method, which I like for multiplication of polynomials, because it helps keep them straight, is also a good help to reverse the multiplication, which is similar to the Algebra tiles.
Learning experiences that involve rigor … | Experiences that do not involve rigor … |
challenge students | are more “difficult,” with no purpose (for example, adding 7ths and 15ths without a real context) |
require effort and tenacity by students | require minimal effort |
focus on quality (rich tasks) | focus on quantity (more pages to do) |
include entry points and extensions for all students | are offered only to gifted students |
are not always tidy, and can have multiple paths to possible solutions | are scripted, with a neat path to a solution |
provide connections among mathematical ideas | do not connect to other mathematical ideas |
contain rich mathematics that is relevant to students | contain routine procedures with little relevance |
develop strategic and flexible thinking | follow a rote procedure |
encourage reasoning and sense making | require memorization of rules and procedures without understanding |
expect students to be actively involved in their own learning | often involve teachers doing the work while students watch |
Critique and Feedback: The Story of Austin's Butterfly from Expeditionary Learning on VimeoThis is a fantastic story about learning through observation, and making many drafts before you are through.
Inspired by Nelson Mandela's claim that the impossible is just waiting to be done, this blog chronicles my own journey to do the impossible. I am embarking on another new career as a high school math and science teacher . . . and I don't really think it's impossible - just really hard these days to land a job.
I finally became a credentialed "single-subject" teacher of math, science, physics, chemistry and biology in 2011--but finding the job to use my skills to help motivate students to enjoying my favorite subjects was difficult. I ended up at a different school each year.
So I am now retired, but still working with some kids and books.