There is something about the first of every school year that has always frustrated me. It seems to me that the first two or three weeks that we spend reviewing topics from previous years is such a waste of time. Students either enter Algebra I with a good foundation on things like integer operations, distributive property, collecting like terms or they don't. Two or three weeks of reviewing these topics seems to do nothing for those who are lacking these skills and only seems to bore the rest of the students.
Last summer, I heard a fantastic speaker at CAMT (Conference for the Advancement of Mathematics Teaching) and she challenged us to begin our year differently. She talked about how many students will give their maximum effort in the first grading period of the year, yet we waste this prime learning time teaching old material. She urged us to make the most of this maximum effort that most students bring to a new school year by beginning the year with challenging material and fill in any gaps as we went.
When I came back to my campus and said I wanted to skip our "Algebra Foundations" unit also known as Chapter One in your textbook, most the teachers were very opposed to the idea. It took a little convincing, but we finally decided to begin the year with the topic of functions. We jumped right in to rich mathematics and never looked back.
Challenging the students with new material from the first week of school on seemed to help with the complacency that some students seem to experience when presented with material they have already mastered. I want them to get the idea early in the year that they will need to put forth effort in order to be successful.
So how did this new approach affect the struggling learners? Surprisingly, most of the students were able to fill in their gaps as we went. After an entire year of solving linear equations, inequalities, and systems etc, they became quite proficient in the areas they were weak in when they entered algebra I. I admit, they are probably still behind their peers when it comes to being prepared for the next level, but I don't think spending three weeks teaching them how to add and subtract signed numbers would have increased their knowledge base.
So, think about your first few weeks of school carefully. What can you do to challenge your students and make the most out of the first few weeks?