My apologies for the late entry to the discussions...I shall begin with a brief summary of thoughts on the prior prompts.  First of all I currently serve as an Assistant Principal at Lawrence HS overseeing both the Mathematics and Science Departments.  I began my career in the early 1980's teaching both Computer Literacy and 9th grade HS Math classes (Algebra I and General Math).  After 14 years in the classroom I accepted a position as a JH Principal where I stayed until I joined the staff here at LHS in 2005.

I will endeavor to “take a task or item you would typically use with your students and "take it to the alternative."  What did you learn?”

 

Meanwhile, I am writing now because I have an issue with the second example on page 37.  I believe the store clerk correctly computed the amount that you would be charged in any store with the same advertisement.  I am confused by how the example given shows the additional 10% based on the original price, not based on the adjusted sale price.  In my experience, stores always give the “additional discount” on the lower price.  Perhaps a better example would be to have students explain why the excerpt on the top of page 29 (jet lag recovery) has used the wrong math and how to correct the mistake.

 

More to follow…  :)

Susan Hillman wrote:  I wish I could attach some files here, since I could then show you the examples I provided the students. 

Susan and others,

As an introduction to exponential functions and equations, instead of jumping right to the algebraic form, I used an "alternative" activity based on population growth.  I will e-mail the document to Pam Rawson and ask her to post it here for those interested.  As I expected, students struggled with setting up the graph (units, scale) and reading large numbers expressed as scientific notation on their calculators.  These students are college prep juniors and have done lots of graphing and calculator work, but still without specific detailed step-by-step instructions they flounder.  I was surprised however by their extreme reluctance to estimate, from the given data, future population.  A few even refused to answer the question until I told them how to do it.  Over and over I emphasized that there was no right or wrong answer, that there was not an equation or formula, that their answer depended on how they interpreted the data, and that whatever their estimate they needed to have some explanation of their reasoning.  I tried to relate the situation to a job -- that the boss has asked for a prediction and their job depends on a well thought out response.  Reluctantly they did find a way through to an answer.  Interesting class experience for me and the students both.  

I too am joining these discussions late and apologize.  I'm enjoying the book and it aligns nicely with the changes being initiated in RSU 10.  I know the math curriculum must shift and it became very clear to me as a teacher of high school mathematics when I had the opportunity to teach Core Plus Mathematics and Honors level classes at the same time.  What I mean by this is that I really felt that the investigative approach of the Core Program allowed students to gain a much richer understanding of the content being taught and the assessments confirmed that with the explain and justify questions, where the honors students wanted to memorize everything, just to score well on an assessment.  I have worked very hard to incorporate that change with the honors students. I have shifted the old curriculum to a new approach that has given students a deeper understanding. An example that I'm trying now... In my Honors Algebra II class the students can choose between a paper and pencil assessment or a project on Quadratics. In this class I'm dabbling a little in Mass Customized Learning (MCL) so not everyone is at the same place.  The project is that students must choose a quadratic in either art or architecture, do some research, create an equation in standard and vertex form, and find an additional point on the graph of their subject.  They are to use graphing calculators to confirm their calculated equation as correct or incorrect, after they have done their calculations by hand.  They have the choice to write a one page report, create a poster, or use technology to turn in for grading.  They must show all their work, but even more challenging is they have to determine where their errors are in their application and explain them.  What I have seen so far is that it is giving them a much richer understanding about quadratics in the real world and why precision in the equation is essential.  Not all students have completed the unit but all of them so far have chosen the project.
The book confirms that "teachers need time and support to analyze these changes" and that a school leaders must support this movement, but the question is how do we get that support?  I do feel fortunate that I have a great department to work with and a supportive administration, but it is the time and financial piece that is a road blocker.