Pilot Recap, Week 11: Intentional development

I feel like we got back on track this week after the test.  Basically, Heather and I sat them down said, "it's time to work."  We gave them specific strategies for learning the material each class, after class, before tests, and after tests.  Not all that advice was new but it was repeated and elaborated on so students could use it to their advantage.  We built in some small incentives but the main incentive is passing gets them into a college level class next semester.  We reminded them that had they taken beginning algebra this semester, they would have had 3 semesters before college math (beg. algebra, geometry, intermediate algebra).  Illinois requires geometry but this course satisfies that so it really shortens the sequence if they will work.  Otherwise, it doesn't.  Right away, I saw a huge improvement in terms of work, questions in class, and questions between classes.  I think it being this point in the semester wakes them up too.  Time is running out to raise their grade.

On another up note, the lessons for this week worked excellently.  Debate was lively, students were engaged, and progress is being made mathematically and in terms of student success.  This week we saw a recurring theme that is good to see, especially in the midst of the constant mistakes lessons learned this semester.  Our development of content has worked incredibly well.  Our approach has been go slow in terms of how long it takes to accomplish all facets of a topic.  Also, start with numbers and learn them well before attempting algebra.  For example, with equations and proportions, we started solving numerically for a while and then eventually solved equations with algebra.  But we stayed with proportions using numerical techniques for quite a while.  This week we got a proportion that couldn't be solved with numerical scaling, so we used algebra.  Eventually, cross products being equal came out of it.  And they were easy.  But what was great was that students had no difficulty setting up proportions or using units by this point.  And cross products are easy to find and solve.  Building a good foundation proved incredibly helpful.  By the time we got to something that required more theory, that was easy.  Also, they saw value in both techniques (using proportional reasoning and using algebra).

Same with dimensional analysis.  That topic is usually forced on students and they resist.  They just want to multiply or divide.  Plus, we do it once and rarely do it again.  Our entire semester has had problems with conversions.  So we started the semester learning how to do them just in terms of multiplying and dividing as well as judging which operation is appropriate and if our result makes sense.  This week, we got some conversions that were very involved but asked them to use that technique (multiplying or dividing) to answer the question.  And it was very frustrating.  So we offered dimensional analysis and it was very welcomed.  Not only did they use it, they understood it, and have continued to go to it since. 

Again, as a math teacher, that is music to my ears.

We closed today with a lesson that integrates lots of content.  That's something we do constantly as well.  We wanted to know if the reduction in plastic made by water bottle manufacturers amounts to much and if so, how much?  We couldn't find the volume of a water bottle cap so we had to use its density and weight.  We weren't given the original amount of plastic, just the new amount and the fact that it's 30% less.  Once they found the original amount, they found the amount saved for one bottle and then all the bottles in the U.S. for a year.  That number is large so we converted it from cubic centimeters to cubic yards (still too big) to Olympic swimming pools (9, by the way).  Not trivial, interesting, and integrated.  I'll take that every day.

Heather and I will be AMATYC next week presenting a workshop on the course.  We hope to see you there!