How can we use math to determine whether or not a company wrongfully laid off its workers simply because they were older than others? Where does polling data come from, and can it be trusted? Do the students of MHS feel that there are cliques and are they part of one? What are the style preferences of MHS females? Do private lessons really give you an edge in competing for "chairs" in orchestra? Can people really tell the difference between a name brand coffee versus a store brand; does the name brand really taste better? What keeps MHS students up at night, and does the answer differ by age or gender? These are just a few of the questions my Advanced Quantitative Analysis and Mathematical Modeling (AQAM) students have been investigating this year.
Yes, this year I was one of the "chosen”, a never-give-up-self-punishing-perfectionist who was asked if I would be part of the blended learning pilot program for Medina High School. And I, never afraid of a challenge, said "ok, but I would like to create a course from scratch". As you can see from the title of this course, my mantra was go big or go home. And so here I am, at the end of the first grading period, in the middle of what you could call a perfect storm of mathematics educational technology delight...or dread. I took this unique opportunity to try, without real penalty, to teach a version of a course that I have been envisioning for the last decade of teaching. A course that ALL students would find something to take away for the future; a course that would not require (or allow) a mathematics cookbook in which to solve problems; a course that would be relevant for 21st century learning and a small step toward what I believe is what is meant by educational reform.
I have learned a great deal in a very short amount of time and since I have had zero time to really sit and put my thoughts down on paper, I realize that I could write more than any one person would stand to read in one sitting. Some of what I have to say will make you laugh, some will make you scream, some will make you take pity on myself and my fellow blended learning cohorts - but mostly I hope that some of what I have to say will inspire you and save you from making some of the mistakes I have made. For now, I will just introduce you to the course that I am creating and tell you about the basic structure and how it is different from the other courses I have taught.
Students are taking this course as a 5th year course after successfully completing Precalculus. They may choose to take this instead of OR in addition to a Calculus course. This year, the majority of my students are hoping to pursue careers in a health-related, business, or engineering field. When you read this, you might be thinking, “Wow, you have a dream job with dreamy students!”; don’t forget, while I do have fabulous and bright students, they have all been taught traditionally for 12 years and change is tough!
My initial plan for content was one semester of Elementary Statistics and one semester of selected Finite Math topics, all under the idea that we can use math to model a variety of situations in the world of healthcare, business, finance, and science. At this point, I will be happy to get through the Statistics portion. Fair enough, I am trying to teach for depth through problem solving and collaborative projects and that takes time; the inner math geek feels disappointed though.
Each week, I post a lesson for students through Blackboard. This lesson contains readings and supplemental videos. These videos are short, meant to supplement the reading; watching only the video would be tragic on the student’s part. Built within each lesson are concept checks through short multiple-choice quizzes, hotspot activities, matching, sorting, etc. These purely check for basic understanding of what they are reading; and to keep them honest. Students work through the lesson, at their preferred pace, for the week. In class, we problem solve and work with datasets using Minitab. I teach them how to do all computations by hand with small “irrelevant” datasets and then I show them how to ask Minitab to do the same thing with real data (our first dataset contained 1450 observations). Students are assigned something additional to practice each week: group discussion questions, group problems to solve, group/individual lab assignments, and always a end of week private journal entry.
The main form of assessment is team projects. Instead of a unit test, they design and carry out a project (with guidelines of what to demonstrate mastery with), they write a formal paper, and they give a brief presentation to the class. The majority of students have said that they enjoy the projects since they get to pick the topic/research question. Through these projects, they are learning the additional skills of collaboration (either face-to-face or via technology), public speaking, writing, professionalism, and how to use digital tools effectively. Team projects come with their own set of challenges; the biggie is equal division of labor. This part will be a work in progress for me, in the mean time I still give an end of quarter traditional exam. The exam has things like computations, reading computer output and writing interpretations in context, and case scenarios that they analyze or answer questions about.
In future posts I will write about the challenges that I have faced in implementing this model. I consider myself tech-savvy – but I have still had trouble in implementation. I have a solid record of students reaching high-achievement on high-stake assessments, but teaching in any online environment is very different from the face-to-face environment and so I struggle to feel confident that my students are achieving the same level of success I have come to expect. In a face-to-face math course, you typically deliver a lesson with whatever method you feel most effective and then you send students home for 30-45 minutes of drill-and-kill problems; but do they really learn? Do they develop conceptual understanding? Do they understand not only how to get the right answer, but how to get the best and most efficient answer? I say no, not always. My course focus is conceptual understanding and finding the best answers to real problems, and some students (and parents) want a textbook and drills, and points; if they understand it, well that is a bonus. All of our courses represent change, and as the previous post "Transition" by Shannon Conley discussed, transition and change take time.
(Christina Hamman can be followed on Twitter: @hammanmath)