What have I learned about my students?

I’ve learned that students from all backgrounds, grade levels, races, ethnicities, socioeconomic status, and so on are first and foremost adolescents with adolescent interests, resources and challenges.

I’ve learned that students want to be successful, to be liked, to be recognized, to be supported, to be challenged, to be appreciated, and to be tolerated for their frequent albeit minor behavioral transgressions.

I’ve learned that students in algebra intervention, algebra 1, or even AP Calculus can feel excited about their success or overwhelmed by their failure.

I’ve learned that while most students say they want to lead better lives, to attend college, or to succeed in high school that many do not know how to fulfill those desires, or if so, are unable to devote the time or effort to doing so for a variety of reasons.

I’ve learned that many students have been promoted from one grade level to the next without retaining the concepts and procedures they were taught in prior years, some of whom never truly learned key fundamentals such as subtraction. These students continue to struggle year after year with more and more challenging concepts that require mastery of earlier concepts in order to succeed.

I’ve learned that in spite of their challenges in school and out of school, students come to class mostly to learn, if they feel there is a chance they may learn the material. If they do not feel there is a chance, I’ve learned that is when students give up.

What have I learned about myself as a teacher?

I’ve learned that I start the year full of hope and anticipation that students will successfully learn the curriculum for their course once I develop trusting relationships with them and bring as many of them as possible to mastery of the prerequisite material.

I’ve learned that within a week or so I have a solid idea of who knows what and how to proceed with filling in the gaps in their understanding.

I’ve learned that even after several weeks of review, reteaching, and re-reteaching, that I am still stunned at how many students continue to struggle with the prerequisite concepts and procedures, thereby limiting their ability to be successful with the specific content in the course.

I’ve learned that no matter how hard I work to plan, create, deliver, assess, reflect and repeat this process, that many other factors impede students’ ability to attain the outcomes we desire for them.

I’ve learned that in spite of this seemingly insurmountable challenge, much of which is out of my control, that I need to find ways to stay invigorated, passionate, and committed to reaching every student in some way to help them improve in some amount, even if it is simply in believing in themselves enough to keep on attempting the course content in spite of what seems an impossibility to them.

I’ve learned that while teaching is one of the most arduous, draining, and sometimes thankless jobs I’ve ever experienced, I continue to give my best effort every single day even if I sometimes consider leaving the field.

In short, I’ve learned that I’m a thoughtful, caring person who brings tremendous energy and knowledge to my students nearly every day in hopes that in some way I will leave them better off at the end of a class than they were at the beginning.

I do not know if all students benefit from my being their teacher.  I do hope that nearly all do benefit though.  And with that hope, I continue to work at improving their knowledge about mathematics, its applications, our society, and life itself.

Is it Worth 12 Hours to Grade a Test?

Feeling a bit better after two months of recovering from the flu while juggling three preps, BTSA, and other teaching tasks, I took a moment to pen the kernel of the following for my Facebook friends.  Sharing an expanded version now with those who follow my blog.

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The two charts below depict my AP Calculus AB students’ performance (N=35) on a cumulative test covering second semester topics: 1) integration techniques; 2) applications of integration; and 3) separable, first order, ordinary differential equations.

The first chart depicts scores as a histogram using 10% bins.  The second chart shows scores using my rating scale spanning categories from far below basic to advanced.  These correspond to letter grades of F through A, respectively.  My cut scores break at 15% intervals from 40% to 85% corresponding to far below basic to advanced, or F to A.

The results include distributions of the total score as well as sub-scores for Integrals, Applications of Integration, and Differential Equations. The overall average was 47%. High score was a 95%; low score was an 8%.  I am not pleased with the results; however, I am not surprised.  I do wish I knew how best to motivate these advanced students to invest more time in their studies; it seems the majority of them are so accustomed to minimal effort out of class based on earlier successes in mathematics that they simply do not know how to do so in an advanced course like calculus.  A few have simply given up, which takes more time and energy from me to get them to re-engage.

It took 12 hours to score this test, as I needed to read the written work from 700 problems for maximal partial credit. As you might imagine, that is a considerable investment on a teacher’s part for one course (aka prep); I have two other preps. It is very worthwhile if students are investing significantly in their preparation for a test, and their learning, but not so much otherwise. I’ve asked my students to please consider this as they progress in their education.

BTW, the overall score is the only score that counts towards their grade at present. At some point, I will compare each of their sub-score percentages to earlier test scores to replace those that are higher, which helps late bloomers. I’ve also suggested that students look at their sub-scores and use them to guide subsequent studying for the course and AP Exam.

Let’s hope they do so!