Exam Design

It is almost spring break, which for me means designing my exams for the courses that do not have a state or national exam.  Over the years, my exam format has changed, but I now believe that I have a strong, concise, format for exams.

The first consideration is exam length.  Yes, my exam has to be long enough to take an amount of time close to that provided by the school.  That being said, I also need an exam length that I am willing to grade.  What I have established is the follow.

• 30 Multiple choice questions
• 5 Short answer questions
• 5 Free Response questions

Yes, this is only a 40 question exam, which is short; however, it isn't the amount of questions you have, it is the quality of the questions that counts.

The thirty multiple choice questions comprise 50% of the exam grade.  These questions are basic computational or recall problems.  Each question has 4 to 5 possible answer choices, and yes, answers that would be obtained if a student made a common error are some of the choices.  Though these are the most basic of questions, it takes real thought to answer them correctly.

The five short answer questions are conceptual in nature and comprise 20% of the exam grade.  Students have to explain, in two to three sentences, the concept being discussed.  My favorite type of short answer question is error analysis, where I give to sample sets of work and the student must identify which one is the correct method.  Another popular style of question involves applications to mathematics; for example, I show students a graph discussing a companies profit, then ask about the significance of the slope or the y-intercept of the graph.

The five free response questions consist of multiple parts and comprise 30% of the exam grade (for those keeping count, this should be 100%).  This is the part of the exam where students combine their computational and conceptual skills.  Each part of each question builds off of the previous part, but if a student gets part (a) incorrect, they can still earn the points in part (b) if they use their answer from part (a) correctly.  For these questions, a strong, but consistent rubric is designed that requires them to show their work in each question.

Prior to the exam, I tell students how many questions are on the exam, what percentage each group of questions count, and the topics that will be covered.  I do not, however, conduct a formal in class review.  I can get away with this "lack of compassion" (as one parent described it) because all of my test are cumulative, therefore I should not have to review extensively in class if every student has completed their corrections from previous test.  I do make myself available before and after school, meaning that the two weeks before the exam I arrive at 7 AM sharp and leave a 5-5:30 PM every day, regardless of if a student has come for a review.

One final note, the first year I formatted my exam like this, one student looked at the number of questions and said he would be done in twenty minutes.  One hour and forty-seven minutes after the exam started he turned it in and said "I have never had an exam that short that involved so much thinking."  Remember, quality is far more important that quantity.

Goals for Next Year

Here are my plans for this summer.

1. Write all exams for all courses
2. Write all test for all courses
3. Create/update pacing guides
4. Create/update unit plans
5. Fix nuclear physics and differential equations lessons

This list is daunting, but manageable.  Also, if I get through all of this in the summer, then next year will be so much easier on me.

I find it amazing how the last part of the year in teaching seems to always be focused on the next.

Geometry... well this is Different

For the first time since my student teaching, I will be teaching geometry.  Now I am very knowledgeable about geometry, I understand the subject, and I am very competent when it comes to working with geometric principles; however, I do not enjoy geometry.  I am a strong believer in the principle that if you do not enjoy a topic, then you will not be as good of a teacher of that subject.  That being said, I do not have a choice, I will be teaching geometry because one of my colleagues will no longer be with the school.

So now I need to get back into the mindset of geometry.  For me, this means spending time this summer focusing on planning my geometry course.  I say my geometry course because, as I have stated before, I do not teach kids to the test, I teach the kids mathematics.  Yes, I will cover all of the topics and standards covered in state standards, but I will cover it my way.

I believe I will start the year off with constructions.  If the students can construct any geometric object, I think this will give them a better understanding of the information covered in the course.  This would mean a lot of up front work and a hard road as far as pacing is concerned, but if they can build the situation, then they can work with the situation more affectively.

The Importance of Foundation

When I went into teaching seven years ago, I did not know (even with the education degree) exactly what it meant to be a teacher.  I am hoping that I will never truly know what it is to be a teacher, but I do like having a better idea about it at this time.

As a math teacher, I am really an architect, building manager, construction worker, and psychotherapist.  As an architect, I design my lessons, assessments, tutoring sessions, and the like with a clear goal in mind; that goal is NOT having students pass an End of Course Exam.  Instead, that goal is to get the students to the point that they can perform well in a mathematical environment.  If they can do this, then any test should be a piece of cake to pass.

I am a building manager because I oversee everything that is done throughout the mathematics department (and science department for that matter).  At my current school, the person who teaches the highest level of the subject is the "department head;" since I teach AP Calculus AB and AP Physics B, I am technically the head of both the math and science department.  As such, I oversee all of the other math and science teachers, making sure that the overall design is kept in mind as teachers do their jobs.

I am a construction worker because I sit in the trenches everyday and slowly build the knowledge of students and help them hone there skills.  The key to this, in my experience, is providing students with a solid foundation to build themselves up from.  For example, I refuse to teach the ever popular FOIL method for multiplying binomial expressions because I view it as a crutch that makes it more difficult for students to have success when they reach multiplying true polynomials.  The stronger the foundation, the less chance that the house will crumble in a storm.

Finally, I am a psychotherapist because I continually council students out of their fear of mathematics.  As the title of this blog indicates, mathematics is art.  It is a wonderfully beautiful collage of logic, problem solving, poetry (yes, I said poetry), and images.  I am happy to say that many of my students have seen the beauty of mathematics.

In short, I am a teacher... and I am always looking to improve.