## A Assignments

I have a problem-solving approach to teaching.

By this I mean that I try very hard to identify the problems of teaching and I look for solutions to these problems. Each solution creates new problems, for which I seek new solutions. Etc. It’s part of what keeps the job interesting for me.

One of the problems I have always had-in my middle school and my college teaching-is how to use the drive to achieve that some of my students have to get them involved in doing interesting mathematics.

This is different from the problem of trying to get the whole class doing interesting mathematics-that’s a curricular problem. I’m talking about getting my high achieving students to do some original and independent thinking.

These are students who are used to getting A’s for mastering techniques. If the teacher tells them what to do, they’ll do it. They are accustomed to meeting external expectations and to being rewarded for it.

I have tried many things to engage these students in thinking beyond the curriculum and I have failed many times.

But now I have something that seems to be working. I call them A Assignments.

Leave aside the rest of my quirky grading system. We’ll begin with the system of A Assignments.

In my courses, there are 100 points in a semester. If you get 60 of those points, you earn a grade of D. 70 is a C. 80 or more is a B. And if you get 80 or more points and complete two A Assignments, you earn a grade of A.

There are four A Assignments to choose from, and they are made available (ideally) at the beginning of the semester. Each A Assignment requires students to dig deeper into some aspect of course content than is required in the standards for the course.

Students read over the assignment, discuss it with me if they like and get to work. They submit a first draft, get comments and feedback from me, then revise and submit a second draft. If this draft is satisfactory (see below for definition of this), then they are done. Otherwise, they do a third draft, etc.-as many as necessary. When in doubt, we return to the definition of satisfactory completion.

Completion of two A Assignments and B work at the level of 80% or better in the rest of the course earns an A in the course.

A Assignments are optional in the sense that they are not required for completion of the course, nor for credit. Students with 95% of the points who have not completed two A Assignments receive a grade of B (but this is extremely rare).

A Assignments have solved my problem. There is enough structure for students who need external direction, but there is enough openness to the task that I feel I am getting these students to push beyond their intellectual comfort zone.

And now the next problem I am working on is how to engage the students who would benefit from working on the A Assignments, but who don’t care about the A. I was that type of student.

### Satisfactory completion

Satisfactory completion denotes mathematically correct responses to all prompts in the assignment and adherence to academic norms for written work-including grammar, presentation and academic integrity.

### Sample topics

College Algebra: Investigating non-linear asymptotes, Writing an equation modeling the pH of water mixed with orange juice concentrate, Determining a rule for when a^b>b^a for a, b positive integers, etc.

Math for Elementary Teachers: Determining whether all multiples of 12 are abundant, Developing number language for Mayan numeration, Determining under what conditions the standard algorithm for 2-digit by 2-digit multiplication will give identical partial products, etc.

In college, students and teachers have differing expectations of technology. Teachers typically expect one of two things from online technology:

1. Increased content consumption by the student, and/or

Students typically expect one of two things also:

There are outliers in both groups, of course. I make a gross generalization in order to make a point-there has been great attention to and investment in educational technology in recent years, but teachers and students are not in agreement on what purposes that technology should serve.

I have written recently about Sophia, an online social learning platform, that relates to the first expectation of teachers and students above.

Every college subscribes to one or another Instructional Management System. Ours is Desire2Learn and it is a mess. (I have complained about it in writing before, and on the radio.)

So I do not post grades on D2L. My students are critical of this and I have wondered why.

I contend that their discontent goes deeper than their expectation of being hyperconnected and instantaneously updated.

I contend that teachers have used electronic gradebooks to make their grading schemes too complex for students to understand. I contend that students don’t expect to be able to figure out their own grades, so they look to D2L to figure those grades for them rather than looking at their scores on work that has been returned to them.

Consider an example.

My first semester at my current institution, I had a student whom I will call Aaron in my Math Center course. The Math Center is where we teach our developmental math courses. It is a carefully constructed machine in which each individual teacher has a narrowly defined role to play, and where there is little autonomy. In particular, the grading scheme is standardized across all sections: 60% tests, 20% final exam and 20% participation points.

Aaron was shooting for an A in the course. He had scored an 89 on the first test, a 65 on the second and he wanted to know what average he needed in order to get the A that was his goal. Our conversation began something like this…

Well, you are averaging 77% on the first two tests. There are five tests for 60% of the grade, so you have 77% of the 24% of the grade determined by these two tests. Let’s assume you get all of the participation points, so you have 100% of that 20% of the grade. So we need to figure out what percent you need of the remaining 36% of the grade that comes from the tests, and what percent you need of the 20% that is the final in order to get 90% or better in the course.

Even I was confused.

So we thought about it algebraically. If we let x be the average on the remaining tests and final exam, then we need to solve the following inequality:

0.6*(89+65+3x)+0.2*(100)+0.2*(x)≥90.

But in order to solve this inequality, Aaron would already have to have passed the course in which he was enrolled.

In the courses I teach outside the math center, I take a different approach. The semester has 100 points. The weighting is built into the point values of each graded item. So if I want exams to be worth 60% of the grade, then I have 60 points to distribute across however many exams I am giving. At any moment in the semester, a student can simply add the points they have gotten, the total points, divide one by the other and consider the quotient as a percent.

I can figure these grades quite easily without my computer and I can answer a question like Aaron’s quickly and easily.