Archive for the ‘Math’ Category

Teach like I say, not how I teach

January 24, 2015

As usual, the week before classes start, we had meetings. Some of presentations at these meetings are designed to help us teach better. In one meeting, the speaker said that for teaching math, the students should have lectures for only a third of the time. The rest of the time they should be actively working, instead of passively listening. He actually had us actively working now and then for a minute or two. I didn’t time these sessions, but it was between five and ten percent of the total time.

If a class runs for 100 minutes, they schedule it for 110 minutes and tell us to give the students a ten minute break. Meetings often run longer than that in practice, and in theory one speaker was scheduled for two and a half hours without a break. Do they really think we have that long an attention span?

Most speakers had good Power Point slides that were legible, but when I have sat in the back of the room, some speakers have slides I can’t read. A speech teacher I know once said that any visual aide should have two characteristics: people should be able to see it and it should help. We had some in the meetings that were too long to read without ignoring the speaker. What do they think they are accomplishing? Do they wish to be ignored? Or, do they want us to be impressed when they put long paragraphs on the screen?

If these speakers believed what they said, we would have very different meetings.



The quality of students at the community college

October 19, 2014

Two recent incidents in Intermediate Algebra (high school Algebra II) help explain the low pass rates of students.

In the first case the student was trying. He was supposed to be working on an online assignment which involved factoring of trinomials. I saw he had another screen up and asked him about it. He said he was working, which was true. He Googled the factors of 45.

In the second case, the student arrived fifteen minutes late to a computer classroom, where beverages are not allowed, carrying a cup of Starbucks coffee. When I reminded him of the rule, he put his coffee cup next to the wastebasket. I threw it away after he left without it. This would not be a particularly significant incident except the fifteen minutes he missed of class was from a test which was 16% of his grade.

These two incidents display the major reasons students don’t pass, lack of prerequisite knowledge and lack of commitment.


What are tests for?

August 30, 2014

The last line in an article from The Washington Post was a quote from a Chinese official: “The habit Chinese students have formed is that they only memorize things but not absorb them. They forget about everything once the test is over.”

Most people think tests are there to measure students’ progress. That is not the only reason for tests, but some think it is.

The measurement of progress is reported to many people:

1. The student. This is often skipped in standardized tests designed to measure the teachers or the schools more than individual students, but the tests that are most important to the student should be reported to him.

2. The student’s parents. Obviously, this step should be done only if the student is a minor.

3. The teacher. Usually, the teacher grades the test, but with electronic and standardized testing something else grades the test. As a teacher, I’ve often used test and quiz results to modify reviews for the final exam and to change the emphasis the next time I teach a course.

4. Where the student goes next. This could be a job or simply the next semester’s course. Usually, the report is only a single grade.

5. Society. This helps judge the quality of the teacher of the school. It rarely names individual teachers or students.

A second goal of tests is to help student learning. Students often think they know a subject until they are tested on it. If the student doesn’t get feedback, ideally quickly, that student will have difficulty learning. How the students use the results of the test often determines how well he does in school. Graded homework, quizzes, and tests give the students an idea of how much they know. If they only study to do well on tests and forget about it afterward, they are not studying properly. Their actual learning will be incidental, not the goal of the work they are doing.

Unfortunately, American students have formed the same habits as Chinese students. If we want any real progress in education, students need to know things after they take their tests.


I do not want this student

September 21, 2013

She asked me if she could observe my class. I am not supposed to let anyone in who isn’t registered, but I was tempted to say yes. Why not? It wouldn’t hurt. But instead of giving way to temptation, I told her I wasn’t accepting new students. Three weeks of class passed. It was late to start.

She said she was already registered for another section of the class and she just wanted to change sections. What she did not tell me revealed more than what she told me. She did not tell me she had a conflict with work or child care. She did not give me a reason for her desire for a change of section. She was not going to ask me to accept her as a student until she observed me.

She was teacher shopping. I don’t want someone who was teacher shopping. They tend to be picky. If it took her three weeks to find out the teacher was bad, it wasn’t because the teacher’s foreign accent wasn’t understandable. It could easily be because the student had a bad grade or did not understand the material.

Another student asked me to let him join my class after two weeks of class. When I told him it was too late, he started to explain. “My psychiatrist said” were the first three words of his explanation. I don’t want to deal with a student whose psychiatrist is telling him something that makes him not follow the rules. The rules say one should register before the semester starts, not at the end of the second week of class.

I did give permission for one student to come in late. It was a student I had in a previous semester and a work conflict made him have to change sections. This student had two things going for him: I knew he wasn’t a problem student and he had a good reason for the change in sections.

I can’t keep problem students out of my class if they register on time, but I no longer invite them in when they want to come in late.


I’m mean again

July 9, 2013

On the first day of summer school, a student wanted me to arrange for a quiz to be taken early because of a doctor’s appointment. The quiz was for the next day. I refused. I was told appointments were only available when class met. I still refused.

Quizzes are five percent of the grade and I give at least eight quizzes and drop two of them. Individually, they aren’t important. This grade is very unlikely to have any impact on the student’s grade. It would not be difficult for me to arrange for the quiz to be taken, but I didn’t want to set a precedent for this student or for the rest of the class.

The student did not show up for class, even though the doctor’s appointment was for 9:45 and class went until 1:05. Maybe it was a long appointment. But I can’t help thinking the student didn’t put a high priority on class. That is all right. I don’t expect math class to be important to everyone. I do expect the student to understand there are consequences for the chosen priorities.

Are we supposed to be encouraging or honest?

April 19, 2013

We have a computer course covering Pre Algebra and Algebra I. There are twelve tests, and it is supposed to take two semesters, six tests a semester. I have a student who is taking it for the second semester. She finished five tests the first semester. Eleven weeks in her second semester, she added the sixth test and is almost ready to take the seventh test. I told her that she would probably need a third semester to finish. She got angry with me for discouraging her.


The semester is fifteen weeks long (including final exam week.) If she can pass five tests in four weeks, why hasn’t she been doing it earlier, when the material was easier? Are these students so used to people being positive and encouraging that they can’t accept honesty?

False Assumptions

March 25, 2013

A student sent me an email after I went to bed last night. It said that he was Jewish, Passover started in a few hours, and he would miss three classes due to Passover. He knew that the absences would be excused.

Really? I suppose he didn’t know it was coming until last night.

I will not excuse the missed work. He could have emailed me the homework that is due tomorrow. I don’t have the assignments for the next classes, but if he told me early enough, I would have something I would accept. I’m not going to bother now, since apparently he’s not allowed to use electricity for much of the time and won’t be able to communicate with me. If he is going without electricity, he will be cold, since it is 35 degrees now, and will get colder tonight.

He is missing more than ten percent of the classes, since it is a twice a week class. One of my colleagues commented that this would make it hard for him to function in the modern world, since there are many Jewish holidays.

If he had told me the first week of the semester, I would have gone out of my way to accommodate him. He didn’t and I won’t.

I’m not sufficiently sympathetic

March 16, 2013

A student told me that he had health problems and financial problems. He was doing fine in his other courses, but had difficulty in mine. He asked me to tell him honestly if he should drop. I said yes, he should.

He continued with his sob story. I think he hoped I would tell him not to worry. That I would give him a C even though he did not do C work. When I was a new teacher, I might have felt guilty about following the rules. Maybe I’m old and cynical, but I don’t feel guilty anymore. If he has health problems and can’t keep up with college, he should drop the one course that he is unlikely to pass. It is not my job to solve his problems, nor to give him a grade he hasn’t earned.

Just because I can do it doesn’t mean I should do it. Besides, unearned grades shouldn’t go to students with the best sob story.

Mathematics Prep, Part 3

February 16, 2013

I’ve now taught the prealgebra/algebra I course for three weeks. The course is taught on computers, meaning very little of my time is spent actually teaching. The computers do a good job and the students who try to learn can do so. When they need help, it is usually done in a couple of minutes. Often it is finding a mistake they overlooked.

Saying this isn’t a strain on my mathematical abilities is an understatement. I’m teaching basic algebra down to basic arithmetic. Recently, I helped a student find the remainder for long division. I spend my time checking the workbook pages the students are required to do before they can take a test, unlocking tests, once the students have completed the prerequisites and the workbooks, and solving minor technical problems. The major ones are solved by lab aides.

Outside of class, I have to check to see the students are doing their weekly lab time, send them two emails a week commenting on their progress or lack of it, and make certain the students are actually attending class. I’m also supposed to call students into my office for individual counseling if they haven’t made progress or refer them to a counselor. I haven’t done that yet. I hope to do that next week.

Many schools are running courses like this with teachers with less education than I have. All the skills I have in lesson planning, test design, and finding the right examples are wasted here. It’s been done for me. If this method of teaching becomes standard, I expect that the teachers would benefit more from education in counseling than in mathematics.

Is this a better way of teaching? The students appear to be working, which means we tend to feel good about it. We will find out whether they are actually learning more when the statistics are gathered showing if these students do better in subsequent courses.

Mathematics Prep, Part 2

January 25, 2013

Classes start Monday, but I’ve been working on the course, and getting my first introduction to my students. Because we want the students to move smoothly from one semester to the next, they should start where they left off the previous semester. Apparently no one has been able to program the computer to do this, so I spent a few hours this morning going through the records, one at a time. I haven’t seen faces yet, but I’ve seen students who progressed slowly, quit before the semester was over, and gotten very little out of the course. I’ve seen a few students who progressed quickly.

I know nothing about the students who are new to the course. Many teachers look up students’ records before the semester starts. I prefer to judge entirely on each student’s performance in my class. If I knew they failed the class twice before, I might prejudge them.

I was aware when I agreed to teach the course that there would be a lot of clerical work. This is not teaching, but necessary to teaching. There has always been a certain amount of this type of thing in teaching, but this is more than usual, and the semester starts Monday. I will be interested to see how much of my time is spent teaching and how much of my time is spent doing clerical work.

As a clerical worker, I’m overpaid.