Homework

Part 1 - Observation 

1. Describe the content of the homework 
Today's homework consisted of 5 trigonometry problems. 3 involved using sin cos or tan to find the missing side of a right triangle, 2 involved using arcsin arccos or arctan to find the missing angles of a right triangle.
a. Discuss the apparent purpose of this particular homework assignment (i.e., review of previous day’s work, motivation for new lesson, etc.) 
This homework was designed to help show the connection between trig functions and inverse trig functions.
b. Describe the quality and quantity of the problems 
There were 5 total homework problems. These problems seem like they'd be effective in showing the connection between trig functions and inverse trig functions.
2. Describe the procedure used for going over the homework 
My CT did not go over the homework.
a. During what time period of the class was it reviewed? 
N/A
b. How long did it take? 
N/A
c. Comment on the efficiency and the effectiveness of the homework review 
N/A
3. Describe the procedure used for checking the students’ homework. 
My CT would go through the homework and mark each problem correct or incorrect. On incorrect problems he would write a little note about what they did wrong.
a. Was individual work checked? 
Yes, he evaluated the work of each problem.
b. How many students had their homework examined? When? 
The roughly 12 students who turned their homework in had their homework checked. It took about a week for the assignment to get returned to them.
c. What criteria (e.g. accuracy, completion, neatness) were used for checking the work? 
Accuracy was the main criteria. Any problem that had an incorrect solution was marked wrong regardless of the reason it was marked wrong. However, students are allowed to correct their work to receive full credit on the homework.
d. Comment on the efficiency and the effectiveness of the homework checking. 
I feel like this is a good method of allowing students to learn from their mistakes. However, the time it takes to make comments makes it take a long time to get assignments back to students. I'm not sure what my overall feeling on the matter is.

Part 2 - Interview 
1. Interview the teacher to find out more details about the homework procedures that may not have been observable to you. Use the following questions as a guide:

a. How frequently do you assign homework? 
Roughly 3 times a week, though I expect students to make corrections on previous homeworks on those off nights.
b. How do you create the assignment? What types of questions are assigned? How long are the assignments? 
I generally try to find several problems in the textbook that get to the core of the concept. I usually aim for the homework to take no longer than 20 minutes though in that time I want them to really think about what they're doing. Sometimes this means I have to come up with my own questions.
c. What methods do you like to use to go over homework? Do you go over all the problems? 
I don't like to go over homework in class. I much prefer to allow students to correct their own assignments. I allow them to turn in corrected homework for full credit. This allows them to learn from their mistakes and I wouldn't be able to do this if I went through the answers in class. However, if I have a class where the vast majority doesn't do the homework I will go over it so they at least get exposed to the assignment.
d. Do you check the work that students do on their homework? If so, how? Is it graded? If so, what criteria do you use? Is it officially recorded in the grade book? 
I do check their work but if the answer is wrong I mark it as wrong. I try to give constructive feedback on each missed problem so that they can retry and get the problem right. I'll record the initial grade they receive in the grade book but then change it later if they make corrections.
e. Do you ever assign problem-solving projects, research projects, or term papers to the students? If so, please describe them. 
My most advanced class has to write a 10 page paper at the end of the year. In this paper they are supposed to come up with a question and then explore it. Last year I had a student discuss how if you take a polygon with n sides and take the limit as n goes to infinity, you can derive pi from the perimeter. The point of this paper isn't for students to demonstrate their math ability, but their math understanding.

Part 3 – Reflection 
3. Use your responses to the questions above to also respond to the following question: 

a. Based on your observation and interview, how are you thinking about dealing with homework in order to achieve your goals? 
I think my CT's method of allowing for corrections is brilliant. Their are many occasions where I've received work back and when I saw the mistake noted suddenly understood the concept that I had missed before. However, I was never given the opportunity to demonstrate this new knowledge. I also like how he focuses on assigning fewer but more meaningful problems. This makes students less shy of doing homework (since it won't take more than 20 minutes) and if a student stops after just a few problems they get more out of it than if the assignment was 30 problems and they just did the 10 easy ones. I plan on testing his methods out for myself when I student teach. The biggest issue is staying on top of grading which my CT admitted to me he wasn't great at. He usually has a turnaround time of about a week, but to benefit the most from the graded comments you really want the students to see them the next day. I think I'll need to allocate a specific part of my day to grading. This will be hard to do but will keep things from piling up.