Getting to Know Your Students Through Reflective Writing Assignments Dr. Dana Olanoff Widener University dolanoff@widener.edu

About Me Dr. Dana Olanoff, Associate Professor of Mathematics and Mathematics Education, Widener University. In my sixth year of working at Widener teaching both mathematics content courses for prospective elementary and middle school teachers, as well as calculus, precalculus, and a general education mathematics class. Many of my students are not interested in STEM and do not have the strongest math backgrounds. Prior teaching experience at Hobart and William Smith Colleges (Visiting Assistant Professor, Instructor), Syracuse University (Graduate Teaching Assistant), and Michigan State University (Graduate Teaching Assistant).

The Premise Research has shown that building on students’ prior knowledge and understandings is beneficial in helping them develop more advanced understandings (Whitacre, 2013.) However, in order to do this, it is important for instructors to understand their students’ incoming knowledge and how they learn best. Research has also shown that reflecting on one’s teaching and learning is beneficial for positive change.

The Questions How do I as an instructor learn about my students’ current understandings and feeling about mathematics and my courses? How can I find out this information before the end of the semester course evaluations? How do I get my students to be reflective about their own mathematical thinking and learning?

The Answer Through Reflective Writing Assignments: Mathematics Autobiography Post-Exam #1 Reflection Questions

Mathematics Autobiography Homework #1—due the evening of the second class day Write a short math/education autobiography. The point of this assignment is for me to get to know you and learn about your experiences with education and math up to this point. In your autobiography I would like you to discuss your education and math history up to this point. Tell me your feelings about math. Do you like it? Have you been successful with math so far? What kind of experiences have you had that have shaped your opinion of mathematics? What are your expectations for this math class? What are you hoping to get out of it? Do you have any concerns about math or this class that you would like me to know about? Also include your feelings about college in general, what other classes you are taking in addition to this one, and what kind of extracurricular activities you are involved in. If you have taken Math 112, include a paragraph or more about your experiences in that class. What did you like about it? What didn’t you like about it? What did you learn? Has taking Math 112 changed the way that you think about math? I expect your responses to be at least a page in length and contain proper grammar and punctuation.

Mathematics Autobiography Scoring Rubric _____  Feelings about math/Do you like it? (2 pts) _____  Have you been successful with math so far? (2 pts) _____  What kind of experiences have you had that have shaped your opinion of             mathematics? (2 pts) _____  What are your expectations for this class? (2 pts) _____  Do you have any concerns about math or this class? (2 pts) _____  Extras (2 pts) _____  At least 1 page (1 pt) _____  Grammar/Punctuation (1 pt)   Total _____________ /14 pts

Responses Generally, a mix of students who like math and don’t like math. (Surprisingly more students who like math than I originally expected, especially in a group of prospective elementary teachers.) Most define “success” based on grades in previous classes. Good/bad experiences in mathematics tend to come from having good or bad teachers. Most students seem to have a positive attitude coming into the class—they seem to find that the first day wasn’t too bad, so they are hopeful for being able to succeed.

Responses The only concern I have about this class is that I have not taken a math class since my senior year in high school and I am nervous that my knowledge about math may have been lost during that time.     You should probably be okay on this front. Nobody in the class has taken elementary mathematics in a super long time, so everyone is learning as they go for the most part. My only concern with this class is that I may not do well.     This is always a possibility, but if you keep up with the work and ask for help when you need it, you should be able to be successful.

Responses Ever since I was in elementary school, I struggled in math class. I actually enjoy math, but I just am not good at it.  Math has been my own worst enemy because every other subject I excel at, but math has just never been my strongest point. Up until high school, I had always managed a B or better, but intense algebra and calculus is where everything went wrong. I don’t necessarily agree with this. I think that you can be good at math, but you probably have to work harder at it than you do for your other classes. My experience with Math 111 was a positive experience. Since math does not come easy to me, I definitely had to work hard and go to office hours in order to achieve the grade that I did. It was a really proud moment for me when I was breezing through the final with barely any problems at all. I believe I only answered two questions incorrectly, so I still cannot believe that I did that well on a math final in college! This experience has definitely made me more confident about my mathematic skills.

Feedback I try to provide feedback and encouragement. I always encourage students to ask for help whenever they need it (usually more than once for each student.) I try to be sympathetic with negative experiences, since although my experiences with mathematics have generally been positive, I do know what it is like to struggle with a topic. I am able to save these autobiographies to refer back to them throughout the semester, to refresh my memory. I use the students who have taken the prior class as information to help me shape the current classes.

Post Exam #1 Reflection (Math for Teachers) Completed as homework right after taking Exam #1, before they get the exam back: 1) How did you study for the exam? 2) How did you feel while you were taking the exam? How do you think you did? 3) In class, I generally: a) work with my group on all of the problems b) sit with a group, but mostly work on my own c) do the problems on my own 4) How often do you ask for help in or out of class? Is there anything that stops you from asking for help? 5) One topic that I understand and felt successful on the test was. . . 6) One topic that I still don’t understand very well and struggled with on the test was. . . 7) What aspect of class so far is the most beneficial to your learning? 8) If you could change one thing about the class, what would it be and why? 9) What will you do differently from now in class and/or when studying for the next exam? (The answer can be nothing, but this implies that you are happy with how you did and would like to perform similarly on the next exam.)

Post Exam #1 Reflection (Calculus) 1)  How did you study for the exam? Did you do the practice questions? 2)   How did you feel while you were taking the exam?  How do you think you did? 3)  How often have you gone to office hours or the math learning center?  Is there anything that stops you from doing this? 4)   One topic that I understand and felt successful on the test was. . . 5) One topic that I still don’t understand very well and struggled with on the test was. . . 6)  What aspect of class so far is the most beneficial to your learning? 7)  If you could change one thing about the class, what would it be and why? 8)  What will you do differently from now in class and/or when studying for the next exam? (The answer can be nothing, but this implies that you are happy with how you did and would like to perform similarly on the next exam.)

Post Exam #1 Reflection Purpose of this assignment is four-fold: To get students to think about their own learning and study habits and whether or not they are working for them. For me to see what aspects of the class are working and not working for students. (By only asking for one from each student, I am not overwhelmed with criticism (or praise.)) For me to be able to reflect on my teaching based on student feedback, and think about why I do what I do. For students to see that I am taking their concerns into consideration, and working to make the class better for them.

Responses I feel like I did okay on the test, but sometimes I say that and I end up doing worse. So, if I end up doing well, I would hope to do the same come the next test. If I did not do so well, I will spend more time studying and practicing problems. I would get more help outside of the class, I did go to office hours but I just want to have a better understanding and I would also study more in advance I started 3 days before the exam but I feel that for the next time I will give myself more time to prepare. I will set a little more time aside to study. I will focus on the information and break it down more so I am 100% confident going in to the next exam.

Responses I don’t like that our homework gets graded on correctness and not completion because when I am home alone working on it and am not sure how to do something I know I will get a lower grade on it because I don’t know how to do it. I feel that homework is practice, and it is hard to do practice perfect on the first time.  I understand this concern, and other people often feel the same way. However, I grade homework for a few reasons: 1) There are some students who will not try as hard on homework that is not graded for correctness—they will just give up if they can’t figure something out. 2) If you are going to make mistakes, I want you to make them on the homework, where it doesn’t count as much, rather than on the tests, where it counts a lot more. That way, you can correct mistakes. If I didn’t grade for correctness, you wouldn’t be as aware of the mistakes. However, I am happy to go over anything that you are struggling with on the homework, so that you can get a better grade on that too.

Responses I didn’t feel as prepared as I should have been because I did not get to study as much as I would have liked to. I think I did pretty poorly on this exam. If I study like I should have, I think the exam would have been fairly easy.  (DO)  In general, you seem to have a pretty good idea of what we are doing. I think that you can do much better on the subsequent exams, but I would like to see you in class a bit more often. (S) I really appreciate this feedback! I apologize about the amount of classes I have missed, there is no excuse for it. I will make a conscious effort to be at every class from now on. The last thing I would want is for my absences to effect my participation grade, or my grade in general. Thanks again for the feedback. It is very helpful.

Responses (Not trying to earn brownie points, I promise) Your teaching is the most beneficial part of class to me. You are so approachable and do not make me feel dumb when I ask a question, as some math teachers in the past have made me feel. In my last math class at [a different school] I used to literally come home crying because the professor was so mean and when we would ask a question after class he would say, “you have a book for that”. He went so fast through things he had the attitude that because he thought it was simple so would we. By the last day of class there were only a handful of student’s left. But you take your time while explaining and it helps keep me from getting overwhelmed when I don’t understand something. Although I do not like group work, I like that you do not just teach us something and then send us home with homework. You give us a chance to work on everything in class so that we can do it on our own while you are there in case we need help. This is the first Math class in a while that I am actually happy to be in… so thank you for that !  I’m so glad that you are feeling comfortable in the class. I really wouldn’t guess that math makes you anxious, since you are doing very well figuring things out. I would like to see you work with other people just to bounce your thoughts off of them, but I understand that there are some people in the class that you are at a different point in your life than they are, and it makes working with them difficult.

Using the Students’ Writing Thinking about why I do what I do: Students who complain that I grade homework made me consider the reasons why I grade homework. While it would be much easier for me not to grade the work for correctness, it is not as beneficial for them in the long run. Incorporating more guided instruction and more practice: Many students in the math for teachers classes said that they wished that I gave more notes during class, as I do mostly student-guided learning. In Calculus, the students wanted fewer notes and more time to work through examples, so I was able to incorporate both of these into my classes.

Incorporating Reflective Writing into STEM Classes Because my class sizes are relatively small (max 20/25), I am able to use reflective writing assignments like these, as well as personally respond to my students (although it does take a lot of time.) What can instructors with larger classes do to incorporate some of these ideas into their courses?

Thank you! For questions or copies of the assignments, email me at dolanoff@widener.edu.