Learning Mathematics Sarah Stover Literature and Society Dr. Sherry 10/03/11

THE QUESTION, BACKGROUND, AND METHODS CLUE Project

The Question (kivettbednar.com) (edudemic.com)

Background This is not the first study on student-teacher interaction. In her novel, My Freshman Year, Dr. Rebekah Nathan, a professor for 15 years, decided to study college life by enrolling as a student at her own university. Chapter 4 of My Freshman Year focused on international students and how they viewed American culture. Nathan asked the international students about teachers, and this is what she found: Quote: “U.S. professors were described by different international students as ‘laid-back,’ ‘helpful,’ ‘open,’ ‘tolerant’ (of scant clothing and sleeping in class), ‘casual,’ and ‘friendly,” (Nathan, 2005, pg. 78). Quote: “For other students, it was the interest in listening to students’ problems and opinions and in helping students that was refreshing,” (Nathan, 2005, pg. 78) Goal: I wanted to see if teachers could influence they way students learn or how well they do in a class through they way they interact. Maybe students are more motivated to do well if their teachers have the qualities described in these two quotes.

Methods I decided to use the ethnographic approach because I though it would be most effective in gathering data, since it is “a theory-building enterprise constructed through detailed systematic observing, recording, and analyzing human behavior,” (Heath and Street, 2008, pg. 29). I observed two college-level math classes, which allowed me to study how teachers interact with students in two different settings. I interviewed five college students, a high school student, and a high school math teacher. The interviews gave me different perspectives on how students learn, and I focused, in particular, on how they learn math.

FINDINGS CLUE Project

Findings: College Interviews Interview Question #1: In general, do you consider math classes to be difficult or relatively easy? Answer #1: Not too hard, but it's really easy to make stupid little mistakes. Answer #2: I've always liked them, but it depends on the teacher. The class is harder if the teacher isn't good. But once I get it, I get it. Answer #3: In the middle. I don't have too many problems. Answer #4: Depends on the class and the professor. The teacher always influences how well you do. Answer #5: Somewhere in between; it depends on the class. As you can see, for most students, how well they do depends on the class and the teacher.

Findings: College Interviews Interview Question #2: How do you best learn/study math? Answer #1: I'm a visual learner, so examples with pictures are great. I draw pictures for a lot of problems. Answer #2: Practice over and over. Sometimes, I rewrite notes. Answer #3: By practicing problems in class. I don't like homework problems because you can't get instant feedback. Answer #4: By listening or having visuals. I do practice problems. Answer #5: I'm a visual learner. Another thing was that in high school, I could do the work while I was in class, but once I got home, I got confused. All of these students said it was better to learn math by using visuals or doing practice problems.

Findings: College Interviews Interview Question #3: Is it helpful to have homework to do after every math class? Answer #1: It's helpful once you understand how to do the problems. If you don't, it's frustrating. Answer #2: Yes, definitely. The more practice the better. It gives you more examples on the same material. Answer #3: It's necessary, and yes it helps. Answer #4: Yes, that way you can ask questions the next day. You can check to make sure you really understand the material. Answer #5: It is helpful; I just wish that there was time at the end of class to at least start your homework so you can ask questions. Students answered how homework is helpful because it gives you a chance to ask the teacher questions. This emphasizes the importance of student- teacher interactions and how the teacher is instrumental in helping students understand material.

Findings: High School Student Interview Question #1: Generally, do you consider math classes to be difficult or relatively easy? Easy. There’s always a definite answer, and I’ve always been good at it. Question #2: How do you best learn/study math? Practice problems. Teachers shouldn’t ramble on about themselves or repeat the same thing all the time; it gets boring and is not as effective. Question #3: Is it helpful to have homework to do after every math class? Yes, especially if you are learning new material. Theses answers are similar to the college interviews. The high school student also learns math by doing practice problems, and she agrees homework is helpful.

Findings: High School Teacher Interview Question #1: Why did you choose to become a teacher? I'm a people person, and I like the interaction I have as a teacher. Question #2: How do you teach math? Students learn in all different ways, and you have to provide for each way. Some students see you do it, and they learn that way. Others like to do it themselves, so it's better to introduce it and give them opportunities to work on it in class while you monitor. Some students learn better from each other, so you give them time to work with another person or group in class. You can't do the same thing every day. The most effective teachers use a combination. Question #3: Do you assign homework every day? Does it help your students to have homework to do after every math class? Absolutely. Practice makes permanent. Homework is about practicing the skills you learn in class. Sometimes all you need to give is five problems for them to practice it enough. When student ask why I give them homework, I ask them if they play an instrument or a sport. If they say yes, I ask them why do they practice if they already know how to play? (thepartnership.us) These answers also show the importance of student-teacher interaction and how it’s a part of every class.

Findings: Students vs. Teacher When I compared the students’ answers to the teacher’s answers from my interviews, I found some interesting correlations. Comparison #1: Most students said how practicing problems was a helpful way to learn math concepts, but each of them added to that. Some said they like doing the problems in class, some said they like using pictures with the problems, and another student said they like to listen while the teacher does the problems in class. The teacher I interviewed talked about how each student learns differently so you have to present the information in several different ways. Some like to watch the teacher do the problem, while others learn better in groups. Comparison #2: Students said how homework is very helpful because it gives them a chance to ask questions and make sure they understand the material. The teacher agreed that homework is extremely important, and he said how homework is more of a chance to practice the information they already learned in class and make sure they understand.

Findings: Classroom Observations I observed a Calculus 2 Class for one period to see what sort of data I would collect. The professor began class by giving notes on the overhead projector. She would introduce a concept or theorem, and then give several examples for the class to do together. She made sure the material made sense before moving on to the next concept. She explained concepts by giving real world examples, which was helpful. The professor went over the material that would be on next week’s test, and several students asked questions. Since the test is scheduled outside of class time (due to the flood), she said she would work out another time for anyone who couldn’t make the test date. Then, there was a quick review session. Students asked questions about homework, how to do certain problems, and about how the test was set up. Throughout the class, the professor gave examples for the students to do so they could practice each concept, which is what students prefer according to the interviews. There was also time during class to ask questions either about homework or the new material. This in addition to the information from the interviews shows the importance of student-teacher interaction.

Findings: Classroom Observations I observed a Discrete Math Class as well to see if I found similar observations. At the beginning of class, the professor handed out quizzes as well as a copy of the answer sheet for students to have. He asked if there were any questions on the quiz. Only one student had a question. Then, students were free to ask any homework questions. Several students had questions, and the professor showed how to do them on the whiteboard. Then he went into the notes, which he wrote on the whiteboard. He started with a concept, and then gave several examples. As he did the examples, he asked the students what he should do next in the problem to make sure they understood the concept. He asked if anyone had questions before he moved on. As in the Calculus 2 class, the professor gave examples for the students to do so they could practice each concept. There was also time during class to ask questions either about the quizzes, homework, or the new material. This class also shows how student-teacher interaction is an important every-day thing.

CONCLUSION CLUE Project

Conclusion A teacher’s attitude and teaching style can affect how well students do in the class. 4 of the students I interviewed said that how well they do in the class depends on the teacher. The high school student said she is less motivated to do the work if the teacher rambles on about herself. The high school teacher I interviewed said how the most effective teachers use a combination of teaching styles to help their students learn since each student learns differently. This information suggests that students are more likely to take an interest in the class if the teacher is willing to take an interest in them or provide for their learning needs. * *The 3 IN’s

Conclusion Students learn in different ways, but many students find visuals and practice problems the best way to learn math. o 3 of the students I interviewed said they were visual learners and that pictures helped them with math problems. o 3 of the students I interviewed said that they learn concepts or study by doing practice problems. o In both of the classrooms I observed, the professors gave many examples in class for the students to work on. This suggests that math is a subject in which students learn best by doing or seeing rather than listening. This is probably because math consists of a lot of processes or theorems that are then applied to math problems. Examples show students how to apply these theorems. * *The 3 IN’s

Works Cited Heath, Shirley and Brian Street. On Ethnography. New York: Teachers College Press, Nathan, Rebekah. My Freshman Year: What a Professor Learned by Becoming a Student. New York: Cornell University Press,