Academic Exchange Quarterly Winter 2007 ISSN 1096-1453 Volume 11, Issue 4
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Dealing with Anxiety and Attitudes Towards Math
Schmidt, Ph.D., is an Assistant Professor of Mathematics.
When teaching a general education course, we encounter students with various backgrounds and dispositions. Our main general education course in mathematics is Introduction to College Math. Unfortunately, the majority of dispositions are unfavorable and most students enter the class with negative attitudes and anxiety. The purpose of my project is to study the impact of self-reflection, subject relevancy and group work on anxiety and attitudes in an algebra classroom.
Although this is the first algebra course that counts as general education credits, it is rarely the first mathematics course they take at the college level. Many students place into remedial mathematics courses where the credit does not count towards their graduation. They complete the remedial courses and then take our Introduction to College Math course to receive their required credits for graduation. As stated earlier, most students believe they cannot do math or cannot succeed; they have high anxiety and a lack of motivation (Farrell, 2006; Hilton, 1980). On the first day of class you will often hear comments such as; “I’m only in this class because it is required”, “All I want to do is pass”, “I have never been good at math”, “I’ll never use this material for my job”. The goal is to change the assumptions and beliefs students have about themselves and mathematics. For half of the students this course is their final mathematics course. The remaining students will continue on to trigonometry, calculus or finite mathematics if their major is related to technology, business, engineering or science. It is important to give students a good experience in mathematics, especially if it is their last one, and to instill confidence for future studies.
Key Learning Activity
Utilizing a course management system, I implemented a series of online surveys to enable students to discuss self-reflections of their learning. A background information survey was administered on the first day. This survey included questions about the students’ presumptions, mathematics course experience, expected hours of work, and any related concerns. At the end of the semester, the students completed a similar survey to explore any changes in student opinions. Each week the students were assigned readings, followed by survey questions on the readings due before Monday’s class. The reading surveys included questions about least/most difficult topic, assumptions, and thoughts on that weeks’ content. Based on those responses, the content of the class was adjusted and discussed during the week. On Thursday’s class a group worksheet was designed reviewing what they had learned and challenging them to use the concepts to application problems. These weekly group activities provided students with a chance to solidify their understanding and ease their anxiety by working problems out with others. The students were tested on weekly quizzes where groups were further utilized on alternating weeks. They ended the week with another survey taking a look back at what they learned and reflecting on any changes in their assumptions or thoughts. They were asked questions about which activities engaged them in class, when they felt most puzzled or distanced and if their earlier assumptions had been alleviated during the week. I discussed with the students the responsibility of their responses and emphasized the importance of being honest and to not respond with what they think are my expectations. Their responses were read before the following week and discussed at the beginning of the next class. Any concerns the students still had were addressed and then the new week’s material began.
To increase subject relevancy, the course included four projects incorporating the students’ majors and “real world” problems. The directors of the appropriate majors were asked to submit questions that would apply the algebra techniques the students learned in the class. These questions were transformed into projects/worksheet questions that the students completed. After each project the students completed a survey including questions about what was least/most difficult, what they enjoyed, and if the project changed their assumptions or thoughts about mathematics.
Students were assigned a few points for each completed survey for the course. At the end of the semester the students were asked to write a reflective essay based on how they believe their knowledge, skills, and dispositions have changed. This was one of the most rewarding aspects of the investigation. The responses were insightful and the assignment helped the students to understand the purpose of the surveys they had been completing throughout the semester.
When the background surveys were compared with the final surveys (52 responses total), 63.5% of the students’ assumptions and thoughts changed positively, 30.8% remained the same, and only 5.7% (3 students) changed negatively. When the students had the chance to reflect back on their learning throughout the semester, many common themes appeared in their reflective essays. The top four themes were -- they understood more mathematics (89%), developed greater confidence in their mathematical skills (70%), have a greater understanding of the applications involving mathematics (52%), and think that mathematics is more fun (38%). These results demonstrate the effectiveness of self-reflection, increased subject relevancy, and group work on the students’ dispositions. The percentages are based on the students’ survey responses. At this time, there is no data to deduce which aspect of the course was most responsible for the overall change.
The top four student responses (listed first to fourth) for each project are listed after the project description for the following two questions. 1) What did you enjoy about the project? 2) Did the project change your assumptions about mathematics? The student responses are italicized.
Project #1: The purpose of this project was to develop problem solving skills with word problems. The student was to write up their own word problem with solution related to their program of study. I compiled the submitted problems and distributed the collection. Their groups chose three problems, which were not their own, and solved the problems. By the conclusion of the project, students had solved one problem from their program of study and three from other programs.
1) Working in a group -- reading other peoples questions -- difficulty level -- creating my own word problem related to my major.
2) No changes -- math is applicable -- easier working word problems now -- developed a greater respect for why we learn how to solve word problems.
Project #2: A manufacturer takes many things into consideration in designing a product and presenting the product to the public. For example, the appearance of the product is important to the consumers and the cost of manufacturing the product and its packaging. For this project, we considered the design of a soda can. The object was to compare the size of a can with the optimal size of a right circular cylinder for a given volume.
1) Fun and creative -- working in groups – challenging -- “real world” math application.
2) Math is applicable -- no changes -- it was a difficult project -- that a difficult project is solvable.
Project #3: This project was written as a letter from a sociology professor who needed help solving a budgeting problem. The students had to read through his request and then reply in a letter back explaining their answer.
1) “Real world” math application -- fun and creative -- difficulty level -- nothing.
2) No changes -- math is applicable -- good practice solving word problems -- the existence of interesting math problems.
Project #4: The purpose of this project was to use a graphing calculator to fit a model to quadratic data. The student was permitted to complete this project in pairs or individually.
1) Graphing using technology -- working in groups – nothing -- “real world” math application.
2) No changes -- learned more about graphing technologies -- it was a difficult project -- math is applicable.
What I discovered with these projects is that the more creative and relatable the project is, students devote more effort and perform better (Hilton, 1980; Felder, 2007). It was rewarding to notice the applicability of mathematics mentioned often, which I believe led to 52% of the students having a greater understanding of possible applications using mathematics.
Weekly Survey Findings
The weekly survey results were compiled and the top three results for each question were added together for all 14 weeks. The comments are based on repeated results (when more than one week had a similar response). In general, students’ assumptions at the beginning of the week depended on the level of difficulty of the material. If the material was a review they were more confident, if the material was new or looked difficult they would often express anxiety and discuss how they will have to work harder that week.
The students were asked several questions, the first of which was: At what moment in class did you feel most engaged in your thinking? Students commented that they were most engaged when the class was going over examples, whether it was the teacher demonstrating them or the students working out examples themselves. They were particularly engaged when they would see a problem worked out step by step and then would try a similar one on their own. They frequently mentioned they were engaged when learning new material and when working on the worksheets with their group. For 5 weeks, students also said they were engaged while taking the quizzes. Interestingly, this response was given when the week was a group quiz week. Therefore, it appears that if the students were working in groups, whether it was on the worksheet or a quiz, they were more engaged.
The second question was: What action that anyone took did you find most affirming or helpful? The number one response, occurring every week, was when someone in class would ask a question and they had the same question as the student who asked. They mentioned that this eased their anxiety because they felt that they were all in this together and that they were not the only one having difficulty. The second highest response indicated that working on the worksheets in their groups was helpful and the third response was the teacher discussing the homework problems.
The third question was: When did you feel most puzzled/confused/distanced from what was happening in class? The responses were approximately 50/50 that they were not puzzled at all or were puzzled with a specific topic from the week’s material. This was an expected result since students tend to be puzzled when learning a new concept. The third response was they were puzzled when working on their homework. This was also expected since they are trying problems on their own for the first time without support and explains why they found going over the homework problems afterwards helpful.
What was interesting to read were the responses when asked: What happened in class this week that alleviated any of your assumptions from the beginning of this week? They had several responses such as recalling previous courses material to aid them, having the pace of the lectures slow enough, going over problems, working on the worksheets, and understanding a concept that they found to be difficult at the beginning of the week. However, the response that occurred the most (10 weeks) was that nothing alleviated their previous assumptions. That is not entirely bad, for some of the students this was because they already had positive assumptions about the week, however there were other students who said the opposite. In future courses, I will add to the survey another question asking them to explain their answer so that I can decipher what a “nothing” means. The weekly survey responses have been extremely enlightening and demonstrate that students asking questions, going over/working on examples and collaborative group work seem to help ease their anxiety and improve their understanding.
There were several challenges that I encountered while working on my project. Since I implemented the project in two sections, I had 68 surveys to manage throughout the semester for 70 students. Making sure that the availability of the surveys were up to date, reading a total of 9000 responses, grading each response and compiling the data were extremely time consuming. The students were very willing to participate in the investigation; however soliciting “good” student responses on the surveys was difficult in the beginning. A “good” response was discussed in class when the course began and they were reminded again after midterms. It took a few weeks to really convince students that the more thought they put into their responses the more value they received afterwards. Another challenge was constructing meaningful and relevant projects/worksheet questions for over 12 different majors. Without being an expert in each field, it becomes difficult to make sure that the question is realistic. This is where the responses from the directors were helpful. However, I still needed several extra examples that I had to develop on my own. A final challenge was convincing students of the effectiveness of working in groups. I had several students (in particular non-traditional students) who were weary of group work because they wanted each person to give an equal share of work and were afraid the other student would not contribute their share (Davidson, 2001). Since the students were allowed to choose their own group members this challenge was overcome fairly early in the course and the group interactions were successful.
In future courses, I will incorporate these components with a few changes. I will definitely reduce the number of surveys so that it will be easier to manage and edit the surveys so that the questions are more specific to each week’s content or project. Asking the students why something was difficult or why they were engaged at that moment would be another element that I will change on the surveys. Finally, based on the responses from the project surveys, I will try to devise more creative and applicable projects to more programs of study.
Comments from Students
Below are examples of students’ responses taken from the project surveys.
“I enjoyed that it challenged me and gave all of these math concepts some practical application in real world scenarios, especially because we were assigned to do something relating to our major.”
“It kind of gave me a better outlook on the fact that the stuff we learn isn’t just pointless; it is applicable and useful to the fields that we’re going in to. I’m really glad I was able to realize that and I really think it will help give me a better outlook and attitude in the future towards math.”
Below are examples of students’ responses taken from the weekly surveys.
“I felt most engaged when we went through examples from all the different kinds of ways to solve quadratic equations.”
“I thought it was most helpful again when classmates asked questions about problems that they were confused on and also that it was helpful when you would put problems on the board and make us work them out first before you worked them out so we had to do it ourselves.”
Below are excerpts from students’ reflective essays.
“I now have a clearer picture of what algebra is used for. Before I really had no idea about what a lot of mathematics was used for. I didn’t think that a lot of this had any use. The projects we were assigned this term really opened my mind to see the applications of different and more complex algebra skills.”
“I feel that math isn’t as hard as it once used to be, and I no longer feel lost and overwhelmed with math problems. I never felt stressed because of math and that was very rewarding. I think Math 120 was a great class to take, and has helped make my math skills, knowledge, and attitude change in a positive way.”
Overall, I believe the project was a success. Students left the class with greater confidence in themselves and their mathematical abilities and realized the wide variety of applications in the “real world” using mathematics.
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