CESTL paper-Helping Students Understand Math

“I don’t Hate Math, I just don’t Understand it!”
Helping High School Students Understand Math

By Eldon J. Clark
EDCI 4322-60 Human Development & Instruction

School of Education
University of Texas at Brownsville
Spring 2008

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This Paper was presented at the 2nd Conference of Elementary Secondary Teaching & Learning (CESTL) in April, 2008, Brownsville, Texas. If you have any questions or comments regarding this paper, please contact the authort directly at eldon.clark@utb.edu .

Acknowledgements

I would like to thank two of my peers from the Human Development & Instruction class, Juanita Torres and Claudia Lopez. Both of them shared their own experiences in math with me and provided me their opinions related to my research during the individual interviews I conducted with them. Their insights greatly influenced my understanding on math motivation.

Background

Ever since I was 12 years old, I have always dreamed about becoming a teacher. This early-developed interest in teaching has motivated me in learning and understanding about how to teach. Since I was a student, I have informally observed my teachers in all subjects, focusing on how they teach. I have learned what is effective and what is not. I have also paid close attention to how students responded to different approaches and teacher personalities. These informal observations have greatly influenced my philosophy and understanding on education today. Now as a college student, I am still constantly developing and fine-tuning my ideas and plans for my future teaching. The findings presented in this paper are based on my own learning experiences and reflections, my field-based research, and insights from my peers and professors.

Literature Review

Motivation in math has become a very crucial issue in today’s high schools. Math is considered as one of the most important and yet also the most difficult subjects taught in the high schools. All high school students are required to learn math well since it is used in many fields and in daily activities. Also, with the NCLB putting more emphasis on math and making schools more accountable, students who fail math on the state exams will not be able to graduate from high school. However, Regardless the importance of math, majority of high school students showed demotivation, fear, and even resentment towards math.

Why are high school students not motivated to learn math? Research shows that two areas of mathematics pose the biggest hurdle in mathematics for secondary-age school children: fractions and algebra (Steen, 9). To help illustrate just how big of a problem fractions represent, Steen says that on an international test, for a question asking what whole number is 19/20 + 23/25 closest to, more than 50% of 8th-Graders answered 42 or 45 (9). This is not because the students are not intelligent, but simply because they do not have a good grasp of the concepts. Steen concluded, “These students had no idea that 19/20 is close to 1, as is 23/25” (9).

Another valid point Steen makes is that even though most people understand that 1/5 is the same thing as 20%, they have a very difficult time interpreting it in complete sentences in real contexts. This is because too often in math classes, teachers focus mostly on calculation rather than on interpretation, but in order to be effective, both should be used (Steen, 10). Algebra is especially important. Those who pass algebra, particularly Algebra II, are better qualified for high paying jobs and will not need to take remedial math courses in college. Unfortunately, a third of students entering college need to take remedial math courses (Steen, 11).

These problems are alarming, and finding solutions to these problems is more challenging. According to Larry Cuban, a professor at Stanford University, one key thing to solve this problem, is by making a connection between math and students’ daily life experiences. He shared his experience of teaching a high school math class:

“If I wanted those students to be engaged intellectually, then every day – and I do mean every day – I had to figure out an angle, a way of making connections between whatever we were studying and their daily lives in school, in the community, or in the nation.” (Snowman & Biehler, 388 [emphasis in original])

In order to be motivated to learn math, students need to be able to see how math connects to the real world. They need to see that math is useful and needed in all aspects of life. One factor that causes students to become demotivated is that they do not see the connections between math and their own life and they do not see a need for learning math. “Students need to see all their teachers using math to explain their subjects when appropriate” (Steen, p.12). This is important since math is used in all types of fields and careers.

Methodology

Research Question

What motivates high school students to learn math?

Hypothesis

First, my interest in student motivation in math is based on my own experience that in general, students either like math or they hate it with few in-between. For me, this is very understandable since mathematics is a very difficult subject. However, I do not believe that is the sole reason why so many students dislike math and perform poorly in it. Instead, I strongly suspect that in many cases it is the teacher’s fault for not taking the necessary steps to ensure students’ understanding of mathematical concepts. For example, in many of my own math classes, I have heard the teacher say to us, “Come on, guys, this is easy!” Then, when some students do not get it right away, they begin to think that since it is easy, they must be dumb if they do not get it. Even if teachers do not verbally express this kind of negative comment, often their non-verbal language conveys the message to the students.

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In many cases the math teacher, since he is already an expert and has already studied and “knows everything”, he forgets that it is something new and challenging for his students. He forgets that the students have not studied those concepts before. He forgets that they do not know those information which looks simple for himself. Too often, the teacher assumes that students have a prior knowledge of things; he tries to build a house with the students where there is no foundation for it yet. As a result, the students lose the confidence in themselves, lose interest, and eventually lose their motivation for math.

In contrast, if a math teacher is willing to explain math to the students patiently, and show them the connection between math and their real life, then the students will be able to understand math with hard work, perseverance, combined with the assistance received from the teacher despite the fact that math is hard. Of course, this requires a lot of planning on the teacher’s part such as designing engaging lesson plans, hands-on activities, peer tutoring, and teacher tutoring. Lastly, the teacher must also have high expectations for his students. Mutual respect must be established so that students feel comfortable going to the teacher with any questions whenever needed.

Research Methods and Participants

My field research took place at Border High School. I observed three classes, all were 9th-Grade TAKS courses and were taught by the same teacher. These three courses were intended for the students who failed the math of the TAKS test from the year before.

Research methods included classroom observation, questionnaire, and individual interviews. A total of six hours of classroom were conducted in these three classes (two hours in each class). A questionnaire regarding students’ attitudes towards math was also conducted with one class of students comprising of a total of 45 students. Lastly, I also interviewed the teacher, who had two years of teaching experience. The second teacher I interviewed also was teaching at Border High. He had 27 years of experience and had taught all high school math courses, including dual enrollment and pre-AP, with the only exception of Calculus. Lastly, I also interviewed my own peers from various fields in order to gain their perspective on high school math experiences.

Findings

De-motivator I – Ineffective Instruction

Through one semester’s intensive investigation, I first found that one main reason that this group of high school students were not motivated to learn math was because of the instructional approach the teacher employed in the classroom. Through my observation, I found the teacher’s teaching strategies had the following characteristics.

First of all, my overall impression of the class was that the instructional method the teacher used was very traditional (e.g., lecturing) and it did not provide enough stimulation to engage the students. For example, the teacher gave a lot of time for students to work out the problems on their own, but I feel he could have more dynamic lessons. I often observed that his students were off task and I believe the reason was because the students were not receiving stimulating lessons. If the teacher could have had the students go up to the board and work out problems, or work in teams, they would have been much more engaged. Also, the teacher did provide enough individual help. The teacher normally lectured for the first half the class, then went around the room helping students individually as they were working on the assignments.

Most of the class was on task today, which is impressive, considering it is a Friday! However, one student in particular really seemed to have a real problem understanding today’s assignment. He asked more questions than most, but the teacher did not give him very much of his time. It really gets me when teachers say, “You should know this by now.” That only discourages the students from asking questions. (Class Observation Fieldnotes, March 7, 2008)

Secondly, the learning tasks that the teacher gave were not challenging enough. For example, one day I observed the teacher gave the last twenty minutes to the students to work on the assignment, which did not need to be turned in for another two days; and the teacher told them to finish it before the end of class. I observed that since they had so much time, the students decided that it was social hour and started to chat with each other!

For the last twenty minutes of class, the teacher had the students work on the homework. It was not a lot of homework (he told them they should be able to finish it before the bell rang), and yet it was not due until Friday (in two days). While I think it is important to give time during class to work on math homework, I think it sends the wrong message to give so much time for something so little. As a result, the students did not take the homework seriously – instead it was social hour. During this time the teacher let them work on their homework, about only half of the students were actually working on it. Others talked, went to the bathroom, or just stared off in space. (Class Observation Fieldnotes, Feb 20, 2008)

Thirdly, interaction and group work in the class was seldom observed. As a matter of fact, the teacher gave me the impression that he seemed to discourage group work. For example, one day when I was observing his classes, there was a group of four girls sitting close to each other. When another teacher came to room to talk to the teacher whom I was observing, the students kept working on their assignments. Then I noticed that four girls in particular started to work on the problems together, discussing and consulting each other. I could tell they were not copying off of each other but learning from each other since I was sitting right next to them. When one girl did not understand something, the other three explained the concept to her so she could get the right answer. Then, when the teacher came back into the classroom and saw the students were talking among themselves, he just assumed that they were off task. He broke up their conversation and told the class they would have to stay a few extra minutes since they were wasting time. I was very surprised to see that these four girls were punished for working together.

Lastly, discipline problem was not severe but did exist. For the most part, his students were well behaved. Unfortunately, however, I feel that the teacher did not emphasize enough on that, and the instruction was frequently interrupted during the discipline problems. For example, one day I observed that the teacher had trouble continue his teaching because of the students’ being late.

The class took a long time to settle down today. There were many distractions. People came in late throughout the whole period. As the teacher would begin to give the lesson, there was a knock on the door. He stopped the lesson, let the student in, and then scolded the student in front of the whole class before going on with the lesson. Sometimes he would only get a few sentences out before there was another knock on the door. I think that he should either unlock the door, or have a policy already in place for the students to follow so that class is not disrupted so often. Also, several students did not have pencils while others were noisy with the pencil sharpener. All of this took far too much time. Some of the students were disruptive on purpose because they knew it would annoy the teacher. I think the teacher needs to set higher standards and procedures starting from the very first day of class to minimize these distractions as much as possible. (Class Observation Fieldnotes, March 7, 2008)

Lastly, my overall impression of the teacher’s class was that his lessons were not engaging enough and the students seemed to be unmotivated almost every time I observed his classes, about half of the students were just staring off in space and waiting for the class to be over.

After a day like today, I do not know how anyone in that class could have been motivated to learn math. For the last ten minutes, the students just waited for the bell to ring, with nothing on their desks. Even worse, the teacher was also waiting. (Class Observation Fieldnotes, Feb 20, 2008)

De-motivator II – Lack of Understanding for Math

My second findings regarding students’ motivation towards math was to my surprise. I first found that most students did not hate math as I strongly suspected to be the case. During conducting the questionnaire, I asked the students to describe their attitudes towards math. I told them that they could choose from choices such as a) they love it, b) it is okay, c) it is a necessary evil, d) they hate it, fear it, or e) they have no need for it. I was expecting more students to report that they hate it or feel they have no need for it, which to me would make most people unmotivated to learn about it. However, 42% of the students reported that math was okay, many giving reasons that even though they did not like it much, they realized that math was important and useful in their daily lives.

Another surprising finding was that these students did seem to have good motivation. 87% plan to attend college, and 38% are interested in careers in the sciences. Also, these students did spend a certain amount of their time studying math. The results of the questionnaire showed that nearly 50% of the students reported spending at least thirty minutes on homework. For those 20% who reported that they did not spend any time on homework, it was because they finished their work in class already. Also, the grade distribution for the students’ math classes is about normal: students who received D’s and F’s were 11% each and students who received B’s in their math classes was about 22%.

Given that the students’ responses on what motivates them and their attitudes toward math exceeded my expectations, I would expect their performance and understanding to be much better. However, almost half of the students still reported that they did not understand math, which I found very surprising.

So what is the reason that students do not do well in math? My research showed that it is because they “do not understand math.” When asked why they do not do well in the areas that they struggle in, 71% of the class reported that it is because they do not understand the material. Also, when asked the reasons for not doing their homework, instead of saying that they hated math, that they forgot, that it is boring, or that they had other things that they wanted to do, 46% of the students reported that it was due to their lack of understanding of the material. Another interesting finding is that only 4% blamed it on poor explanations from the teacher. Most students blame themselves for being “stupid” to understanding the material! One college students recalled her high school math experience:

“I always blamed myself for my inability to perform well in math, and having my teachers tell me ‘How come you don't do well in math? Your mother is a math teacher, so why aren't you a good math student?’ did not make me feel very good about myself either. I felt like since I wasn't super awesome in math I was dumb. But I know now that I’m not dumb. ”

A possible barrier for why students were unable to understand math, according the second teacher I interviewed, is “mental block.” During my interview with the second math teacher, we discussed the biggest barrier for high school students in understanding math. This teacher told me that it was because of the mental block most students had that “math is hard.” He agreed that a teacher should not say things like “it is easy” and show frustrations and impatience in front of the students why they still do not understand, which can only make the students feel stupid and dumb.

Math Motivation – The Solution

What can teachers do to motivation students to learn math? Based on my interview with the second math teacher, there are several things a math teacher can do. First, the math teacher should use different approaches and strategies to help the students understand the concepts. Students should know how the math applies to everyday situations. Tools like the internet should be used to help them along the way. Math teachers should also be patient with them. Give students less amount of work which are more meaningful and hands-on. Teachers should also create more opportunities for one-on-one instruction. For students to understand and remember math, math teachers have to make it important for them. A great example this teacher gave is that students have no problem remembering the name, birthday, favorite color, and phone number of their boyfriend or girlfriend. The reason is because it is important to them.

Teachers should show that they care for the students. “I treat my students as if they were my own kids,” he said. When we show our students that we care about them, they are more prone to be motivated. One of my peers shared an important insight: “A teacher could determine whether the student will love math or not… It is really important to change the student's mentally that math is difficult,” she said. She commented that hands-on activities and giving real-life applications to the problems being solved are important motivating factors.

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Lastly, it is very important for the teacher to be willing to explain math to the students, be patient and let them think at their own pace. I interviewed one of my friends who used to hate math. When I asked her why she hated math. She said she just could not understand it. After a little prompting, she told me that fractions just drove her crazy, and so I spent a few minutes with her explaining fractions to her. At first she did not want to, but after a while, she was engaged in the lesson and ended up saying that she wanted to buy a notebook just for math lessons that I would give her. Why changed? I asked her why all of a sudden she was motivated to learn math, and she said that it was because I allowed her to take control. She asked the questions, not me. As educators, we need to teach by guiding our students to the answer, and the students should be in control of their education. That way, when we are not there to help, they will know how to do it, satisfaction will follow, and they will be motivated to continue.

Conclusions

From my research, I found that in order for students to be motivated to learn math, teachers need to design effective and engaging instruction. Also, even though students do put a lot of effort into their math homework, it is often still too hard for them. This is often due to a “mental block” that the students might have, and teachers need to be more patient and understanding, trying many different approaches to help each student overcome their difficulties in math. Lastly, teachers need to help the students see the connection between math and their own life experiences to make them understand it in a more meaningful way.

Application

This study provided a deep understanding regarding high school motivation. Based on the findings of this study, the following suggestions can be made to classroom math teachers. First, the teacher must take an active role in creating interactive, engaging, and thorough lesson plans. This can be done by integrating technology, dividing the class into groups, using hands-on activities, etc. Second, the concepts must be presented in a way which helps the students to see how it can be applied to their own lives and how it can benefit them by knowing the material. Third, the homework should be challenging so that it stimulates the students intellectually, but at the same time it should not be too difficult as the students can become overwhelmed. Along with challenging homework, the teacher must set high expectations for the students. Lastly, a teacher must be committed to his students and his teaching. If the students see that their teacher cares for them, then they will feel comfortable going to that teacher for help. The teacher and students then become partners in education. Because of the stimulating class, high expectations, and teacher support, the students will be motivated to learn math.

Limitations and Future Research

This study had several limitations. One thing I found interesting and surprising was that the first teacher’s answers in the interview conflicted with my observation. For example, he mentioned that he promoted cooperative learning, but in the six hours I observed, he not only did not promote it, but he scolded students who were working together. This may be because I only observed his class for six hours, and I was unable to gain a full picture of his teaching style.

Also, this study was completed in a very short period of time. If I had more time to conduct the questionnaire with the students, my data could be a lot more in-depth, because some students did not have time to finish the questionnaire.

In the future, I would like to expand my research by giving the questionnaire to more students and from a variety of classes. After I have their responses, I would like to come up with a follow-up questionnaire to dig deeper into their perspectives on math motivation based on their responses in the questionnaire.

References

Snowman & Biehler (2006). Psychology Applied to Teaching, (11th Ed.) Boston:
Houghton Mifflin Company.

Steen, L A. (2007). “How Mathematics Counts.” Educational Leadership. 65 (3) (Nov
2007): 8-14.