A National Math Trail Evaluation 

Teacher Interviews and Site Observations
Part of the evaluation activities of National Math Trail during the 2001-2002 school year involved gathering detailed information from teachers and students in the classroom who participate in National Math Trail activities. In order to see first-hand how math trails were being used in the classroom, several site visits were scheduled with teachers in Georgia who had volunteered at one of the National Math Trail’s 2001 summer training sessions. A combination of site observations along with telephone interviews were used primarily to determine how teachers decided to use math trails with their students and how well this form of instruction fit with their current teaching practices. The results of those interviews and observations are presented thematically below. 

Preparing to Use National Math Trail Resources
National Math Trail Institutes provide teachers an opportunity to learn how to create math trails with their students and how to take advantage of the National Math Trail web site. Overall, teachers regarded their Institute experiences with a high degree of satisfaction. Teachers pointed to several aspects of the training that they felt were particularly helpful. Teachers indicated, for example, that the facilitators at the training offered practical recommendations about how to direct students through the creation of a math trail. 
 
Teachers expressed a particular appreciation for having the opportunity to go through the entire process of creating a math trail with a small group of peers. In this environment, teachers were able to learn not only from the facilitators but also from the ideas they shared with other elementary and secondary school teachers. Teachers felt that by going through the process they could more easily anticipate any problems that might be encountered in the classroom.
 
Because the National Math Trail Program encourages the use of technology throughout the process, the training was designed to address the technology questions and concerns of the teachers. Teachers who did not consider themselves experts in the use of technology were pleased by the pace of the Institute when it came time to learning about the role and use of digital cameras as well as other kinds of equipment. The presentation made by Casio representatives to show teachers how to use the digital cameras was cited as both useful and interesting. Even teachers who had already used a digital camera before indicated that they were able to learn a variety of functions and techniques that they had not previously known. 
 
In addition, teachers were pleased that the Institute taught them a spectrum of approaches for completing a math trail. One teacher, for example, explained that some relatively simple tips, such as substituting magazine pictures for digital camera pictures, gave him some flexibility if the classroom activities were taking more or less time than he had anticipated. 
 
Considerations Made in Integrating National Math Trail Activities
Faced with limited time and resources, K-12 teachers carefully considered whether to incorporate National Math Trail activities into their curriculum. Before introducing National Math Trail into their classrooms, teachers that were interviewed identified the following three areas of concern: time, technology, and state content standards.
 
a. Time
Because teachers face pressures to cover a certain amount of academic material with their students each year, they do not have a lot of time to spend on activities that do not directly relate to their curriculum. Teachers agreed, however, that math trails are a good way to introduce and review the math content they are already required to teach. 
 
Teachers also reported that the time needed to develop a math trail was quite flexible. Since the number and complexity of problems as well as the presentation can be controlled, it is possible to do a whole math trail in just two or three class segments or over a number of weeks. Some teachers indicated that they would use math trail activities to review material before a major test while other teachers did math trail activities after their major tests near the end of the school year. The adaptability of the National Math Trail Program has proven to be a great strength in the eyes of instructors.
 
b. Technology
While some teachers have extensive experience using technology for educational purposes, many teachers still feel uncomfortable using even simple computer functions in their classes. For this reason, teachers who were doing math trails thought that other teachers might be intimidated by the technology used in preparing a National Math Trail. After learning about math trails, however, math teachers concluded that the amount of technology used was completely subject to their own preferences.

“The great thing about the National Math Trail is that you can do it in a high-tech or low-tech way. Students can draw pictures of things around them and create a math trail even if there isn’t any special equipment.” 

Although technology use is not a necessary component of forming a math trail, the program is designed so that students can gain experience using technology as part of their K-12 education. Teachers recognized that when doing a math trail in the classroom it is a good opportunity not only for the students but also for the teachers themselves to learn some basic skills that can be applied to a number of other areas and activities. 
 
To take full advantage of National Math Trail, teachers reported that it was advantageous to have access to computers with Internet connectivity. With this access, both teachers and students can explore the National Math Trail web site to see what students in schools around the country had created to challenge their peers. In the classrooms observed during this study, the students were fortunate to have several computers inside of their classrooms. Although not necessary, the teachers interviewed also said it was convenient for them to have a personal computer at home to do some preparation and exploring of math trails outside of school.
 
c. State Content Standards
Because of the self-directed nature of National Math Trails, teachers reported that they do not have a problem ensuring that their math trail activities follow the guidelines of their state’s curricular content standards. In Georgia, for example, teachers are using National Math Trail to address areas of state-wide academic weakness that have been recognized. As part of that state’s Quality Core Curriculum, students are expected to progressively develop their problem solving skills, which historically have remained below the expected standard. Realizing this weakness, many teachers have used National Math Trail as a vehicle to improve their student performance. 

“It [National Math Trail] is designed to incorporate any standards you want such as problem solving which has become an area of concern in our state of Georgia.” 

Creating Math Trails in the Classroom
Student math trail activities varied greatly during site observations. Despite the various stages that the classes were at when creating their math trails, several common elements were observed. These observations mirror much of the feedback offered by instructors.
 
First, students demonstrated an eagerness to both create and solve math trail problems because, as one student described, “they are real.” Teachers supported this notion and maintained that by directly applying mathematical concepts to the surrounding world, students can more easily understand the value of math in their every day lives. Furthermore, teachers reported that their students enjoy the opportunity to work outside of the textbook. 

“Math trails help students see math in the real world. Not necessarily new content, but a new perspective to the content that is already taught.”  

In addition, students who created their own math problems seemed enthusiastic to share their work with other students and adults. Students exhibited a great deal of pride in the math problems they created and enjoyed challenging their peers to solve these math problems. The students as well as their teachers also expressed excitement at the prospect of seeing their math trails put up on the Internet so that local schools and even international schools could see their work.
 
Perhaps the greatest excitement in the classroom was observed, however, when students were given the opportunity to use the digital camera provided by National Math Trail. After receiving detailed instructions from their teacher, students at one elementary school in Georgia were allowed to take digital pictures of the things that they based their math problems on. Trees in the playground, windows in the classroom, and doors to the gymnasium were just a few things that the students had created math problems about and then took pictures of. In one third-grade elementary school class, students applied their study of multiplication, addition, subtraction, time, estimating, place value, and lines of symmetry to the math problems they created.
 

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