# Discussion between Colleagues

*What is your philosophy of teaching mathematics?*

My philosophy for teaching mathematics is simple. I believe deeply and truly that all children can be successful in mathematics if they are provided with the necessary motivation and scaffolding. I believe that children have a love of math, but many just do not know it yet. I believe that if I believe in students and their ability, they will succeed. Finally, I believe that a teacher’s role is to provide students with lessons that are fun, engaging, and challenging while at the same time being their number one cheerleader.

*Explain what you do in the lesson in light of the cultural makeup of your students?*

Because of my students’ need for specific information regarding the usefulness of the information that they are learning, we spend a great deal of time working on the practical applications for the information. It is important for me to work to make the lessons not only applicable but also accessible. The lessons generally are scaffolded quite extensively in the beginning and then less so as the unit of study progresses. My units generally have a project component built in that provides a hands-on way of applying the knowledge they have gained.

*Are there any teaching practices that you consistently apply based on the culture of your students?*

The concept of the “whole being greater than the one” is a part of the Native American culture at our school. I consistently use this worldview by having children work as part of a group toward a common goal. I also tend to tie the lessons into the world of my students. In the case of rockets, we not only find the altitude of the rockets but also apply it to finding the height of trees. Lumber and the forests are a big part of our students’ lives; therefore, they can see a real value in learning how to perform these measuring skills.

*How did you come to understand your students’ cultural background?*

Although I am not from the same culture as the Native American students in my class, I have a great appreciation for and a deep understanding of the culture. Growing up in Arizona, and as spending a great deal of my time on the Hopi and Navajo reservations, have given me a greater

understanding of the culture of my students. Although I am still an outsider, I have an appreciation for their culture that comes through to my students and their parents. I think the parents’ acceptance of me shows up in the extent of their involvement with my class projects. They would not so eagerly come to school unless they trusted that I have their children’s best interests at heart.

*Tell us more about the parents’ involvement in the project.*

My students’ parents are an interesting mix of people. Most are from lower socioeconomic levels, and many of them are not used to volunteering in the classroom. Parents come in 30 minutes or so before the launch (the launch traditionally takes place after the lunch break). During this time, they are trained on the use of the walkie-talkies and the protractor, as well as given a quick overview of what is going to happen. I am very proud of the fact that a full one-third to one-half of my parents participate on any given project, including Native parents. In some cases, coming to my classroom is their first time in a classroom for a positive experience.

*How do you generally assess students?*

Students are assessed in a number of different ways, both formally and informally. The end result of their projects serves as an assessment (i.e., their rockets and finding the altitude and velocity of their rockets). Observational information is also used in the assessment of my students. Finally, I spend a great deal of time talking with my students and asking questions of them while they are in the midst of their work. This is probably the most useful form of assessment that I use.

*How does this lesson fit into your general curriculum?*

The Rocket Unit fills two very important needs in my classroom. First of all, it is a great way of getting kids to work together to use formulas and to manipulate numbers. They see the way that formulas work along with the value of algebra. Second, it fills the need of being something very exciting for the kids to do that keeps them motivated at the end of the school year. It also serves as a culmination of all of the mathematics that we have done since the beginning of the year: multiplication, division, fractions, decimals, and geometry. Year after year, students of all levels, of all abilities and backgrounds, have been successful in this unit. One of the greatest things any teacher can hear is that his/her lessons made a difference. An e-mail I received from a former student said it all. David said that because of the math that we did in fifth grade, he feels successful and smart in his math classes in middle school. What could be better?

*What experiences using mathematical formulas have your students had prior to this unit?*

We work with a number of different formulas throughout the year. We use s = h/m to find the strength-to-mass ratios of bridges we build, a = (l)(w) to find the area of our gingerbread houses’ walls and roofs, x = c/d to find pi, p = (e/t)(100) to find the percent chance of an event occurring, and, of course, v = d/t for velocity and a = (tan angle)(b) to find the altitude of a right triangle.

*How is a calculator used in this unit?*

It varies with the grade levels. Fourth-fifth-grade students have not yet had experience with multiplying decimals, so I would let them use calculators for calculations and to help with understanding and verifying the formulas. For fifth- and sixth-graders who may need more practice developing fluency with decimals or fractions, then, once they understand the concepts, I have them do the calculations by hand and require that they show the work. In all cases, the calculator is used to help students quickly verify that the tangent formula really works and to also eliminate manual errors that may hinder students from verifying their measurements.

*What recommendations would you make to a teacher who is about to begin teaching in your school?*

My first recommendation would be to value the culture of the students in his/her class. This is a key. Second, I would tell a new teacher not to fall into the trap of stereotyping students. These stereotypes, which include Native American students’ being poor performers, can have a devastating effect on the performance of the students. Finally, I would urge a new teacher not to put artificial boundaries on the students. We often feel that fifth-graders are not able to learn certain topics. I feel that all children can learn anything if they are provided with the necessary motivation and scaffolding.