NNER Teacher Case Story

The Applied Math Caste

Nicole Smith

My first year of teaching has been a collision of theory and reality. I started the year with a brain full of what “should be” and was soon bombarded with what “could be”. In a desperate attempt to appear competent, keep up with my peers and learn on the job, I’ve struggled to maintain and practice my ideals. However, as time goes on, it is becoming clearer which ideals I absolutely cannot sacrifice.

In May, almost four months before I would begin my first teaching job, I spent the day at my new high school to meet some of the other math teachers, get my text books and chat a bit about the first few days of school. My schedule for the year would be four sections of geometry and one section of Applied Math II. My teacher-edition geometry text book was brand new and came with software for worksheets, test generators and activities to enrich the content. My teacher-edition Applied Math II text book was actually a student text, about 60 pages long, which looked like it had been teleported to me from the 1980’s. It turns out that this text represented just one of the eight or ten units I would be expected to cover over the year and thankfully, most other units had a teacher-edition.

The contrast between my geometry and my applied math II text books was remarkable and disappointing. My geometry book, which included a myriad of extra resources, was new and filled with current pictures and examples. I was told that applied math II (a continuation of applied math I and prerequisite of applied math III, all using the same antiquated textbook series) was a class designed for students who typically participate in a vocational program. I looked inside the book and found sketches of builders putting on a roof and about ten to fifteen pages of writing in 1980’s font (at the time of print I imagine the font choices were limited).

The retiring teacher whom I was replacing showed me a closet of rulers, micrometers, dowels and other things I didn’t recognize that could be used to do the labs in the text book. He explained to me that each unit had a few labs to do and that the students, being hands-on learners for the most part, enjoyed the labs over traditional assessment measures. My skepticism of the value of the textbook was momentarily assuaged by the fact that the series was offering a different mode of assessment at least, showing some consideration for the different learning styles of their typical students.

I left the school that day loaded with textbooks, handouts and hope that I could somehow make this content more exciting and interesting for my students. The task ahead was daunting but my success in teacher’s college had given me the belief that I could live up to the challenge. I wasn’t prepared for the war of ideals and pragmatism that awaited me.

That summer, I read through both the text books and started preparing lessons for both classes. Geometry was fairly easy to plan, the textbook was divided into chapters and subdivided into topics, neatly followed by worksheets and activities to re-enforce the content. My ideas were flowing and I was excited to get started. The applied math text book on the other hand was more difficult to use. The chapter was called “Ratios” so I tried to divide the 15 pages of writing into subtopics that I could tackle each day. I made notes and tried to match up the questions at the back of the book with what I would be teaching that day. I also tried to find real-life examples on the internet of what we were learning to make the content more interesting. What really struck me at first, was how disorganized the book was and how difficult it was for me to identify the key points from the text. One day when I was particularly frustrated I remember thinking that I would end up spending more time preparing for this one class than I would for my four geometry classes that year.

When school finally started on August 27th I was ready, syllabus in hand, to greet my students. The first day of school was for freshmen only so I only saw a few geometry students that day and no Applied Math students. I had been assigned a mentor who taught the other section of Applied Math II class and a section of geometry. At the end of the first day I showed her my syllabus for Applied Math II and asked what she thought. She said it looked a lot like hers but that she didn’t have “applied kids” do journal entries.

This would be the first time I would hear the term “applied kids” and definitely not the last. As I would later learn, “applied kids” has the opposite connotation of, “honors kids”. Where it was safe to leave “honors kids” in your room between classes, “applied kids” must be supervised at all times. “Honors kids” could be trusted to go to the nurse and their lockers but “applied kids” need to be tracked by emailing the nurse and timing locker visits. “Honors kids” are respectful, want to learn and should be challenged but “applied kids” are disobedient, hate learning, easily frustrated by challenging material and should never be assigned homework.

I told my mentor of my plans for how to teach the first chapter and she was quick to say that applied kids don’t respond well to traditional lectures. The textbook series comes with study guides (which I hadn’t received on my May visit) for each unit and she strongly recommended that I use them. “Definitely try your lessons if you want”, she said “but the ‘applied kids’ really don’t have the attention span to sit through a lecture and take notes.”

And so began the first battle of my ideals versus reality. Was it true that kids in my applied class would struggle with my lessons? Would they really prefer to read the text on their own and fill out the study guide instead of having me teach the content to them? My mentor said that she felt she was “copping out” of teaching when she first started using the study guides but that the kids really responded better to them. “They’re more independent learners”, she said. At that point I didn’t know what to think or feel about the study guides and thought the best thing to do was to wait until I had met my students.

As a side note I think it’s important to mention here that my mentor is, what I believe to be, a wonderful teacher. She desperately cares about her students as is evident by the flock of students who have formed a sort of entourage around her. In her “traditional” math classes she provides many types of assessments to allow students to show their knowledge in different ways and is very open to collaborating with other teachers on activity or project ideas. She is a graduate of the same teacher Ed. Program as I, having graduated only about three years ago, and has clearly tried to incorporate some of what she learned into her teaching. She is an incredibly supportive person and although I may not fully agree with her views on the kids in the applied math program and therefore risk portraying her as a bad teacher, I want it to be clear that I respect her as a professional and believe her to be one of the more progressive teachers I work with.

Back to the story: At this point in the first few days of school, I was completely torn about how to handle my applied math class. The first class after our initial class I had my students write me a journal entry on how they learn math best. I then taught my first prepared lesson which was an introduction to ratios. I had made some practice worksheets for use in class and assigned some problems from the book for homework. The kids seemed only marginally interested in the lesson and although they dutifully filled in the worksheets, they made many mistakes and asked very few questions. At the thought of homework, they moaned but I thought at least they might try it. I could see already that this class was going very differently than my geometry classes.

The journal entries were interesting to read. Many students said they learned best by “doing”, some said they learned best when the teacher gave examples on the board. However, I knew that I was in a foreign situation; this was a different sort of class that I hadn’t had experience teaching before. I started to question my lessons, maybe this really wasn’t the way to go about it. If the students were used to study guides, and this had worked for other teachers, who was I as a first year teacher to balk at the system?

The next class I had fourteen fresh copies of the study guide ready to go. I passed them out to the tune of more moaning and complaining. I heard things like “I hate the study guides” and “study guides are so pointless and stupid”. I told them we would just try them out and if it didn’t work, we’d try something different for next chapter. They seemed satisfied with that and got to work.

It struck me at this point that the “independent learning” experience designed by these books were not at all appropriate for these students. One thing I was told about students in the applied program was that they aren’t strong readers for the most part. And yet, this learning method required them to read to access the material. What would I be assessing them on- reading comprehension or math? Why throw another hurtle in front of these already struggling students?

And the result was what you would expect from students who are more challenged by reading than most; they copied answers directly from the book without reading. Their understanding of the math content was virtually non-existent; many were unable to answer questions that they had already answered in their study guides a few minutes before. It was becoming obvious to me that these students had been cast aside and forgotten by being given a math curriculum they can’t access.

The videos were almost worse than the book. At the beginning of each unit the teacher is expected to show a short video which poses a problem to introduce the students to the new unit. It’s not a bad concept so after a few classes I tried it out. The video opened with upbeat synthesized music and showed a mustache-sporting-tight-jeans-wearing man from the 1980’s stirring a huge pot in the middle of an industrial kitchen. “I’m making a roux” he said as the word “Roux” went across the bottom of the screen. “My roux has 2 parts margarine to 1 part flour. How many pounds of margarine do I need if I have 2 pounds of flour?”. The numbers were displayed on the screen as he solved the problem and poured four pounds of margarine in his huge pot. As if the sight of so much margarine wasn’t disgusting enough, the thought that these students were supposed to take this video seriously and learn from it was downright offensive. I laughed it off and made fun of the host’s mustache but didn’t get much reaction from my straight-faced students. I could tell that they didn’t see the situation as a laughing matter. So far, these materials were proving to be ineffective and insulting to my students.

As a new teacher, I’m new to the math curriculum and the different options students have. My impression of the applied program was that it was for students who struggle in math; the kids were quick to point out that it was the “stupid math” within the first week of school. When I asked the department head what students we should be recommending for the applied math program she told me that voc students were the best candidates not regular students who struggle. This struck me as a little bit odd, it’s not like we’re doing on the job training in applied math; the biggest difference is that each concept is tackled one at a time for an extended period of time instead of for one class period like in the traditional math stream. On top of that, only one out of my fourteen students is actually taking vocational classes. So why is applied math reserved for “voc kids”?

There’s something I’ve noticed about the kids in my applied math class versus the kids in my geometry class. I have students who attend voc in my geometry class and I have struggling geometry students who would probably do a lot better with the pace of the applied math class. I also have some strong student in my applied math class who would do fine with the pace of my geometry class. The common factor seems to be their socioeconomic status and I can’t help but wonder if these students aren’t being tracked according to their financial situation. Of the students in my applied math class, one has already been to court on drug charges (he’s actually one of my top students) another has confessed to stealing from goodwill and apple orchards, another has spoken about their “psycho” mom who hasn’t had contact with him in months but who showed up to open house, and who knows the problems the others are facing. I can’t help but feel as though these kids have been written off by their parents and now, the school.

I started asking around about getting new text books to replace the applied series but there was little interest among the other math teachers to get the ball rolling. I was told that the newest edition of the current series was in a textbook format that kids in the applied math program found intimidating. I’ve ordered two sample text books from other companies but each could only be used for a few years and the applied series needs to have three classes (so that a student could conceivably do all three required math credits in the applied track).

In the meantime, I’ve scrapped the textbook and, by the request of my students, I’ve proceeded to give short lectures in class followed by activities and practice. I’ve tried to use the internet as my resource for materials. For our unit on scale models and drawings I showed pictures of scale model Volkswagens and BMW’s made from wood that are used by the company during the design process. I had them use real maps to map out a route and estimate travel time based on speed limits (just like MapQuest does). When we learned about vectors I used online applets from NCTM which illustrate vectors and vector addition using airplanes and wind vectors. However, I still don’t feel that I’m doing justice to the “applied” goal of the class because of my lack of experience and resources.

Over the last five months I’ve managed to develop solid relationships with the students in my applied math class based on respect. Some of them have thanked me for not using the textbook and one even thanked me for making their tests harder than the other applied math teacher does. Some students have said that they actually look forward to coming to class which for me, is one of the most important outcomes. It’s hard to tell how my methods have affected their mathematical development but I know my students performed well on the common midterm assessment we used for both applied math II classes. I feel that if I were to teach this class again, I could expect my students to be even more successful than this year’s students because I will be starting with more resources and ideas for new approaches. My goal is for my students to feel successful in math but most importantly, I hope they come away from the class feeling as though they had a teacher who expected more from them and cared whether or not they succeeded. And now that I’m using the needs of my students to guide my instruction, my ideals have never seemed more practical.

Discussion Questions:

In your school, do you feel teachers have different academic expectations for students from a lower socioeconomic status? If so, how does this affect the students?
How do the expectations/hopes that parents have for their children affect the way teachers view their students? (i.e. Could a struggling student from an affluent family be pushed through the mainstream math program because parents expect that student to go to college even if, academically, they might do better in the applied class setting?)

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