Darryl Yong is a professor of mathematics at Harvey Mudd College in Claremont (CA). For the entire PDF, see rtx121001408pDarry Yong
During the 2009–2010 academic year I did something unusual for a university mathematician on sabbatical: I taught high school mathematics in a large urban school district. This might not be so strange except that my school does not have a teacher preparation program and only graduates a few students per year who intend to be teachers.
Why did I do this? I, like many of you, am deeply concerned about mathematics education and I wanted to see what a typical high school in my city is like. Because I regularly work with high school mathematics teachers, I wanted to experience the life of a high school teacher for myself. I had neither a research project nor an agenda for changing schools or teachers.
I kept a blog during my adventure, but it took some months after that experience before I could begin to process all that had happened. Four lessons emerged from my experience that I hope will give college and university educators a clearer view of what teaching high school mathematics is like.
Before we get to those four lessons, some background information might help. First, you should know that my story is not going to turn out like Stand and Deliver, Dangerous Minds, or any other inspirational Hollywood movie about a teacher who helped students achieve great things through painful sacrifice and struggle. The Hollywood idealization of a teacher as a martyr who sacrifices her personal life for the sake of her students propagates unrealistic and unhealthy expectations. Teaching is hard, but it shouldn’t have to be that hard.
This is also not the story of a professor coming down from his ivory tower and becoming outraged by the horrors of how children are taught in schools. I find these narratives unproductive.
This article conveys one person’s perceptions of the struggles that novice teachers face in one school and discusses what the general public rarely hears about public education.
I applied for teaching positions just like other teachers in my district, though I did not take all of the necessary steps to become credentialed.
Visiting Faculty Permits, which were authorized between 2007 and 2013 through California Senate Bill 859 by Senator Jack Scott, gave me a convenient way to teach in the California public school system without a credential.
I was hired at a school that serves about 1,100 students. It is one of three high schools in a working-class neighborhood. Roughly 40 percent of the students at this high school are English language learners, 80 percent qualify for free or reduced meals, 85 percent identify as Hispanic or Latino.
In 2009 only 3 percent of students at this school were deemed proficient on the Algebra 1 California Standards Test (CST). That year, I taught Algebra 1, Algebra 2, Geometry, and a math intervention class (an additional period of mathematics for students who are struggling in mathematics). Even though I taught four different classes, I did not teach a full load (six classes at this school). One of my Algebra 1 classes was an inclusion class—half of those students had learning disabilities or some other reason to warrant having an Individualized Education Program (IEP). In that class, all students, with IEPs or without, learned math together….
In many respects I got what I wanted that year: an authentic experience of teaching in a high need urban school. I didn’t want to teach calculus or teach only “gifted” students. I didn’t want to receive any concessions because of my qualifications.
My experience was closer to that of a new high school teacher with no prior experience than that of a seasoned educator moving from one institution to another. I had to cut my teeth on many things like a rookie teacher. For example, I had to learn how to avoid taking things that students said or did to me personally. I learned that my students’ behaviors in class were often a result of grave personal issues (violence, gangs, fear of deportation, etc.). I made many mistakes that year, but I was also spared many more mistakes because of trusted friends who are or were high school math teachers.
Lesson 1: Schools Are Complex Systems Involving People, Culture, and Policies
The news is full of stories about how our school systems are failing along with accompanying claimed explanations. There is a lot of blame that goes around, even at schools. I have heard some university mathematicians blame high school teachers for the poor preparation of their students. At this high school, I heard teachers blaming elementary school teachers for the poor preparation of their students.
During my short high school teaching experience, I learned that most explanations for why our schools are failing are simplistic and inadequate.
For example, consider this frequently cited reason for our underperforming schools: bad teachers. We need to “hold teachers accountable” and “get rid of the bad teachers”. I have yet to meet a teacher who willingly wants to be an ineffective instructor—every teacher I know has a desire to do a good job. Of course, I met math teachers at my school who didn’t know their subject area as well as they should have. Nevertheless, the idea that we can simply replace “bad teachers” with enthusiastic new ones ignores the reality that years of hard work and experience are required to become an effective teacher. In addition, our schools and districts are not doing enough to help teachers grow in their content knowledge and teaching practice.
Some place blame on bad school administrators. In my opinion, our high school was poorly run, but our administrators didn’t always have the resources to do their job well. Our administration mostly reacted to events and crises instead of implementing sensible practices. There was very little feedback given to us teachers about our teaching.
In fact, over the entire year I had an administrator in my classroom observing me for a total of about ninety seconds. I received no meaningful feedback on my teaching. But it’s difficult to blame him when you consider how understaffed the school was. Because the school lacked a counselor at the beginning of that school year, the assistant principal had to take on those responsibilities while supervising students during breaks, dealing with disciplinary issues, communicating with parents, and putting out fires.
Some people have asked me whether it was difficult to teach in a school with lots of poor families who didn’t care about education. Not only is that stereotype inaccurate, it represents another line of reasoning that is simplistic. During that year I encountered some families who didn’t seem to care about their kids’ education and many that did. Sometimes when I called a student’s home I would get a parent who was involved and would intervene, sometimes not. I encountered one young woman who returned to high school as a senior after having taken some time off to care for her baby. Unfortunately, right at the end of the school year, this woman’s mother stopped offering to take care of her baby and she had to quit school.
Does that mean her family didn’t care about education? I don’t think we can tell. I think the best we can say is that each student is a person whose attitudes and capacity for learning is greatly shaped by past and present circumstances.
Simplistic diagnoses are dangerous because they encourage quick fixes. Instead of long-term plans for systemic change, school reform becomes a series of short-lived fads that cause teachers to become jaded by unfulfilled promises of improvement.
At my high school, la mode du jour was project-based learning (PBL). All teachers were trained in PBL (oh, how schools love acronyms) and required to design and implement one project for a class that year. The potential benefits of authentic problems that engage students in meaningful thinking and help them to develop useful life skills are great, but the program was not implemented wholeheartedly. When I talked to one of my colleagues at this school a year later, I found out that PBL was no longer being practiced schoolwide. How can we expect to see meaningful improvement when we change from one fad to another every few years? The unfortunate truth is that the work of improving schools is long, arduous,and not at all sexy….
Lesson 2. Student Self-Concept Is the Best Explanatory Variable for Student Success
I have won teaching awards at the institutions where I’ve worked, but I intentionally held low expectations for my effectiveness as a high school teacher. Even so, I felt depressingly ineffective as a teacher most of that year. While it’s not wise to generalize from a single case, my experience shows that having strong content knowledge in one’s field is a necessary but insufficient condition for student learning to take place.
In the education research literature there are some econometric studies that attempt to measure how different variables (district spending per student, parents’ education level, past academic performance, training of teacher, students’ socioeconomic status, etc.) correlate with student achievement. So, which variables matter most?
According to John Hattie, the variable that correlates most strongly with student achievement is student self-concept. This is a very robust finding. His amazing book  synthesizes over 800 meta-analytic research papers on education (thereby covering over 15,000 journal articles!) to determine the variables that most strongly correlate with student achievement.
Self-concept is a person’s concept of “self” in a particular domain. The difference between self-esteem and self-concept is that the former is an overall view of oneself, whereas self-concept is domain specific. For example, I see myself as a successful learner of mathematics but a pretty poor painter and basketball player. The vast majority of people in our country have a low math self concept—many almost see it as a badge of honor to be bad at math….
Self-concept is shaped by prior academic achievement and one’s beliefs about who has access to mathematical skill and what it means to be “good” at mathematics. During this year I repeatedly observed that my attempts to make learning engaging (by using fun activities, putting mathematics in contexts that students could relate to, making connections to prior learning) were helpful, but not nearly as helpful as attending to students’ self-concepts as learners of mathematics.
If a student’s self-concept is based on past academic achievement and future performance correlates strongly with self-concept, how can we break this cycle? I learned that, regardless of how “tough” some students are or how weak their math skills are, teenagers still love feeling successful when they become good at something or when they figure something out. A sequence of small successes can lead students to develop intrinsic motivation to learn and take risks in a classroom. One way to stage these sequences of successes is through minute, detailed, careful scaffolding of mathematics content….
Lesson 3. Teaching Is a Far Less Respected Profession Than It Should Be
Many parents of school-age children will tell you their kids’ teachers are great but that “bad teachers” are part of the reason why the school system as a whole is failing. To me, this is one of many indicators of the level of respect that we afford teachers and teaching as a profession. In my opinion, discussions about teacher compensation just scratch the surface. I believe that the deeper issue is that our society, including some people in the school system, doesn’t see teaching as a growth oriented, intellectually demanding career deserving of our nation’s best and brightest individuals.
Teachers receive messages every day about how much they are valued as professionals. The way students and parents talked to teachers at our school, the process of signing in and out of work every day, down to the inconvenience of not being given a key to the school office (where the copier was) were examples of such messages. But the most disturbing messages came from the weekly professional development meetings that all teachers had to attend…..
Only rarely did I leave one of these weekly professional development meetings feeling invigorated. These were usually meetings in which teachers shared information about the students that we had in common or when the mathematics department met together without an administrator present. Unfortunately, the vast majority of these professional development meetings made me feel as if I had been babysat for an hour. And many of my teacher friends tell me that my experience is not unique….
Lesson 4. It’s Not the Written Curriculum That Matters, It’s the Assessed Curriculum
Many university mathematicians who take an interest in mathematics education tend to focus on mathematics curricula. For instance, university mathematicians feature prominently in debates about reform versus traditional textbooks that fuel the “math wars”. Perhaps the reason for this interest is that textbooks give us an easy way to join conversations about mathematics education.
Each of us learned mathematics as children, so feel we have something to contribute to the choice and design of math textbooks. Unfortunately, most of us university mathematicians are very different from the majority of students in our nation who have to study mathematics in high school. I, too, am interested in mathematics curricula and was excited to teach a range of classes and to use both reform and traditional curricula. However, at the beginning of that year I greatly overestimated the impact of textbooks on student learning.
The word “curriculum” has various meanings. The intended curriculum comprises state, district, and school standards that dictate what students are supposed to learn and when they are to learn it and, to some extent, how they are to learn it. The new Common Core State Standards are an example of this. Written curricula are the textbooks that schools and districts choose for teachers, but since teachers vary greatly in their adherence to and usage of textbooks, it is important that we pay attention to the curriculum that they enact. All of these lead to the attained curriculum, a construct for what students actually learn.
And then there’s the assessed curriculum. I knew little about this concept before my adventure started, but by the end of the school year I became keenly aware of it. Because we live in an era of accountability and standardized testing, my state and district use various assessments to measure how much students have learned. In a perfect world, the intended curriculum would align with the written and assessed curricula, but in practice they often do not agree. When this happens, teachers find themselves in the awkward position of having to decide how to sacrifice one set of learning intentions for another.
My principal was enthusiastic about a reform Algebra 1 curriculum. I was impressed by many wonderful features of this curriculum and wanted to follow it faithfully, but it did not align with our district’s periodic assessments. For example, there was a moment during that year when I had to decide whether to teach my students how to blindly follow a recipe to use the quadratic formula (since they weren’t yet ready to understand the derivation of that formula) or continue along the path set by our textbook and let them get all of those questions on the periodic assessment wrong. I chose the former and to this day still feel horrible about that decision. Over time I found my teaching becoming increasing aligned with the assessed curriculum: I reorganized the sequence of topics in this reform curriculum and altered how certain topics were introduced or emphasized. This led to a rather weak implementation of the written curriculum and a less coherent Algebra 1 course.
I believe that assessment is crucial to knowing whether students are learning and whether the strategies that schools and districts employ are working. However, we need to remember that these assessments enforce standards for student learning more powerfully than written curricula.
While that may not be a bad thing, thoughtful, well-aligned assessments tend to be expensive and labor intensive (both to develop and to grade). And the likelihood of creating and implementing these kinds of assessments is low given the severe financial condition of most states and districts….