In an era of mathematics reform, classroom practice is of the utmost interest to mathematics reformers, policymakers, parents, students, school administrators,
community members, and most notably, teachers. Classroom teachers determine the extent to which practice changes or remains the same. This circumstance has been studied by researchers for quite some time. In fact, as the preceding chapter showed, what
teachers espouse about mathematics and mathematics pedagogy has been studied. However, much of that knowledge has been obtained through methods that fail to confront why teachers make the decisions they make.
This study attempts to discover how teachers understand the state standards, as well as how their understanding translates into classroom practice. Do teachers truly support the Standards and strive to provide standards-based instruction to their students, and if so, what is the evidence of this in their classrooms? (It is possible that this is not the case.) For those teachers who advocate for the Standards and standards-based instruction, what circumstances inhibit them from successfully implementing standards- based instruction in the classroom?
Prior Research Focus Groups as a Backdrop for the Study
This study was based on the researcher’s personal prior teaching work with practicing teachers, and reading of current literature on classroom practice. What began as an inconsistency in my view of effective mathematics teaching and my observations of the instructional practice of mathematics teachers during a research study became a quest
for understanding. I decided to interview other teachers to see if I could make sense of this evident discrepancy.
Initially, my sense making led me to conduct a focus group of mathematics teachers to find out how their knowledge of the mathematics standards affected what happened in their classrooms. I wanted to know how knowledgeable teachers were about the Standards, how they meshed the Standards with their instructional strategies, and how the Standards had (or had not) changed their teaching. Basically, I wanted to know how mathematics teachers defined what they do in the classroom.
Focus Group Alpha
The first focus group consisted of 11 teachers of Grades 2-7 from three different school districts within a single county. The majority of the teachers were teaching in self- contained classrooms in Grades 3-5. The teachers were together on this occasion to attend the last session of an eight day sustained professional development series training
arranged by their county educational service center. The eight professional development days were spread over a five-month period of time and were held during the teachers’ work day.
I began the discussion with a request for them to share their thoughts with me. The question I asked the group was, “When you first start planning what you are going to teach and do in your mathematics classroom, what do you think about? Tell me about your planning.”
Answers were short with little to no elaboration on the ideas put forth. Some of the considerations mentioned were the goals of the lesson and what they had to do to
achieve those goals, the indicators, what the state says they have to teach, time constraints put upon them by the need to prepare students for state achievement tests, lack of resources, and their student demographics. The teachers, for the most part, were hesitant to elaborate on their responses when I probed for additional comment. They were uncomfortable, fidgeted, and displayed signs of uncertainty and hesitation, so I ended the conversation. I surmise that my presence at a workshop arranged by their district
leadership may have compromised the rapport needed for a more frank discussion. I did not feel I learned much about teacher practice by conducting this focus group. In addition to what I interpreted to be feelings of mistrust, I hypothesized that much of the problem had to do with the grade levels taught by the majority of these teachers. Mathematics is only a part of their teaching responsibilities, and many of them had expressed a dislike for mathematics. Perhaps the opinions of this group of teachers were atypical of educators specializing in mathematics.
Focus Group Beta
I chose to attempt another focus group with mathematics teachers who taught in departmentalized mathematics classrooms. I contacted a colleague who was preparing to facilitate a 2-week summer institute, primarily but not exclusively, for middle-school mathematics teachers. I arranged to attend the second day of the institute prior to most of the instruction that would take place since I did not want the content from the workshop to influence teachers’ conversations with me. I conducted two focus groups, which allowed me to meet with all teachers in attendance.
The teachers ranged in experience from a new teacher seeking employment for the upcoming school year to a teacher who had taught for 28 years. The incentives for participation in the workshop were such that the motivation for attendance was quite varied. Teachers, self-reportedly, participated for various reasons--free graduate credits for licensure renewal, stipends, free resources and materials, information, and
networking. All were from rural school districts in southern Ohio.
The workshop participants divided themselves into groups by choosing when to meet with me. This accident of timing prompted an interesting split between the
participants as they self-selected their groups. The beta group was made up of 11 novice teachers--newly licensed teachers (some with and one without employment for the coming school year) and teachers who had some experience but generally no more than 5 years. The gamma group was made up of nine more experienced teachers.
I met with the beta group over an extended lunch. I started the conversation with the same question from my earlier focus group. “When you first start planning what you are going to teach and do in your classroom, what do you think about? Tell me about your planning.”
The first person who spoke said, “The [Ohio Academic Content] Standards. I think I can speak for all of us here. That is the first thing that comes to mind. The Standards.” Everyone around the table nodded their agreement. This group continued to talk about the Standards and the accountability system the state has adopted and how it has made teachers more accountable for teaching what is required. Many recounted using previous Ohio Achievement Tests to determine the testing emphasis placed on individual
indicators. Indicators that were most often addressed in testing questions were chosen as “power indicators.” When asked to explain further, they explained that power indicators helped them know exactly what indicators to hit the hardest. It helped them focus instruction. One teacher stated,
I took the achievement tests over the last few years and mapped out what questions they asked. I matched them to the indicators. Those are the power standards. It helps me because I know what I can leave out and what I need to teach.
All but two of the eleven teachers at the table had done this as part of their planning. This naturally led to a conversation about short-cycle assessments, which are a direct result of school districts trying to focus instruction on the Standards and grade- level indicators. All teachers from the beta group spoke favorably of this practice. They were cognizant of the importance of alignment of practice and assessment. “I know what’s on the short-cycle assessment tests. I know what is on the achievement test.” Another teacher offered her perspective, “We all have our favorite things to teach. I like algebra. If I like teaching algebra, is that going to affect how I teach geometry? With what I like to teach…I can be more creative.”
With no more prompting from the interviewer, the group eventually turned to a discussion of pedagogy. Most talked about different strategies for instruction, which included hands-on activities, worksheets, and making “real-world” applications. They agreed that what they actually do in the classroom is affected by time, cognitive ability levels of students, and students’ behavior. Teachers reported using a variety of strategies
based on those considerations, and they seemed to doubt the existence of “one right way” to teach. They admitted that strategies they employed were not even consistent
throughout the day. “I might teach using a worksheet one period and then try something else the next.” Another added, referring to behavior, “What can you trust your kids to do?” Yet another added that it often happened that she found herself saying, “…This is second period and that didn’t work so now I will try something else.” The only male teacher in the group mentioned that he tried to find “real-world” applications for each topic he taught to which someone quickly added that it was important to make it meaningful to students. The beta group teachers spoke with animation and seemed confident in their classroom practice.
Focus Group Gamma
At the end of the day, I met with another group of teachers. This group consisted of more experienced teachers. Most of them had taught for many years. The exception was a middle-aged woman who was teaching a high school geometry course under alternative licensure while completing course work to obtain her license to teach. There were nine teachers in this group.
Posing the same question, I expected a repeat of the beta group discussion. Things, however, were not exactly as I anticipated.
Teachers began talking about the “big picture” and breaking down the year into “chunks” by grading period and then further by week. One teacher talked about self- evaluating what she had done the previous year and thinking about her weak areas and considering how to change or strengthen those. Several teachers talked about how
important it is in planning to know your students. “You have to pre-assess your students. I don’t need to spend time going over things they can already do.”
Interestingly, they were 19 minutes into this conversation before anyone brought up the Standards. “They gave us a copy of the Ohio Academic Standards on a worksheet. And now, any time I talk about something on the sheet, I put a check by it so they
[administration] know at the end of the year that I ‘covered’ everything.”
Someone else reported, “Our new textbook has the Ohio Standards right in the front of the book. I made my kids sit down and read the indicators. They were bored and didn’t want to do it, but I made them anyway.”
According to the gamma group, many of the school districts seemed to be taking measures to force students and teachers to focus on grade-level indicators. One teacher reported that the students in her school had to keep a check-sheet of the grade-level indicators in the front of their notebook, and whenever the class covered one of the indicators, the students and the teacher both had to initial that indicator on their check- sheet. “That way they can never say they didn’t cover it when we get to the test.” Several teachers reported that although their schools were not currently following this procedure, they were planning to implement this for the next school year. Some reported they were required to write on poster paper and to highlight which indicators they were “covering” each day. Some reported that they had commercially made posters they were required to display in their rooms listing the standards and indicators.
A few teachers discussed short-cycle assessments. One of the teachers said she did not use the short-cycle assessments because they were not aligned with the state tests.
(Incidentally, this person worked in the same school as one of the beta group
interviewees who talked about the short-cycle assessments favorably citing them as well aligned to state indicators.) Another said she worked in a county where they used a pacing chart that dictated what each teacher on a grade level would be teaching on any given day along with prescribed and mandated short cycle assessments. She liked the pacing chart because many of the students in this county moved from school district to school district and claimed that the pacing chart helped to make sure “huge pieces of the curriculum” were not missed.
In discussing what they did in the classroom, most teachers described classrooms where there was great disparity between the students’ ability levels. They talked about the difficulties they faced in meeting the needs of all their students, now and in the future. While most teachers talked about their struggles to meet the expectations of the state and their superiors, two admitted they were failing to meet the needs of both advanced and lower-level students because they felt they had no choice but to “teach to the middle.” They just hoped they could find time to help the others.
The conversation then moved to how, in the next few years, all students will be required to take Algebra 2 as part of the core courses in high school. Several teachers expressed concern for their students who have individualized education plans (IEPs) and those who are struggling with more limited mathematics ability. Such students, they observed, had little recourse when it came to securing additional help. More than one teacher reported trying to make time outside of class to work with students who were struggling, since their parents were unable to help them with mathematics.
Teachers discussed the need to make mathematics meaningful for their students. One teacher said, “I try to use ‘real-world’ applications whenever I can. You know…. I don’t care how many golf ball problems there are. My kids don’t golf. Put it back on the farm. Take it back to everyday.” Another expressed concern, “What if they don’t want to go back and farm? They may go cut timber or tobacco.” The group erupted with
indignation that what students want to do with their lives is not honored within the educational system. The conversation was not moving forward in a way that I could determine what was actually happening in the classroom and why they chose certain instructional practices.
Intervening, I asked the gamma group, “When you think about your instruction, what kinds of things are you doing in your classroom?” Teachers talked about paper- folding, acting out problems, trying to use “real-world” applications, using tangrams to prove the Pythagorean Theorem, and using dry erase boards for group computational activities. While these were strategies reported as a direct result of a specific question, throughout earlier discussion, most talked about doing problems on the board for students to copy and starting assigned homework problems by working problems together as a group before giving students time to work on the problems prior to leaving the classroom, indicative of traditional methodology.
After much venting of their frustrations over testing, one teacher suggested that value-added evaluation would be beneficial to their students as the value-added system judges performance as individual growth (over time) rather than in reference to a norming group. One teacher expressed her thoughts on the matter.
It will also help these kids. Even though they don’t make the score, they can see that they have come up from here to here (using hand motions). They compare them to themselves. It is important for that kid to realize the growth they have made. I mean why compare these kids to kids in California? I have kids who have never been to a mall. I had a kid who didn’t know what a pineapple was. You tell me, is it fair to compare that kid to some kid in Sandusky? Those kids don’t know what a farm is and could never milk a cow but my kids…. Well….they can take care of a cow!
Another teacher told about a student who had no interest in school but sure knew how to hotwire a car. This group seemed to me to have a whole-child view of the purpose of education.
Summary of Focus Groups: What Does It Mean?
When I thought about the differences in these three focus groups, what kept coming to mind were their attitudes and feelings about the Standards. It was not even something they all identified as such. The first group seemed to view the Standards as an administrative mandate to which they were being held accountable. Although they indicated some appropriate supports were being offered, they were concerned that the expectations set forth by administrators were unrealistic and that teachers would be viewed unfavorably if test scores were not acceptable. The beta group interpreted their responsibility to students in terms of the Standards: This is what we are supposed to be doing and these are all the ways in which we are accomplishing this goal. The gamma group, by contrast, seemed to see the Standards as almost a hindrance to preparing their
students for life. As one teacher explained, “When I started, I felt like I was preparing the kids for their life. Now I feel like I am preparing the kids for a test.” These teachers seemed not to doubt that this change was a disservice to their students but they also seemed at a loss as to what they might do about it. For this group of teachers, the
Standards seemed to be an obstacle to overcome. Their stories were about the challenges they faced due to changes they seemed to consider a detriment to education. These challenges made their jobs much harder. With this group, I never really could decide if they truly understood what was meant by the term “standards” as they seemed to use it loosely and sometimes erroneously.
The discussions with practicing teachers did little to alleviate my confusion about what teachers did in their classrooms and why. It did confirm that teachers seem to have differing degrees of understanding and that they place differing degrees of value on mathematics standards. This is not surprising as, according to research, one would expect debate and difference. The discussions did not give me great insight in to what part mathematics standards play in determining classroom practice because, although all the teachers in the focus groups reported teaching according to the [Ohio] Standards, their