### Fast kids, slow kids and lazy kids

Educators would never use such labels within earshot of students because they know the power of language to influence how students feel about themselves and about their ability and desire to learn.

But, educators should be just as careful about language when they speak with one another about educational reforms because the words they use can influence what actions are taken to change teaching practices and implement those reforms, according to a recent article in* The Journal of the Learning Sciences.*

“As numerous research studies have documented, many equity-geared mathematics reforms are transformed in the process of implementation, often due to teachers’ apparent misunderstandings of, or outright resistance to, the reform’s intent,” says researcher Ilana Seidel Horn, who analyzed recorded conversations at 2 high schools implementing math reforms.

The language or the labels or categories that were used in the discussions of implementation at each of the high schools could help explain why reforms were more successful at one than the other, she writes.

“Because these category systems provide a vocabulary for fleshing out problems of practice, any solutions that emerge are informed by these underlying conceptions, providing a resource for teacher learning and for making choices about practice,” she says.

At one high school, which the researcher calls South High School, mathematics teachers were asked to eliminate remedial math courses from their curriculum and were given a paid work day to meet and finalize their response to the mandate.

At the other high school, called East High School, teachers were in their first year of full-scale detracking in their mathematics courses. The previous year two teachers had piloted the effort by teaching Algebra 1 content to their pre-algebra students in Math A.

### The mismatch problem

Horn analyzes the educators’ language when discussing what she calls the “Mismatch Problem”–the perceived gap between a proposed curriculum and the students’ abilities. How teachers frame the Mismatch Problem, she says, “resides at the heart of equitable teaching.

“As long as teachers believe that some kinds of mathematical activity are not viable for certain groups of students–whether because of students’ prior preparation or innate abilities–teachers will have little impetus to seriously engage in developing their pedagogy in ways that will reach all students with richer, more challenging content.”

At South High School, educators not only had a mandate to eliminate remedial math classes, but also to provide 4 years of mathematics for all students. Before the start of their 1-day meeting, the math department had already decided to replace two pre-algebra courses, Math A and Math B, with a 2-year algebra course. Now the question was what would happen after that.

The researcher notes the following statements at the beginning of the meeting:

“I don’t think we can fly geometry.”

“You brought it up, and you’re telling the truth” that “our kids cannot get through our geometry as we teach it now.”

“What you’re doing is figuring out our hierarchy and that’s good.””What they won’t be able to handle is the logic in the two-column proofs.”

“Our regular kids can’t handle that.”

“One of the problems with the kids we’re putting in (the 2-year algebra course) is they don’t have the logic component.”

### New bins, old conceptions

The researcher notes that the remedial courses can be thought of as bins that hold certain kinds of students. Although the bins might be changing, in this discussion the conceptions of students are not being challenged, she notes. One math teacher from South High commented that until the district started enforcing its policy of holding back 8th graders who were not ready for 9th-grade work, “we’re not going to be getting the quickest kids.”

As the teachers continued to discuss how they would eliminate remedial courses and offer 4 years of mathematics courses, the researcher notes the following comments:

“Where will we send the kids who aren’t ready for geometry?”

“Should we keep Math C?”

“We can call it Integrated Math Concepts?”

“If you taught a hands-on geometry, if you took Discovering Geometry (a hands-on geometry textbook) and spread it out over 2 years, the district would buy that. That’s not a remedial course.”

“A 1-year hands-on geometry class would not be a pathway to advanced algebra.”

“I say that the kid is ready for advanced algebra at a community college level.”

Horn observes that the educators view hands-on geometry as less legitimate because of its different method of presentation, and describe the course as geometry with a lot of algebra support. As their discussion proceeds, they try to agree on a name and discuss how to distinguish this 2-year geometry course from the college-bound geometry course.

“Integrated Math/Geometry Concepts.”

These are the kids who “forget (about concepts) if they’re not reminded every week, every day.”

“We have to fancy up the name.”

“As far as the names of the math classes, I don’t think we should change it so colleges can recognize it on transcripts.”

“Our lazy kids will sign into it. If the way it’s written says (the state universities) accept it.”

“The college-bound kids won’t take it.”

“Even a lazy kid who wants to go to college won’t take it.”

“If they want to screw up and take two years to get through one year’s worth of work they have the right to screw around.”

Although the mandate forced the teachers to rework the course structure and eliminate the remedial classes, Horn writes that the old bins are maintained under new course names and the distinctions merely blurred.

### How the discussions differed

At the other high school, East High, which was more successful in implementing reforms, Horn says those existing conceptions were challenged as teachers discussed working with students in a detracked curriculum.

One difference in the discussions was that at the first high school the discussion was about students in general while at the other high school it was more particular, more focused on individual students. Another difference is that responsibility for the Mismatch Problem was placed more on teachers at the second high school than on the students.

Both high schools were in California and serve a diverse, largely working-class and middle-class population. East High’s students come from groups that have been traditionally underrepresented in higher education (59% of students from East High identify themselves as Latino or African American vs. 27% from South High.) In a department meeting at East High, teachers discussed how teaching the detracked math courses was progressing.

These are some of the comments from this discussion:

“My students, I don’t know where they’re from, they’re doing so well, I mean they know the difference between a linear graph versus exponential. But the thing about my students is that there’s kids that know a lot and then there’s kids that, you know, feel like they’re slow learners.”

Teacher adds she is looking for group activities “so that the kids that are slow learners can contribute and can you know feel smart, but I don’t know if I can find activities that are group-worthy activities like that. Because I can feel the um frustration of the fast learners.”

“‘This is easy ! I already know the answer!’ And then there’s kids that are slow learners that are like, ‘Give me a chance to find the answer!’ and it’s almost like they kind of give up because they feel like it’s a speed competition, like who can get the answer the fastest kind of thing. And I’m trying to close the gap….”

Horn says the teacher whom she calls “Tina” opens by saying something positive about the students. When she reluctantly categorizes students as fast or slow, a more experienced teacher, “Carrie,” who piloted the detracked curriculum, is visibly uncomfortable with the language. By bringing the issue to the group as a problem to be addressed, Horn says the teacher is taking responsibility for the issue, not just placing it on her students. She seeks help in finding a group-worthy task that will involve all students.

Horn quotes other comments from the discussion:

“I wonder if it’s not just the activities you’re doing but also just status.”

“I mean even if you did give them a group-worthy task, those kids who feel like they have low status will just continue to play that role.

“So that’s what my struggle is, what can I do to make them feel motivated? Make them feel like ‘I’m a part of this group,’ make them feel like ‘I’m smart, too.'”

Carrie, the more experienced teacher, introduces the notion of the status in the discussion, suggesting to Tina that instead of “fast learners” and “slow learners” maybe what she is seeing is learners who are “high status” and “low status”.

“My prediction is that you won’t be able to do anything about it. But that, I think that’s from thinking about a group of kids as slow learners…and that’s how we’re acclimatized to think about learning…..what I find is that when I have mindsets like that that they get in my way in terms of thinking about the curriculum.”

Another teacher, “Guillermo” says: “One thing I’m thinking about is the ones that are moving through things really quickly often they’re not stopping to think about what they’re doing, what there is to learn from this activity. So one thing to think about is, uh, helping kids who are not stopping to see their own learning agenda…Because even if you have great activities, if the perception in the class is um, I’m fast, I’m not as fast, it’s not going to help with the status issues I don’t think.”

### Speed as a liability

This last remark, Horn observes, suggests that speed may be a liability as fast kids often are not stopping to think about what they’re doing. Their focus on task completion may be adaptive to schooling, but not necessarily to complex thinking. The teacher “explodes the scheme altogether by complicating the single dimension of speed (fast-slow), transforming it into a multiplicitous, relational category,” Horn writes. The teacher recommends that Tina consider a problem of the week, a group activity that students can work on independently.

“One thing that I learned in the 8th grade is that kids work the same complex problems but independently they can see other kids’ strategies for how they approach the problem and how they show their reasoning. That maybe they wouldn’t have thought of because they’re too busy like playing school? I’ve got the answer? I’ve got it done quickly. So they’re slow at something. There’s something to get smarter at.”

Guillermo offers support to observe Tina’s class. After observing the class, he mentions a particular student who has a great deal of intellectual curiosity and a lot of background in math and who is “probably going to get most things quickly.” He tells Tina she would have to spend a lot of time looking for a group math problem that is appropriate for this student.

“So you may not be able to really challenge him mathematically, but I think in terms of the complexity of his thinking you can.” He adds that this student seems to be “impetuous” and to get “locked into one thought pattern.”

Horn notes that rather than a 2-track classification of students as fast or slow, the system of classification in this discussion grows ever-more complex and now encompasses qualities such as “carefulness” and “ability to see multiple perspectives.” Tina’s problem, she says, is addressed by examining issues of students (learning agendas, categories of kids), mathematics curriculum (group-worthy problems, problems of the week), and teaching practices (setting learning agendas, incorporating problems of the week, following an experienced teacher).

When teachers meet to discuss reforms, underlying conceptions about students, subject and teaching get built into whatever solutions emerge, Horn writes. By introducing the dimension of academic status in the discussion, for example, a whole new set of responses by the teacher became possible, the researcher says. Many educators’ sequential view of teaching mathematics also needs to be challenged, she says. Horn’s article emphasizes the importance of language not only in how students construct their views of themselves and their potential for achievement, but also in how educators construct practices and solutions to equity-based reforms.

*“Fast kids, Slow kids and Lazy kids: Framing the Mismatch Problem in Mathematics Teachers’ Conversations,” by Ilana Seidel Horn, The Journal of the Learning Sciences. Volume 16, Number 1, pp. 37-79. *