Updated: Mar 11, 2021
At Pear, we’re always looking to evolve our services by incorporating the latest research on equitable teaching practices. The research findings of Jonee Wilson, Mahtab Nazemi, Kara Jackson, and Anne Garrison Wilhelm in their article Investigation Teaching in Conceptually Oriented Mathematics Classrooms Characterized by African American Student Success published in NCTM’s July 2019 Journal for Research in Mathematics Education validate practices we’ve used and impress upon us how important it is to increase the frequency of these practices in order to create equitable outcomes in mathematics. As the researches hope will be the result of their article, these findings inform our approach and focus in the professional learning programs we design and implement. In this post, I provide a summary of the authors’ findings.
"[W]e see value in integrating a focus on the identified forms of practice in preservice and in-service professional learning settings."
- Jonee Wilson, Mahtab Nazemi, Kara Jackson, and Anne Garrison Wilhelm
Investigating Teaching in Conceptually Oriented Mathematics Classrooms Characterized by African American Student Success, published in NCTM’s July 2019 Journal for Research in Mathematics Education Classrooms, outlines several forms of instructional practice that distinguished middle-grades mathematics classrooms organized around conceptually oriented activity and marked by African American students’ success on state assessments” (p 363). Building on research (Walker, 2009) that shows conceptually oriented mathematics classrooms improve the learning of mathematics (as evidenced in improved standardized tests scores) for African American students, the authors studied classrooms in which students were presented “cognitively demanding tasks,” while teachers “maintain[ed] the rigor of the tasks” and “engag[ed] students in whole-class discussions that emphasize reasoning” (p 393) through their implementation of the Connected Mathematics Project 2 (CMP2) curricular materials.
The seven practices described below appear to be key factors in raising the math achievement of African American students as measured by current high-stakes assessments. While these practices were present in all of classrooms studied, these practices occurred, on average, over 2.5 times more frequently in classrooms with the resulting higher-achieving African American students (p 381).
Forms of Practice in Classrooms Characterized by Conceptually Oriented Activity and African American Students’ Success on a Standard Measure of Achievement
1. Making Mathematical Expectations Explicit
Teachers made lesson expectations clear for both social and mathematical behaviors. Not only did teachers make statements about what students were to do and how to act (social expectations) along with reasons why those behaviors would be helpful to students, but also – and more importantly – they pointed out what mathematics students needed to attend to in a task and how students were “to approach mathematical work” (mathematical expectations) (p 376). Teachers’ high-quality expectations were further met with reasons why the expectations were important as well as student accountability in meeting them. Indeed, "teachers took time to check in to see where students were and remind them of the expectations" (p 383).
2. Coaching Students
Teachers provided “clear suggestions and further guidance” to students on how to meet the explicit expectations given (p 393). Coaching students describes when a “teacher explicitly intervenes to support a student or students to meet expectations” with the intent to assist students in participating socially or mathematically during the lesson (p 376). “Specific details or concrete suggestions” that helped students meet expectations occurred over 3 to 6 times more frequently in distinguished classrooms. It is worth noting that teachers helped students meet the given mathematical expectations while also maintaining the rigor of a task by not telling students procedural steps to solve it (p 385).
3. Attending to Students’ Local Contexts, in Service of Mathematics
More effective teachers showed “an awareness of or an attempt to connect to students” using references to students’ own contexts (school, home, community, or pop culture) “explicitly in service of furthering mathematical understanding” (p 385). That is to say, teachers helped students envision the mathematical tasks at hand in a context that made sense to the students’ real experiences or understandings.
4. Attending to Language
Teachers helped students understand words, phrases, and ideas. Assistance took the form of revoicing student responses with formal mathematical language as well as using “gestures, hand motions, and verbal explanations” (p 388). Teachers also had students help themselves and others attend to language by having students “restate, translate, or ‘say it again in your own words.’” Assuring students could understand mathematical ideas and their related terms, as well as contributions from classmates, occurred a median of 13.5 times during a lesson in distinguished classrooms as opposed to 5 times in other classrooms.
5. Attributing Mathematical Authority to Students
Teachers “position[ed] students as being mathematically autonomous." In distinguished classrooms, teachers “h[e]ld students accountable for engaging in rigorous work and for their own learning” (p 388). While teachers compassionately offered students ideas on how they could continue the struggle (i.e., talk to their peers) and reassured them that the difficulties they were facing were the point of the task at hand, teachers did not give answers that would take the thinking out of a mathematical task.
6. Positioning Individual Students as Competent
Teachers in effective classrooms supported individual students in viewing themselves as “capable [mathematical thinkers] and legitimate contributor[s] to the learning environment” (p388). This took the form of praising students for their sharing of ideas and making explicit statements that validated student problem-solving strategies. Recognizing and verbalizing the competency of individual students, not just groups of students, was more frequent in high-achieving classrooms. In fact, the median number of instances of Positioning Individual Students as Competent was 48 per lesson!
7. Attending to Classroom Community
Successful teachers showed evidence of “developing and maintaining a supportive learning environment for students” by “telling personal stories to the students, joking with the students, or making remarks that suggest that he or she relates to the students and cares about them.” Teachers further addressed noncompliant students through discreet relationship-building actions that also contributed to a productive learning environment. It’s important to mention that attending to classroom community alone, however, was not enough to provide the necessary support to improve African American student achievement. This practice was as frequent in at least one other classroom in which students did not outperform the expectation.
The difference appears to be in the frequency and in the quality of the practices.
As mentioned earlier, all of the practices listed above occurred even in conceptually oriented classrooms where African American students did not make expected gains in mathematics. The difference appears to be in the frequency and in the quality of the practices.
The great news is that many teachers in conceptually oriented classrooms are already providing high-cognitive demand tasks needed to build student proficiency in mathematics and are likely incorporating these practices to some extent into their classrooms. The question is, how can we help teachers improve and incorporate these practices more frequently?
In a future post, I’ll provide some of my own ideas for school administrators, looking to improve minority student achievement, to support teachers of mathematics to increase the frequency of these effective practices.