ASU Partnership with Schools Focuses Teachers on Big Ideas in Math and Science
The graph shows state assessments in math and science of students at National Science Foundation-funded math and science partnership schools. National Science Foundation
Since receiving NSF funding and launching Project Pathways in 2003, Dr. Carlson and her research team of a dozen faculty and nearly 20 graduate students, along with professional development staff specialists, have worked with dozens of high school teachers in the five Phoenix-area school districts.
Grouped in cohorts, the teachers are taking a sequence of four integrated math and science courses developed by Carlson’s team. In creating the courses, the team has drawn on years of their own research and that of others into how mathematics and science can be most effectively taught and learned.
As they take each course, the teachers simultaneously work together in professional learning communities (PLCs) supported by the ASU faculty. These PLCs draw on research into the lesson study practiced in Japan, in which teachers design lessons together, take turns practice-teaching and videotaping them, and then regroup to study the videos and refine the lessons based on how well they work in the classroom.
The model for PLCs used in Pathways also draws on a "records of practice" model developed by researchers Deborah Lowenberg-Ball and Hyman Bass at the University of Michigan. In a records-of-practice PLC, communities of teachers study student work and videos of classroom activity.
Four cohorts of Arizona teachers are now participating in the project.
Changing How U.S. Schools Teach Math and Science
"At its root, our project is leveraging a tightly integrated model of coursework linked to PLCs and one-on-one coaching to move teachers to a new way of understanding what ‘good teaching’ in math and science looks like,” said Dr. Carlson recently.
"We have a dysfunctional teaching culture in the U.S. compared to more high-performing countries,” she said. “Teachers are given the mistaken idea—and much research shows it’s mistaken—that ‘good teaching’ means just showing students how to easily get answers to a limited variety of problems. And their own university education and teacher-training often has not given teachers themselves a deep enough understanding of the key ideas they must teach in secondary math and science.”
In contrast, the Pathways project aims to help teachers shift to ways of teaching that catalyze a deep understanding of ideas in their students, along with the critical thinking ability needed to solve new problems the students have not encountered before.
“This is the kind of thinking you need to succeed in industry or advanced education,” said Dr. Carlson, “and our research is revealing important information about what interventions work well in moving teachers toward valuing and being able to deliver this kind of ‘meaning-rich’ instruction.”
It Takes Time, Persistence and Research
Dr. Carlson’s team is finding that “there absolutely are no quick fixes for promoting more meaningful instruction. It takes rigorous, sustained interventions, and the discipline to refine your interventions again and again based on what the research tells you is and is not working.”
“Essentially,” she said, “our research team works from an engineering design model. We design an intervention based on what prior research suggests will produce the desired changes in instruction and learning. We deploy the intervention and carefully research its impact. We refine it in response to what we learn and try it again. Eventually, you have enough confidence in an intervention that you can recommend scaling it up to serve diverse populations in many different school settings.”
Pathways researchers study the impact of their interventions by videotaping every class meeting of the courses and each PLC session. A team of two researchers is assigned to observe the members of each PLC in their course and PLC sessions. These teams code each videotape. Every week, the entire PLC research group meets to view and discuss selected videos.
Out of these discussions comes a variety of useful material---the team will reach consensus as to what various degrees of a desired behavior looks like, for example, which allows for consistent coding of the behaviors among all the coding teams.The term has become a mantra for Pathways researchers and teachers. In PLCs, teachers remind one another to “speak with meaning.” School leaders report cases of teachers writing “speak with meaning” on their chalkboards as an exhortation to their students to think about the meaning of the mathematics they are learning.
Recent Findings
In a recent report to the National Science Foundation, Carlson’s Pathways team reported the key findings that are emerging from the first three years of their research:
Courses that engage teachers in activities in which they wrestle with grasping and communicating the fundamental ideas of high school mathematics and science are a critical piece of the intervention.
“It’s not enough to help teachers practice pedagogical methods like open-ended questioning,” said Carlson.“Teachers also need time and support to really dig into the math and science content. Our courses help them develop a deep understanding of the concepts they are expected to teach, and to see the connections among the concepts, as well. “
For example, the four Pathways courses are tied together by the mathematical idea of covariation, based on the research of CRESMET Research Director Pat Thompson and Les Steffe (University of Georgia). As the teachers deepen their understanding of covariation and related ideas such as rate of change and function, they are able to use these ideas to model scientific phenomena, and thus to begin to see how they can help their students to make a similar jump from grasping a concept to applying it.
Professional learning communities are most productive when teachers are engaged in some shared intellectual activity, such as taking a graduate course together or teaching the same or related courses. This promotes rigorous discussions about ideas and teaching practice in the PLC meetings, rather than chatting about day-to-day school business.
The Pathways PLCs center on the content being studied in the Pathways courses. Project faculty design a general agenda for each PLC session. The agendas are designed to improve the teachers' ability to have substantive discussions about the ideas of the courses, student thinking and their own instruction. The agendas also provide time for the teachers to practice developing lesson plans that encourage student inquiry and focus on concepts more than procedures and drills.
Training teachers to interview their students to probe how the students are thinking about specific concepts (such as rate of change) has proved to be a profoundly important intervention. It prompts teachers to examine how their teaching promotes or unwittingly hinders student understanding. And getting a precise picture of what the students do not understand can help teachers to design more effective lessons.
Math and science teachers who acquire knowledge about mathematical and scientific concepts in well-designed coursework (as opposed to drill sessions for memorizing formulas and procedures) are better equipped to reflect and speak meaningfully about their own teaching and learning.
PLCs work best when led by one teacher who has been trained as a PLC facilitator. With direct coaching, ineffective facilitators can improve. In Pathways PLCs, research faculty select a teacher to serve as facilitator in each group. The research team developed an 18-hour training workshop that facilitators take in the summer. Faculty also meet with each facilitator weekly to plan for each upcoming session. Between sessions, faculty and professional development staff review videotapes and coach the facilitators on ways to improve the interactions in their PLCs.
Coaching the facilitators in two particular practices seems to be critical:
1. “Speaking with meaning” is a term coined by Dr. Carlson to describe a way of talking about mathematics and science that goes beyond reciting formulas and procedures.
The term “speak with meaning” implicitly reminds teachers and students that mathematics models physical realities. Reciting equations is not meaningful unless students grasp the physical reality that the equations model.
When we “speak with meaning” we “decode” a mathematical formula and look at the physical quantities, relationships and changes that the mathematics models.
Only when teachers (or students) have clearly communicated that physical reality do the researchers have them go on to speak in the mathematical symbols that model the reality.
In this way, the researchers constantly make clear what the numbers, variables, equations and graphs of mathematics “mean” as symbolic representations of something physical.
Teachers and students come to understand that mathematics encompasses a continuum of meaning that begins in the real world of objects, motion and change and culminates in algebraic formulas such as y = 5000 2x + 382
The researchers also use the term “speak with meaning” to prompt teachers to provide a logical rationale for why they choose a particular solution approach to a problem.
2. Decentering, a term borrowed from Piaget, is used in Pathways to describe the mental action of trying to discern and understand someone else’s perspective, with the ultimate aim of influencing it.
Decentering is at the heart of what researchers mean when they speak of “student-centered instruction” or teaching that focuses on student thinking. To influence a student’s thinking, teachers must first have the ability to create a mental model of how the student is understanding a situation or problem—a cognitive version of standing in someone else’s shoes.
The facilitator of an effective PLC must cultivate a similar ability to decenter and discern how PLC members are understanding topics under discussion.
As Project Pathways enters Year 4, the research team will continue to research the impact of its interventions on teachers. But they are also moving into the teachers’ classrooms, preparing for comparison studies between students of Pathways teachers and control groups of students whose teachers are not participating in the project.
"We can see teachers changing in Pathways,” said Dr. Carlson, “and as we investigate their students over the next year it will be even more encouraging if their students show improvements that exceed what NSF is recording at the national level.”