By Laurie Speranzo, Lilia Garcia, Carol Jones, Sara Trail, Dina Conzone & Denise Collier
The Institute for Learning works in collaboration with educators to use insights from educational research in their local contexts through the use of professional learning opportunities and materials. After all, it is educators who are doing the work in schools every day! Teachers try new pedagogical moves and get to witness the impact on student understanding and student agency in the classroom. Administrators support teachers and students by encouraging the implementation of research-based practices that lead to deep learning. Read about what teachers have tried recently and how administrators can foster environments of best practice.
CASE STORY 1: STUDENTS OWNING LEARNING OF THE MATH
My name is Lilia Garcia. I have been in education for the last 17 years. Prior to working with the IFL, I felt isolated with limited resources and support. Previous training that was provided was redundant and, at times, not grade-level appropriate.
Now, working with the IFL, I have expanded my network with teachers from other districts that have helped guide me into venturing off into the higher-level methods of thinking. The work has provided me with many resources and ideas that I have implemented in my classroom and found them to be very effective. For example, the use of different representations (Lesh, Post, and Behr, 1987). These provide opportunities for students to show mastery of the concept in different ways. I used to underestimate my students. Now, they produce pictures, graphs, and explanations that impress my peers and myself. They take ownership of their learning.
Another way that my students show ownership of their learning is the opportunity for them to create charts. In the past, I used to create them myself which increased my workload. Now I let the students do it. They are proud of their products. The posters became proof that learning is taking place in my classroom.
Viewing Lilia’s classroom with an equity lens:
By encouraging students to use multiple representations, all students are able to represent their thinking in the way that makes sense to them; they are viewed as mathematicians whose lived math experiences and ways of understanding are seen as assets. When students are asked to create classroom charts, their voice is honored and they are honored as knowers and doers of math.
CASE STORY 2: IMPLEMENTING HIGH-LEVEL TASKS
We know that in order for students to be able to leverage the representations that Lilia referenced, students need to be presented with high level tasks. In the City of York, teachers have been focused on the importance of the task the students receive and Dina Conzone shares the work of implementing high-level tasks.
I have been implementing more and more high-level tasks, like the IFL task Scuba Math. I have found that these are a great way to entice students, to elicit their thinking, and to honor and see what their ways of thinking are. It’s the design of the high-level tasks that provide real-world and mathematical problems that can be solved in many ways. With the increased use of high-level tasks, I have seen an increasing number of students showing their own work and making connections between each other’s solution methods. Students are seeking patterns and explaining the mathematical reasoning behind the different ways of thinking and solving. In the Scuba Math task, the students who used tables and graphs to solve the problem made connections to what justifies using the substitution method that other students used.
I have also seen that engaging students in high-level tasks and providing time for students to generate and discuss their solution paths has strengthened the community of problem solvers in my classes.
Viewing Dina’s classroom with an equity lens:
The QUASAR project, a pivotal research study in the movement towards conceptual mathematics instruction, lays out that a high level of student learning is only possible from a high-level task; low-level tasks (such as procedural worksheets) only yield a low level of learning. In Dina’s class, the same high-level task was given to EVERY student. Every student had the opportunity to share their solution path with equal validity (because each of them is a valid pathway to solving systems) and every student was afforded the opportunity to engage in productive mathematical discussions. Every student was an honored mathematician.
CASE STORY 3 and 4: FOSTERING PRODUCTIVE STRUGGLE
In Morgan County, TN, teachers have been studying ways to support students as they engage in productive struggle around a high-level math task. Sara Trail, a middle school math teacher, shares what happened in her class.
One of my most enjoyable teaching experiences this year in 8th grade math class was when I allowed the students to struggle as they completed a math task. This sounds really odd, a teacher enjoying watching her students struggle. I had so many doubts and honestly, I didn’t want to lose the instructional time. I also didn’t want the students to become frustrated and just give up. But I will admit, I was curious: would productive struggle work well in the classroom of 8th graders? I seated the students into groups of three and I provided the math task. The only group guidelines were that everyone must contribute and have an opportunity to participate. Here is when the fun began: after several minutes of the students sitting in shock and disbelief, they asked “Is Ms. Trail not going to help get us started with the task?” I have always read the task and reminded the students of their prior learning. This was very difficult for me to let go of the reins and it was difficult for the students to just start the task all on their own. However, after a few minutes of me walking around the classroom, I witnessed students collaboratively sharing ideas, solutions, and strategies as they were completing the math task on transformations. My role in supporting the productive struggle task was to go to the different groups and ask questions with limited assistance. Then, I stepped back and watched the students discuss with one another and allowed conceptual understanding to unfold right in front of my eyes. My students were engaged (even the ones that typically do not contribute), my students were participating, and my students were eager to share with their classmates. The students were still discussing the task and their accomplishments when exiting my classroom. My big takeaway from allowing productive struggle in math class is that the struggle allowed the students to build their confidence and deepen their understanding of math and how to approach problems.
Carol Jones, another middle school math teacher in the district, had similar experiences and realizations about her students.
As I have tried and continue to try supporting students in productive struggle within my classes, I am constantly amazed at the students who CAN actually come up with the answers! Students I knew usually did not engage, are now actually trying and surprising themselves with correct answers! They grin so big, and it makes them want to work harder! It makes my heart happy to see them finally excited about math!
Viewing Sara and Carol’s classroom with an equity lens:
…productive struggle comprises the work that students do to make sense of a situation and determine a course of action when a solution strategy is not stated, implied, or immediately obvious. From an equity perspective, this implies that each and every student must have the opportunity to struggle with challenging mathematics and to receive support that encourages their persistence without removing the challenge. (Boston & Dillon, et al., 2017)
In both classrooms, every student was provided the opportunity to grapple, collaborate, and succeed. But, in addition, the role of the teacher’s expectation that students can and will be mathematicians was crucial. They saw that by not doing the heavy lifting and by requiring students to take on the responsibility of productively struggling with the math, students who may have previously been reticent to engage, defied the passive role and shined!
THE CASE FOR ADMINISTRATIVE SUPPORT:
SUPPORTING RISK-TAKING IN TEACHING PRACTICE
As we have learned from a growing body of research from the Wallace Foundation, school leadership is second only to classroom instruction in affecting student learning, and may matter even more than previously thought (Grissom, et. al., 2021). In other words, what principals do really matters. One important role of school leaders is that of inviting and supporting a school climate that is conducive to learning, both at the student AND the teacher level. Denise Collier, a leadership fellow and former district administrator, shares.
The impact of principals on the learning culture was made clear to me in a recent conversation with a team of middle school math teachers. When asked what worried them the most about trying out a new instructional strategy—engaging students in collaborative group work around a challenging task—they jointly voiced a concern that their principals wouldn’t understand or support what they were doing, especially if the new strategy wasn’t immediately successful. The teachers raised questions like:
- Will my principal trust me enough to let me try something new if it takes some time to get good at it?
- What if my principal comes in for a walk-through or observation and the students are loud or it looks like they are off task?
So, if one of the risks to continued learning is fear of failure or criticism, one of the key roles of principals should be creating a climate of trust, support for learning, and innovation in their classrooms.
The experiences that these teachers shared validates that implementing research-based practices works! The teachers spoke to both the learning as well as the excitement and ownership of the math. Taking on new practice served the students, but also the teachers as they learned more about the students’ assets and honored them as doers of math! Thanks to the teachers who take risks to serve their students and the administrators who support them.
References:
- Boston, M. D., Dillon, F., Smith, M. S., & Miller, S. (2017). Taking action: Implementing effective mathematics teaching practices in grades 9-12, (p. 208). Reston, VA: National Council of Teachers of Mathematics.
- Grissom, Jason A., Anna J. Egalite, and Constance A. Lindsay. (2021). How principals affect students and schools: A systematic synthesis of two decades of research. [Research Report] New York: The Wallace Foundation. http://www.wallacefoundation.org/principalsynthesis.