Future Implications
Prior to my experience in the classroom this year, my vision, which was rooted in the independent research I gathered through reading works such as Jo Boaler's Mathematical Mindsets, was mainly theoretical. I was excited to have many opportunities to put aspects of my vision into action this year during student-teaching. The experience I had as a student-teacher also exposed me to the multitude of challenges, setbacks, and constraints that come with attempting to implement a reform to the traditional teaching model. Along my journey, I encountered challenges from teachers, prescribed curriculum, and students.
The NCTM stresses that procedural fluency should be built upon a strong foundation of conceptual understanding. While I tried to provide time in every lesson for deep conceptual understanding, I found that constraints from the scope and sequence timeline as well as pressure from higher personnel to get standardized test scores up through rote practice presented an obstacle. I also learned that spending an entire lesson on conceptual understanding without practice doesn't allow students opportunities to master fluency. Once students have a conceptual understanding time for practice of the skill is vital. Finding the balance in lessons and the curriculum between procedural fluency and conceptual understanding is something I look forward to exploring deeper in my career as a math educator. Hand-in-hand with this balance, is the balance between learning goals and performance goals. As I mentioned in my Learning Goals Artifact Analysis, performance goals can be more measurable than learning goals sometimes. This is another balance I am excited to experiment with as an educator.
For students who have had prior math experiences where they were spoon-fed information or taught math within a GRR model, my vision can present a steep learning curve. In these types of prior experiences, students might not have had opportunities to discuss their mathematical ideas with classmates or might not have been pushed to clearly explain their thinking. Some students might have been used to being praised for the high speeds at which they could do arithmetic. Their teachers might've tried to "make the math easy" by over-explaining and giving students the formula to set up to solve a problem, therefore taking the cognitive load off of the students, and depriving them of opportunities for productive struggle. As explained earlier in the site, I am curious how to re-engage a learner in a high-level task after they have disengaged out of frustration of the cognitive challenge. I learned that getting students used to a You-do We-do I/Me-do model takes time. Things will not flow perfectly smoothly the first time implementing this model with students who are new to it. For example, I encountered resistance from students the first times I asked them to work collaboratively with a partner. There were students who just gave up when they weren't first provided a formula to plug numbers into. The model takes time for students to get used to.
This project and research has pushed me to explore additional questions such as:
The NCTM stresses that procedural fluency should be built upon a strong foundation of conceptual understanding. While I tried to provide time in every lesson for deep conceptual understanding, I found that constraints from the scope and sequence timeline as well as pressure from higher personnel to get standardized test scores up through rote practice presented an obstacle. I also learned that spending an entire lesson on conceptual understanding without practice doesn't allow students opportunities to master fluency. Once students have a conceptual understanding time for practice of the skill is vital. Finding the balance in lessons and the curriculum between procedural fluency and conceptual understanding is something I look forward to exploring deeper in my career as a math educator. Hand-in-hand with this balance, is the balance between learning goals and performance goals. As I mentioned in my Learning Goals Artifact Analysis, performance goals can be more measurable than learning goals sometimes. This is another balance I am excited to experiment with as an educator.
For students who have had prior math experiences where they were spoon-fed information or taught math within a GRR model, my vision can present a steep learning curve. In these types of prior experiences, students might not have had opportunities to discuss their mathematical ideas with classmates or might not have been pushed to clearly explain their thinking. Some students might have been used to being praised for the high speeds at which they could do arithmetic. Their teachers might've tried to "make the math easy" by over-explaining and giving students the formula to set up to solve a problem, therefore taking the cognitive load off of the students, and depriving them of opportunities for productive struggle. As explained earlier in the site, I am curious how to re-engage a learner in a high-level task after they have disengaged out of frustration of the cognitive challenge. I learned that getting students used to a You-do We-do I/Me-do model takes time. Things will not flow perfectly smoothly the first time implementing this model with students who are new to it. For example, I encountered resistance from students the first times I asked them to work collaboratively with a partner. There were students who just gave up when they weren't first provided a formula to plug numbers into. The model takes time for students to get used to.
This project and research has pushed me to explore additional questions such as:
- How can I create more meaningful math experiences for my black and brown students?
- How do Projects/assessments factor into or extend this You-do We-do I/We-do framework?
- How can I fully support my students who have IEPs and provide appropriate accommodations while also not lowering the cognitive demand of math tasks?
- How can number sense routines be implemented into high school math classrooms?