In the fall of 2014, I had an amazing professional opportunity to join a venture called the Cross-State Mathematics Teacher Leader Project. There were teachers from Iowa, North Dakota, South Dakota, and Montana who formed a collaborative group. Our mission was to assist teachers in rural states with professional development to improve mathematics instruction. We were interested in creating professional development modules to best support teachers in implementing the Common Core Standards for mathematics. I had an awesome opportunity to work with educators from various size schools as we collaboratively studied the book Principles to Actions: Ensuring Mathematics Success for All to guide our work.
Before reading and discussing Principles to Actions, I would usually want my students to enter a problem the same way and to use one pathway to the solution. This was convenient for me as an instructor because there was a set script for solving problems. I realized that I was doing what was best for me, not what was best for my students.
Learning through Principles to Actions made me realize that my students needed to have multiple entry points to the problem and be able to develop their pathway to the solution. Now, students are presented with the problem and allowed to determine where they want to enter the problem and what pathway they will take to get to the solution. Students share their solutions with each other and justify why they chose their pathway.
My students are frequently heard saying “Here is how I solved the problem.” Instead of following my old method to solve the problem, students are devising their own path, which has led to a better understanding of math concepts.
Reading and learning about the mathematics teaching practices outlined in Principles to Actions caused me to ask questions. Was I doing each of these practices on a daily basis? If so, which ones did I do well and which ones do I need to do better? How do I know if I am doing things better? Getting the answers to these questions required me to learn more about these practices. My own questioning caused me to choose to focus on posing purposeful questions. I wanted to effectively use purposeful questions to formatively assess the reasoning of my students and allow them to make their own sense about really important mathematical ideas and relationships.
As I was learning about posing purposeful questions, I reflected on my practice and asked if I was using questions that would allow me to determine what my students know so I could differentiate instruction to meet everyone’s needs. Was I helping my students to make mathematical connections? Was I supporting students to pose questions of their own? Was I using the different question types at the appropriate times for my students?
I realized for time and efficiency, I was asking questions that were lower order and required answers that were more about gathering information. Students gave answers and I informed them if their answer was correct or not. By changing my practices and asking probing, thinking questions, I required my students to defend their answers and explain how they arrived at a solution.
Now when a student gives an incorrect answer, the student, in explaining his thought process, will usually discover his error and correct it. Students also discuss among themselves their misunderstandings. Instead of being the giver of information, I have become the facilitator of learning. Students are also making mathematics visible through their discussions of problem solutions.
Through learning about Posing Purposeful Questions and applying this practice, I have found that my students are able to understand mathematical standards and standards for mathematical practice at a higher level of rigor. This ties different areas of mathematics together and allows a focus on the skill our students need for the real world – problem solving, communicating their ideas and solutions, and modeling with mathematics.
Additional Resources for Principles to Actions and the Eight Effective Teaching Practices for Mathematics can be found on the Iowa Core Website for Mathematics. See links below:
- Instructional Practices
- Reflection Guides
- Learning Modules
- Strategies to Implement Principles to Actions
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