A team of us received funding through a TLLP grant previously to do a book study on Douglas Clements’ math learning trajectories. We learned more than we could have imagined about how to help move kids through the stages in their math learning, and it was an amazing experience. We ended up creating a website which brought the first four trajectories (chapters) to life by adding actual videos of students in action at EACH stage, in EACH of the four trajectories. We also created links within the website to games and activities teachers could use at each stage to help move students. We had the opportunity to share this website with many teachers and have received some wonderful feedback on how helpful it was for teachers to help their students move through the stages on the trajectories due to the fact that they could “see” what their students needed in order to move to the next stage. Although we spent a lot of time learning about how to help our students move through the trajectories and developing this site, we are not finished! We still have eight chapters/trajectories left, and we want the opportunity to not only finish the website, but to branch out so that we can have more teachers involved in developing and, in turn, owning this website.
Team Members
Cheryl Teolis
Rainbow District School Board
Daria Dziuba
Rainbow District School Board
Karen Peck
Rainbow District School Board
Quinn Buck
Rainbow District School Board
Debbie Buott
Rainbow District School Board
Professional Learning Goals
- Understood learning trajectories in math and how to use this information to determine students’ current learning and next steps
- Continued to develop interview questions to determine student learning
- Added videos to current website in order to have a more thorough, online, easy-to-use resource to help teachers help their students
- Created a list of appropriate games and activities students could play at each stage in order to move them along in the trajectory
- Had more teachers involved in development of the website in order to create more spread and ownership of Douglas Clements’ learning trajectories in math
- Shared the website with as many educators as possible
- Continued to learn from feedback given about the website in order to create a more effective resource
- Found connections amongst and between Douglas Clements’ trajectories and others (e.g., Alex Lawson)
Activities and Resources
- Readings of excerpts from Douglas Clements’ resource, Learning and Teaching Early Math
- Collaboration of the teams’ understanding of each stage description in the spatial thinking trajectory
- Brainstorming of potential activities, games or topics of discussion that students could engage in to move children’s conceptual understanding to the gradual next step
- Executing these potential activities into the classroom
- Team meets again to debrief on observations of movement in students’ conceptual understanding
- Revisit the trajectory and gain further understanding of the next natural next step to which the students need to be introduced
Unexpected Challenges
- Interpreting Douglas Clements’ trajectory as some of the language is difficult to decipher his message
- Meetings were spaced monthly as funding was limited so therefore momentum was lost with the large amount of time between each session
Enhancing Student Learning and Development
This project builds, in teachers, content knowledge as well as further understanding of how children come to acquire concepts in mathematics. As teachers further develop these areas within their teaching practice, it is then that educators will have the greatest impact on student learning.
Sharing
My team headed a half-day professional development for our staff. We reviewed the spatial awareness trajectory and shared multiple activities and games with the staff that we felt would have the greatest impact with students to move them through the learning trajectory.
Project Evaluation
Once again, we have completed a portion of our website (spatial thinking). Our learning journey began back in 2013. We set out to bring light to all of Douglas Clements’ trajectories for early math. This project was a success because we were able to build professional content knowledge around spatial thinking, we were able to implement this progressive approach to moving students thinking, and we were able to capture this trajectory on our website under the tab “Spatial Thinking.” We still have lots to accomplish, but having this grant has aided us in completing another portion of the big picture in how students come to acquire math concepts.
Resources Used
Please visit our website Learning Trajectories: Spatial Thinking to access activities and games useful for moving students through Douglas Clements’ spatial awareness trajectory.