As I have visited with staff in workshops sponsored by the Virginia School Consortium for Learning, it’s quite apparent that our workshop leaders understand that participants must be actively engaged and focused on how they will use practices to make sure that transfer occurs. This is the essence of professional development that gives good bang for the buck!
In a recent workshop, professors Jennifer Suh and Padhu Seshaiyer of George Mason University worked with educators to focus on mathematical modeling as an “unique opportunity to engage … students in this creative process of mathematizing their world.” Despite varying background knowledge in mathematics, participants worked together to explore why math modeling is critically important in the curriculum. Math modeling engages learners in analysis, critical thinking, logical reasoning, problem-solving, and sorting and selecting relevant data.
However, as educators know, curriculum is a frame that only becomes accessible when a teacher selects instructional strategies that will help young people, whether 5 or 18, to make sense of what adults believe they should learn. Dr. Suh and Dr. Seshaiyer spent the day engaging staff in a series of math modeling activities that were anchored in creativity, critical thinking, collaboration, and communication as teams worked together to make sense of math in the context of relevant and rigorous work that backward mapped from a question to the math needed to find solutions to a multitude of potential problems and challenges generated by the team.
For example, the workshop participants were asked to consider that every trip we make is grounded in math modeling processes- getting to work in the morning is one such example. What do we think traffic will be like? Do we need to stop for coffee? gas up the car? drop off a child at school? How much money will we need to spend on the way? Will we take the same route or a different one from yesterday? What impact might traffic have depending upon when we leave? To contextualize a similar example for elementary school children, they took the group though a similar approach to simulate what children might generate to math model a trip to the pumpkin patch.
When we wonder why learners seem to develop little capability over time to translate and transfer deep conceptual understanding, number sense competencies, and problem-solving capabilities forward in more advanced and complex mathematics, it likely has to do with the limiting factors of how we choose math standards and assess math procedures both of which drive how mathematics are taught. What participants learned from the workshop leaders is that to teach mathematics well, we must work together to study how children learn math, what strategies deepen understanding in powerful ways, and how to engage learners in increasingly complex and interesting challenges to their mathematical thinking and reasoning. Children like challenges in their work but they also need to make sense of math in the context of the world around them. That’s the workshop focus provided by Dr. Suh and Dr. Seshaiyer.
To increase your own understanding of mathematical modeling you can read more in their research article linked here:
” mathematical modeling.. as an iterative problem solving process that includes posing authentic, open-ended problems, making assumptions, identifying constraints and variables, building mathematical solutions and, finally, analyzing and interpreting these solutions. It is iterative because once the initial solution is tested and translated back to the real world, revisions usually need to be made and the process continued until a satisfactory solution is reached and can be justified. This iterative process not only helps to validate the model but also helps to optimize the method and the process in the context of the real-world problem.” ( “Engaging Elementary Students in the Creative Process of Mathematizing Their World through Mathematical Modeling”, Suh, Matson, Seshaiyer, p. 2, Education Sciences 2017, 7(2), 62; doi:10.3390/educsci7020062 )
What’s Happening Next for Consortium members?
Inquiry Learning! The DBQ Project Part I and II will address both strategies to engage learners in the Document Based Questioning process and how to use performance assessments with DBQ responses.
The Trauma Sensitive Classroom! Cultivating mindfulness and compassion is critical to managing stressful demands so that educators can cultivate an exceptional learning environment and ultimately revitalize the learning opportunities of all students. Participants will gain valuable knowledge, develop new skills, and have time to collaborate effectively with other attendees.
Plans are in the works for several additional professional development opportunities after the winter holidays. Information will be posted on the website as soon as plans are complete.