Note: These thoughts are strictly my own and do not represent the vision, mission, values, and goals of St. Vrain Valley Schools. Several of the ideas below are contrary to the Colorado Academic Standards for Mathematics and our legal obligations as a local education provider in Colorado.
Thinking about educational and curriculum reform for a rapidly changing world, these are questions I often wrestle with and don’t have clear answers.
- What is the appropriate balance between using district adopted, commercially produced instructional materials vs. teachers curating and creating their own lessons collaboratively with colleagues that are aligned to standards? What should we encourage as a system to ensure access and equity and recognize the amazing talent and professionalism of teachers?
- At what point should we give simply give students calculators in upper elementary and middle school to ensure they can access grade level tasks and content and not get bogged down in potential computational fluency shortcomings?
- At what point do we “give up” on having students master computational fluency in elementary school (and long division in 6th grade) in order to focus on critical thinking, understanding, and problem solving (i.e. things that require human capacity and cannot be optimized with technology)?
- How do we cultivate curiosity within students around mathematics when most adults learned mathematics in a prescriptive, procedural way?
- Do teachers and students see mathematics as a place for creativity, beauty, and joy?
- What would happen if we thoughtfully and strategically eliminated a third to a half of the standards at each grade level (or high school course) to spend more time developing mathematical reasoning and problem solving with non-routine, large-scale problems and tasks? Would we get the same or better outcomes than we’re getting today based on how academic achievement is measured?
- How much symbolic manipulation is required for demonstrating “mastery” of algebraic concepts? When do we unlock the power of graphing utilities and other technology tools to explore relationships and solve relevant and interesting problems using algebraic concepts?
- Is there a compelling reason why all students must study polynomial, rational, logarithmic, and trigonometric functions in high school? Would we be better off focusing on linear, exponential, and quadratic functions for all students, and leaving these other families of functions to advanced mathematics courses based on student interests and postsecondary goals?
- What if we retooled the “traditional,” required high school course sequence of Algebra 1, Geometry, and Algebra 2 with the following sequence of one year courses: Algebra 1 (focusing solely on linear, exponential, and quadratic functions), Geometry, and Statistics & Probability? Would this better serve all students for a variety of contexts beyond high school?
- Why is practice-based homework a quintessential part of learning mathematics in school? How might changing the role of homework drive changes in instruction and uses of class time?
What are your thoughts? We always have to work within constraints beyond our control, but that doesn’t stop the design thinking process from creating a better outcome or tweaking part of the whole. What questions do you wrestle with? What would you add to this list?