You've just explored a problem with triangular and square numbers and a conjecture that relates them. Now we'd like to write about your own classroom practice with relation to this activity. Please reflect on the following questions and choose one or two to answer in your journal.
Questions to write and reflect about:
Three ways to write and reflect:
- Some otherwise successful mathematics students can be both intimidated and potentially stymied by working with formal proof. Does you personal experience working with proof in mathematics offer any insights into how you can help these students?
- Mathematics involves working to foster factual knowledge, procedural ability, and conceptual understanding. Do you believe it's possible and desirable to integrate elements of reasoning and proof into all these areas? Why or why not? Are some a more natural fit than others?
- As students progress through the high school curriculum, mathematical terminology and definitions typically become more precise and abstract. How can you guide students in a way that encourages them to think flexibly and fluently about mathematics, while simultaneously fostering the ability to understand and present formal mathematical proof of a rigorous standard.
- When explaining reasoning or developing a proof for students, teachers often hear a student say, "I don't understand where that came from" or "how did you get that?" Have you had that experience firsthand in this activity or in your mathematics learning or teaching in general? How did you respond to it? How can you help students respond to it? What role do such questions play in mathematics learning?
Be sure to save what you have written before you navigate out of the journal section.
- Use pen and paper.
- Use a word processor.
- Use the form below.
Thank you for writing in your journal. Please keep your entries in whatever format you choose -- you will find them useful for reference later.
Learn how the Standards define connections