Rationale: Good! You have identified natural patterns related to trig functions, and some important pedagogical approaches you plan to use. Trig identities are a bit different from trig functions, as you’ve noted, but it looks like you will be bringing the two topics together in interesting ways.
Project: Excellent! These topics are interesting, and there are others that you and the students can find as well. It’s great to have students connect knowledge about mathematics with knowledge of how to do mathematics. This looks like a well-thought-out project plan.
Assessment plan: Very good — well planned and balanced. I’m glad to see ‘respectfully critiquing arguments made by others’ as an important criterion for mathematical thinking and learning.
Unit elements: Good!
Lesson plans: #1: The Geogebra applet and TED-ED film are very good choices — brief and to the point, with lots of clear visual representations. Good to include student research on Pythagoras as part of an active learning plan. Will everyone be focused and find interesting facts? Is there a way to give students a more focused task for their research, to keep them on track?
Will students understand that there are other Pythagorean identities possible — i.e., the basic Pythagorean identity in other forms?
An interesting lesson!
#2: Good to engage students in finding that this common misconception is untrue, and why. I find these two Geogebra explanations a lot less transparent than the last one…Are there any other resources that might help students understand these identities? You are depending on the Geogebra as a source for a large part of this lesson, so do make sure that it is accessible and understandable for students!
#3: Very interesting — I hadn’t heard the term ‘Guilloche patterns’ before, though I knew of a number of drawing linkages that produce these patterns. I also didn’t (and still don’t) really understand how one can generate these patterns using trig identities. You haven’t explained this in detail in your lesson plan, and I hope that you do understand it well; do you think that students will be able to work with this in the course of one lesson to be able to create these intriguing patterns? I’d love to learn more about this relationship!
Overall: Very well planned unit with lots of intriguing mathematical knowledge and patterning, great use of dynamic geometry, animation and film, and very good planning for student engagement. I would only suggest that you have ‘plan B’ ready in case students need help deriving and manipulating trig identities all on their own. Excellent work!
Thanks for this thoughtful unit outline, Murugan.
ReplyDeleteRationale: Good! You have identified natural patterns related to trig functions, and some important pedagogical approaches you plan to use. Trig identities are a bit different from trig functions, as you’ve noted, but it looks like you will be bringing the two topics together in interesting ways.
Project: Excellent! These topics are interesting, and there are others that you and the students can find as well. It’s great to have students connect knowledge about mathematics with knowledge of how to do mathematics. This looks like a well-thought-out project plan.
Assessment plan: Very good — well planned and balanced. I’m glad to see ‘respectfully critiquing arguments made by others’ as an important criterion for mathematical thinking and learning.
Unit elements: Good!
Lesson plans: #1: The Geogebra applet and TED-ED film are very good choices — brief and to the point, with lots of clear visual representations. Good to include student research on Pythagoras as part of an active learning plan. Will everyone be focused and find interesting facts? Is there a way to give students a more focused task for their research, to keep them on track?
Will students understand that there are other Pythagorean identities possible — i.e., the basic Pythagorean identity in other forms?
An interesting lesson!
#2: Good to engage students in finding that this common misconception is untrue, and why. I find these two Geogebra explanations a lot less transparent than the last one…Are there any other resources that might help students understand these identities? You are depending on the Geogebra as a source for a large part of this lesson, so do make sure that it is accessible and understandable for students!
#3: Very interesting — I hadn’t heard the term ‘Guilloche patterns’ before, though I knew of a number of drawing linkages that produce these patterns. I also didn’t (and still don’t) really understand how one can generate these patterns using trig identities. You haven’t explained this in detail in your lesson plan, and I hope that you do understand it well; do you think that students will be able to work with this in the course of one lesson to be able to create these intriguing patterns? I’d love to learn more about this relationship!
Overall: Very well planned unit with lots of intriguing mathematical knowledge and patterning, great use of dynamic geometry, animation and film, and very good planning for student engagement. I would only suggest that you have ‘plan B’ ready in case students need help deriving and manipulating trig identities all on their own. Excellent work!