Haha! Get it? Straighten out the vectors? It's been a long week.

As usual, it's only when it's too late for this year's students that I have clarity on what to do, but in my defense, seeing so many possible wrong ways to do it today was what guided me to writing this hinge question.

To generate the wrong answers, I used today's mistakes. The 3 big ones I saw today: not taking absolute value of components, wrong order of ratio, wrong quadrant formula. I saw one person using the y-axis as a reference instead of the x-axis, so I'll put that in just a few answers.

If they get 294 degrees, they're right.

If they get 426 degrees, they did 360 - arctan (-20/9), ie didn't take abs value of 9

If they get 335 degrees, they did 360 - arctan (9/20), ie wrong order of ratio, OR they did 270 + arctan (20/9)

If they get 66 degrees, they did arctan (20/9), ie wrong quadrant

If they get 384 degrees, they did 360 - arctan (9/(-20)), ie didn't take abs value of 9 AND wrong order

If they get -65 degrees, they did arctan (-20/9), ie didn't take abs value of 9 AND wrong quadrant

If they get 24 degrees they did arctan (9/20) wrong order and wrong quadrant

If they get -24 degrees, they did arctan (9/(-20)), ie wrong ord, wrong quad, no abs val

If they get 204 degrees, they did 270 + arctan(-20/9) ie used y-axis as reference AND no abs val.

Love the idea about looking at what student thinking caused each outcome . Thanks for sharing your thinking. Can you tell me more or send me some place I could go to learn about what a "hinge" question is? Thanks!

ReplyDeleteSure, Amy, it's from Dylan Wiliam's book Embedded Formative Assessment. It's called "hinge" because its outcome determines the direction of the lesson. Ideally, it's a multiple choice question in which each wrong answer is interpretable by the teacher, students can respond in 2 minutes or less, & the teacher can see all responses in 30 secs or less. Thanks so much for reading my post and commenting, it means a lot to me!

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