This year’s Mathematics Assessment Project Hopewell Triangles task on similarity and right triangles played out differently than previous years.

2013 – Right Triangle

2013 – Similarity

2014 – Misconceptions

In general, students didn’t have as many misconceptions as the prior year.

As students were working by themselves, I did see one misconception that I was sure to bring out in our whole class discussion.

(Look at ∆D above.)

On another trip around the room, I saw this on his handheld, which helped him correct his own mistake for ∆D.

I particularly enjoy seeing different ways that students explain why the triangles are similar (#3) and why or why not the triangle is a right triangle.

I sent a TNS document with questions to collect student responses for some of the questions. When I collected it after students worked individually, we had a 70% success rate. (I’ve changed the Student Name Format to Student ID to keep student names concealed.)

At that point, we changed to Team mode, and students talked with each other about their work and I told them that they could change answers in their TNS document as they discussed their work. Students are making it a practice to not mark an answer unless they have an explanation to go with the answer. When I collected their work the second time, I knew that our whole class discussion needed to start with the third question. (I also knew who needed to come in during zero block for extra support.)

Also of note is that the first collection of question 3 had these results:

But the final collected had these results:

Why is ∆1~∆A?

Why isn’t ∆1 similar to ∆F or ∆E?

We finished the discussion by discussing a misconception that students had last year. Anna thinks that ∆2 is a 30-60-90 triangle. Do you agree? Why or why not?

And so the journey continues, using formative assessment to make instructional adjustments to meet the needs of the students who are currently in my care …

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