Report 6: Evaluate & Revise
To review, the following objectives were developed for this instructional unit:
- Given a word problem, students will be able to draw an appropriately labeled diagram of the problem with 90% accuracy.
- Given a word problem or diagram, students will be able to identify whether it is necessary to use the Law of Sines or the Law of Cosines to solve the problem with 95% accuracy.
- Given a word problem or diagram, students will be able to apply the Law of Sines or Law of Cosines to correctly solve for the missing side/angle with 95% accuracy.
- Given 15 minutes and access to their notebooks, students will be able to solve three word problems using the Law of Sines or Law of Cosines with 90% accuracy.
Assessment of Learner Achievement
The objectives represent cognitive skills and thus lend themselves well to traditional test items. I created the following quiz:
- Without actually solving the triangle, determine if you should use the Law of Sines or the Law of Cosines to solve for the indicated variable:
2. Manny and Gracie are standing 10 miles apart on the seashore. The both look out and see a ship. The angle between the shore and the boat from Manny’s spot is 35o. The angle between the shore and the boat from Gracie’s spot is 45o. How far is the ship from Manny? Draw and label an accurate diagram as part of your answer!
3. Caris, Gabe, and Josiah take their cars to the local car show and park. If the distance between Caris and Gabe is 153 ft, the distance between Caris and Josiah is 201 ft, and the distance between Gabe and Josiah is 175 ft, what is the angle between Caris, Gabe, and Josiah? Draw and label an accurate diagram as part of your answer!
4. A triangular playground has side lengths of 475 ft, 595ft, and 401ft. What are the measures of all the angles between the sides, to the nearest tenth of a degree?
Evaluation of Methods and Media
The assessment showed that the instructional materials were generally effective. Students were effective at drawing and labeling diagrams and successfully using the Law of Sines and/or Law of Cosines to solve problems. An area of weakness was revealed to be students being able to recognize which formula to use initially (ie, identifying if it is a Law of Sines or Law of Cosines problem). I believe this can be improved by making some changes to the stations (which focused more heavily on the procedural skills in solving the problems). From an instructor’s perspective, I believe the use of station rotations (with the in-class flip) was an effective strategy for teaching the Law of Sines and Cosines to this group of Algebra 3 students.
After the quiz, I asked the students to complete a short reflection about the unit. I asked what they thought about the strategies used, and students were generally positive in liking the station rotation. Students indicated they especially appreciated Station 3 everyday (the small groups) as a way to get more one-on-one attention. They were also positive about Stations 1 and 2 (video notes and DeltaMath). Many indicated less enthusiasm for Station 4 (one student wrote “I don’t think Station 4 hurt me, but I don’t think it helped me either.”). I think there is still revision needed with Station 4.
Revision
As the main struggle on the assessment appeared to be recognizing which formula to use, I will revise the instruction for next time by including this skill more explicitly. In this case, I think it will work best to revise Station 4 on Day 2, and instead create an activity (such as a matching activity/card sort) where students will have to determine which of the two formulas to use to solve a given triangle. I can also address this in the small groups (Station 3) on Day 2. I believe these two changes to the station rotation will result in more success on the quiz next time.
Instructional Insights 