Katie Braunschweig
EdPsy 391 HW #6
1. Work in groups to define and identify permutations and combinations.
2. Understand and explain formulas for permutations and combinations.
3. Distinguish between the two, why use one or the other, when.
4. Discover how to apply permutations and combinations to probability.
The following are questions that could be asked to test student’s knowledge on the above learning objectives. I do not think that all of these would be necessary as some repeat concepts found in others, it is simply different ways of asking these questions to gain different aspects of a student’s comprehension on the topic.
Test Item #1: Define permutation and combination and state the formula for each. Rationale: This item tests simply knowledge level skills that the students need to know for the remainder of the test. It links to learning objective number 1 directly.
Test Item #2: What is 2P5? What is 2C5? Compare these two answers and explain what you find. Rationale: This question goes one step beyond knowledge and tests knowledge and also synthesis because students have to know how to do it and also explain it. Students have to take what they have found and put it together. It applies to learning objectives 1 and 2.
Test Item #3: How many ways can the letters I L L I N I be arranges to make new “words”? (Recall “words” implies different orders, not real words). Explain why this answer is true and why you did what you did. Rationale: This question applies to learning objectives 2 and 3 because it makes you explain why you do what you do and not just do it. It tests for comprehension, analysis, and evaluation because students have to explain and verify their answers and strategies for solving.
Test Item #4: Which word can be arranged in the most number of ways,
A L G E B R A or C A L C U L U S? Rationale: This item applies simply to objectives 2 and 3. Students have to do just a bit more than understand the formula they must also know when to use it. It tests both knowledge and comprehension, however not much else because it simply asks the student to apply general knowledge to a simple question.
Test Item #5: Give an example of a situation when you would need to find a combination of items (other than one in this test!) and explain why and how you use it. Finish by finding the answer to your combination.
Test Item #6: Give an example of a time when you would use a permutation to solve a problem (other than one on this test). Explain why you would use it and solve it. Rationale: These 2 test items, #4 and 5, relate to both learning objectives 2 and 3 and if the student is good, they even provide an example that could relate to objective 4. These questions make the students do more than just supply knowledge. They need analysis, comprehension, application, and evaluation in these questions to receive full credit.
Test Item #7: Explain the difference between a permutation and combination. How are they alike and how are they similar? When is one used over the other and why? Explain their importance. Rationale: This relates directly to objective 3, by asking the student to explain exactly what the objective desires. This item requires evaluation, application, and synthesis because it asks the student to apply what they know and form general explanations as to what exactly is going on between the two concepts.
Test Item #8: Explain how both permutations and combinations are used in probability. Include examples of each and specifics as to why they are needed. Include when permutations are used and why and when combinations are used and why. Explain how this can be helpful in problem solving probabilities. Rationale: This question directly relates to objective #4, which is to apply to probability. It tests evaluation, synthesis, and analysis. Students are asked to explain why these concepts are used and synthesis and analyze what is being done, along with explaining why.