ELN 122 37714 Lesson 1
Martha Knox
Describe the difference between learning outcomes and performance objectives. Include the different categories of learning outcomes and types of performance objectives. What are their roles in assessment?
The categories of Learning Outcomes are: declarative knowledge, procedural knowledge, and problem solving. Declarative knowledge is knowing, recalling and verbalizing specific facts. Procedural knowledge is knowing how to identify, demonstrate and classify the knowledge. Problem solving is knowing how to strategically apply known procedures to solve unknowns in a problem.
Performance objectives asks what observable events can the student demonstrate by using specific behaviors to prove they have learned the indicated knowledge. What specifically can the teacher see the student after they have been taught the concept. They include: capability, behavior, situation, and special conditions.
Problem solving is my favorite method of assessing knowledge. I always tell my math students there are no answer books in real life. The answer you give is the answer, whether the bridge falls down, someone gets too much medicine, or you have to pay for the wrong change out of your own pocket as a cashier. The answer you find is the answer. The most important thing is can you analyze your answer in terms of what you know to prove to yourself that your answer is correct?
One of the most common math problems from ancient times to modern day cray computers is to find prime numbers in a random list of numbers.
It relies on declarative knowledge: multiplication tables, procedural knowledge identifying classes of numbers, and problem solving: generating a solution from the knowledge they have about the characteristics and relationships of numbers. (Solving this classical problem has resulted in many new theories about how numbers are related.)
Let's try a list of numbers , not in any particular order: 56, 34, 73, 29, 81, 22, 55, 69, 2, 15, 1010, and a big one 70600809789664532.
Declarative Knowledge: First we or an explorer of math has to know multiples. We have to know for example multiples of numbers from at least 1 through 10, (although 11, 12, and 13 would be great).
Procedural Knowledge: Then we have to classify the list of numbers, maybe using the knowledge of prime numbers. 2 is the only even prime number. So if a number is more than a googleplex , it still is not prime, if it is even. This means any number no matter how many infinite digits is not prime if it is even; so we have eliminated half of all the possible integers.
Then we need to classify numbers as odd or even, since even numbers are multiples of 2 thus 56, 34, 22, 1010 could be eliminated, also the biggest one.
So the numbers 73,81,55,69, 15 are left. Let's work on the odd numbers. We reason that 5 would be a great number to try. Maybe the other fairly easy numbers could be tried for example: If a number ends in 5 then it is not prime. So now we're left with 73,81,and 69. So we reason that 81 is a multiple of 9x9, and 69 is a multiple of 3x23, thus neither are prime.
Problem Solving: so we are left with 73. Now comes the problem solving part. We need to prove 73 is prime. We reason that 73 could be a multiple of any prime number between 2 and 37 since anything equal to or above 37 as a factor would result in a fraction.
73 is not even, dividing by 3 is a fraction, it doesn't end in 5, it's not a double digit 77 so that means 11 is out of the running, 13 is out because 13 numbers in a deck of cards and 52 cards in a deck plus 26 is 78, 37 is out because 37 x 2 is 74 which is more than 73, the upper limit, so we only have to guess and check: 17, 19,23,29,and 31; of which none are multiples.
The prime numbers between 2 and 36 are 2,3,5,7,11,13,17,19,23,29,31 and 37 none of these are factors of 73 so 73 is prime. Fun. Like a puzzle.
So how can we assess learners? Information, concept, and rule
First, find out what information they already know.
Second, ask learners to classify different examples of the same concept.
Third, give learners a brand new example so they can apply the rule to a brand new example.
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