Describe the various types of constructed response assessments. What are the advantages and disadvantages of using these types of assessments? Include pros and cons of making the exam as well as grading and feedback.
One type of constructed response assessment is completion or fill in the blank. The questions are easy to write. They are not multiple choice, only one answer is needed. Next a teacher can include many questions in a test. However the level of knowledge tested is usually on the lower end of Bloom's Taxonomy, such as remembering facts and definitions. Although in mathematics precise definitions of terms is necessary. There is a big difference between the term minus and the term negative. These terms although sometimes represented by a similar symbol are not interchangeable. I liked the example given in the text about sometimes there is more than one answer to a question.
"Who discovered America?" is really too broad a question. Whole archeological dissertations have been written in trying to answer that question. It depends on when, who, where, and other qualifying statements. Also maybe the answer changes depending if you are Norwegian, Italian, Spanish or Native American. One of my student's answer to an essay question about the Pilgrims wrote "They should have stayed home." This from a Native American viewpoint. When I visited Ireland I went to Galway. There is a place there called the Spanish gate. Christopher Columbus came there to Ireland to do research and gather maps before sailing West across the Atlantic. He knew other people had been there before him. He had great PR in my view.
Another question I think is rather humorous is , "There are ______ planets in the solar system."
That's not exactly a one line answer. Depends on when you are asking that question. When I was young it was nine. This is an especially touchy question if you are from Arizona, that question is not exactly popular. Pluto named after Percival Lowell, and discovered by an Arizona astronomer, working in Flagstaff Arizona, is my states' favorite planet. But now it's merely been downgraded to a planetoid. Sigh.
I would not score a fill in the blank with a computer. I think a teacher needs to use judgment when grading an answer.
Essay question are another form of constructed response questions. Especially in mathematics essay questions allow the learner to explain the logic behind their answers. Sometimes essay questions in mathematics involve writing. Written reports are a very common way to express mathematical conclusions. My students used to complain about journal writing and essay questions, and projects in math class. They used to say this isn't English class. However unless a student can articulate what they are doing, why they are doing it and why their answer is correct they don't know how to do math. Even though essay questions are harder to grade I think they give insight into how the student thinks. Although I recently read an article on gender bias in mathematics where teachers were given similar tests to grade with boys names and girls names, although the answers were all correct the teachers gave girls a lower score than boys. The only solution is to have blind grading. Definitely a rubric helps very much to keep the teacher bas out of the grading. Sometimes I used to grade the papers, then sort them into piles regardless of whose name was on the paper. Then I would group like grades with like grades. 1 being 5 being the highest 0 being the lowest. The hardest thing to grade was not an outstanding the difference between an good paper vs. a failure paper but it was in the middle range 4, 3, 2. What was it that made the difference between a 4 and a 3, or a 3 and a 2? Grammar ? Legibility? Logic? ESL ? Diagrams? Arithmetic Errors? I would also allow a day between grading papers and going back for a second look. Sometimes I would even ask a student verbally why they did something. Sometimes they could explain themselves out loud better than on paper.I know this is difficult to do in an online class, but maybe a podcast would help.
Essay questions allow math students to explain their logic. I have told my students that people don't think alike.
How one person solves a problem might not be the same as another person. I like a format such as:
Draw a picture.
Restate the problem in your own words.
Can you write a similar problem using simpler numbers? (1, 2 5, or 10).
What facts are given to you? (Sometimes there are too many facts).
What other background knowledge do you need to solve the problem?(for example when doing a measurement problem you need to know there are 12" in a foot.)
What formulas do you need?
Does the answer make sense?
Check your math!
Can you prove you are correct?
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