Assessment Rubric and Constraints

Rubric

Testing Constraints

Before the test:

• The test will be announced one or two days in advance to give students time to prepare.
• Instructions for behavior during the test and directions for turning it in will be given prior to handing out the test.

During the test:

• Students will be allotted 25 minutes to complete the test.
• Calculators, textbook, and equation sheets are not allowed.
• Students are not allowed to talk to others or share answers.

Rationale for Test Items

In my previous post, I have written learning outcomes and test items to support those outcomes. In this post I will give my thought process and rationale behind the creation of these items.

 

Test Item One

My first item relates to my first outcome listed. The outcome clearly indicates that the student will need to be given a point and a slope in order to develop the equation of a line. The type of test item that best fit this outcome is a completion item. Therefore, I developed an item that will require the students to take what they know about the equation of a line and develop this equation themselves and write it on a line provided. For this outcome, a true-false, multiple-choice, or matching item would not allow the students to develop the equation themselves.

 

Test Item Two

The second test item is based on the second learning outcome. When figuring out how I should write this item, I was deciding between multiple-choice and completion. Neither format is better than the other in terms of the learning outcome. Therefore, I ultimately selected multiple-choice for speed; it is quicker to circle a letter than to write out the word. In the book by Kubiszyn and Borich, it is mentioned that multiple-choice items should avoid “multiple defensible answers” (2010, p141). Thus, I noted in the directions that the student should only select the “intersecting” option when the lines are neither parallel nor perpendicular. I made sure that this note stands out in the directions by capitalizing the note.

 

Test Item Three

The third test item corresponds to the fourth learning outcome. Based on the outcome, I needed to provide a word problem with an embedded linear equation. Then the student would need to develop the equation. I decided to use a multiple-choice answer format since the first item was a completion item, thus giving a level of variance to my test. In order to keep this item difficult enough, I needed to keep the options similar to each other, make each answer plausible for someone who may be guessing, and only give one correct answer (Kubiszyn & Borich, 2010, p. 147-148). By mixing around the letters and numbers, the student will not be able to guess the correct answer without knowing the material. I only used letters and numbers that were provided in the word problem so each option could be plausible.

 

Essay Test Item

The final item is the essay item. It was difficult to come up with an essay item for a math class since most of the problems involve numbers and drawings. However, there are ways to accomplish this. My essay item covers the third and fourth learning outcomes. First, it gives a scenario of a word problem. Then it asks the student to develop the linear equation and to graph it on the axes provided. After that, the students are asked to describe how they developed the equation and their process for graphing the line. This item does not have a “single response or pattern of responses that can be cited as correct to the exclusion of all other answers” (Kubiszyn & Borich, 2010, p. 158). The students are able to select their own variables in the equation and no two students graph lines in the same way. Therefore, each response will be unique. The textbook also mentions that essay items need to set an acceptable length and be clear on what is required of the response (Kubiszyn & Borich, 2010, p. 164-165). I accomplish this in the last sentence of the prompt.

 

Rationale for the Essay Item

The first part of the prompt, including developing the equation and graphing the line, is merely done to set the student up for the second half. It is possible to write objective test items that assess these skills. The second part of the prompt allows the student to expand on the deeper understanding of the pieces of linear equations. It also gives the teacher a way to see how each student graphs the line and to make sure each student knows how the pieces of the linear equation are represented in a graph. I did not want to ask the students to solve the problem since that was not one of my learning objectives. 

References

Kubiszyn, T., & Borich, G. (2010). Educational testing and measurement: Classroom application and   practice. (9th ed., pp. 141-165). Hoboken, NJ: John Wiley & Sons, Inc.

Assessment Plan

Purpose 

Students will learn how to develop, write, and graph linear equations

Grade Level:            9th-10th grade
Unit of Study:    Algebra - Linear Equations

Learning Outcomes:

• Given a point and a slope, the student will develop the equation of the line 80 percent of the time.
• Given the equations of two lines in slope-intercept form, the student will determine if the two lines are parallel, perpendicular, or intersecting with 80 percent accuracy.
• Given the equation of a specific line, the student will draw a graph of the line on paper with 80 percent accuracy.
• Given a word problem, the student will be able to form the corresponding linear equation 80 percent of the time.

Test Items Supporting the Learning Outcomes

Completion

Using the given point and slope, write the equation of the line on the blank provided.

1.    Point: (2,3)    Slope: -3                _______________ 

Multiple Choice

Compare the two linear equations listed for each problem below. Then circle the letter that best describes the relationship of the two lines. 
NOTE: Only select “intersecting” if two lines are neither parallel nor perpendicular.

3.    y = 4x + 5     y = 4x - 10
a. Parallel   b. Perpendicular   c. Intersecting

4.    y = (1/2)x + 3     y = 2x - 2
a. Parallel   b. Perpendicular   c. Intersecting

5.   y = x      y = 2x + 4
a. Parallel   b. Perpendicular    c. Intersecting

6.    y = (3/4)x - 1      y = 3x - 2
a. Parallel    b. Perpendicular   c. Intersecting 

Multiple Choice

Read the word problem below. Write the letter that corresponds to the correct linear equation on the line provided.

2.   Mary's plant is currently 5 inches tall. It grows 0.5 inch per week. What is the linear equation that represents the height (h) of the plant after w weeks?
 
      a.    h = 5w + 1/2
 
      b.    w = (1/2)h + 5

      c.    h = (1/2)w + 5

      d.    w = 5h + 1/2

Essay Item

­­­­­­Read the scenario below and follow the direction provided.

Kyle needs to buy wrapping paper for the upcoming holiday season. He finds the style of paper he wants at a local store. The retail price of the paper is $1.00 per yard. Thankfully, he has a coupon that will take 25% off the price. Write the equation of the line that represents the amount he will pay using this coupon in terms of yards of paper. Using the set of axes provided, graph the line and label the axes. Then in the space below, use complete sentences to answer the following questions in detail. What variables did you use for the equation and what do each represent? What is your step-by-step process for graphing the equation? Your score for this item will depend on the accuracy of your equation and graph and the organization and detail of your answers to the questions.