Math Assessment: An analysis of raw data

This article contains a presentation of raw data from a Grade 5 level math assessment. I analyzed this data to determine student strengths and learning needs, from which I could continue lesson planning and instruction development.

Grade 5 Summative Assessment

Problem 1.

Look at triangle ABC. 

What are the coordinates of points A, B, and C?

A.)  A (2,7), B (4,3), C (5,6)
B.)  A (2,7), B (5,6), C (4,3)
C.)  A (7,2), B (3,4), C (6,5)
D.)  A (7,2), B (4,3), C (5,6)

Problem 2.
Connor is buying tickets to a play. The play he and his friends want to see costs $4.75 per ticket. Connor has $26.00 in his pocket.

What is the greatest number of tickets Connor can buy?

A.) 4
B.) 5
C.) 6
D.) 7

Problem 3.
Rob is calculating the area of this rectangle. His strategy is to multiply the whole numbers first and then multiply the fractions. 

Since 3 x 5 = 15 and 1/3 x 1/4 = 1/12, he concludes that the area of the rectangle is 15 1/2 square feet.

Find the correct area, in square feet, of the rectangle.

[_______________] 5 1/4 feet

3 1/2 feet

Problem 4. 

This line plot shows the heights of the bean plants in a garden after 3 weeks.

             Table of Raw Scores and Percent:

Student	Question 1	Question 2	Question 3	Question 4	Total	Percent
Andrew	1	1	1	1	4	100%
Analy	1	1	1	0	3	75%
Liz	1	1	1	0	3	75%
Jazmin	1	1	1	0	3	75%
Draven	1	1	1	0	3	75%
Adam	1	1	0	0	2	50%

 

Answer Key

Problem 1.
Answer:

A.) A (2,7), B (4,3), C (5,6)

Problem 2.
Answer: 

B.) 5

Problem 3.

Answer:

17.5
(Preferred: 17.5 square feet)

Problem 4.

Answer: 

7 1/2
(Preferred: 7 1/2 inches)

Analysis of Results: Student Strengths and Weaknesses

I have organized and reported sample student scores in the order of highest scores to lowest. For my analysis of these results, however, I would like to address student work in terms of lowest scores to highest scores. This is because students who scored higher were able to do so by utilizing strategies and skills that lower-scoring students did not. 

Using the example of the fourth question, each student except for Andrew missed the question. When I looked at the student work, I could see that Andrew was the only student to utilize lining up the fractions horizontally in order to add them together. Not only this, it is clear that Andrew knew he would need to generate improper fractions, and make the denominators the same. This type of strategy was missing from the work of the other students on this problem. Other students attempted to line up the fractions and add them just like they would any normal numbers—and likely the way they were taught to add numbers when they first learned addition. This tells me that students understand a way for performing addition tasks, but lack the knowledge to understand fractions conceptually in order to manipulate the numbers so that they become friendly for addition. For most students, this was the difference between performing at 100% proficiency and 75% proficiency.

Adam had the lowest scores of the group, which in this sample meant he missed one question more than his classmates. This is because he made a mistake while calculating the area of a rectangle with a length of 5 1/4 and a width of 3 1/3. After I examined his work, it is clear to me that Adam attempted some long division within his problem, and likely found that his answer would be 17.5. However, instead of understanding that 0.5 means 1/2, Adam instead put this as his numerator of 5/12.
As a general assessment, it is clear that when students are successful, it is because each student is aware of how to line numbers up correctly so that they are easy to work with. This is apparent in the problems which show students numbers that are neatly graphed, and in instances when students are performing multiplication tasks involving numbers with multiple place values.

Generally, I would say these students have a weakness with long division, which I can see in the student work where students attempt long division without having the knowledge to carry out the process fully. Students also lack the acumen to know when long division would be most useful—such as Liz’s example while solving Problem 2. Her skills in multiplication eventually lead her to the correct answer; however if she knew to divide the total amount of money by the cost of each ticket, she would have been able to reach her answer quicker and more efficiently.

These students would also benefit from understanding more about fractions from a conceptual standpoint. The student work shows attempts at utilizing algorithms for solving problems containing fractions. However, as was the case with Adam’s answer, understanding what numerators and denominators represent is still a challenge for these students.