Pre-assessment on graphical mathematics skills among physical science students
A pre-assessment in mathematics skills was administered to 23 students in SC 130 Physical Science on the first day of class. The pre-assessment differed from prior terms. This term the first question more no longer used a density of soap example. Instead the graph and questions referred to an algebraic xy labelled scatter graph. Question two was also simplified with the answers to 2e and 2d being able to be read from the table directly rather than calculated from the equation of the line. This term the slope formula and point-slope form were not provided.
1. Answer the following questions based on graph one.
a. __________ What is the slope of the line?
b. ______________ What is the y-intercept of the line?
c. y = _________ x + __________ Write the y = mx + b slope-intercept equation for the line.
2. A student rolled a ball along the sidewalk measuring the time and distance that the ball rolled. The data is recorded in the table below.
a. Plot the data on graph two.
b. __________ What is the slope of the line?
c. __________ What is the y-intercept of the line?
d. __________ How far will the RipStik travel in 20 seconds?
e. __________ How long in seconds for the RipStik to travel 50 meters?
The students were unaware of the pre-assessment and thus were taking the pre-assessment without any preparation.
Many of the 23 students had all completed MS 100 College Algebra, MS 101 Algebra and Trigonometry, or MS 150 Statistics. One student had completed only developmental mathematics at the college. Three students had completed only high school mathematics. Of the three students who had completed only high school mathematics, two had placed into MS 101 Algebra and Trigonometry and one had placed into MS 100 College Algebra. Given that the mathematics on the pre-assessment is high school algebra one level material, all of the students had encountered this material at least once and most had encountered this material more than once.
Percent correct with the questions asked:
Answer the following questions based on graph one.
43% a. What is the slope of the line?
39% b. What is the y-intercept of the line?
30% c. Write the y = mx + b slope-intercept equation for the line.
2. A student rolled a ball along the sidewalk measuring the time and distance that the ball rolled.
70% a. Plot the data on graph two.
43% b. What is the slope of the line?
22% c. What is the y-intercept of the line?
83% d. How far will the RipStik travel in 20 seconds?
70% e. How long in seconds for the RipStik to travel 50 meters?
Note that both graphs involved a direct relationship with a y-intercept of zero. A simple rise over run calculation yields the slope, the fundamental coefficient that characterizes a direct relationship. Noting that the first graph provided a graphical image of the line and on the second graph 70% plotted the coordinates correctly, the inability of over half of the students to then arrive at the slope - given the mathematics courses completed is, to me, surprising.
Note that this term 2d and 2e could be answered by reading the table (see the image above) as the table contained the answers. This led to an improvement in answering 2d and 2e. In the past terms the questions required use of the equation to calculate the solutions. This term I wanted to see what would happen if the answers were available in the table.
Performance across multiple terms on the pre-assessment
Overall performance was up term-on-term, but this boost was due both to an unusually weak performance in the fall term and a stronger performance on 2d and 2e than seen in the past.
One reaction might be to call for more mathematics requirements and courses, but consider that the three students who had not yet taken college mathematics courses had a 63% average success rate while the students who had completed a college level mathematics course (MS 100 or higher) had a 49% average success rate.
One intent of the physical science course is to engage with mathematics in contexts that give the mathematics meaning. Rather than "even numbered problems one to thirty" the course generally focuses on a single equation each week, more often a single linear equation. An equation that has a slope with a physical meaning - density, velocity, coefficient of friction, speed of sound, index of refraction. The hope is to make the mathematics more approachable and to provide the concrete systems of physical science as cognitive hooks on which the mathematical knowledge can be hung.
1. Answer the following questions based on graph one.
a. __________ What is the slope of the line?
b. ______________ What is the y-intercept of the line?
c. y = _________ x + __________ Write the y = mx + b slope-intercept equation for the line.
a. Plot the data on graph two.
b. __________ What is the slope of the line?
c. __________ What is the y-intercept of the line?
d. __________ How far will the RipStik travel in 20 seconds?
e. __________ How long in seconds for the RipStik to travel 50 meters?
The students were unaware of the pre-assessment and thus were taking the pre-assessment without any preparation.
Highest math class taken
Many of the 23 students had all completed MS 100 College Algebra, MS 101 Algebra and Trigonometry, or MS 150 Statistics. One student had completed only developmental mathematics at the college. Three students had completed only high school mathematics. Of the three students who had completed only high school mathematics, two had placed into MS 101 Algebra and Trigonometry and one had placed into MS 100 College Algebra. Given that the mathematics on the pre-assessment is high school algebra one level material, all of the students had encountered this material at least once and most had encountered this material more than once.
Performance by item on the pre-assessment n = 23
Percent correct with the questions asked:
Answer the following questions based on graph one.
43% a. What is the slope of the line?
39% b. What is the y-intercept of the line?
30% c. Write the y = mx + b slope-intercept equation for the line.
2. A student rolled a ball along the sidewalk measuring the time and distance that the ball rolled.
70% a. Plot the data on graph two.
43% b. What is the slope of the line?
22% c. What is the y-intercept of the line?
83% d. How far will the RipStik travel in 20 seconds?
70% e. How long in seconds for the RipStik to travel 50 meters?
Note that both graphs involved a direct relationship with a y-intercept of zero. A simple rise over run calculation yields the slope, the fundamental coefficient that characterizes a direct relationship. Noting that the first graph provided a graphical image of the line and on the second graph 70% plotted the coordinates correctly, the inability of over half of the students to then arrive at the slope - given the mathematics courses completed is, to me, surprising.
Note that this term 2d and 2e could be answered by reading the table (see the image above) as the table contained the answers. This led to an improvement in answering 2d and 2e. In the past terms the questions required use of the equation to calculate the solutions. This term I wanted to see what would happen if the answers were available in the table.
Performance across multiple terms on the pre-assessment
Overall performance was up term-on-term, but this boost was due both to an unusually weak performance in the fall term and a stronger performance on 2d and 2e than seen in the past.
One reaction might be to call for more mathematics requirements and courses, but consider that the three students who had not yet taken college mathematics courses had a 63% average success rate while the students who had completed a college level mathematics course (MS 100 or higher) had a 49% average success rate.
One intent of the physical science course is to engage with mathematics in contexts that give the mathematics meaning. Rather than "even numbered problems one to thirty" the course generally focuses on a single equation each week, more often a single linear equation. An equation that has a slope with a physical meaning - density, velocity, coefficient of friction, speed of sound, index of refraction. The hope is to make the mathematics more approachable and to provide the concrete systems of physical science as cognitive hooks on which the mathematical knowledge can be hung.
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