Author: Jim Ham Date: May 20, 2006 Type: Course Assessment

Project Description: The Delta College (Michigan) mathematics department conducted a course assessment project in Elementary Algebra (MTH 097). Here are some characteristics of the course:

• MTH 097 is a developmental mathematics course. Its content parallels a traditional (early) high school first-year algebra course.
• MTH 097 is Delta College's most popular mathematics course, followed closely by Prealgebra (MTH 096). In 2005-2006, about 1200 students enrolled in MTH 097 (59 sections) during the fall and winter semesters.
• The prerequisites of MTH 097 are either a C grade or higher in Prealgebra (MTH 096) or a suitable COMPASS placement score. About 39% of the MTH 097 students (n = 1186) took the prerequisite course, MTH 096. About 61% did not take MTH 096.

• Have MTH 097 students achieved the outcomes of the course as measured by final exam questions?
• Does MTH 096 (the prerequisite course) sufficiently prepare students to succeed in MTH 097? What grade should students receive in MTH 096 so that they are successful in MTH 097?
• Based on their responses to the final exam questions, what can we learn about our students learning in elementary algebra?

1. DEFINE / REFINE student learning outcomes based on input from stakeholders.

You will recognize the learning outcomes from a traditional elementary algebra course.

• Simplify numerical expressions with multiple operations and grouping symbols using the order of operations.
• Add, subtract, and multiply polynomial expressions.
• Simplify algebraic expressions with multiple operations and grouping symbols using the order of operations.
• Simplify algebraic expressions using the rules of exponents.
• Simplify algebraic expressions using the distributive property.
• Simplify rational expressions.
• Factor polynomials by taking out a common factor.
• Factor trinomials.
• Factor binomials of the form x^2 - y^2.
• Solve a variety of linear, quadratic (using the factoring method and the quadratic formula), radical, and rational equations.
• Solve a variety of linear inequalities.
• Solve a variety of systems of linear equations.
• Compute the slope of a line in a variety of contexts.
• Compute the y-intercept of a line in a variety of contexts.
• Construct the graph of a line if given the equation of the line.
• Identify an appropriate scale for both axes when constructing a graph.
• Set up an equation or expression if given a word phrase.
• Solve a variety of real world problems using the tools of algebra and mathematical modeling.

2. DESIGN assessment tools, criteria and standards directly linked to each outcome.

There were 14 questions that each faculty member added to their final exam. Some faculty members used only these questions as their final exam. Others attached these 14 questions to the back of their longer final exam. And yet others cut and pasted these 14 items into their final exam to make a more coherent exam.

For the purposes of this assessment project, the student responses were scored correct or incorrect.

Our standard was set to be 75%. That is, we would be happy if 75% of all students taking the final exam would answer correctly each of the common final exam questions.

3. IMPLEMENT assessment tool(s) to gather evidence of student learning.

The common final exam questions were administered to all sections of MTH 097 (Elementary Algebra) during the Fall, 2004 and Winter, 2005 semesters.

Each (full and part time) faculty member was sent a spreadsheet for their section(s) listing each student and each common final exam question, and was asked to complete the spreadsheet as follows: a 1 was entered when a problem was completely correct, and a 0 was entered when the problem was not correct. For the purposes of the assessment project, partial credit was not awarded.

4. ANALYZE and evaluate the collected data.

Download the following documents to see the project results.

• Final Exam Items: A list of the common final exam items.
• Participation: A summary of the student cohort and the number of full and part time faculty who participated in the project.
• Additional Summary Tables: The data were analyzed in several ways. Group comparisons, item analysis, impact of prerequisite course, and relationship between reading placement score and success in course were all considered to try to make sense of the data.

5. IDENTIFY gaps between desired and actual results.

The data revealed several gaps between the actual and desired results.

• Only the A students achieved the 75% standard for the most part. A students achieved the 75% standard on 14 of the 17 common final exam questions.
• Students who earned less than an A grade in MTH 097 achieved the 75% standard on only one of the common final exam questions.

• If partial credit was given, students would have scored much higher. It was clear that many students did lots of correct mathematics on their way to their final incorrect answer.
• Student algebraic skills and understandings are very fragile after completing the elementary algebra course. It may require several additional semesters in college-level mathematics courses before students master algebra.
• A multiple choice format may have lead to additional correct answers and higher scores.
• Because MTH 097 is a developmental course that does not count toward graduation, it is the lowest priority course for students with several courses; it is the first course that students will drop if they encounter one of the many unexpected events that they will experience in their work or personal life.
• Students who take a similar course in high school (or junior high) have an entire year, or 180 days, to learn the skills and concepts of an elementary algebra course. We require students to learn the course content in one semester, or 45 hours. Perhaps the pace of this course is too fast for most students.
• Because of the gap between how students score on the common final exam questions and the grades student receive in the course, some wonder if grade inflation is an issue.
• Most of our students who are successful in our elementary algebra course go on to be successful in Intermediate Algebra, other math courses, or courses with an elementary algebra prerequisite. So we should be concerned, but not overly concerned about our students' performances on the common final.

6. DOCUMENT results and outline needed changes in curriculum, instructional materials or teaching strategies.

The elementary algebra course has the lowest success rate of any of the mathematics courses. Only about 55% of students who begin the course will pass with a C or better. This assessment project confirms that the course is not as successful as the mathematics faculty would hope. In addition, students who passed elementary algebra are leaving with very fragile algebra skills. Additional data collection revealed that only 30% of Elementary Algebra C students passed Intermediate Algebra.

So, what are we going to do about it?

During the department discussions the following proposals were made:

• Offer an extended elementary algebra course that would contain the same outcomes as elementary algebra, but would meet for one additional hour per week.
• Offer a two course sequence of elementary algebra, each worth 1.5 credits each. The first module would contain the first half of the elementary algebra course, and the second module would contain the second half of the elementary algebra course.
• Make better use of the College's peer mentor program and assign peer mentors to more of the elementary algebra sections.
• Experiment with higher prerequisites in elementary algebra or intermediate algebra.
• Offer a couple of sections of the course so that they span an entire year.
• Experiment with a continuous review model to teaching the course. That is, assess students on the most important topics, skills, and concepts several times during the semester after they are first introduced.
• Create an extended hour intermediate algebra course to accommodate students who need additional time to master the course content.

The mathematics division decided to take the following actions:

1. Experiment with alternate teaching strategies to help students develop the algebra skills necessary to be successful in future courses.
2. Create an extended-hour (6 contact hours) intermediate algebra course. The prerequisite of this course is C or better in elementary algebra.
3. Increase the prerequisite of the 4-credit intermediate algebra course to B- grade or better in elementary algebra.