
































Microsoft Word - 2. Atkins-Dec 2016.docx


Vol. 5, No. 1, Dec 2016, pp. 13-25   

 

 
 
 
 
A Co-Requisite Model for Developmental Mathematics: Innovative Pathway Leads to 
Positive Outcomes for Education Majors 
Charlene Atkins and Ann McCoy 
University of Central Missouri 
 
 

Abstract 
 

The traditional mathematics pre-requisite model creates obstacles for pre-service 

educators by increasing the number of semesters to graduation.  Extended time results in 

additional financial burdens for students in developmental courses along with increased risk of 

student drop out.  Education majors, with little or no room for electives in their programs of 

study, have been particularly impacted. The pilot of a co-requisite model, involving the 

collaboration of two academic departments, has proven successful in enhancing students’ 

academic achievement while addressing social and emotional needs of students. 

 

  



14	
     C. Atkins & A. McCoy	
  
 

 

Introduction 
 

A popular saying often attributed to Albert Einstein speaks of the futility of expecting 
different outcomes without changing the process or procedure being followed. In other words, if 
we are dissatisfied with the results we are experiencing, we must be willing to make changes. 
Such dissatisfaction with student performance in developmental mathematics courses and 
subsequent credit-bearing mathematics courses led faculty at a public mid-western university 
(MWU) to examine the university’s approach to developmental education. 
            Historically, MWU had taken a traditional approach to developmental education in 
mathematics. Students who failed to meet an established cut-off score on a standardized test 
were required to successfully complete a series of pre-requisite courses prior to enrollment in a 
credit-bearing mathematics course. A lack of success in pre-requisite courses or in the 
subsequent credit-bearing course meant additional semesters at MWU and increased financial 
burdens for many students.  

A number of MWU education majors, especially those pursuing degrees in elementary or 
special education, scored below the established cut-off score required for credit-bearing 
mathematics courses and were required to enroll in developmental education courses. Because 
these education students have few or no electives in their programs of study, the additional 
developmental education pre-requisite courses impacted their progress towards graduation and 
teacher certification. Consequently, MWU faculty made the decision to pilot a co-requisite 
model as an alternative to the traditional pre-requisite model for education majors. Promising 
results from the pilot led to the recent formalization of the model and the courses that are part of 
the model. 
            This article will provide a brief overview of developmental education, a discussion of co-
requisite models for developmental education, a description of the process followed in 
implementing a co-requisite model at MWU, and a summary of the results from the pilot of the 
model. Finally, a discussion of the lessons learned by MWU faculty is provided. 
 

Developmental Education 
 

History of Developmental Education 
 When universities were initially established in the United States, over 200 years ago, the 
only admission requirement of students was the ability of their families to pay tuition fees.  It 
was not unusual for a student from a wealthy family to be accepted for enrollment even though 
the student lacked the academic preparation necessary for success at the college level (Arendale, 
2011).  Accepting students who were academically underprepared for the rigor of post-secondary 
coursework contributed to the financial stability of the institution; however, this practice caused 
great concern for the success of these students.  Eventually, institutions found it necessary to 
offer college-preparatory courses, to a large population of entering freshmen.  As this population 
continued to grow, institutions established full college-preparatory programs and departments to 
assist underprepared students in achieving their academic goals.  Over time, such assistance 
became known as “remedial” education, having a focus on building content knowledge that 
students had not yet mastered due to a lack of prior schooling or to students’ fragmented 
understanding. 
 Through the years, America witnessed numerous historical events having a direct impact 
on education at secondary and post-secondary levels.  Following World War I (1914-1918), 



 

  Co-Requisite Model for Developmental Mathematics  15 
 

education systems began to require formal schooling through the 12th grade, a recommendation 
made by education reformer John Dewey. This change generated an increase in college 
enrollment causing colleges “to lower standards to accommodate many of the applicants” 
(Tucker, 2012, p.4).  World War II (1939-1945) generated a demand for mathematicians causing 
a need for increased numbers of mathematics teachers at the secondary level and encouraging a 
larger enrollment of college freshmen in calculus courses.  Those students unprepared for 
calculus studies were enrolled in remedial college-level algebra courses.  A greater number of 
military veterans began to enter college following the creation of the G. I. Bill, though many 
lacked academic preparation due to their military service.  The launching of the Russian satellite, 
Sputnik, in 1957 brought about political concern for the Soviet Union’s lead in the space race 
along with public blame on American education.  Each of these events, along with others, 
brought about education reform at both the secondary and post-secondary levels. 
 Reform at the secondary level seemed to occur consequently with societal needs.  
Lambdin and Walcott (2007) described reforms at the secondary level as six phases: drill and 
practice, meaningful arithmetic, new math, back to basics, problem solving, and the current 
standards and accountability phase. Instructional practices in American high schools experienced 
change through each phase; however, university classrooms remained unchanged causing a 
growing gap between high school achievement levels and expected college entry levels.   
 
Traditional Pre-requisite Model 
 Developmental mathematics education originated as remedial courses designed to 
address academic deficiencies, due to the lack of preparation of students entering college. 
College Algebra began as a remedial course serving to prepare students for calculus. 
Traditionally, remedial courses were pre-requisite courses for an algebra intensive pathway. 
Eventually, College Algebra became the required gateway course for most major programs of 
study.  Students unprepared for College Algebra were enrolled in pre-requisites of Intermediate 
and Introductory Algebra. In addition to the number of high school graduates entering college 
underprepared, the number of non-traditional students continued to grow creating a diverse 
population of students with academic deficiencies.  Educational doors opened to a new 
population including immigrants with language barriers, military veterans, and those seeking a 
career change. 
 Those serving this diverse population realized that these students shared additional 
characteristics, aside from academic deficiencies.  Students enrolled in remedial pre-requisite 
courses reported a lack of self-esteem, lack of support from family and friends, trouble adjusting 
to university culture, time-management issues and mathematics anxiety (Bitner, Austin, & 
Wadlington, 1994; Boylan, 2009; Castator, 1995).  The traditional pre-requisite model of 
remediation was not designed to offer student services in addition to academic courses.  In the 
last 10 years, such traditional models have been accused of creating obstacles for students, 
preventing students from reaching their academic goals.   
 Traditional pre-requisite remedial algebra preparation models have been identified as 
creating financial burdens on students and institutions by extending time to graduation.  Those 
opposing college-preparatory programs argue that such programs “cost taxpayers twice” and 
only serve to re-teach what should have been learned in high school (Saxon & Boylan, 2001, p. 
2).  Those supporting such programs argue that the traditional system is flawed and should be 
reformed to eliminate obstacles and address student needs beyond content understanding.  For 
these reasons, remedial courses and programs have evolved into developmental courses and 



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programs designed to address the social, emotional and intellectual needs of students while 
removing unnecessary obstacles. 
 Another obstacle, cited in current research, is the tradition of requiring all students to 
complete a college-level algebra course (Cooper, 2014).  College Algebra was once the pre-
requisite for calculus, as calculus was the required gateway course for many majors  for most 
university students.  Eventually, College Algebra became the acceptable gateway course for most 
students.  Students unprepared for College Algebra were placed into developmental algebra 
courses, based on scores earned on a standardized assessment such as the ACT.  Higher 
education has since seen a demand for mathematics courses that more appropriately align with 
and prepare students for chosen careers and professions.  As a result, institutions have begun to 
offer basic statistics and quantitative reasoning courses as alternatives to College Algebra for 
students not entering a science, technology, engineering or mathematics (STEM) field.  Though 
these new gateway courses are now available, the pre-requisite algebra pathway has seen little 
change.  Until recently, developmental algebra courses have been accepted as appropriate pre-
requisites for a variety of gateway courses, even though developmental algebra courses were 
designed to prepare students only for college-level algebra. In addition, the ACT was designed to 
measure preparedness for college-level algebra and there is no evidence it will predict success in 
other gateway courses (Clough & Montgomery, 2015).   
 
Co-Requisite Model 
 One result of current research in developmental education is the effort to enroll students 
directly into college-level courses rather than expecting students to complete a sequence of one 
to three developmental courses prior to the gateway course.  Rather than following the pre-
requisite model by re-teaching high school mathematics content in preparation for college-level 
content, co-requisite models allow students to immediately begin work at the college-level while 
receiving just-in-time academic assistance along with support and services designed to address 
social and emotional needs as well.   

Co-requisite models can be implemented using a variety of structures. For example, 
students may be required to enroll in parallel, supplemental courses or to participate in non-
course-based options such as self-paced instruction hosted in university computer labs.  
Mandatory tutoring that accompanies the credit-bearing course is another strategy used as part of 
co-requisite models.  Some institutions offer developmental support immediately after the 
scheduled credit-bearing course ends while others add additional hours to courses (Core 
Principles for Transforming Remediation, 2015). 

 
Changing the Model, Changing the Outcomes 

 
 The Department of Academic Enrichment at MWU has been serving students with 
developmental needs for more than 50 years.  Traditionally, students have been placed into 
developmental algebra courses when the reported ACT math score was below the placement 
score required for all gateway mathematics. Depending on the reported ACT score, students 
were expected to complete from one to three developmental algebra courses before enrolling in 
the required college-level course, offered in the Department of Mathematics and Computer 
Science. As noted earlier, a number of education majors were placed in these developmental 
courses. 



 

  Co-Requisite Model for Developmental Mathematics  17 
 

 Each year the MWU Department of Academic Enrichment holds a department retreat 
where members of the entire department come together to share program reports, research, 
legislative updates, and university goals.  At the spring 2014 retreat, members reviewed and 
discussed the implications of an education bill recently approved by state legislators. This bill 
requires higher education to identify and reduce the use of methods shown to be ineffective in 
supporting students or that delay student enrollment in credit-bearing courses. Best practices in 
developmental education were discussed at the spring retreat and ideas for improvement were 
shared among faculty and staff.  In an attempt to meet the expectations of the state bill and the 
MWU vision to improve graduation rates, members of the department agreed that steps should 
be taken to reduce time to graduation by decreasing time spent in developmental mathematics 
courses.   

Academic advisors identified education majors as having the least time for elective 
credits in the current program of study. In addition, new state level teacher certification rules 
require all prospective teachers to pass a series of rigorous assessments, the first of which is an 
assessment of general education knowledge and skills. Initial pass rates for the mathematics 
portion of this assessment were very low. These two factors, along with the knowledge that pre-
service teachers maintain the highest levels of math anxiety compared to students of other 
undergraduate majors (Gresham, 2007), led to the suggestion that a co-requisite model be 
implemented for education majors to provide these students with a successful pathway through 
their required gateway mathematics courses, while reducing time to graduation and alleviating 
financial burdens.   
         The next step was for the Academic Enrichment mathematics program coordinator to 
consult the mathematics education coordinator in the Department of Mathematics and Computer 
Science. Though the two academic departments had occasionally worked together to ensure 
curricular alignment from pre-requisite courses to gateway courses, the departments had not 
worked collaboratively on such a huge project.  Changing the developmental model would have 
an impact on both departments so it was imperative that both departments contribute to the 
foundation of this project.   

 The Department of Mathematics and Computer Science offers several mathematics 
courses that fulfill the general education mathematics requirement at MWU. It was agreed that a 
co-requisite developmental lab would be paired with a Contemporary Mathematics course. 
Contemporary Mathematics is a mathematics survey course focused on quantitative reasoning. 
Topics in the course include set theory, statistics, probability, measurement, and geometry, and 
students are assessed through course assignments, projects, and tests. Contemporary 
Mathematics (CM) is required of all MWU elementary, middle school, and special education 
majors because the topics studied are more relevant to future educators. In addition, the course is 
a popular general education option for students in other teacher education programs. Historically, 
Contemporary Mathematics had been one of the general education mathematics courses for 
which Introduction to Algebra was required as a pre-requisite.   

The co-requisite model for the CM course was piloted over four semesters, beginning the 
fall 2014 semester. Students who did not meet the required ACT mathematics placement score, 
or did not have a score on file, were enrolled in a CM course, carrying three college credit hours, 
meeting on Monday, Wednesday, and Friday each week.  These students were also enrolled in a 
developmental mathematics lab (DML), carrying two elective credit hours, meeting on Tuesday 
and Thursday of each week.  Students enrolled in the DML received traditional instruction, 



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alongside students who met the recommended placement score, in the program specific CM 
course.  

 Just-in-time content support was provided through student-centered activities and tasks 
in the co-requisite DML course.  For this to be successful, instructors of the gateway CM courses 
shared course objectives, syllabi, and instructional schedules with the DML instructor.  This 
allowed the DML instructor time to plan appropriate activities that would align with the content 
covered in the CM course at the appropriate time.  The DML instructor was able to identify 
student prior knowledge and implement pre-teaching tasks to prepare students for instruction 
received in the CM course.  If a CM instructor needed to alter the schedule, he or she simply sent 
a short email notifying the DML instructor so that adjustments could be made prior to lab 
meetings. 

 
Co-requisite Lab Description and Example Activities 
  In addition to academic deficiencies, students with developmental needs deal with 
mathematics anxiety, low self-esteem, time-management troubles, and other non-cognitive 
issues.  The DML course was designed to address the social, emotional and intellectual needs of 
students while supporting the development of both conceptual and procedural content 
knowledge.  In addition to helping students develop understanding of the mathematics 
curriculum, the DML served to provide students with materials, tools, and resources for success 
in the gateway course and, in a broader sense, in all university courses and experiences. Because 
teachers who suffer from mathematics anxiety unintentionally transmit their fears to students and 
rely on traditional methods of instruction (focusing on algorithms, expecting seatwork, relying 
on lectures), the DML also served to expose education students to a variety of instructional 
strategies appropriate for use in future classrooms (Aslan, 2013; Bekdemir, 2010). 
 Though there were many areas of importance, instructional activities in the DML course 
focused heavily on mathematical language development.  Stahl, Simpson, and Hayes (1992) 
emphasized the importance of student ability to understand and use the language of mathematics 
including mathematical symbols.  Student ability to draw from multiple definitions and examples 
including synonyms and antonyms is vital for effective communication in current courses and for 
success in subsequent courses.   

For this reason, each new unit was introduced in the DML by focusing on vocabulary 
fluency through student-centered activities.  For example, a unit on geometry was introduced 
first by establishing definitions of specific terms that would be used throughout the unit.  
Students were given a list of important terms along with the textbook definition of each term.  In 
small groups, students worked together to develop their own appropriate definitions of these 
terms so that they could personalize the definitions and make connections to their own prior 
knowledge and experiences.  Finally, students were asked to take photos of objects representing 
each term and to share with the class their reasons and justification for selecting the objects 
photographed.  This activity allowed students to personalize their learning of the vocabulary 
while building an understanding of mathematical language through communication with 
classmates. 
 Allowing students to work collaboratively promotes communication in a non-threatening 
situation where students can receive feedback and accept responsibility for their learning 
(Osterholt & Barratt, 2010).  For example, while completing a lesson on probability, students 
were randomly placed into small groups and each student was randomly assigned a specific 
responsibility (driver, recorder, starter, or judge) within the group.  The task of each group was to 



 

  Co-Requisite Model for Developmental Mathematics  19 
 

participate in a remote control car race, in order to collect data that would later be used to 
investigate the probability and odds of different cars winning a race.  While in the small groups, 
students encouraged their team drivers by providing driving tips, cheers, and pats on the back.  
They also worked together to ensure data was recorded correctly and that decisions were made 
fairly.  The activity provided an opportunity for students to become comfortable with their 
teammates and to build relationships that would be supportive in the future as well.  After the 
activity, teammates worked together to solve mathematical problems.  During this time, 
communication was comfortable for students because the teams had shared in the fun activity 
first.  Students felt comfortable in asking mathematical questions and offering suggestions to 
their teammates.  Discussions moved through phases that started with the activity itself, turned to 
the mathematics content and language, and ended with plans to collaborate for other shared tasks 
and courses.  Students not only developed conceptual knowledge but learned the value of 
cooperation as well.  At the same time, these education majors experienced instructional 
strategies they can eventually implement in their own classrooms once they become in-service 
educators. 
 Formative assessment was used daily in the developmental lab, often through the use of 
technology including iPad apps such as Kahoot and Nearpod.  Students often reported, through 
anonymous course evaluations, enjoying the use of technology and the participation in simple, 
friendly, no-pressure competitions.  Regular formative assessment provided information to the 
lab instructor that was then used to develop new tasks to address content areas where students 
continued to struggle. Grade evaluation in the developmental lab was based only on class work, 
lab attendance and summative assessments completed in the gateway course.  No summative 
assessments were administered in the developmental lab.  Rather than spending valuable class 
time on additional summative assessments, the time was spent on building content knowledge 
and understanding. Student performance on unit exams was assessed in the gateway course and 
scores were then shared with the lab instructor. 
 
Pilot Results  

In order to determine the effectiveness of the co-requisite model, faculty at MWU 
designed a study to investigate the relationship between student participation in a developmental 
lab and student achievement in the associated Contemporary Mathematics course.  The study 
also sought to examine the relationship between possible placement variables and achievement 
of education students enrolled in Contemporary Mathematics and participating in the co-requisite 
model of instruction.   

A total of 54 education majors participated in the co-requisite pilot; however, for the 
purpose of this study, students without both an ACT mathematics score and a high school grade 
point average on file with the university were eliminated from the study.  The subjects of this 
study were 43 education majors having both an ACT mathematics score and a high school grade 
point average on file.  Two of the 43 participants were males.  All subjects of this study had a 
reported ACT mathematics score less than 22, placing these students into the developmental 
mathematics program.  Education majors with areas of emphasis in elementary, early childhood, 
middle school, music, art, special education, and career and technology education participated in 
the study. 

Quantitative data for this study came from a total of four semesters of a pilot co-requisite 
mathematics program.  The data include student high school grade point average, ACT 
mathematics sub-scores, daily attendance rates in the developmental mathematics lab, and final 



20	
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gateway mathematics course scores.  All quantitative statistical analyses were completed using 
the SPSS Statistics 23 software package. 

A descriptive analysis found the mean ACT mathematics score to be 17.33 with a 
standard deviation of 1.44.  The mean high school grade point average was 3.13 with a standard 
deviation of 0.48.  The mean daily lab attendance rate was 0.79 with a standard deviation of 0.17.  
The mean gateway course score was 2.95, on a 4-point scale, with a standard deviation of 1.17.  
Descriptive data is displayed in Table 1.1. The Pearson Product Moment Correlation was 
computed to describe the strength and direction of the linear relationship between each pair of 
variables.  An analysis of the data revealed a  and positive correlation between attendance in the 
developmental lab and gateway course scores (r = 0.644, p < 0.001**).  The analysis revealed a 
moderate and positive correlation between high school grade point average and gateway course 
scores (r = 0.451, p = 0.002*).  The analysis also revealed a moderate and positive correlation 
between ACT mathematics scores and gateway course scores (r = 0.403, p = 0.007*).  A 
correlation matrix is provided in Table 1.2. 
 
Table 1.1 Descriptive Statistics 

Variable Mean Standard 
Deviation 

ACT mathematics score 17.33 1.44 
High School GPA 3.13 0.48 
Lab Attendance Rate 0.79 0.17 
CM Course Score 2.95 1.17 
 
Table 1.2 Correlation Matrix 

 
  

ACT 
High 

School 
GPA 

 
Lab 

Attendance 
CM Course 

Score 

ACT 
mathematics 
score 

Pearson Correlation 
Sig. (1-tailed) 
n = 43 

1 0.176 
0.259 

0.053 
0.734 

  0.403* 
  0.007 

High School 
GPA 

Pearson Correlation 
Sig. (1-tailed) 
n = 43 

0.176 
0.259 

1 0.226 
0.145 

  0.451* 
  0.002 

Lab Attendance Pearson Correlation 
Sig. (1-tailed) 
n = 43 

0.053 
0.734 

0.226 
0.145 

1   0.644* 
<0.001 

* p<.01,  ** p<.001 
 

To determine the value of using multiple measures as course placement tools, regression 
analyses were conducting using ACT mathematics scores, high school grade point averages, and 
DML attendance as the independent variables, and gateway course scores as the dependent 
variable.  Using the Enter Method regression model, a significant equation was found (F(3, 39)= 
20.877, p < 0.001) with an R2 of 0.616.  The model summary is provided in Table 1.3 and 
theresults for independent variables in Table 1.4. 
  



 

  Co-Requisite Model for Developmental Mathematics  21 
 

 
Table 1.3 Model Summary 
 

Model Summary 
Model R R Square Adjusted R 

Square 
Std. Error of 
the Estimate 

 

1 0.785 0.616 0.587 0.75483  
ANOVA 

Model Sum of 
Squares 

df Mean 
Square 

F Sig. 

Regression 
Residual 
Total 

35.686 
22.221 
57.907 

3 
39 
42 

11.895 
0.570 

20.877 <0.001 

 
Table 1.4 Coefficients Table 
 

Coefficients 
Model Unstandardized 

Coefficients 
Standardized 
Coefficients 

t Sig. 

B Std. Error Beta  
 

(Constant) -6.639 1.536  -4.323 <0.001 
Lab 
Attendance 

3.737 0.671 0.567 5.568 <0.001 

ACT 
Mathematics 
Score 

0.265 0.082 0.326 3.231 0.003 

High School 
GPA 

0.653 0.254 0.266 2.570 0.014 

Dependent Variable: CM course score 
 

 
  The quantitative data analysis indicates that there is a correlation between attendance in 

the developmental lab and performance in the gateway course.  The analysis also indicates that 
using multiple measures, rather than a single measure alone, will contribute to CM course scores.  
All independent variables were significant predictors of CM course scores:  Lab Attendance (t = 
5.568, p <0.001), CT Mathematics Scores (t = 3.231, p = 0.003), High School GPA (t = 2.570, p 
= 0.014).  Although all students in this analysis had complete data, unfortunately, not all students 
are able to report those scores.  Students who did not complete high school in the United States 
may not have a traditional high school grade point average to report.  Non-traditional students 
who completed high school many years ago may have a high school grade point average to 
report, but those high school GPAs may not parallel those of more recent high school graduates 
as graduation requirements and course offerings have changed over the years.  Along with these 
issues is the concern over the possibility of grade inflation that could impact the reported high 
school grade point average. 



22	
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In addition to the quantitative analysis, another indicator of program success may be the 
overall course completion rate for the subjects of this study.  MWU monitors the DFW rate of 
each course offered.  Courses with fewer than 30% of students earning a letter grade of D or F or 
having withdrawn from the course are considered successful courses.  Of the students 
participating in this study, approximately 86% successfully passed the gateway course with a 
letter grade of C or higher leaving only 14% in the DFW category.  Of these students, 67% 
earned a letter grade of D meaning less than 5% of the students in this study either failed or 
dropped the co-requisite courses.  The reported DFW rate for students enrolled in the same 
sections of the CM course but participating in the traditional pre-requisite instead of the co-
requisite pathway was 25%. 

 
Lessons Learned from Implementing the Pilot 
 As the results above indicate, MWU’s co-requisite model has been effective in terms of 
promoting student success and completion of a gateway mathematics course while reducing time 
to graduation and financial burden. The pilot of the model has also provided faculty with a great 
deal of insight into the successful implementation of a co-requisite model. First, if multiple 
sections of the co-requisite courses are offered, the model works best when each section of the 
gateway course is paired with a specific DML section. When this is not possible, then all sections 
of the gateway course associated with a specific DML course should have the same instructor. 
When students in a DML course have different instructors for the gateway course, different 
topics are often being studied. Just-in-time content support really only works if all students are 
studying the same content. 

Frequent communication and ongoing collaboration between the instructors of the 
gateway and DML courses is essential. Face-to-face meetings prior to the beginning of the 
semester have allowed faculty to plan together and to establish means of communication. A 
weekly email from the gateway course instructor provided the DML instructor with an update on 
the topics to be covered during the week, and this allowed the DML instructor to plan 
accordingly. Adding the DML instructor to the course management site of the gateway course 
was another strategy that helped to facilitate communication. Having access to the site allowed 
the DML instructor to access student grades, and thus, monitor student progress and performance 
in the gateway course. 
 In addition, assessments must be carefully planned and coordinated between the gateway 
course and DML instructors. In the MWU model, summative assessment occurs exclusively in 
the gateway course and formative assessment is a major component in the DML course. 
Interestingly, students in the DML course have asked for graded quizzes that help them practice 
for the summative tests given in the gateway course.  This assessment plan has worked to 
provide students with the information they need to monitor their progress without overwhelming 
them with multiple summative assessments. 
 Monitoring attendance in both the gateway course and the DML course has proven to be 
an important aspect of the model. Not surprisingly, students who were successful in the gateway 
course attended both the gateway and DML course regularly. In addition, instructors of the 
courses must communicate with each other on a regular basis about student attendance. 
 The logistics involved in ensuring students are enrolled in the appropriate gateway and 
DML courses proved to be more challenging than initially anticipated. Several different 
processes were investigated and tried before a workable procedure was identified. While course 



 

  Co-Requisite Model for Developmental Mathematics  23 
 

management and enrollment platforms vary from university to university, spending time upfront 
to address enrollment issues is essential. 
 Finally, many models for co-requisite programs are in use at universities. In some of 
these models, the same instructor teaches the gateway and DML course.  For the model 
described here, a deliberate decision was made to involve two different faculty members 
representing two departments of the university. Doing this has provided students the opportunity 
to experience the content from two different perspectives and through two different teaching 
styles. This practice supports a variety of student learning styles and needs. 
 

Next Steps - Extending the Model 
 

 Based on the success of the pilot of a co-requisite model for the Contemporary 
Mathematics course for education majors, the co-requisite option has been opened to students 
with majors other than education. Enrollment in the co-requisite sections of the gateway course 
and the DML course has grown tremendously and several sections of each course must now be 
offered. In addition, the success of the pilot has led MWU to begin offering a co-requisite option 
for a second course, Introduction to Mathematical Modeling. The same structure of offering the 
gateway course through the Department of Mathematics and Computer Science and the DML 
course through the Department of Academic Enrichment is being utilized with this new course. 
The DML course is structured in a similar manner as the course used with Contemporary 
Mathematics. This fall, the Department of Mathematics and Computer Science will use a co-
requisite model for Basic Statistics. For this course, both the gateway course and the DML will 
be offered in the Department of Mathematics and Computer Science. Data will be collected and 
analyzed for each of these new models. 
 
Conclusion 
 The co-requisite model implemented by the MWU has resulted in positive outcomes for 
students. Education majors have been supported in achieving success in gateway mathematics 
courses and in gaining the knowledge required for successful completion of required teacher 
certification assessments. In addition, the credit hours previously devoted to pre-requisite 
developmental math courses can now be spent on other required or elective courses. The success 
of the pilot of the model has resulted in the model being extended to include majors other than 
education and to additional mathematics courses. A deliberate, yet informed, move away from 
traditional practices and the willingness to undertake the work involved in trying something new 
has led to very different, and very positive, results for students. 
 
 
 
 
 

 
 
 

  



24	
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References 

 
Arendale, D. R. (2011).  Then and now:  The early years of developmental education. 

 Research and Teaching in Developmental Education, 27(2), 58-76. 

Aslan, D.  (2013).  A comparison of pre- and in-service preschool teachers’ mathematical 

anxiety and beliefs about mathematics for young children.  Academic Research 

International, 4(2), 225-230. 

Bekdemir, M.  (2010).  The pre-service teachers’ mathematics anxiety related to depth of 

negative experiences in mathematics classroom while they were students. Educational 

Studies in Mathematics, 75(3), 311-328. 

Bitner, J., Austin, S., & Wadlington, E.  (1994).  A comparison of math anxiety in  

traditional and nontraditional developmental college students.  Research and Teaching in 

Developmental Education, 10(2), 35-43. 

Boylan, H. R.  (2009).  Targeted intervention for developmental education students (T.I.D.E.S.).  

Journal of Developmental Education, 32(3), 14-23. 

Castator, M. M.  (1995).  Identifying high-risk courses for underprepared students.   

 (Unpublished doctoral dissertation).  University of Kansas, Lawrence, KS. 

Clough, S., Montgomery, S.  (2015). How ACT assessments align with state college 

 and career readiness standards. Retrieved from ACT: http://www.discoveract 

aspire.org/pdf/ACT_Alignment-Whte-Paper.pdf 

Cooper, K. J.  (2014).  Remedial rescue: New approaches to developmental education have 

proved successful for several two-year colleges.  Diverse Issues in Higher  Education, 

31(18), 14-15. 

 



 

  Co-Requisite Model for Developmental Mathematics  25 
 

Core principles for transforming remediation within a comprehensive student  

success strategy:  A joint statement.  (2015).  Retrieved from 

http://completecollege.org/wp-content/uploads/2015/12/Core-Principles-2015.pdf 

Gresham, G.  (2007).  A study of mathematics anxiety in pre-service teachers.  Early 

 Childhood Education Journal, 35(2), 181-188. 

Lambdin, D. V., & Walcott, C.  (2007).  Changes through the years: Connections  between 

psychological learning theories and the school mathematics curriculum.  In W.G. Martin, 

M.E. Strutchens, & P.C. Elliott (Eds.), The learning of Mathematics: Sixty-ninth 

yearbook (pp. 3-25).  Reston, VA:  The National Council of Teachers of Mathematics. 

Saxon, D. P., & Boylan, H. R. (2001).  The cost of remedial education in higher education.  

Journal of Developmental Education, 25(2), 2-8. 

Stahl, N. A., Simpson, M. L., & Hayes, C. G.  (1992).  Ten recommendations from  

research for teaching high-risk college students.  Journal of Developmental Education, 

16(1), 2-10. 

Tucker, A.  (2012). The history of the undergraduate program in mathematics in the United 

States. Retrieved from the Mathematical Association of America: 

http://www.maa.org/sitesdefault/files/pdf/CUPM/pdf/MAAUndergradHistory.pdf 

  



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