Chief Dull Knife College
PO Box 98   Lame Deer, Montana  59043   406-477-6215





Pathways to Success in Pre-College Mathematics
by Bob Madsen, Ted Hodgson, and Carol Ward

(Editor’s note: “Talking Circle” is a new department in Tribal College Journal. It features tribal college faculty and administrators discussing their lessons learned and best practices for teaching and operating tribal colleges. We invite submissions.)

    Like most tribal colleges, Chief Dull Knife College (CDKC, Lame Deer, MT) offers a sequence of pre-college mathematics courses – Basic Mathematics, Introductory Algebra, and Intermediate Algebra – to assist students who lack college-level skills. Unfortunately, 60-70% of our students typically failed or withdrew from these courses. Moreover, those passing often emerged with weak skills and poor retention. To address these problems, CDKC is reforming its pre-college mathematics. Those enrolled must be able to pass, and those passing must emerge with college-level skills. In this article, we briefly describe our reform efforts and offer preliminary evidence about their impact.

Course Revisions
    We identified four factors that affect student success and are within our power to control: inadequate preparation, inappropriate student placement, inadequate out-of-class support, and promotion without content understanding. To address the first two problems, we tested each entering student on pre-college mathematics content (see Table 1). To bypass Basic Mathematics, students now must correctly answer 80% of the Basic Mathematics exam questions. If a student does so, he or she attempts problems from Introductory Algebra. Similarly, students must correctly answer 80% of the Introductory Algebra exam questions to skip Introductory Algebra. Students bypass the entire sequence only after demonstrating content mastery. Thus, the exam identifies students’ skills and places each into appropriate courses. 

Basic Mathematics

Introductory Algebra

Intermediate Algebra

Whole Number Operations

Real Numbers

Systems of Equations


Variable Expressions



Linear Equations

Factoring Polynomials

Ratios and Proportions


Quadratic Equations


Graphing Equations

Rational Expressions



Radical Expressions

Table I.

Pre-college mathematics content.

To enhance student support, CDKC created the Student Learning Center, which is staffed by instructors and student interns and offers computer work stations. During spring 2006, more than 300 students logged over 3,000 visits to the center. To improve students’ retention of mathematics, we discarded our traditional, lecture-based approach to the pre-college sequence and adopted a curriculum that delivers content through text and computer activities (Wright, 2005; Wright, 2006). For each section, students read the text (or corresponding computer material) and complete computer-based problems. Correct work allows students to quickly progress. Those that struggle, however, can view worked examples, re-read sections, or seek outside assistance. The software then presents additional problems to ensure the students’ readiness to proceed.
After completing each section, students must pass a computer-based assessment at the 80% level. Failing that, a student receives additional instruction or practice. Students demonstrating section mastery must pass the chapter test at the 80% level. Those unable to pass may review information and complete additional problems before retaking the test. Pre-project interviews revealed that student success would increase if partial credit were given for the work they complete. Therefore, we developed a “Math Seminar” consisting of three sections – one for each pre-college course. Students enroll in a section, based upon their placement scores or prior work, and receive credit for making “adequate” progress. They may re-enroll in any section to complete the seminar. Thus, students receive seminar credit until they are prepared for college-level mathematics. 

Project Impact

Combining computer-based instruction, mastery learning, and adequate support offers distinct advantages to CDKC students. For one, the revised structure increases the likelihood that students will retain concepts. Students no longer pass with partial understanding, only to be unprepared for the next course. To complete the Math Seminar, students must demonstrate 80% mastery of each section and chapter. Problems created by absenteeism, such as students returning to unfamiliar content, are also addressed. With self-paced coursework, a student starts where he or she left off. Within a traditional classroom, teachers assume primary responsibility for students’ learning. As a result, students often attribute their difficulties to the teacher (Brint, 1998). Within our revised structure, the teacher is not the ultimate content authority. Rather, teachers serve as facilitators, working with students to prepare them for chapter assessments. The resulting relationship is less authoritarian and more consistent with the collaborative ways that Cheyenne elders instruct Cheyenne youth (Northern Cheyenne Follow-Through, 1980). Two years of preliminary data indicate that these revisions facilitate student enrollment and success (see Figure 1). While enrollments at CDKC and in college-level mathematics remain steady, pre-college enrollments have significantly increased. Moreover, the percentage of students successfully mastering pre-college mathematics has also increased. Prior to 2004, approximately one-third of the students enrolled in a pre-college course received a C or better. During the first year of computer-based instruction (AY 2004-05), 50% of those in a pre-college course received a C or better. In fall 2005, the pre-college courses were reorganized into the Math Seminar, and 85% of those enrolled successfully completed at least one section of the seminar. Though one section is only comparable to approximately one-third of the material in a traditional pre-college course, students passed each section at an 80% proficiency level and demonstrated increased mastery of the mathematics. 

Figure 1. Pre-college enrollment and success.  Students also perceive the revisions favorably. A recent survey (Brown, 2005) indicates that 73% of the students evaluated their math classes positively, and half view the Student Learning Center as “very helpful.” Students are also positive about faculty availability and the revised instructional approach. Seventy percent indicated that revised courses “did a good job of covering material,” 55% viewed course assignments as appropriately related to course objectives, and most reported that they were “confident” approaching instructors and discussing mathematics with others.


While preliminary results are encouraging, our approach is not flawless. Brown’s survey, for instance, revealed some frustration with the rigidity of the software. Likewise, although an increased percentage of students make “adequate” progress, many take more than one semester to complete each section of the seminar. Still, increasing numbers of students are succeeding and convey satisfaction with pre-college mathematics. For many, mathematics is no longer an impenetrable barrier but one step toward educational success.

Acknowledgements: This work was supported by the National Science Foundation. The ideas are those of the authors and do not represent the views of the National Science Foundation. Bob Madsen is a science instructor at Chief Dull Knife College ( Ted Hodgson is a professor of mathematics  at Montana State University (Bozeman, MT, Carol Ward is an associate professor at the Brigham Young University Sociology Department (Provo, UT,


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