

TALKING CIRCLE DEPARTMENT
Pathways to Success in PreCollege 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.)
Introduction
Like most tribal colleges, Chief Dull Knife College (CDKC,
Lame Deer, MT) offers a sequence of precollege mathematics courses – Basic
Mathematics, Introductory Algebra, and Intermediate Algebra – to assist students
who lack collegelevel skills. Unfortunately, 6070% 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 precollege mathematics. Those enrolled must be able to pass, and
those passing must emerge with collegelevel 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 outofclass support, and promotion without content
understanding. To address the first two problems, we tested each entering
student on precollege 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 
Fractions 
Variable Expressions 
Polynomials 
Decimals 
Linear Equations 
Factoring Polynomials 
Ratios and Proportions 
Inequalities 
Quadratic Equations 
Percents 
Graphing Equations 
Rational Expressions 
Integers 
Functions 
Radical Expressions 
Table I. Precollege 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, lecturebased approach to the precollege 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 computerbased problems.
Correct work allows students to quickly progress. Those that struggle, however,
can view worked examples, reread 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 computerbased 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. Preproject 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 precollege course. Students enroll in a section, based
upon their placement scores or prior work, and receive credit for making
“adequate” progress. They may reenroll in any section to complete the seminar.
Thus, students receive seminar credit until they are prepared for collegelevel
mathematics.
Project Impact
Combining computerbased 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 selfpaced 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 FollowThrough, 1980).
Two years of preliminary data indicate that these revisions facilitate student
enrollment and success (see Figure 1). While enrollments at CDKC and in
collegelevel mathematics remain steady, precollege enrollments have
significantly increased. Moreover, the percentage of students successfully
mastering precollege mathematics has also increased. Prior to 2004,
approximately onethird of the students enrolled in a precollege course
received a C or better. During the first year of computerbased instruction (AY
200405), 50% of those in a precollege course received a C or better. In fall
2005, the precollege 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 onethird of the material
in a traditional precollege course, students passed each section at an 80%
proficiency level and demonstrated increased mastery of the mathematics.
Figure 1. Precollege 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.
Conclusions
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 precollege 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 (bmadsen@cdkc.edu). Ted Hodgson is a professor of mathematics at Montana State University (Bozeman, MT, hodgson@montana.edu). Carol Ward is an associate professor at the Brigham Young University Sociology Department (Provo, UT, carol_ward@byu.edu).
References
Brint, Stephen (1998).
Schools and Societies. Thousand Oaks, CA: Pine Forge.
Brown, Bertha (2005). Math Evaluation Report: 2005 Spring Semester. Lame
Deer, MT: CDKC Internal Document.
Carpenter, Thomas & Rich Lehrer (1999). Teaching and learning mathematics with
understanding. In E. Fennema & T. Romberg (Eds.), Mathematics Classrooms that
Promote Understanding (pp. 1932). Mahwah, NJ: Lawrence Erlbaum.
Herriott, Scott (2005).
College Algebra Through
Functions and Models.
Belmont, CA: Thomson
Brooks/Cole.
Northern Cheyenne FollowThrough (1980). U.S. Department of Education Proposal.
Lame Deer, MT: CDKC Internal Document.
Small, Don (2004).
Contemporary College Algebra:
Data, Functions, &
Modeling. Columbus OH:
McGrawHill Primis Custom Publishing.
Wright, D. (2005). Introductory and Intermediate Algebra. Charleston, SC:
Hawkes Learning.
Wright, D. (2006). Basic Mathematics for College Students. Charleston,
SC: Hawkes Learning.