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Math Focus Group Study
For some years American leaders and educators have noted the decline in the degree production of the so-called STEM disciplines, sciences, technology, engineering, and mathematics. Indeed, as one article suggests, China and other developing countries may be producing more graduates in the STEM disciplines than the United States. Over the long-term the decline could jeopardize American leadership in research and development, with further ramifications regarding our global competitiveness and standard of living.
Introductory college Math courses may pose a particular barrier to graduation in the STEM disciplines. College level algebra, trigonometry, and calculus courses are often considered as “gateways” to bachelors and higher level course work in these four disciplines. Unfortunately, numerous studies have shown that students coming to college are poorly prepared to succeed in introductory Math courses such as algebra. Nationwide, success rates in introductory Math courses are notoriously low. Many who fail these courses refuse to re-take, and move off into other majors and programs which have little or no Math component. Still other students delay taking these gateway Math courses until later in their college careers, delaying progress toward a STEM or other degree requiring some Math.
At the College of the Sequoias MATH-360 is the barrier course for most students. This course is entitled “pre-algebra.” It is four units or credit hours in scope. If passed, the units earned are not associate degree applicable. Upon successful completion of MATH-360 (with a “C” or better) or eligibility determined by COS placement exams, the student may then take MATH-200 or MATH-205, “elementary” and “beginning” algebra courses.
Table 1 below shows the placement rates for “first time” students at the College of the Sequoias. (First time students are those who, upon admission, indicate that they have not attended college before.) For each of the terms approximately 75% of the students who took the Math placement test tested into a pre-college-level mathematics course or were “required to see a counselor.” Only 25% of the students placed into intermediate Algebra or above. (Note: students entering a number of vocationally-oriented certificate programs are not required to take the placement test.)
Table 2 below shows the rates of success in two Math courses, Math-360 and Math-200 over several semesters. (Students who earned a “C” or better in the courses are considered successful.) In Fall, 2005, 47% were successful. In both the Fall 2006 and Fall 2007, however, only 35% of the students who attempted Math-360 were successful, underscoring the notion that Math-360 is a barrier to future Math success.
Planning and Research conducted a mini-study to determine if students unsuccessful in Math- persisted and enrolled in a higher level Math later in their college careers. Table 2 shows that 363 students were unsuccessful in Math-360 in Fall, 2006. Of this number only 61 enrolled in a higher level Math class over the next five semesters, a rate of less than 17%, as shown in Table 3.
Table 1 – Placement Tests Results in Math
Fall, 200 6 Fall, 200 7 Fall, 2008 TOTAL See Counselor 82 4% 85 4% 85 3% 251 4% Math 360, 361, or 365 884 42% 889 41% 950 38% 2,69 1 40% Math 200, 201, or 205 637 30% 631 29% 772 31% 2,004 30% Math 230 or 235 275 13% 324 15% 365 15% 937 14% Math 21, 45, 110, or 154; or Bus 20 or 19
184 9% 194 9% 256 10% 609 9%
Math 61 or 75 29 1% 31 1% 36 1% 91 1% Math 70 26 1% 30 1% 53 2% 102 2% Total 2,117 100% 2,184 100% 2,517 100% 6,685 100%
Table 2 – Success in Key Math Courses
Fall, 2005 Fall 2006 Fall 2007 Fall 2008 Success No S. Success No S. Success No S. Success No S. Math- 200 403 449 317 459 361 457 357 539 % 47 53 41 59 44 56 40 60 Math- 360 234 308 191 363 180 287 197 337 % 43 57 34 66 36 64 37 63 Total 637 757 508 822 540 744 554 876
Table 3 – Unsuccessful Math-360 Students in Fall, 2006 Who Attempted
Higher Level Math Classes in Subsequent Terms
Spring 2007 Summer 2007 Fall 2007 Spring 2008 Summer 2008 TOTAL MATH 230 0 3 9 13 4 20 MATH 205 1 0 1 0 0 2 MATH 200 35 8 21 16 6 59 MATH 021 0 0 1 1 1 3 MATH 010 0 0 0 1 0 1 Total 36 11 29 30 11 61
Despite this gloomy picture, students are testing into Math-360, taking it (often more than once), ultimately successfully passing it, and taking higher level Math classes. What can we learn from their experiences which might raise the success rate? What has helped these students to succeed?
With the support of the President and Math Department, the Office of Planning and Research undertook a qualitative research project to help determine the answers to these questions, from the perspective of our students. An overview of the project process and findings of the project are below.
Project
In March, 2008, the Office of Planning and Research conducted a search of the student database to identify students who met the following criteria:
- The student tested/placed into MATH 360;
- Everyone is expected to contribute to the discussion;
- Focus on what helped in Math 360…stay positive;
- Do not mention faculty or other names at any time;
- What is stated in the focus is not to be repeated later.
The topic “success in Math 360” is a broad one. Realizing this, the Office of Planning and Research and the Math Department developed four “sub-questions” to assist the facilitators and participants to pace the discussion through the hour:
- What one thing did you do personally which helped you succeed in Math 360?
- What one thing did a Math 360 instructor does which was instrumental to your success?
- What role, if any, did the Math lab play in your success?
- What one thing would you recommend to MATH 360 students in order to succeed?
Often the facilitators chose to use the four “sub-questions” to divide the hour long sessions into 15 minute segments, the last question becoming a wrap-up.
Analyzing the data
The Office of Planning and Research analyzed focus group success and the data in two ways. First, several days after the final focus group session, the facilitators and the Planning and Research staff met for a morning to “debrief.”
By all accounts the focus groups were successful. Those at the debriefing felt participants appeared to freely state their views, respect other views, and address the topic and the sub-questions in a forthright manner. Many participants shared quite personal moments of success and break-through. At no time in any of the sessions were names mentioned, all contributed, and the sessions were positive in tone.
At the debriefing the facilitators and staff then took time to organize the focus group discussions into themes or theme-areas. For example, in each of the focus groups there were numerous comments about “homework” and its importance to Math 360 success. Other theme-areas included scheduling, the role of study groups or study “buddies,” how a class session is organized, and the importance of “flexibility” to success.
Finally, the facilitators and staff reached consensus perspectives on each theme-area, and a consensus on the project’s central finding. These are discussed below.
As a second analysis step, the staff of the Office of Planning and Research transcribed each of the five focus group sessions from the recordings. This was an extremely time-consuming, labor-intensive task. Because of audio quality, length of statements, and other factors, the transcriber sometimes had to “interpret” and paraphrase the student on the tape as best possible.
Central Findings
Some 18 to 20 year old students attending college have the experience and self-discipline necessary to succeed in a relatively unstructured collegiate environment. They attend class, take notes, study those notes, do homework on their own, go to the library well before an assignment is due, study for exams, and organize. Although it might be vague, these students each have a view of their future; hence has a semblance of a plan for their academic careers.
Often older students returning to college bring with them a confidence and discipline stemming from their work and home experiences. These students may lack some self-confidence having been out of the educational environment for a period of time. However, responsibility gained from holding a job, managing a budget, raising children, and organizing daily time and tasks, often compensate for the lack of academic self-confidence.
If the 42 students participating in the focus groups are representative, many students enrolling (and often re-enrolling) in Math 360 at COS are not the “mature,” self-disciplined learners described above. In fact, many of those participating in the focus groups had failed or dropped the course at first, only to come back for another try. The important, underlying theme evident in the focus groups was the need for structured learning. Students felt they succeeded when:
The class syllabus was clear, and there were no deviations from the schedule day-to-day;
The class hour was structured the same every day. (For example, the first 15 minutes for reviewing and grading the homework and answering questions, the second fifteen… and so on);
Time and time again students mentioned that problems (and problem-solving) need to be broken down into steps;
Homework should be mandatory, reviewed in class, and graded, otherwise students will not do it;
Conversely, providing options and alternates – while it may be appealing to a mature learner -- apparently may not lead to success in Math 360:
o Providing a variety of ways to solve a problem may confuse, rather than help, a number stated;
o If attendance is not taken students do not feel the need to come;
o If the Math lab is not required or attendance enforced, many students do not use it.
In summary, the Math 360 focus groups held during Spring, 2008, indicate that many students entering the class are not self-disciplined learners. Instructors can help their students succeed by provide the discipline and structure needed.
Group work “My mother took 360 at the same time. We couldn’t study together much, though, because her teacher taught her differently and we studied different things at different times.”
Math Lab “Teachers could make the MATH lab mandatory, but it is really best if the students learn the stuff in class.” “I found several of the software programs helpful, but the tutors taught different ways to solve problems. That confused me more than helped.”
Time to study “After flunking MATH 360 two times, I realized I could not pass it without setting aside two hours every night to study – in a quiet place where I would not be disturbed. I studied from 12 midnight to 2 am. Now I can pass anything.” “360 instructors must tell the students that they have to set aside time every night to study. Otherwise students think they can play. This isn’t high school.”
Dealing with troublemakers “What helped me was the teacher throwing disruptive students out of class and dropping them. It gave the rest of us time to review the homework.” “What every Math 360 teacher should do is have someone who passed MATH 360 come talk to the class about what to do, how to study and spend the time. I would do it. I would tell the bums just to drop out right now and come back and take it when they were older.
