Preparing Students for College-Level Math
Portland Adult Education (PAE) is the adult learning division of the Portland Public Schools. In existence for over 150 years, the program now serves over 6,000 students a year with an array of academic, vocational, and enrichment courses. PAE’s academic program consists of English for Speakers of Other Languages (ESOL), basic- through college-prep-level reading and math, adult high school diploma completion, and GED preparation and testing.
In January 2003, with support from the New England Literacy Resource Center and funding provided by the Nellie Mae Education Foundation, PAE launched an ABE-to-college transition program, the College Connection Certificate Program. The program includes skills assessment and testing, academic counseling and support, and classes to improve basic academic skills. To be eligible for the program, students must have a high school diploma or GED.
PAE has a four-member math faculty and offers Math Basic (ABE level), Consumer Math (basic computation skill development and application), Math Concepts (GED prep/pre-algebra), Algebra A and B (to prepare students for the college entrance exam) and Math Brush-up (a computer-based lab option that covers basic math through algebra). The focus of this Promising Practice is Algebra A and B.
Rationale and Background of the Practice
To prepare students for college-level math, I use an array of strategies in my Algebra A and B courses. When I first started as an adult-education math teacher, I actually had a student lie down on the floor because she was so stressed out by the math. Math anxiety like that has been around for a long time. I want to break down that level of anxiety and help students make a transformation.
But it’s more than the math. They need to learn to be good students, meaning they need to learn how to take notes, be organized, come prepared. We would find that if someone came and just passed the GED and went on to college, they weren’t successful because they weren’t prepared to be college students. Students need to know how to work in groups, and how to network and advocate for themselves. If you can’t ask a question when you get to college, you’re sunk. When students challenge me and say they have another way of doing a math problem, I know they are ready for college.
I’ve been teaching math for 20 years but I still keep going to workshops, learning whatever I can to really help students learn. I read all kinds of research and, lately, I have been focusing on the research on brain-based learning. I still turn to K-12 research because there is not a lot on adults yet. But I really want to focus on adult learners, so I read the information coming out of Australia and Great Britain, where more research has been done. I go to as many workshops as possible. One turning point for me was encountering Marilyn Burns’s Math Solutions organization,which is when I started to see the importance of using manipulatives.
Description of the Practice
I have two main goals for my classes:
- students will really understand the math they are doing, and
- students will be successful in college.
These are specific strategies that highlight my teaching approach.
Make Students Comfortable
My first strategy is the way I approach the student when I first meet them. I want to make students comfortable, and that starts as early as the placement test. I interview each student and let them know that the placement test is not the be-all and end-all of who they are as a student. It is only a guide for me, so I know what skills they have.
I also work to break down barriers by laughing, building rapport with students and getting them to talk with one another. At the first class meeting I have students pair up and do Peer Interviews. I might pose a lead-in question like, “It was the best of times and it was the worst of times…” and students share a best time and a worst time in their experience with math. This helps students know they are not the only ones that have had problems in math.
At that first meeting we also do a Goal Setting Activity. This activity is based on John Comings‘s research on learner motivation and retention and my own study based on his work. I ask students, “What keeps you coming? What are the barriers that might get in your way?” And, I also have students do a Learning Styles Inventory.
To read more about Pam’s research, see The Effects of Continuous Goal-Setting on Persistence in a Math Classroom on the National Center on Adult Learning and Literacy website.
Math Murder Mystery
Another activity that I do at the start of each course is a game in which students are given 26 clues and they work in small groups to solve a mystery. It is called the Math Murder Mystery and, like the board game Clue, the students have to identify who the murderer is, the time of death, the murder weapon, the motive, etc. After they share their solution and defend their decision, we then discuss what this has to do with problem solving. There is actually some math involved, but it is mostly designed to get students talking with one another and comfortable in the class. Building a community helps students ask questions because the questions can come from the group rather than a single person.
I do hands-on Labs that I would describe as more like inquiry-based learning. Instead of saying, “A base raised to a zero power is…” students come up with the rules. I ask them, “What did you notice? Why do you think this happens?” See the worksheet for this lab. I try to think of some kind of a hands-on application for each main concept I cover. We do about one lab a week, which means a total of 10 or 11 labs per course. The labs take time, but the whole staff says, at the end, that it was worth the time. Students say that the labs really helped them understand the math. Sometimes in Algebra Part B the math is more abstract and it’s harder to develop a lab. Working with graphing calculators gives you that same effect because students can just try different numbers and see the results.
No matter what the level of math, I have students do Journaling in all my classes. In their journals, students reflect on their learning process, developing their critical thinking. The students really work hard on the journals and I find they are especially difficult for non-native English-speakers. To help with the journals, I developed a rubric [Word] of what I want them to write, but they don’t have to follow it exactly. Sometimes I give students a sample of an exemplary journal. Although it is time consuming to respond to every journal, I am constantly giving and receiving feedback.
The journal has four parts. I start with a question that has to do with a specific concept.
- Explain (or compare, etc.) the specific concept.
- Give an example of the concept.
- Connect or apply the concept to real life.
- Write one or two sentences about how the class is going for you.
After students write an explanation of the concept, I have students give an example so I know they understand the concept. The connection to real life is harder. Sometimes it can be more of an abstraction than an application. For example, one student explained that the number line reminded her of playing the piano—the right hand was the positive integers and the left hand was the negative integers. I use the information from my students’ Learning Styles Inventory, which I keep on an Excel spreadsheet, so I can point out in my response just how their learning styles are reflected in their journals. The students feel that I have taken the time to really focus on who they are as learners.
Quizzes, Tests, and the Final Exam
I give quizzes once a week. The quizzes are scaled so that the lowest grade is a “D.” I tell students, “No one is going to fail a quiz.”
Students have three or four take-home tests because I just don’t have two hours of class time to dedicate to each test. I was very worried in the beginning, but students know they are in school to learn and copying has not been a problem.
The final exam is given in class because they do have to have that experience, too. The final is untimed (as is the college placement test) so that students have a chance to show what they know. If students are in Algebra Part B, they take the computer-based college placement test, the ACCUPLACER, which we are allowed to administer at PAE.
Evolution of the Practice
Over time, the strategies I use have changed and the work keeps evolving. For example, the whole idea of the labs changed from an informal activity to something formal. A recent change is the introduction of graphing calculators. We teach students to use them so they are prepared for college. Traditional students have been using graphing calculators through four years of high school. Lastly, the ACCUPLACER has changed what I teach. For example, I make sure students practice problems with fractions because it is an area on the ACCUPLACER that tends to trip up adult students.
The big issue, I think, is teacher preparation. To teach at this level of math, you do need a strong math background. Some teachers come with no math experience; some have an elementary school background and have not taught algebra concepts. Yet, some teachers with elementary backgrounds do well because they have a better feel for interactive strategies. I am especially concerned that teachers may pass on their own math anxiety or misconceptions.
Another challenge is time. Students could use more time preparing for college-level math but they have goals they want to reach and need to move on. Recently, our program has seen more direct competition with community college developmental math programs. When my students finish Algebra Part B, they still have to take the ACCUPLACER to prove competency in math. Students who complete developmental math at the college don’t have that hurdle. If they pass the developmental course, they go into college-level math.
An emerging challenge is that younger students who have done most of their math with calculators have very little experience with computation. Many have forgotten how to divide, but they can pick it up again. I tell students that even concert pianists practice their scales.
Cost and Funding
The major expenses for the students in the program are the course fee ($40 per course) and the textbook (about $65), although they can use the same book for both Algebra Part A and Part B. There is a fee waiver for students if they need it. In addition, good math resource materials or equipment, like graphing calculators, can be expensive for students and programs. However, this is much less expensive than the cost of remediation in college.
For programs, the primary cost is related to professional development so that math teachers have the time and resources to develop engaging teaching strategies. The PAE administration has been very supportive and the Nellie Mae Education Foundation has provided a grant that underwrites the College Connection program, including professional development activities.
Evidence of Impact and Effectiveness
We have two ways we currently evaluate our effectiveness. The first is how our Algebra Part B students do on the ACCUPLACER and the second is ongoing feedback from students. PAE recently conducted a phone survey of our transition students that showed 86 percent of Algebra Part B students passed the ACCUPLACER to place into college-level math. This may take two tries for some students because the test format is still fairly new to them. This rate of success compares favorably to a national study in which 34 percent of first-time freshmen at two-year public colleges took remedial math.**
Implications for Practice, Policy, and Research
The main implication for practice is the need for strong professional development in the area of math instruction. The Adult Numeracy Network (ANN) is one source for information and collegial sharing. The goal of the ANN is “to share the joys, challenges, problems and insights in the teaching and learning of important math and numeracy skills for adults.” The ANN website includes a variety of resources. Networks, like the ANN, are especially important as a method of supporting teachers who have few math colleagues and/or fewer students ready for algebra.
In terms of research, we know quite a bit about how adults learn to read but very little about how adults learn math. How does an adult learner finally make that breakthrough on a math concept?
**According to a study by Boylan and Saxon, 34 percent of first-time freshmen at two-year public institutions took remedial math in Fall 1995.
Pam Meader, Math Instructor
Portland Adult Education
Pam Meader, a former high school math teacher, has taught math in an adult basic education setting for more than 20 years. She has been NCSALL’s Practitioner Research and Dissemination leader for Maine and is the current president of the Adult Numeracy Network (ANN). Pam’s textbook, Math for All Learners: Algebra, is available from a variety of online retailers.