FFew practitioners have such strong historical overview and such consistent participation in the Massachusetts ABE curriculum frameworks development process as Barbara Goodridge does. I had the opportunity to interview Barbara about how her participation in developing, field testing, and using the Massachusetts Adult Basic Education Curriculum Framework for Mathematics and Numeracy has affected her classroom practice.

Barbara's experience in teaching math spans many years; she started off with junior high kids in the Lowell public schools. Eleven years and one sabbatical later (during which time she obtained a degree in counseling), Barbara made the transition to teaching adults at Lowell Adult Education Center. She has been there ever since.

Some History
About ten years ago, a committee of ABE math teachers, convened by Mary Jane Schmitt, began to meet. Their task was to envision the math curriculum frameworks content and structure by thinking it through together and by bringing what they knew to the table. Smaller subgroups worked on developing emerging content areas: number sense, geometry, data and statistics, algebra . Participants brought different skills to the process and worked from their strengths: some contributed concrete lesson ideas, others stepped back to help design overall structure, and one person assumed the task of proofreading to maintain consistency throughout the document--among and between all the content areas.

Barbara has been involved in the curriculum frameworks process throughout-from brainstorming initial content to editing the final version posted online in 2005. The original frameworks, a highly collaborative effort, resulted in a content-rich, useful document that can help teachers with many aspects of their classroom practice. Over the summer of 2005, Barbara, along with Drey Martone of UMass and Jane Schwerdtfer of the Massachusetts Department of Education, edited the frameworks to make them fully aligned with the newly designed Math Assessment scheduled for release in July 2006.

I asked Barbara how her involvement in the frameworks development affected her teaching. "We were a group of teachers who got together to address what we thought should be done, " she said, adding that "working on the frameworks and creating the document was also an exercise in developing more awareness through the exchanging of ideas."

As Barbara spoke, it became clearer to me that developing the frameworks was its own kind of professional development. In this case, a group of "knowledgeable peers," guided by a leader in prevailing math practices, shared and expanded their knowledge base, and crystallized and deepened their belief systems about teaching math.

"The frameworks reflected what we were interested in," Barbara noted. "For example, one of the habits of mind is developing curiosity. One of the learner questions is 'Do you ask yourselves why this is done?' We wanted to given students an opportunity to question why they were doing something, because we believed that when you understand why, you understand in a deeper way."

Many students initially resist "asking why," Barbara noted. "Just tell me how it's done," students say, "so I can pass the (GED) test." But often this initial resistance softens when other students articulate why they did something a certain way, or when other students express a desire to understand the why of solving a problem a certain way. Since some of the habits of mind are so new to students, it is important to remember the value of patience, and to trust the process, Barbara noted.

Stepping Back: Examining Enabling Skills
"Writing the frameworks was a challenge for me," Barbara admitted. "Especially when I had to step back and think about the enabling skills-that is, what do students have to know already before I can teach them something like percents? I remember in my first weeks of teaching junior high math, I was supposed to be teaching fractions and percents, according to the math text. Then I saw that the students couldn't even do long division. I went to my principal and told him. 'So teach them long division!' He said. I said: "I don't teach long division! I teach fractions and percents."

"Of course I did have to teach them long division. But then, there is so much a student needs to know in order to do long division! In fact, I had to teach subtraction and multiplication which are the basis for the traditional method of long division. I had to look at those enabling skills, too and go back as far as I could."

"So, working on the frameworks helped me to step back a little more and see a broader scope in teaching math. We had to look at students' background knowledge carefully. Tricia Donovan and I worked on the Statistics and Probability strand. Trisha was good at asking what we were assuming about what students brought with them to the classroom and checking the accuracy of our assumptions."

Barbara noted that the leadership of the process, largely provided by Mary Jane Schmitt, provided a world view and theoretical underpinnings about math teaching to the process.

"Mary Jane shared models from the UK, the Netherlands, Australia," she said. "She and Esther Leonelli have an active connection to the National Council of Teachers of Mathematics and the Adult Numeracy Network (ANN)."

"Even though we thought research and looking at other models was important, we all agreed that whatever framework model we came up with, we wanted it to be useful to teachers."

Safe and Challenged
Barbara's background in counseling came to bear on aspects of the frameworks development process. "When we defined the levels,"she said, "we didn't want to overwhelm students, but we did want to challenge them. We wanted to present them with something more than what they thought they might be able to do. I was always interested in the 'safe' part of teaching and learning," Barbara said, "but I wasn't always as challenging as I could have been. Working on the frameworks renewed my interest in challenging students without pressuring them. The challenge part became a more explicit value for me as we wrote the frameworks."

"Developing the frameworks has helped me see that there is more than one way to get to where you are going," Barbara pointed out. "I didn't learn math with a visual component. I have had to try and think, 'How can I make this concrete?' I get excited when I see it and I try to do more of that. I see that manipulatives are OK. In one lesson, I gave students a problem on perimeter and area and they had a certain number of tiles to solve the problem. One student left early, and took the problem with him. But he solved the problem by drawing the tiles rather than having the actual tiles. That was great."

Persistence
"One of the habits of mind in the frameworks is persistence," Barbara said. "I'm still exploring persistence. Math is so easily the subject where it's do or die — I can get this or I'm quitting — instead of 'I'll stick with it.' I think more about what kind of atmosphere to create or allow where students are encouraged to persist.for example, one student who normally gives up easily is highly determined when we work on a puzzle.I try to help students think "I believe I can" when it comes to solving math problems, and for this student, I encouraged her to think of math as a puzzle."

Open enrollment tends to work against a safe and challenging environment. Barbara noted that she always tells students on the first day that the rest of the class has been working on the area in math for some time, so they shouldn't feel overwhelmed; they should try and be patient and they will eventually catch up. It is clear that Barbara takes the "safe and challenged" perspective to heart as she employs these approaches to including students of all levels into doing math.

Overlapping Levels
Barbara repeated that the group working on the frameworks had to examine their assumptions over and over again about different aspects of teaching and learning. This reexamination process showed up when the group decided to create overlapping levels. "The overlap in levels is deliberate and fluid," Barbara noted. "In Statistics and Probablilty, for example, there are eight benchmarks in level 1. In level 2, we repeat some of the benchmarks verbatim, but expand others, then expand into the third level. We cannot assume that a level 4 math teacher is going to read levels 1, 2, and 3, "she said, "so we we repeated many benchmarks in the level 4 section. We felt that the skills in those earlier levels bear repeating. By having them written out, it's a reminder to teachers."

The 2005 version of the Frameworks includes assessment notes to specify the level at which a benchmark is assessed. If a benchmark is repeated in Level 3, but assessed at Level 2,that is indicated by a note in the Level 3 benchmark. This safeguard, "Barbara explained, "allows teachers to look behind for review and ahead for challenge without requiring the students to master skills that are beyond their instructional level.

Role of the Teacher
The math curriculum frameworks emphasizes, as prevailing math pedagogy does, that there are many ways students can solve problems. "When I taught in junior high, I believed the teacher is much more in control of leading the student to the right answer," Barbara noted. "I led the students to where I wanted them to go." Through working with the math team and working on the frameworks, I learned that students might get there another way, and that's a habit of mind, too. As an ABE teacher, I was doing that more and more (encouraging a variety of routes to the answer.)." I asked Barbara if it was scary to teach that way. "At first it is," she said, "but once you know and the students know you don't have to have all the right answers, it's not as scary. My students tell me I can make one mistake every day, and two is getting carried away."

The Value of Peer Investigation
"Mary Jane was always talking about the teacher as learner," Barbara said. "That kind of awareness was clear as we worked as a team to develop the frameworks. We had to step back, articulate our beliefs and approaches, and share ideas." This process sounded a lot like the environment teachers want to encourage among students, I suggested, and Barbara agreed. "Creating the frameworks and using them with other teachers can re-excite you," Barbara said.

It is obvious that Barbara is guided by the habit of mind connected to curiosity. She noted that she experiences the same excitement that came with the group of practitioners developing the frameworks as she does when she works with the Math Group that centers the Massachusetts ABE Math Initiative. (Editor's note: Go to the SABES Web site to read more about the ABE Math Initiative.) "Part of the meeting is to do math together," Barbara explained. "It's fun, and it enhances teaching. We share how we solved the problems and we look at the different approaches people use. Using different ways to get to an answer is also a habit of mind in the frameworks," Barbara noted. "I leave these meetings with my colleagues charged. When we first got a problem it seemed too easy. Then I saw that we came up with eight different ways of solving the same problem! When we were required to solve it in more than one way, it was challenging. I solved it my way then puzzled out another way to do it, one that didn't come naturally. I had to back into it."

My interview with Barbara left me jazzed about teaching and learning in much the same way that she described being charged as result of her participation on developing the curriculum frameworks and in participating in the math team. I can't help but wonder if I would have been less math phobic in my school days with a math teacher like Barbara who had access to a set of guiding principles like the math frameworks, The next time I pick up the math (or any other) of the Massachusetts Curriculum Frameworks, I will be more open to absorbing the energy, creativity, logic, and passion that guided the writers along the way.

Barbara Goodridge teaches math and social studies at the Lowell Adult Education Center in Lowell, Massachusetts. She can be reached at: bbgood2000@yahoo.com