Teachers Investigating Adult Numeracy (TIAN) is a national four-year project that brings ABE math teachers together to strengthen their practice. This year, 40 teachers—20 in Massachusetts and 20 in Ohio—are participating in the first year pilot. In Massachusetts, SABES is helping to facilitate the project.

Conducted as collaboration be-tween the Center for Literacy Studies at the University of Tennessee and TERC, in Cambridge, Massachusetts, TIAN's main goal is to develop a model for standards-based mathematics in-service professional development for ABE teachers. The model, which uses teacher inquiry and reflection, en-gages teachers in learning how to design and implement purposeful and effective standards-based mathematics instructional approaches to algebra and data analysis. (See the last issue of Field Notes for more information about TIAN.)

Connections to Massachusetts Math ABE Framework
The TIAN Project has used several activities to encourage connections with the state standards. In Massachusetts these are the Massachusetts ABE Curriculum Frameworks for Mathematics and Numeracy. For example, in fall 2005, TIAN offered the first intensive in-service institute for TIAN participants. At the end of the two days, participants broke into small groups to review and become more familiar with the Frameworks. Each group took one of the ABE instructional levels identified in the Framework and identified the benchmarks they had covered, through a variety of activities and readings, during the two days of the institute. Then the small groups reported out to all the participants. This activity was effective because it used a well-founded approach to aiding comprehension: reading for a specific purpose.

After the first institute, teachers left with some lessons on graphs and data to try out in their classrooms. When they returned for the second institute in February 2006, the first thing they were asked to do was to select one of the core concepts from the Framework and to write how they saw that concept come alive in their classes since the last institute.

Below are excerpts from the teachers' reflections. (Editor's note: Many teachers refer to specific math activities and lessons by name. Teachers can find these activities in EMPower in the unit "Many Points Make a Point: Data and Graphs." Key Curriculum press.

Teacher 1: Group work was an area that challenged my students. This is my GED, they would ask, Why do I need to work in a group? In the lesson "Displaying Data in a New Way," students were able to speak about the foods most frequently eaten (by referring to) mathematical comparisons. Most of us, some of us, ¼ of us, 50% of us eat a certain food, for example.

Teacher 2: The lessons involving collecting data and making graphic representation really helped the students see the relationships between information, frequency graphs, bar graphs, and then circle graphs. I saw students who had struggled with answering questions about graphs develop confidence and skill from making their own graphs from information we had collected in class (clothing and food.) Since attendance is erratic and students join class at any time, students who have been in class are able to share their knowledge with new students and help them. For example, with the paper plate activity, a student who had previously had trouble with math explained to a new student how to represent the percentages on her plate. Another student explained the step-by-step process of making the circle graphs displayed in the classroom.

Teacher 3: The time in class where we interacted, discussed, (argued), the most was when we did the "Sketch This" activities. The students had never told stories by graphing, and there was a lot of disagreement and coaching going on about what labels should go on the graphs (this was the Giselle/Marathon/Stocks activity) and where on the y-axis the "story" should begin. Although it was very difficult at the beginning, and very difficult for me not to give the answers, by the end of the activity three of the students were able to retell the story while following the graph on the wall.

Teacher 4: In doing the "Clothing from our Closets" unit, students worked cooperatively in gathering data. We used our frequency graph as a group to generate numerical statements about our graph. We made statements about both our country and our continent graphs. Some students did not realize so many items came from China. Some people set up fractions to find what percent of clothing came from a particular country. I think the core concept came alive in the hands on activities in a group setting. They were able to articulate the stories that the quantities told. During the "Countries in Our Closets" unit, students were engaged from the start in terms of predicting geographic clothing manufacturing patterns. Situating mathematical concepts, like distribution, ratio, fractions, and graph making, within other contexts like political power relations, geography, capitalism, and corporate cultures helped build a case for the usefulness of math as knowledge in local and larger contexts. Students' predictions about clothing manufacturing countries validated their intuition and thinking. As students drew graphs comparing continents and measuring data according to different criteria, they asked questions of each other that covered proportion, visual data, and non-mathematical topics.

Teacher 5: Two students used the Crime Watch data to create a bar graph for the midpoint assessment. They had a very animated discussion about how they would display the information. Both participated equally and the end result was a well-designed graph with a color key and an excellent display of the information. Theirs was probably the best group effort I've seen in my classroom.

Teacher 6: During the "Countries in Our Closets" unit, students were engaged from the start in terms of predicting geographic clothing manufacturing patterns. Situating mathematical concepts, like distribution, ratio, fractions, and graph making, within other contexts like political power relations, geography, capitalism, and corporate cultures helped build a case for the usefulness of math as knowledge in local and larger contexts. Students' predictions about clothing manufacturing countries validated their intuition and thinking. As students drew graphs comparing continents and measuring data according to different criteria, they asked questions of each other that covered proportion, visual data, and nonmathematical topics.

Teacher 7: My student was able to draw a graph with a title, labeled axes, and form. This graph was of her life. It told a story of when she felt happy and when she felt sad. Under the graph she wrote a story explaining the up and down periods. This was an example of mathematical thinking in the real world.

Teacher 8: When we were in Lesson 5, "Sketch This," a few of my students described the busy and slow periods of their workplaces, Dunkin' Donuts. They gave information to the class regarding the number of people served in a normal workday from 5 a.m. to 5 p.m. We graphed the data and then discussed why there were peaks and valleys, how many workers were needed at which times, when workers would take breaks, etc.

Teacher 9: One thing that pops into my head in thinking about connections is when we were doing the line graphs. We were doing the lesson with the stories and graphing the stories. I started with a general discussion about line graphs; students knew about them, but no one was getting the idea about line graphs representing the concept "over time." The graphs they were drawing were too finite. We were looking at the graphs and listening to the story again. Then, suddenly, one of the students, who is on the lower end of the ability range, had the "aha." He got excited and realized we needed to show time passing by keeping the line straight. He went up, fixed the graph, and the discussion changed at that point-they started to get it. I think the graphs at that point started to take on more meaning when I reread the stories. The next set of drawings was much more accurate.

Teacher 10: During the categorizing activity (Practice: Thirsty) there was an extended discussion around the proper placement of drinks into categories. Students started out by wanting to create only two categories-the most obvious (hot and cold). The first student who showed me his work was dismayed when I asked if any of the drinks could fit into both categories. He decided he needed to go deeper-find more and better categories. All the students heard us and after a collective groan began a lively discussion about various ways to categorize. They started breaking down the ingredients in the drinks and discussing health merits of each and even cultural preferences. Then they decided how to break things into groups depending upon the criteria they each felt was most logical for the task.

Teacher 11: An exciting moment .came when students were working in pairs to draw graphs based on stories ("Sketch This"). It was eye-opening and fascinating to see how different pairs made decisions and communicated/negotiated how they would create these graphs. The process and dynamics which emerged from each pair was interesting, but also what elements they choose to focus on in representing the stories in graph form was very rich. Some pairs spent a great deal of time on their axis and set up their graph. Others were totally focused on the line representing the story.

As these teachers show, curriculum frameworks or standards can be more than a checklist of skills to be covered. By reflecting on practice, teachers can make the ideas in the standards come alive for them and their students. These Massachusetts teacher insights, as well as similar insights from Ohio teachers, will be shared with teachers from other states. Next year, groups of teachers from four other states will join Project TIAN. How they make connections between their own state frameworks and their classroom practice will be of interest as well.

Project TIAN is based on work supported by the National Science Foundation under award number ESI-0455610. Any opinions, findings, and conclusions or recommendations are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Mary Jane Schmitt works with TERC and is a principle investigator of TIAN. She can be reached at mary_jane_schmitt @terc.edu. The authors of the above reflections, teachers in TIAN, preferred to be identified by number rather than name.