Making Math a Definition of the Situation: Families as Sites for Mathematical Practices

Abstract

We present three cases showing families' competence in mathematical problem solving as a practical aspect of daily life. At home, parents and children engaged creatively in solving math-relevant problems. They used a combination of everyday practices and school forms, but generally did not recognize mathematics in their problem solving. The findings invite new forms of participation that bring families into discussions of math-relevant situations and relates them to their children 's school math. [families, math, ethnography, daily practices, math in context] Karen: Okay, here comes Bernard. Evan: Bernard. What did he hit? Michael: He's got a little bit better average, he's at .277.While the family waited for game action, Michael asked Evan about his Little League statistics, drawing links between Evan's stats and those of professional players. Evan's stats were kept in a notebook he had with him, and he pointed to each column and announced what they represented (see Figure 2). Michael: You want to take a look at your stats? Can you tell me what all these were? Evan: Okay, that's hit by pitch. Goldman and BookerMaking Math a Definition 377Michael: I'm glad there weren't a lot of those! Evan: One. At bats, there were 6, 9, 11. Michael: Oh, you didn't total it? Evan: Yea. That's hits, doubles, triples, home runs, base on balls, which is also known as walks, strike outs, average for the game, average for the season, runs I scored, RBIs, and stolen bases.Charting baseball stats was one way Evan was both becoming a legitimate player and fan of baseball, a process Michael supported during this game. It also practiced Evan on math skills through creating and using charts for record keeping and interpreting his progress. 6 Michael focused on the statistics, asking Evan which was his best batting average. Evan's answer of a .666 average in two games prompted a deeper look.Michael: How'd you get that? Evan: You do your hits, divided by your at bats.Evan used a simple formula to turn his raw stats into a batting average that told him how he did in a single game-or throughout a full season. His data handling indicated that he knew it wasn't just about numbers, but about which numbers were important in particular situations. When Michael asked which "at bats" were counted in the batting average figures, Evan answered:Evan: Yea, you don't count the walks, uhm. . . . Michael: You probably don't count the hit by a pitch. The reason why is, like if you get someone like Barry Bonds, they'll try to walk him all the time . . . and his average shouldn't go down just because they keep walking him.Michael integrated Evan's stats with an explanation of a similar situation for professional slugger, Barry Bonds. They talked about stats when players came up to bat, when there was a hit or an error, and when there was a paucity of game action. They covered Evan's progress, how the pro players were doing, and how the teams were comparing. Topics were generated in the moment and often in relation to what happened in the game. Figure 2. Ev...

Participatory Design Research as a Practice for Systemic Repair: Doing Hand-in-Hand Math Research with Families

“…However, Blesilda's workshop for parents on campus was as far as any parent, teacher, or researcher in the study got with the school, and we saw this pattern with other parents that participated in the project (see Goldman & Booker, 2009 for other accounts). Distance from the academic and intellectual activity in school math classrooms stubbornly persisted, another rift-outside of our project's purview-in need of repair.…”

“…Families on the team began to show us what it looked like to carry that priming into the wider activities of their lives. By the end of the project, parents and their children had taken over directing us to the math that was relevant and important to them (for several examples, see Goldman & Booker, 2009). This change was also reflected in the research team's shift in role from authority to witness.…”

“…We filmed and gathered field notes during these interactions with families, and collected 10-20 hours of videotape for each family. Coding the video and field notes data clarified a wide range of mathematical practices and the circumstances that supported them as occasions for the family to problem solve together (Goldman & Booker, 2009). We also coded when parents discussed the school and life goals they had for their children (see Pea & Martin, 2010), discussions about how they participated in the schools, and ways they supported their children's learning.…”

“…The project developed nine family workshops, a television special on family math, and a resource guide for parents about navigating school math in middle school years. The project also produced articles about family math, design-based research, and methods (Goldman, 2006;Goldman & Booker, 2009).…”

“…The participants, comprised of parents and educators from three Bay Area cities, were there to come to know each other, learn about experiences with math, and move their various personal and project goals forward. The work was based in mutual exploration and experimentation-what we called "hand in hand" (Goldman & Booker, 2009). The approach was ethnographic, participatory, and located at the nexus of ethnography and design-based research (Bang, Medin, Washinawatok, & Chapman, 2010;Barab, Thomas, Dodge, Squire, & Newell, 2004;Brown, 1992;Engeström, 2011;Gutiérrez, 2008).…”