Journal of Urban Mathematics Education December 2013, Vol. 6, No. 2, pp. 81–85 ©JUME. http://education.gsu.edu/JUME JAMES S. EWING is a fourth-year doctoral student in Teaching and Curriculum at the Gradu- ate School of Education at Syracuse University, 150 Huntington Hall, Syracuse, NY 13244; email: jsewing@syr.edu. He taught elementary school in Spain for 24 years. His research interests include elementary mathematics education, English language learners, and pre-service teachers. BOOK REVIEW The Standards for Mathematical Practice and Hybrid Spaces: A Review of Empowering Science and Mathematics Education in Urban Schools 1 James Ewing Syracuse University mpowering Science and Mathematics Education in Urban Schools by Edna Tan and Angela Calabrese Barton with Erin Turner and Maura Varley Gutiér- rez (2012) is a useful and timely book for a broad range of educators. Tan and Calabrese Barton have backgrounds in science education, while mathematics teaching and learning is included with contributions from Turner and Varley Gutierrez, who both have backgrounds in mathematics education. Throughout the book, the authors discuss how teachers might provide equitable access for “urban” students in mathematics and science by creating hybrid spaces—spaces where schools connect with students’ personal and home lives. The authors’ main argu- ment woven throughout the book: to achieve social justice in mathematics and science it is necessary to focus on equity (not equality) and empowerment. Tan and Calabrese Barton intentionally use the phrase “empowering learning envi- ronments” as a means to envision an education that engages youth in learning and using mathematics and science not only as a tool but also a means for change (p. 14). In each of the chapters, there are different iterations of the argument that lit- eracy in mathematics and science should aim for more than mere functional liter- acy but also, and perhaps more importantly, critical literacy. They support their argument with four practical studies described as “hybrid spaces in action” (p. 17). Collectively, the studies are grounded in critical ethnography—a methodo- logical approach intended to expose injustices and break down or blur the re- searcher/researched binary. As an elementary school teacher in Spain for 24 years, and now as a current doctoral student and future teacher educator and researcher who has research in- terests in elementary mathematics education and English language learners, the 1 Tan, E., Calabrese Barton, A., Turner, E. E., & Varley Gutiérrez, M. (2012). Empowering sci- ence and mathematics education in urban schools. Chicago, IL: The University of Chicago Press. pp. 224, $29.00 (paper), ISBN 978-0226037981 http://press.uchicago.edu/ucp/books/book/chicago/E/bo13181197.html E http://education.gsu.edu/JUME mailto:jsewing@syr.edu http://press.uchicago.edu/ucp/books/book/chicago/E/bo13181197.html Ewing Book Review Journal of Urban Mathematics Education Vol. 6, No. 2 82 title of the book alone caught my interest. Many of the pre-service teachers (PSTs) whom I have taught in my elementary mathematics methods courses are from the suburbs. During their field and student teaching placements in urban schools, they struggle to provide environments that nurture their urban students’ empowerment. Furthermore, many of the PSTs have shared that their own ele- mentary mathematics learning experiences were disconnected from their personal and home lives. Therefore, I seek out literature that offers suggestions on how teachers might connect mathematics teaching and learning to students’ lives as well as how teachers might create learning environments that fill students with a sense of (self) empowerment. During my methods course, PSTs are assigned lit- erature to read which they are to connect to the eight Standards for Mathematical Practice as outlined by the Common Core State Standards Initiative (CCSS). 2 These practices are used as an overall guiding framework for the methods course. Here, I use the standards throughout the review to illustrate both the usefulness and timeliness of the book as well as how mathematics classroom that are hybrid spaces might assist in achieving the objectives of the Standards for Mathematical Practice. CCSS for Mathematical Practice MP1 – Make sense of problems and persevere in solving them MP2 – Reason abstractly and quantitatively MP3 – Construct viable arguments and critique the reasoning of others MP4 – Model with mathematics MP5 – Use appropriate tools strategically MP6 – Attend to precision MP7 – Look for and make use of structure MP8 – Look for and express regularity in repeated reasoning Chapters 1 and 2 – Setting the Stage To set the stage, Tan and Calabrese Barton (2012) begin by providing vi- gnettes about two science teachers who changed the suggested district curriculum in order to develop and teach lessons that connected to students’ lives. They show that students were empowered by the lessons because they were allowed to dis- cover science for themselves rather than “practicing the routines of knowledgea- ble others” (p. 12). Tan and Calabrese Barton contend that the discourse of math- ematics (and science) for all “needs to be recast to be emergent of the interest, 2 For complete details of the eight Standards for Mathematical Practice, see http://www.corestandards.org/math/practice. http://www.corestandards.org/math/practice Ewing Book Review Journal of Urban Mathematics Education Vol. 6, No. 2 83 needs, concerns, locations, and conditions of those who participate” (p. 11). Ra- ther than stripping students’ lived experiences from these “technical” discourses, Tan and Calabrese Barton suggest making the discourses accessible to all by in- fusing students’ lives into the discourse as a “process of cultural production” (p. 10). In these hybrid spaces of learning the lines that too often separate schooling from the lived experiences of students (and teachers) are blurred if not altogether erased—and yes, even within the technical discourses of mathematics and sci- ence. Curriculum changes made by the teachers described in the vignettes were in alignment to MP1: Make sense of problems and persevere in solving them. Many of the PSTs that I have observed misinterpret this practice to mean that it is their role to explain the mathematical tasks to their students over and over until they “make sense” of them. During these well-intended efforts, teachers tend to offer too much support and decrease the rigor of the mathematics. If students become too dependent on the teacher, they often do not persevere in solving the problems. In contrast, Tan and Barton’s (2012) equitable approach of empowering students by connecting the discourses of mathematics and science to students’ lives en- courages them to make sense of problems and persevere. When students’ lives become part of the mathematics and science discourse, students are more willing to persist with problems until they are solved. Chapters 3, 4, 5, and 6 – Reporting Four Studies In chapter three, Turner (2012) discusses findings from her study of pre- dominately African American sixth graders from an overcrowded school. In a class discussion, students complained that their school’s facilities were inferior to a magnet school located in the same building with a high population of white stu- dents. The teacher and students designed and completed mathematical projects to support their hypothesis that the resources in their part of the building were infe- rior. These projects were examples of “critical mathematical agency” (p. 53): stu- dents not only learning a deep understanding of mathematics but also applying mathematics to right an injustice. One student’s project posited that the girls’ bathroom shared among students and adults was too small to meet their needs. She used mathematical concepts such as area, ratios, and fractions to support her hypothesis. Turner also provides an example of when critical mathematical agen- cy was not possible because it did not fit the guidelines of being mathematically rigorous (i.e., critical mathematics is not less rigorous mathematics). Two boys wanted their project to focus on the idea that there were too many poles where they played basketball. Although this problem tied into their personal lives and was an act of social injustice—other schools have more space to play basketball— counting poles was not a rigorous mathematical approach for sixth graders. Ewing Book Review Journal of Urban Mathematics Education Vol. 6, No. 2 84 Turner’s explanation of critical mathematical agency aligns with MP4: Model with mathematics. In chapter four, Tan and Calabrese Barton (2012) report on how a seventh- grade science teacher told stories, referred to as narrative pedagogy, to capture her students’ interests. They make the point that in “traditional” science classes the textbook (and/or teacher) is typically the authority, whereas storytelling introduc- es students to multiple points of view. Thus narrative pedagogy encourages stu- dents to be more critical as they determine which of the stories might be the most accurate. Tan and Calabrese Barton find that storytelling builds stronger ties be- tween and among the teacher, the students, and the content. Here, the teacher ini- tiates a story and students are able to critique her (or his) story and construct their own stories using the discourses of mathematics and science. Tan and Calabrese Barton contend that students are empowered “when individual narratives are wo- ven into the educational content of the curriculum” (p. 81). The focus of this chapter, narrative pedagogy, aligns with MP3: Construct viable arguments and critique the reasoning of others. In chapter five, Tan and Calabrese Barton (2012) provide details of another example in which students are empowered through hybrid spaces. A community club allowed youth to use “slang” and music in their science video projects. As opposed to traditional classes where the teacher is the expert and students listen passively these students acquired an expertise in their projects as a result of the teacher linking science to the students’ lives. As previously noted, being empow- ered in hybrid spaces has implications for MP1: Make sense of problems and per- severe in solving them. It stands to reason that students cannot make sense of problems and persevere if their culture is not considered. Thus the argument by Tan and Calabrese Barton that teachers should consider urban students’ culture is both appropriate and consistent with MP1. In chapter six, Varley Gutiérrez (2012) discusses her findings from a study about fifth-grade girls who protested the closing of their school in which they cal- culated the time and money it would take for students to travel to the new school. The students constructed a persuasive argument to convince the school board to change their decision. In order to do so, the girls had to understand the board’s argument at a deep level to develop counter arguments. The mathematical activi- ties described in this chapter align with several of the MPs. For example, being able to understand the school board’s point of view and developing a viable ar- gument to convince them not to close the school aligns with MP3: Construct via- ble arguments and critique the reasoning of others as well as MP4: Model with mathematics. Ewing Book Review Journal of Urban Mathematics Education Vol. 6, No. 2 85 Chapter 7 – Summarizing the Book Tan and Calabrese Barton (2012) conclude the book by summarizing the importance of empowering youth by creating hybrid spaces in mathematics and science classrooms. According to them, there has been recent attention in the lit- erature about such spaces (see, e.g., Gutiérrez, Baquedano-Lopez, & Tejeda, 1999), especially as a proposed solution for closing the so called “achievement gap” between white students and students of color. Nonetheless, Tan and Calabre- se Barton claim that their book is one of the few that goes beyond explanations and offers concrete examples of students actually engaged in hybrid spaces in mathematics and science. Concluding Thoughts I have shown how the mathematics (and science) activities and learning en- vironments (in school and out of school) discussed throughout Empowering Sci- ence and Mathematics Education in Urban Schools might be aligned with some of the Standards for Mathematical Practice. Here, I have highlighted only a few such cases; in truth, a close reading of the book reveals that hybrid mathematics (and science) classrooms align with all eight of the standards. But these hybrid spaces go beyond the standards in an important way: hybrid spaces can/do facili- tate students (and teachers) empowerment. For example, the use of tools in math- ematics is discussed in MP5: Use appropriate tools strategically. The students (and teachers) described throughout the book did indeed use tools appropriately and strategically. But the authors illustrate how students (and teachers) might go deeper; students (and teachers) not only use tools, mathematics and science be- comes a tool. In the end, empowering mathematics and science hybrid learning spaces are those that engage youth in learning and using mathematics and science as both a tool and a context for social change (p. 14). I strongly recommend this book to teachers, teacher educators, parents, and anyone interested in looking for ways to (self) empower youth in and through the discourses of mathematics and science. References Gutiérrez, K., Baquedano-Lopez, P., & Tejeda, C. (1999). Rethinking diversity: Hybridity and hybrid language practices in the hybrid space. Mind, Culture, & Activity: An International Journal, 6, 286–303. Tan, E., Calabrese Barton, A., Turner, E. E., & Varley Gutierrez, M. (2012). Empowering science and mathematics education in urban schools. Chicago, IL: The University of Chicago Press.