Teachers as Listeners of Student Noticing

1. Teachers as Listeners of Student Noticing Higinio Dominguez, PI Kenneth Bradfield, Jose Martinez-Hinestroza Michigan State University

2. In many classrooms with racially diverse and socioeconomically disempowered students, instructional interactions remain unaffected by these students’ perspectives

3. How does listening to student noticing impact instructional interactions in mathematics?

4. Theoretical Approach • “Students and teachers need to learn how to find answers to the problems that confront them” (Kincheloe & Steinberg, 1998, p. 2) • Example of teacher-identified problem: “I feel like I am not thinking deeply enough about their knowledge. Or not knowing how to frame questions in a way that goes deep.”

5. Theoretical Approach • Students notice multiple dimensions in their experiences learning mathematics in classrooms (Lobato, et al., 2013) • Eliciting student noticing (Dominguez & Adams, 2013) can help teachers revisit the seriousness of problems in their classrooms • “Learning to listen is at the core of a teacher’s ability to use knowledge of children’s mathematics productively” (Empson & Jacobs, 2008, p. 259)

6. Participants • Lansing: one first-grade teacher (4 years exp.); one second-grade teacher (7 years exp.). 43 students in a Spanish immersion program (math in Spanish), 100% free lunch program; working class parents (many are unemployed); parents support the bilingual program • Austin: one fourth grade teacher (3 years exp.). 20 students in a district-mandated “bilingual” program; gentrified community; parents support bilingualism.

7. Methods and Data Sources • Bilingual interviews with 63 students • Developed interview questions with teachers • Read and coded responses with teachers • Gave one teacher the other teacher’s student responses • Used open coding process but with general purpose of finding out student perceptions about resources used when learning mathematics in their classrooms

8. Interview Questions With summarized main findings and examples

9. Classroom Practices Questions • How is your math class? What do you do? • Tell me something that you really like (and something that you really don’t like) to do in math class and why. • Who do you understand better, your math teacher or your classmates? Why? Finding Students reported a sense of resourcefulness for navigating classroom practices, a perception that converged with that of the teachers. However, students did not see the teachers as influential figures in this self- and peer-oriented resourcefulness.

10. What students said • A vecescuandohagonumerosgrandes, paraque no se hagandificiles los separo, comoque los rompo en mitadparaque se me hagafácil, luego de sacarunarespuesta, séque no es exacta, peroluegopuedosumar lo quequité, al último. Y dóndeaprendisteesaestrategia? No la aprendí de ningúnlado, pensé en maneras de hacertrabajomásfácil, pensé en muchasmaneras--HD • La claseesdiferenteporquenosdejantrabajar con parejas, y en otrasclasescasino—HD • Cuandolleguéyo no le entendía a lasmatemáticas, yo no era inteligenteparalasmatemáticas y Sandra se paró y me ayudó en matemáticas y noshicimosamigas y empezamos a ayudarnos, y ahoraqueella me dio ideas yopuedoayudar a otras personas de lo queella me enseñó--HD

11. What students said • Understand students better because: (a) Speak same language, (a) are Mexican; (c) we’re best friends; (d) we help each other. • Understand teachers better because: (a) She knows everything. Example: “…I don’t know, she’s just good at it, might be magic powers.”—KB • My teacher because she’s the one who made up the problems, so she must know the answers—HD • Yoa veces le tengomiedo a los números, no confio mucho en los númerosgrandes, a vecescomoque me desespero, no me gustahacerestosnúmeros y escomo, comoesque no le entiendo a esosnúmerosperosi me gustanlasmatemáticas. A mi los númerosgrandes me hacen revolver, me confundo mucho. Como un millón, mil. Me da miedoporquepiensoque no voy a pasar mi gradosi no hagomismatemáticasbien. Las matemáticases un pocomásimportanteque la lectura. No me gustaconfundirme.--HD

12. What students said • No me gustannúmeros tan pequeñosporque no tienencomo mucho interés, lo puedeshacerrapidito, a mi me gusta a vecescomotardarme y quitarnúmeros y asi—HD • A mi me gustacompartirmis ideas y élcomo no sabetantomatemáticas me gustaayudarlo. Y en qué lo hazayudado? Le he enseñadocasitodo, comoseparar los números y luego romper otrosnúmeros y sumarlos. Y élte ha enseñadoalgo a ti? Pues, él no me ha enseñado mucho, bueno nada, porqueélcasi no sabemuchasestrategias—HD

13. What students said • Quémáshaces en la clase? Pongoatención y hago lo que la maestra me dice. Tegustahacer lo quetumaestrate dice? Sí me gusta, porque hay algunascosasquehacenque mi mente se olvide de todasmispreocupaciones. Quétepreocupa? Me preocupaque me vuelva a quedar en 4to. Quémástepreocupa, Juan? Quetalvezalgúndía no le voy a entender a algunapregunta de la maestra—HD • Notoque la maestracadavezquenecesitoayuda, ella me mira, y ellasabecuandonecesitoayuda y cuando no. Y tegustaque la maestro te mire? Me gustaporquesinecesitoayudaya no tengoquelevantar la mano y pediratención. Ella misma me mira y asisabesinecesitoayuda. Y has notadoque la maestramira a los demásniñostambiénparaversinecesitanayuda. Sí, ella los mira a todos (demonstrates by slowly moving head from one side to the other)--HD

14. Influence over Classroom Practices Questions • Tell me something that you notice when you solve math problems that you haven’t told anyone. • What do you enjoy better, learning math in Spanish, in English, or both? Why?  • What is easier for you, explaining a math problem in Spanish or English? Why? Finding Students’ responses converged to strong connections to their learning processes, their peers as resources, and their bilingualism. Yet for some, these connections were not as evident.

15. What students said • Avecesmirocomofotos en mi cabeza, like a mental help, comoparaayudarme… me veoasicomo en un ladoaqui(referring to yesterday’s problem about cost of homes in the east vs. the west side)—HD • I like understanding people and talking to people. In math I get pumped up when I can understand other students--JM • I don’t know how to do math; I don’t know how to do English or Spanish. I don’t like both because I’m a Detroit boy—JM • Yo lo leo (el problema) en inglés. Porquees mas facil leer en inglés y luego lo escribo en español. Y porqué lo escribes en español? Porquecreoque me gustamás el españolporquees de dondevengo. (peer agrees)--HD

16. Academic Status Questions • Who do you like to work (and who would you like to work) with in math class? Why? • Who’s good in math? Who’s bad? What about you? • Have you ever had a good idea or have you noticed something in a problem but you were not given the chance to say it? Finding Students’ perceptions of themselves and peers as either good or bad in math caused teachers to begin to talk about ways to address status through more equitable participation.

17. What students said • Somoscomolasmismas personas perodiferentescuerpos, son dos corazones en uno—HD • I’m a milk and she’s a cookie, and so when we get partner up we get to do math with each other—KB • Nosayudamos lo mismo entre las 4. Y se habíanayudado en añosanteriores? No, esteañoempezamos--HD • I’m the only person that is not good in math—KB • En México yaiba a pasar a quinto, llegó el añopasado a EstadosUnidos, al llegar lo pusieron en 4to. Quésentiste? Senticomosiyotuviera la culpa de regresar a 4to grado--HD

18. Home and School Math Question • Have you seen activities at home that have to do with math? If so, who participates in these activities? Finding Students unanimously responded that math is only at school, not at home, thus prompting teachers to infuse instruction with relevant home connections.

19. Implications • Emerging results: • 1. Teachers’ awareness “I am having a hard time letting go of this direct instruction.” • 2. Change in teachers’ lessons • 3. Change in teacher-students interactions • Future plans: • Analyze and generate more data • Connect results to teachers’ decisions to transform their practice

20. References • Dominguez, H. & Adams, M. (2013). Más o menos: Exploring estimation in a bilingual classroom.Teaching Children Mathematics, 20(1), 36-41. • Empson, S. & Jacobs, V. R. (2008). Learning to listen to children’s mathematics. In D. Tirosh & T. Wood (Eds.), Tools and processes in mathematics teacher education (pp. 257-281). Sense Publishers. • Kincheloe, J. L., & Steinberg, S. R. (1998). Students as researchers: Critical visions, emancipatory insights. In S. R. Steinberg & J. L. Kincheloe (Eds.), Students as researchers: Creating classrooms that matter (pp. 2-19). London: Routledge. • Lobato, J., Hohensee, C., & Rhodehamel, B. (2013). Students’ mathematical noticing. Journal for Research in Mathematics Education, 44(5), 809-850.