Varieties of Language Observed During a math lesson in a Traditional Classroom



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Constructionism


In the 1980s, Seymour Papert delivered a speech via video conference about constructionism and the possibilities computers offer for a constructionist learning space to Japanese educators. In Papert’s own words, constructionism entails "Giving children good things to do so that they can learn by doing much better than they could before."4 In light of that belief, it is interesting to note that Carrasco includes constructionism in his weekly lesson planner under the “valores y actitudes”, or values and attitudes fostered in the classroom. Additionally, in Mindstorms, Papert discusses an “object to think with” as a physical tool that allows the assimilation of an abstract concept. This concept is integral to contextualizing learning tasks.

Zone of Proximal Development (ZPD)


Vygotsky defines the zone of proximal development as:

The difference between a child's actual development as determined by independent problem solving and the higher level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers.5


Legitimate Peripheral Participation (LPP)


In the book Situated learning: Legitimate peripheral participation, Jean Lave and Etienne Wenger define the term legitimate peripheral participation as:

A concept that denotes the particular mode of engagement of a learner who participates in the actual practice of an expert, but only to a limited degree and with limited responsibility for the ultimate product as a whole.6


In my observations of the repaso lesson, the students were all legitimate members of their math community within the classroom since they were all given access to opportunities for participation. Nevertheless, the students actually involved in the discourse were boys meanwhile the girls abstained from participation.

The Three Focal Aspects:

  1. The practice of “Repaso” in a math lesson


Everyday activity vs. abstract concepts

The first topic is the tension and interplay between colloquial and formal language during the classroom discourse. There is a switching from contextualized to de-contextualized tasks that clearly distinguishes this interplay during the repaso. Moreover, the technical mathematical discourse register that he expects the students to assimilate reveals yet another variety of language to learn that serves to promote a proper way with words in the community outside the classroom.


  1. The ubiquitous “minuend syndrome”


a.k.a. Dividendo syndrome

The second focus will be an episode I observed during the wrap-up of the math lesson that mirrors the minuend syndrome discussed in Laserna 1988. The importance of this aspect is to demonstrate how the practice of giving a procedure, or proof to the students to memorize and apply as a way of ascertaining a correct answer is also found elsewhere and appears as a cross-cultural phenomenon in traditional classroom settings.


  1. From group instruction to individual feedback,

Time constraint embodied in “rubber stamp” ritual


The third focus is the issue of time and how it affects the language formalities the teacher uses and the individual feedback each student receives as a consequence. The importance of this aspect is to analyze the manifestations of the constraint of time in the actual discourse of the classroom during the closing of each lesson.

Description of the field site

The school


The Fidel Chaves school is an elementary school in Heredia located within the domain of the newly established Intel Corporation semiconductor assembly and test plant in Costa Rica. Intel emanates a strong presence in the school as evidenced by features of it physical exterior and by the excitement of the teachers and student population about personal computers in the classrooms due to the One-to-One classroom in which each student uses their own laptop. During an interview of the teacher, Carrasco, he brought up how Intel has workshops for the students; during these “talleres” the students learn how to construct their very own “empresa.”

Besides Intel, other businesses also contribute to the school’s resources by means of equipment or other economic benefits. The Corporación Pipasa recently donated a large sum to the school for a “bodega” as well as for other construction projects for the school campus. Another company called Pedregal provides construction materials to the school, such as cement, and other equipment for the students to use in classes such as “Artes industriales.”


The Classroom


When first entering the classroom, the blackboard is placed to the immediate right and the teacher’s desk is to the immediate left. The students are in three rows of eight students each and the adecuación curicular students are two set off in the far right corner of the classroom, sequestered from the rest of their classmates. There are very few posters and signs on the walls of the classroom. The teacher Carrasco explained to me that this is because the parents of the students, or the teachers themselves must put in money from their own pockets in order to decorate their classroom.

The classroom is rather large, but with all of the seats arranged in rows and with the space that separated adecuación curricular students from the rest of the class, there was very little space left to maneuver throughout the classroom when attempting to go through, or along the rows; in fact, the students barely have enough room for themselves to move about the classroom. This physical layout lends itself to close contact between students and facilitates a lot of note passing and side conversations during the lessons since it is so easy for the students to distract each other.





Above to the left is a picture taken from the entrance of the blackboard during English class.

Above to the right is a picture taken of the seating arrangement and the far corner of the classroom.

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