Literature Review
When students are learning a new language it is only natural for language production to take time. Students are absorbing information about the new language and understand much more than they can produce. When language production is paired with the philosophy for teaching mathematics called CGI, exciting things can happen. CGI requires students to explain their thinking process of how they solved the problem, something that demands language production.
Cognitively Guided Instruction
Cognitively Guided Instruction is based in the idea that students come into the classroom with high levels of background knowledge (Fenema,1992; Lane, 2006). As Elizabeth Fenema, one of the founders of CGI explains, the focus is not an objective of what students should know by the end of a lesson. Rather, students are to build upon what they already know to improve their learning. This is very different from the classroom that teaches the procedures of how to solve certain problem types and then expects students to replicate that process. When applying CGI, teachers must allow the students to create for themselves new processes of how to solve problems. Something important to note about CGI type problems is that most can be solved by modeling the actions portrayed in the problem. For example, Mary has 8 fish. Mary would like to buy 5 more fish. How many fish would Mary have? Students can use tactile things to figure out how to solve this problem, which is what students at lower developmental levels usually do, as when they are in kindergarten. As students continue to develop they will be able to solve the problem by simply adding the two numbers in their head. However, what is important is that they did not simply learn an algorithm to solve the addition problem. They understand what addition actually is and when to apply the algorithm (Fenema, 1992).
Thomas Carpenter and others explain that a large part of CGI relies on “particular knowledge about the development of children’s thinking” that teachers must understand when applying this philosophy. Teachers must use what they know about their student’s knowledge base and use that information to make instructional decisions about what students need (Carpenter et. al., 2000; Lane, 2006). CGI is heavily student centered and directed in this manner. As mentioned before, mathematical thinking is developmental and not all students will solve problems the same way. As student thinking becomes more sophisticated they will not need to us manipulatives, drawing, or the like, rather they will be able to apply the algorithm to solve the problem. Even though they may be able to do this, it is still imperative for these students to explain and justify their rationale for however they solved the problem. That explanation is key to the CGI philosophy, whether kindergarteners explain the why they drew the picture they drew or more sophisticated students explain the algorithm they used and why they chose to use it. Not only does it make students think critically but it also aids the teacher in gaining knowledge about the development of the student’s thinking, which Thomas Carpenter writes is important to the CGI philosophy.
Dual Language Immersion and Spanish Language Acquisition
However, in this class special circumstances exist as the students learning CGI are also emergent language learners. The class is part of a Dual Language Immersion Spanish program following 90/10 Model. The 90/10 model means that when students begin the program the emphasis is on the minority language as it is not supported in society and therefore requires more support, especially in terms of academic use (Alanis, I. & Rodriguez, M., 2008). It is labeled the 90/10 Model because in the first year the goal is to present 90% of the content in the minority language. With the progression of each year, English presentation of content is increased by 10%, so that in the second year of the program 80% of the content will be presented in the minority language and 20% of the content will be presented in English. This continues until there is a 50/50 balance and from there on this balance is maintained until the end of elementary school (Alanis, I. and Rodriguez, M., 2008).
According to the American Council on the Teaching of Foreign Languages, speech development is divided into five major levels of proficiency: Distinguished, Superior, Advanced, Intermediate, and Novice. The major levels of Advanced, Intermediate, and Novice are further divided into the sublevels of High, Mid, and Low. The focus of this work will be within the sublevels of Novice and Intermediate proficiency. As outlined by the ACTFL Proficiency Guidelines 2012-Speaking, speakers of a foreign language in the Intermediate level of proficiency will be able to be somewhat creative with the language as long as topics are related to their daily life. They will also be able to “recombine learned material in order to express personal meaning. A key component for the purpose of this research is that speakers at this level are understood by those who are accustomed to communicating with non-native speakers of the language. Speakers at a Novice level will be able to communicate short messages through isolated words and phrases that they have frequently encountered and may be difficult to understand. Most of the students in this study fall in either the Intermediate or Novice proficiencies, as mentioned above and are not able to be very creative with the language, meaning that they are unable to produce much language. They are at this level because they are at the beginning of learning a new language and have only been in the Dual Language Immersion Environment for about eight months. Even those who speak natively have a difficult time being creative with the language as they are still very young and developing language.
How They Intertwine
Cognitively Guided Instruction integrates easily with pedagogies in language production because the philosophy dictates that it does not introduce unknowns to students. Instead, students use what they already know to solve problems. I anticipate, that in this study, students who are asked to use their own prior knowledge, will to be able to explain themselves better. Since CGI works with what they already know, students do not need to try to remember new vocabulary; instead they only need to learn a word that they already know the meaning of in a new language (Gerena, 2011). This will allow for more authentic production by the students in whatever language they choose to use.
How the Literature Influenced This Investigation
Reviewing the experiences and interpretations of other experts influenced the direction and organization of this investigation. Moreover, this in-depth review has enhanced the focus of this inquiry as to what aspect of language I would be focusing on. From the CGI standpoint students will have a grasp on the content based on their background knowledge. In terms of language, students will not be producing complete sentences in fluent Spanish. Rather, students will be trying to piece together words and ideas based on the Spanish I have modeled and what they have come to understand. The goal is for students to begin practicing thinking in this new language.
Alanís, I. and Rodríguez, M. (2008). Sustaining a Dual Language Immersion Program: Features of Success. Journal of Latinos and Education. Retrieved from http://0-web.b.ebscohost.com.sally.sandiego.edu/ehost/pdfviewer/pdfviewer?sid=267e4c18-5750-4626-af91-8bdcc50b3bf2%40sessionmgr111&vid=18&hid=119
American Council on the Teaching of Foreign Languages. (2012). ACTFL Proficiency Guidelines 2012. Retrieved from http://www.actfl.org/sites/default/files/pdfs/public/ACTFLProficiencyGuidelines2012_FINAL.pdf
Carpenter. T. et. al. (2000). Cognitively Guided Instruction: A Research-Based Teacher Professional Development Program for Elementary School Mathematics. National Center for Improving Student Learning and Achievement in Mathematics and Science. Retrieved from http://files.eric.ed.gov/fulltext/ED470472.pdf
Fenema, E. (1992). Cognitively Guided Instruction. National Center for Research in Mathematical Sciences Education. Retrieved from http://files.eric.ed.gov/fulltext/ED372929.pdf
Gerena, L. (2011). Student Attitudes toward Biliteracy in a Dual Immersion Program. The Reading Matrix, 10, 55-78. Retrieved from http://www.readingmatrix.com/articles/april_2010/gerena.pdf
Lane, A. (2006). Professional Development Programs: Cognitively Guided Instruction (CGI) and Math as Text (MAT). Retrieved from http://0-www.eric.ed.gov.sally.sandiego.edu/contentdelivery/servlet/ERICServlet?accno=ED493022
Potowski, K. (2004). Student Spanish Use and Investment in a Dual Immersion Classroom: Implications for Second Language Acquisition and Heritage Language Maintenance. The Modern Language Journal, 88, 75-101. Retrieved from http://0www.eric.ed.gov.sally.sandiego.edu/contentdelivery/servlet/ERICServlet?accno=ED471635
Smith, P. and Hopffer, E. (2000). Exito Bilingue: Promoting Spanish Literacy in a Dual Language Immersion Program. Bilingual Research Journal, 22, 261-77. Retrieved from http://0ejournals.ebsco.com.sally.sandiego.edu/Direct.asp?AccessToken=23L1L9S8S13SMBW1L2L191YW2L2H8SA3L&Show=Object