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Her paper in its entirety is available at http://ell.stanford.edu/sites/default/files/pdf/academic-papers/02-JMoschkovich%20Math%20FINAL.pdf
Give the participants classroom vignettes and discuss them after each recommendation http://ell.stanford.edu/sites/default/files/pdf/publication-briefs/02-JMoschkovich%20Math%20Appendix%20FINAL.pdf
True. This is a myth buster for any language teacher, but should not surprise a math teacher.
The semiotic systems that are involved in mathematical discourse are natural language, mathematics symbol systems, and visual displays. Instruction should recognize and strategically support EL students’ opportunity to engage with this linguistic complexity.
Rather than debating whether an utterance, lesson or discussion is or is not mathematical discourse, teachers should instead explore what practices, inscriptions, and talk mean to the participants and how they these to accomplish their goals.
Both statements are false. P. 7 In many math journal articles, definitions are open to revisions by the mathematician. The problem and the misunderstanding occurs because in the lower level textbooks, definitions are presented as static and absolute.
Recommendations for math instruction for english learners
Recommendations for MathInstruction for English Learners Ruslana Westerlund Adapted from Judit Moschkovich, 2012, Understanding Language, Stanford University
About the AuthorJudit Moschkovich is Professor of Mathematics Educationin the Education Department at the University of California,Santa Cruz. Her research uses socio-cultural approaches toexamine mathematical thinking and learning in three areas:algebraic thinking (in particular student understanding oflinear functions); mathematical discourse practices; andmathematics learners who are bilingual, learning English,and/or Latino/a. She has conducted classroom research insecondary mathematics classrooms with a large number ofLatino/a students, analyzed mathematical discussions, andexamined the relationship between language(s) andlearning mathematics.
Recommendation #1Focus on students’ mathematical reasoning, notaccuracy in using language. Teachers should not be alarmed when they hear imperfect language. Instead, teachers should first focus on promoting meaning, no matter the type of language students use. Eventually, after students have had ample time to engage in mathematical practices both orally and in writing, instruction can move students toward accuracy (p. 5).
Recommendation #2Shift to a focus on mathematical discourse practices,move away from simplified views of language. The focus of classroom activity should be on student participation in mathematical discourse practices (explaining, conjecturing, justifying, etc.) Instruction should move away from simplified views of language as words, phrases, vocabulary, or a list of definitions, which limits the linguistic resources teachers and students can use in the classroom to learn mathematics with understanding (p. 5).
Recommendation #2, cont.Instruction should move away from the interpretingprecision to mean using the precise word, and insteadfocus on how precision works in mathematicalpractices (p. 6). E.g. x+3 is an “expression” , x+3=10 is an “equation”. However, attending to precision is not so much about using the perfect word; but what’s more important is to speak about precise situations.
True or False?Precise claims can be made in imperfect language andattending to precision at the individual word meaninglevel will get in the way of students’ expressing theiremerging mathematical ideas.
Recommendation #3 Recognize and support students to engage with the complexity of language in math classrooms (p. 6). Language in Mathematical ClassroomsMultiple modes Oral, written, receptive, expressiveMultiple representations Including objects, pictures, words, symbols, tables, graphsDifferent types of written Textbooks, word problems, studenttexts explanations, teacher explanationsDifferent types of talk Exploratory, expositoryDifferent audiences Presentations to the teacher, to peers, by the teacher, by peers
Recommendation #3, cont’dInstruction should:a) Recognize the multimodal and multi-semiotic nature of mathematical communication;b) Move from viewing language as autonomous and instead recognize language as a complex meaning- making system, andc) Embrace the nature of mathematical activity as multimodal and multi-semiotic (p. 7).
Recommendation #4Treat everyday language and experiences asresources, not as obstacles. Everyday language and experiences are not obstacles to developing academic ways of communicating in math. Instruction needs to a) Shift from monolithic views of mathematical discourse and dichotomized views of discourse practices and b) Consider everyday and scientific discourses as interdependent, dialectical, and related rather than mutually exclusive (p. 7)
True or False?Mathematical language may not be as precise asmathematicians or mathematics instructors imagine itto be.Definitions are static and absolute facts to beaccepted.
Recommendation #5Uncover the mathematics in what students say anddo (p. 8). Teachers need support in developing the following competencies (Schleppegrell, 2010): a) Using talk to build on students’ everyday language and at the same time develop their academic mathematical language; b) Providing interaction, scaffolding, and other supports; c) Deciding when imprecise or ambiguous language might be okay and when not.
True or False?There is tensions around language and mathematicalcontent and teachers are not prepared to deal withwhen to move from everyday to more mathematicalways of communicating, and when and how todevelop “mathematical precision.”
AssessmentsClassroom assessments based on mathematicaldiscussions need to evaluate content knowledge asdistinct from fluency of expression in English.
References:Moschkovich, J. (2012) Mathematics, the CommonCore, and language: Recommendations formathematics instruction for ELs aligned with theCommon Core. University of California, Santa CruzA complete list of references is available athttp://ell.stanford.edu/sites/default/files/pdf/academic-papers/02-JMoschkovich%20Math%20FINAL.pdf