Week 2: Language and Math

From problem solving to procedures, the idea that mathematics learning is linked to language acquisition appears inherently true as so much of what we do in mathematics is embedded in language. With that being said entering the classroom with strong content knowledge maybe just one facet of your instructional practice, another piece that practicioners must consider is how to provide students with the linguistic proficiency that is needed for mathematics achievement. Language is a tool that organizes one's thinking about a concept and is essential when it comes to mathematical reasoning. How can one explain their thinking or check the validity of their work when they lack the language to make sense of what they are doing. Whether a student is monolingual, billingual or semilingual (lacking first language proficiency) language proficiency is essential for achievement and this component of instruction must be addressed.

Using the lens of Cognitive Theory the idea that information is stored in schemas implies that meaningful learning is essential for students to recall and remember information that is conveyed in the classroom. For the English language learner this can be a more complex task as students often do not have the background knowledge to support them in learning mathematics content and skills.

Scaffolding is an essential part of the process and requires thoughtful planning and individualized instruction. Furthermore teachers need to give students the opportunity to practice and rehearse their new learning otherwise the information will decay or be forgotten. The information processing theory reminds us that students must practice and rehearse new learning in order to recall it. Invariably the idea of multiple representation must be embedded in a teacher's practice as this approach will allow the learner to expand their foundational knowledge, develop more indepth understanding and expand their schemas which will enable students to meet lower lever cognitive demand tasks such as recalling and understanding. When this is achieved students will have the capacity to meet more challenging tasks and persist when they encounter disequilibrium.

I believe that scaffolding is really important in a classroom. If the teacher is providing scaffolding in a classroom to the students, the students are more likely to achieve a better understanding because the teacher would be providing extra help to the students. Furthermore, the teacher can act as a facilitator to guide the students to success. Hence, scaffolding is an essential process of a classroom.

ReplyDeleteI think it is important that teachers use multiple representations to accommodate different students who may have trouble understanding a concept or even a a word in math. They should also have a chance participate in interactive activities that give them a chance to use the word used in different ways.

ReplyDeleteCera I definitely agree with you, we as teachers need to foster multiple representations in our classroom and lessons. After learning more about language and learning this past week it is even more important to use multiple representations in the classroom. As we develop a lesson using multiple representations we can also discuss the particular problem and solution using different forms of language. By doing this students can make connections of words which may be polysemic such as 'mean'.

DeleteLike Lane, I strongly agree with you. I love the usage of multiple representation in the classroom because it assist all types of students, such as the auditory, visual, and kinestentic learners.

DeleteI agree that multiple representations are necessary in a classroom. Especially now days, we have classes where that are a lot of English language learners (ELLs). They need representation models to help them learn because they are more likely to learn faster with representation models.

DeleteOne of the best ways to develop language proficiency in students is by giving them many opportunities to use language in meaningful ways. That means that we must incorporate language acquisition in every class and into every subject so that students can acquire English proficiency. But this can be done simply and easily through thoughtful consideration of language practices. Every math teacher can do easy things like simplifying syntax or giving students access to linguistically proficient peers. Most importantly, students need to have activities that connect mathematical concepts to real world experiences that engage them in meaningful ways. Teachers should construct problems that facilitate open ended discussion and inquiry that delves into real mathematical concepts and provides students with opportunities to construct mathematics and language simultaneously.

ReplyDeleteZach, I still don't understand what you mean by using language in "meaningful ways." For each student, meaningful is going to be something different, and I hate to be cynical, but wouldn't it be difficult to tailor individual activities for each student? Rapping may work for one student, while poetry works for another, etc.

DeleteThe second comment I have to make about what you have said is that how are we as teachers to facilitate open ended discussion and inquiry in a classroom that struggles with discussing their ideas in English? Would you allow them to speak in the language they are most comfortable? And what about those who don't speak that language? What about those students who are soft spoken, or maybe have trouble speaking, would the conversation be dominated by those who do? How would you regulate that?

Surely, I don't want to be a complete negative Nancy, so I would like to add that I did enjoy your perspective that language acquisition should be incorporated into every class (to some extent), which would require large teacher cooperation, but also (unfortunately) some sort of special program (that might result in more tracking and again lower achievement).

I think that scaffolding is a very important technique to connecting with many students from all backgrounds. If the teacher can build on previous knowledge of the student, this means finding out their background and what they do and don't know, then they can gain greater understanding of the problem. Also if the teacher has a few different ways of presenting a problem then possibly students from different backgrounds will be able to pick up on and connect with at least one of the different solution methods.

ReplyDeleteI definitely agree with this point. I think that one of the most crucial parts of teaching in this sense would be assessment because you really need to understand where the students stand in terms of language understanding and what misconceptions they have. The only way that we can address these issues is if we know what they are in the first place.

DeleteGoing off on the idea of Cognitive Theory and understanding that some our students' knowledge and information is stored in schemas, we as teachers need to access this information. If teachers are able to do this then the students will be more able to learn and make connections by recalling prior information. For the ELL student this can be difficult as they may not have the background knowledge needed in mathematics to make these connections. As a teacher I would work with these ELL students to ensure they develop the proper mathematical foundation so then they can also use their prior knowledge to better understand and make connections among the content at hand.

ReplyDeleteI think that metalinguistic awareness into the class will help the students in many ways because metalinguistic awareness will allows students to reflect on the structural and functional features of text as object and to develop a connection between words and images. To achieve this awareness, I think that as a teacher I would use the "Rule of Four" into the classroom because this method offers students to learn in four different ways on one concepts: such as through text, picture, algebraically, and numbers//graphs. Another method that I would use to ensure mathematical understanding in the classroom is group work because I believe that students can share ideas and learn from one another more efficiently than listening to a long lecture.

ReplyDeleteMathematics is a difficult subject to talk about without somehow incorporating language in the picture, after all we truly understand best when we can articulate our thoughts and share them with others. It is then that we are presented with the problem of how to engage our English language learners, while they may not be able to fully understand or articulate their own ideas about the content we are presenting. I have heard multiple perspectives, that we SHOULD help students to learn new words as they navigate mathematics and to also encourage them to express their thinking in English (however limited it may be. But I have also heard that we SHOULD NOT focus so much on vocabulary and language building, but allow our students to explain their thinking in the language that they are comfortable, because they will achieve so much more if they are truly comfortable with it. Rather than exploring a subject they are uncomfortable with in a language they are already even more uncomfortable with, let them explore it in a setting that they can manage, and then let language come as it will. So I am on the border about the issue. I do agree that we should use scaffolding in our lessons, and that multiple representations can be nothing but helpful, but I still have not decided which side of the fence I stand on with regards to ELLs and Mathematics curriculum.

ReplyDeleteI definitely find scaffolding to be crucial in terms of student learning. Especially after the 206 lecture from this week regarding how many times a student must use a word to have command of it, I find it crucial for teachers to incorporate meaningful ways of language learning into their classroom. I found this weeks reading to be extremely helpful in assessing all of the different ways in which language can be confusing for students and also the ways in which teachers can help these students with their language issues. Today's class discussion also really built upon the ideas from the reading for me; I thought it was a perfect example of how student learning is enhanced from personal interpretation and sharing your understanding with others.

ReplyDeleteI also liked the idea, in the 206 lecture, of trying to incorporate higher tiered vocabulary in the classroom. I think that is a good way to get students used to the vocabulary used in mathematics and the terminology hey will see on state tests and in higher level courses.

Delete^I was just thinking about the higher tiered vocabulary. Incorporating this type learning would be beneficial for students, as you said erin, for testing and other courses. If I incorporated this into my classroom I think I would place the tiers on a wall and place new vocabulary at the lowest tier and move them as the students progress to a better understanding. It would be interesting to see how many words we learned at the end of the school year

DeleteWhen it comes to encouraging critical thinking a question asking in your class, it can be very challenging to do that if your students have low language proficiency. One of the things we need to rely on as teachers is to find out how are students are thinking and rationalizing their actions in math. If a student doesnt have the language ability to communicate these to us as teachers, it can prove extremely challenging to adapt curriculum so that those students are learning.

ReplyDeleteI agree that multiple representations and scaffolding can help students who have a low language proficiency. Having a student depict, say a vocab word, in a drawing, the formal definition, symbolically and in their own sentence could help them retain it. We learned in lecture that we have to be exposed to a word at least ten times to actually know it. So, as a teacher, we should make sure we're using new terminology frequently and we should encourage our students to use the correct terminology as well.

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