This week, I read the Murrey and Wiest articles, in addition to, the Five Practices reading. The Murrey article focused on differentiated instruction in teaching mathematics to English Language Learners. A lot of the methods involved teaching students to be more proficient in the English language, both written and spoken. Wiest also mentioned a lot about how teachers need to incorporate language skills in the classroom for ELL students to perform better. I found it odd for both of the articles to touch on language arts so much. I initially thought it would be less efficient for them to do this, until I realized how much language and vocabulary there was in the subject of mathematics. Never really being a fan of math, I hated thinking about the connection between the two, because I understood literacy. I didn't understand math. When I read these articles, I realized that they are closely connected and that they can both play a major role in an ELL's fluency skills.
In Wiest's article, she focused on tasks that demonstrated the importance of language skills in mathematics. The first task was called "The Chickens and Pigs Problem", and it involved the teacher giving the students a word problem. What I really liked, was that she used two students' names from the class in the problem (one boy and one girl). With ELL students, it is important to use vocabulary that they understand in combination with unknown vocabulary. This helps them understand context. This relates directly to Murrey's article. Murrey found contextualized instruction to be a major factor in language acquisition. In addition, she believes it is better to teach and define new math vocabulary after students do the lesson or activity, because they are better-able to connect the term with its context.
In Wiest's second math task, she mentioned that teachers should "have students engage and remain immersed in a single context during a problem-solving session. This way, they can acquire appropriate background knowledge about the context." This is a great variation of how teachers can work on contextualized instruction. Overall, teachers must find various ways of strengthening ELL students' involvement in the classrooms. Both of the articles provided great pedagogical examples of how this can be done.
I thought it was interesting how both of Valand’s articles focused on the importance of ELL students understanding the connection between language arts and mathematics. Valand’s articles were about ELL students while mine (Wilkins & Roberts) were about gifted students and at risk students. Although our articles were about different topics, I completely feel that these topics are interrelated! For ELL, gifted, and at risk students we need to make accommodations for all of these types of abilities and the articles we read were trying to help us identify and create lessons that can be geared toward all different types of students. I completely feel our articles can relate to one another for this reason and that we, as future teachers, have to realize that even though all these students have different abilities level, they are all the same in that they need our help and accommodations in the classroom in order for them to succeed.
ReplyDeleteIn the Wilkins articles, I read about gifted students who need help and accommodations to be successful in a classroom where they may advance much faster than the other students. This article was a bit confusing for me to understand but I tried to understand as much as I could. I believe what happened was that the first MIC unit measurement table that was created was not successful in incorporating ALL students rather it was too difficult for most students and this would lead to gifted students to be singled out. I think in figure 3, “10 criteria for selecting, modifying, and creating activities”, the problems listed seemed to be more open ended tasks that could be arranged for all different ability level students. A teacher could take an activity from this table and change the task to be less difficult or add challenge. I believe this article was trying to show the 4 different ways that researchers have tried to formulate activities for gifted students that would not exclude them but rather challenge them and also could be incorporated into everyday classroom lessons.
In the Roberts article, I REALLY enjoyed reading about the section where Roberts explained how she was going to help at risk students succeed. Her goal was to help the at risk students gain confidence in their work as “creators and problem solvers”. She would do so by having the students participate in very small tasks which would be geared to their learning level. By doing this, these students would begin to succeed at completing these tasks, although small, it would gain the students confidence in feeling as though they can perform the math material. I thought this was an excellent idea and I have never heard a teacher helping students from this angle. Student need to feel as though they can complete the work and have faith in themselves as learners and workers. Not only do the students need to have confidence in themselves but the teachers as well. If they see that we have confidence in their work then they will be motivated to learn how to have confidence in themselves!
This week, I read the articles Helping Students with Disabilities Understand What Mathematics Means by Miller and Hudson (2006) and Problem-Solving Support for English Language Learners by Weist (2008) in addition to Chapter 6 in 5 Practices by Smith and Stein (2011). From all 3 readings, I have noticed a theme of conceptualized understanding of mathematics and how significant this is in helping students develop a deeper understanding of mathematics rather than just memorizing procedures and algorithms.
ReplyDeleteAccording to Miller & Hudson (2006), conceptualized understanding allows students to have a deeper understanding of the meaning of abstract math symbols and operations. The authors provide five guidelines for teachers to ensure that they are helping their students understand mathematics at a conceptual level. The five steps the authors provide include providing various modes of representation, choosing structures to present the concepts wisely, considering the language of mathematics, applying mathematics to the real world, and providing explicit instruction. Although this article was geared towards teaching students with disabilities how to understand math, these guidelines could really be beneficial towards teaching all students to understand math beyond memorization of algorithms and procedures.
Weist’s article also discusses the significance of English Language Learners and their conceptual knowledge of math (2008). Weist claims that conceptualized learning is beneficial because it helps ELLs connect to new math concepts and find value for these concepts to utilize in the future. Throughout the article, Weist discusses the importance of language in math and how it can help students understand what to do. Like Valand, I had never really considered the significance language arts had in mathematics until this course. Although both of my readings discussed the connection between language and math and how they relate to people with disabilities or English Language Learners, the significance of this connection applies to all students. There have been many times as a student where there is vocabulary used in a word problem that I have not understood, making it difficult for me to get past that and focus on what the problem was really asking me to do.
Taking Weist’s ideas about language and its significance in math, we can apply the ideas in the 5 Practices book about how to ask questions and how this can help students develop their ideas of various math concepts. In Weist’s article, she discussed how the teacher, Mrs. Higgins, had her students talk about what the problem was asking the students to do before they actually started doing the mathematics. She asked several questions that were similar to those provided in the 5 Practices book to help push the students’ learning and have them take responsibility for their answers by justifying their reasoning, rather than the teacher directing the questions too much and providing the answer for the students. Mrs. Higgins then had the students work together in heterogeneous groups to promote comfort for ELLs who were weaker (they also had another ELL in the group to help the weaker student). After students worked together and felt comfortable with their answer, Mrs. Higgins would ask students to walk the class through their methods. During this process, more questions were asked by the students and by the teacher in a way that would help students justify their reasoning and push their understanding to a deeper level.
This coincides with the article Valand read by Murrey as well as the Miller & Hudson article that I read for the week. Having students take responsibility for their learning by talking through their ideas is a great way to help develop conceptualized understanding of math, helping them delve deeper than just memorizing math concepts.
This week I read both the Gifted Mathematics Students by Wilkins and the Problem- Solving Support for English Language Learners by Wiest. I was really drawn to the Wiest article because I found it very interesting how students who are not native English speakers learn mathematics. In the Chicken and Pigs problem I loved the way the teacher set up the problem putting students in the class names in the it. I also liked the fact that she arranged the students so that they have an advance ELL students and an English speaker in the group. I think it is important in an ELL setting to both read the problem aloud as a class then silently to themselves just in case students can’t pronounce or understand a word in the problem. The fact that she breaks down certain words to help students make connections to the problem is key. Having students have the discussion time in not only important in a language class but also in Math because it involves language. Making sure that students understand what the problem is asking is very important because you do not want them solving for the wrong thing. I enjoyed this problem and I think it would ne very useful in an ELL classroom.
ReplyDeleteI think that the Wilkins article directly relates to the Wiest article for the fact that more advanced students are placed in groups with students who struggle either academically or linguistically. Often times in classrooms I see this happening and most times these students are left to sit there until everyone finishes their assignments so they become bored. I think it is important for teachers to challenge these students by giving everyone in the class the same math problem but maybe having the gifted students take it beyond what the problem may be asking. The MIC that was mentioned in the article seems like a great asset to the classroom for theses students. I like the fact that students are given the menu as a tool to use during a measurement activity. I feel that it gives them the freedom they need to indentify with the problem and work on their strengths and weaknesses.
I feel that both theses articles are very important to a new teacher because seeing that I would like to teach in an urban area, I know that there will be students who are both ELL and gifted in my classroom, reading theses articles help me to gain the knowledge needed in order to accommodate both students. In many classrooms often times these students are left behind and forgotten about. The gifted, because teachers feel that they don’t need the attention that students who struggle need, and ELL students because teachers feel that they just can not keep up. Theses articles helped me to learn to create that balance for both ELL and gifted students.