Symbolic Representation Competency

Math uses a specialized vocabulary that can only be learned in school. Words in math can mean one thing and have a completely different meaning in everyday conversation. It takes English Language Learners (ELLs) about two years to learn social (everyday) language, but math language takes about five to seven years to learn. ELL students not only have to translate between English and their native language, but also between social and academic language (Janzen, 2008; Slavit & Ernst-Slavit, 2007). In math, we use language to explain concepts and to carry out the procedures, so it is critical to have an understanding of the vocabulary in order to comprehend those concepts. If students do not fully grasp the vocabulary in the problem, then they are at an obvious disadvantage. ELLs may understand the content of the lesson, but inexperience with the language can hold them back from expressing what they know. When students are learning to talk math, it is essential to make the lesson comprehensible for the students, but also to make sure that the students have the vocabulary needed to understand the instruction. It is important for students to not only be able to understand the vocabulary used in the lesson, but also to be able to apply that vocabulary in conversation (Bresser, Melanese &Sphar,

Mathematics is a concept that can be defined as “the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically” (“The Definition of Language”). As a whole, it is a form of communication. The dictionary definition of language is “a body of words and the systems for their use common to a people who are of the same community or nation, the same geographical area, or the same cultural tradition” (“The Definition of Math”). It is clear that both areas of knowledge require a verbal communication used to connect with other people. Presumably, both mathematics and language need each other to be fully understood. This concept can be seen and proven through Chapter 8: Rice Paddies and Math Test in Malcolm Gladwell’s Outliers as well as a real life situation.

Core 2.2 Communication is the ability to talk to another person, and exchange information with one another. Communication is probably the most important skill needed in a job. If you can’t communicate with a person, work will be much harder. You can’t just apply for a job and get accepted. You have to communicate with your boss, and he has to talk to you about the requirements for your job, etc. Having a good communication skill will allow for the company you’re working for to work efficiently and be very productive.

Again, knowing the label “subitizing” aided me in becoming comfortable discussing mathematics. The new vocabulary I learned was an important part of becoming more mathematically fluent, but alone cardinality and subitizing are not enough to fluently compute numbers.

Introductory • In what ways does your curriculum program support student learning and achievement of mathematics? Probing • How have you organized your program to enable student learning of all grade-level curriculum expectations? • How are your lessons designed for student learning of mathematical concepts, procedures/algorithms, and mental math strategies through problem solving? • What ways are the

Personal interview a learner social factors affecting mathematics numeracy learning Introduction Mathematics is a type of reasoning. Thinking mathematically includes thinking in a rational way, developing and checking conjectures, understanding things, and forming and validating judgments, reasoning, and conclusions. We show mathematical habits when we acknowledge and explain patterns, build physical and theoretical models of sensations, develop sign systems to assist us stand for, control, and review concepts, and create treatments to address issues (Battista, 1999).

The Standards for Mathematical Practice are essential tools that will ensure a student has everything they need to improve in their knowledge and understanding in mathematics. Thus, it is highly important that all level mathematical educators try to implement these standards into their classrooms. Ultimately, there are two sections called, “processes and proficiencies” in which the standards are derived from. The practices are depended on these two standards in the mathematics education. For the reason being, that they provide strategies that will help develop a foundation that students may rely on to comprehend and approach a problem. In other words, the standards do not show step-by-step ways on how to solve a problem, but rather help a student feel comfortable and confident in approaching, analyzing, and finishing a problem. The process standards defined by the National Council of Teachers of Mathematics emphasizes a way of problem solving, reasoning and proof, communication, connections, and representations. The proficiencies identified by the National Research Council include, adaptive reasoning, strategic competence, conceptual understanding, productive disposition, and procedural fluency. Knowing how beneficial the Standards for Mathematical Practice is for students, it is clear that as a future teacher I will implement these strategies in every classroom so that all my students may have a chance to prosper.

This is unit one-math 1201 collage algebra math learning journal self-reflection. First, I would like to some way give the personal opinion of which and what really differs mathematics from other subject text. It is a challenging and a difficult question to answer because in my case, I would say reading mathematics text and understand easily would not the same for everyone. I think different from person to person and it is not easy like others regular subject to manage very fast. Because it containing more per sentence and paragraph than any other type of text. They also have specified and written in a very different compact style and each written sentence contended a lot of complicated information, such as words like numeric numbers and non-numeric numbers, symbols, codes, formulas, and continent of the information pages that also laid out in different patterns than the traditional left-to-right of the most reading. Therefore, every math’s text passage would need a lot of time

uhlihl When discussing how students of different mathematical levels solve problems the last sentence stuck out in particular. The statement talking about mathematically proficient students says, “they (the students) can understand the approaches of others to solving complex problems and identify correspondence between different approaches.” This stood out in particular because it should be many people’s goal to have the ability to understand complex problems and find different ways to solve it. A good example of a person who does have proficient mathematical skills despite his amount of education is William Kamkwamba. William was able to interpret and comprehend the science and math needed to make a windmill. Due to his exotic location and

(6) Expressions, equations, and relationships. The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to:

The dialogue of this article is informative but also casual. In the article, the writer uses relatable examples to explain his viewpoints mathematically. As a learner, the dialogue of the article is easy to understand. He gets his point across that learning mathematics isn’t only steps and

Current mathematics researchers emphasize three areas of mathematical abilities. They are procedural knowledge, procedural flexibility, and conceptual knowledge (Kilpatrick, Swafford, & Findell, 2001; Rittle-Johnson & Star, 2007; Bottge, Rueda, LaRoque, Serlin, & Kwon, 2007). Procedural knowledge is the understanding basic skills or the sequence of steps needed to solve math

Similar to Skemp’s definition of mathematical understanding, Hiebert and Leferve suggested two mathematical types of knowledge: conceptual and procedural knowledge. Hiebert and Leferve’s (1986) explanation and definitions of procedural and conceptual knowledge have been reasonably influential in providing mathematics educators and researchers with a well-defined terminology to refer to learners’ knowledge of mathematics (Star: 2005, 406). Haser and Star (2004, 147) believe that proceptual and conceptual understanding are the two main fields that analyse the “nature of mathematical knowledge” while Hiebert and Leferve (1986, 1) attain that with the compact structure and distinctly defined content, mathematics “has provided an arena for much discussion of conceptual and procedural knowledge”.

Mathematics is the one of the most important subjects in our daily life and in most human activities the knowledge of mathematics is important. In the rapidly changing world and in the era of technology, mathematics plays an essential role. To understand the mechanized world and match with the newly developing information technology knowledge in mathematics is vital. Mathematics is the mother of all sciences. Without the knowledge of mathematics, nothing is possible in the world. The world cannot progress without mathematics. Mathematics fulfills most of the human needs related to diverse aspects of everyday life. Mathematics has been accepted as significant element of formal education from ancient period to the present day. Mathematics has a very important role in the classroom not only because of the relevance of the syllabus material, but because of the reasoning processes the student can develop.

I. Introduction In today’s society mathematics is a vital part of day-to-day life. No matter what a person is doing at home or at the workplace, he/she is constantly using different mathematics skills to simply function. Then what does this mean for mathematics education? When someone needs to