Introduction
Charter and public schools in the United States of America are facing a myriad of challenges and pressure from both external and internal sources. Externally pressure dictates that both public and charter schools show good performance during examinations. Anderson and Holder (2012) carried out a longitudinal study to investigate the ten years annual reports of the two local charter schools in the United States of America.
The study used information from different sources including document analysis, site visits, and interviews. The findings of this study revealed that the two schools under study received a lot of feedback about the administration methods, the curriculum, and evaluation strategies.
CER (Center for education reform) describes a charter school as an innovative public school that is accountable to pupils/students outcomes as well as developed to offer programs appropriately modified to meet the desires or needs of the community they serve.
In the year 1992, the first charter school received students in the city of Saint Paul within the state of Minnesota. Presently, there are at least 4,100 charter schools in the United States of America, which accommodate more than 1.2 million students (Bailey, 2009). The District of Columbia and 42 states in the U.S. have enacted laws, which are associated with the charter schools.
In every charter school, there is a board of governors are responsible for making critical decision in the management of the school. Besides, there are also sponsors in charter schools who play an integral role in monitoring as well as approving application to ensure that there is success in this school.
Statement of the Problem
The reasons for initiating charter schools were to improve the academic options in the public school system. Peebles (2004) defines curriculum as the entire issues that take place within the school. They include interpersonal link, guidance, extracurricular activities as well as academic work.
Peebles (2004) further points out that curriculum entails cultural dissonance, academic expectation of the parents, teachers’ support as well as experience in addition to instructional leadership. Peebles (2004) carried out a case study to look at four issues associated with curriculum in the Marblehead charter school. The issues explored included cultural dissonance, academic expectation, teacher training and experience as well as instructional leadership.
Peebles (2004) asserts that, in order for the charter schools to develop, they must move via various critical stages. These stages encompass pre operational phase, operational phase as well as institutional operational stage.
As pointed out by Anderson and Holder (2012), operational and post operational activities have the ability to impede the opening of charter schools and as such, great focus be directed to them in the course of the beginning phases of the charter schools development. The director of Marblehead charter school placed more focus on the survival of the school, such as curriculum development, development as well as staff and instruction supervision.
Background of the Problem
The need to show excellent performance has put a lot of pressure on both, charter and public schools to constantly review their curriculum in an effort to compete effectively.
Skilton-Sylvester(2011) argue that present day principles and managers of public and charter schools are required to constantly monitor and evaluate efficacy of their curriculum, review and implement new strategies and tactics in order to improve the performance of students in schools. Autonomy as well as teachers leadership are critical tenets when developing the school’s curriculum. Several studies have demonstrated that inexperienced teachers do not contribute sufficiently in developing the school curriculum.
Purpose of the Study
Charter and public schools in the United States of America have to combat a number of challenges because of external and internal pressure. Externally, both public and charter schools need to show good results during examinations. Internally, some schools have inexperienced teachers and poor curriculum that does not enhance performance of students. Developing a comprehensive and effective curriculum in both charter and public schools will serves as a platform for the schools to perform well in examinations.
As noted by Peebles (2004), an inexperienced and poor teacher has the potential to negatively affect the outcome of students even after the students have left the class. In the process of defining a curriculum, it is critical that teachers possess a detailed apprehension of approaches for assessing the outcome of students, techniques for assessing curricula as well as instructional delivery and the content of the curriculum.
Besides, when developing a curriculum, teachers should be given sufficient time to plan, to create, to adopt and to assess the curriculum. Numerous studies have revealed that one of the reasons why students migrate from one school to another is mainly due to the students’ poor academic performance. Most parents who are not contented with grades of their children received during the process of studying at school are more than willing to transfer their children to another school.
The significance of the Problem
Students have different abilities in a given or particular classroom. We can hardly have a one-size lesson package which can fit all students in the class. Learning procedures and abilities differ across the classroom. As a result, there is a need for a lesson tailored to fit a specific group of students with a common liability or problem. The lesson must address these needs for effectiveness and benefits of the students.
At the same time, the needs of students are diverse. This means that teachers should tailor their teaching profession in a specific way in order to meet specific needs of the students. The teacher in this case faces a challenging task of ensuring that he or she has the required skills for some particular needs.
Differentiated instruction is an area in the teaching profession which is harnessed for providing specific needs to students. Given that students have specific needs that must be catered for by differentiated instructions, there is the need for developing an area for students’ professional development for the differentiated instruction. In this paper, differentiated instruction for students with difficulties in learning the English language in a mathematics class will be looked into in the process.
Mathematics Learning in English Language
Mathematics is a core subject in all disciplines. The subject is a must-learn for students in various disciplines. Mathematics lessons are majorly taught in English. This is because of the ease with which the language is applied in teaching mathematical expressions.
A gap in understanding the relationship between achieving success in mathematics and individual’s knowledge in English language has not well been defined, but evidence shows that a mastery understanding of mathematics concepts has a strong relationship with the usage of English language and the ability to understand and characterize, express and apply mathematical concepts and expressions.
Correlation with mathematics
The ability to read and understand English and apply the language to learn mathematics has strongly correlation. It is critical to note that the ability to read and understand concepts and solve problems in mathematics is based and influenced by a variety of English language skills (Poglinco, Bach, Hovde, Rosenblum, Saunders & Supovitz, 2003).
That has been evident in different regions in the world. Studies have shown that the United States of America, the United Kingdom, and some countries in Africa use English in mathematics classes.
At the same time, the United Kingdom and the United States of America have non-English speaking population schooling in the same mathematics classes. The challenge is the use of mathematics textbooks written in the English language in this setting. According to Poglinco et.al, (2003), the same text books are used in African countries in the mathematics curriculum.
Teachers in training colleges are taught in English and as a result, they infer the same to students in English. At the same time, there is no discrimination in education settings. Consequently, students are huddled together in the same learning environment irrespective of their ethnic backgrounds (Bender, 2002).
In this case, students find it difficult to grasp and understand expressions in mathematics because the first language of the student is the language learnt from textbooks in the classroom. It has been shown that there is a gap between the language used in class, textbooks, and in social places.
In social places, the gap in the cognitive academic language proficiency indicates that the need for a high degree of proficiency in the familiarity of grammatical patterns, words, and arguments, and the style of presentation, which often appears to be foreign to the user of English as the second language.
Research shows the disparity in understanding the academic language used in mathematics books by speakers of English as a second language. The disparity in understanding mathematical expressions in English as a second language makes it difficult to understand mathematics by second language speakers (Oakes, Gamoran & Page, 1992).
English proficiency
While students who speak English as the second language find it difficultly to cope with the use of English to learn mathematics, research studies show that even students who speak English as the first language need to meet a level of proficiency to optimize the benefits of understanding mathematical instructions given in English.
That reinforces the significance of the relationship between becoming proficient for speakers of English as the second language. Students who use English as the second language find it difficult to cope with instructions in mathematics classes because they encounter two tasks to accomplish simultaneously.
The first task entails learning the English language, and the second task involves learning mathematics. In the first case, the student who speaks English as the second language has to undergo the entire process of learning English as a second language just as one learns one’s own first language.
It entails the complex process of second language acquisition which involves the process of listening to the words and their sounds, followed by the learner’s attempt to speak the words. As is common with all second language learners, the learner makes grammatical errors which include incomplete sentences, poor vocabulary usage and pronunciation.
The process involves the leaner trying to understand the syntax of the language, discovering how the language works, and the rules of organization. That makes the learners using English language as the second language struggle to grasp concepts in the mathematics class.
The need to learn English
It is possible for a student to learn English language as a second language and grasp the vocabulary that is enough to communicate with peers and in other social functions. However, the student might lack the vocabulary and the grammatical organization of words to understand and make sense of the mathematics materials learnt in class.
Examples of learners taught in English in schools who find it difficult to take lessons in mathematics abound. A typical example is where the meaning of the word “term” is not well understood and applied correctly when taking mathematics classes. A student can know the meaning of the word in English but find it difficult to understand and apply the meaning in mathematics lessons.
In this case, many specialized terms such as factor, probability, radius and other terms used in mathematics making it difficult for the student to grasp and apply the meaning in mathematics lessons. This happens because of the fact that when the lessons are delivered, teachers do not discriminate students but deliver the lesson with an assumption that they are grasping the concept irrespective of the language deficiency.
Given that teachers cannot speak and learn the first language for every student in class, there is a need for them to offer differentiated instruction to students in this area. Differentiated instructions are vital to students with learning disabilities as teachers are trained to give instructions in a mixed class environment (American Institutes for Research, 2010).
English language acquisition rate
Research findings show that the rate at which students acquire skills in English varies from one student to the other. Contrary to the earlier belief that the younger the child, the more likely they are to learn English quickly compared with the older people, has been refuted.
An older person has well developed cognitive capabilities and is able to grasp the language faster compared with the younger student. That implies that even speakers of English as a second language are able to acquire English language and mathematics skills much quickly and use them to learn mathematics and other academic pursuits.
Some of the most critical factors that could help the leaners of English as a second language include the type of English language used to provide instructions, the period of exposure to the new language, and different aspects of the learner’s native language.
Differentiating Mathematical Instruction for English Language Learners
A quality and clearly articulated curriculum provides the basis for differentiated instruction. According to Dolan and Hall (2001), content can only be understood when delivered in English for students who are proficient in English when learning math skills. Many mathematics classes have normally students from diverse backgrounds.
Differentiating mathematics instructions can only be successful when connected with the problems students suffer such as anxiety when using English to learn mathematics. Students who use English as the second language suffer from the anxiety of having to communicate and listen to instructions in mathematics as a second language. Teachers in such classes understand very well about the anxiety of such students.
Such classes commonly constitute a diversity of students viewed in terms of ethnic backgrounds. In a mathematics class, about 30% of the students are normally the English language learners. As a result, they differ in the learning abilities, facilities, and styles. The English language learners find it hard to cope with the material in this class. One of the strategies proven with time to offer a solution to the problem encountered by the second learners of English is differentiation.
The purpose of differentiation in a mathematics class is to teach the victimized students with the aid of myriads of techniques and strategies that address their deficiencies. This implies that the main focus is the teacher. The teacher is supposed to come up with strategies to implement differentiation instructions.
In this case, the teacher is supposed to be equipped with professional techniques needed to address the issues (Tomlinson, 1999). In this project, the professionalism involved in differentiation mathematical instructions for the English language learners are going to be discussed and highlighted. Some of the professional techniques employed by teachers taking English learning students in mathematics are discussed below.
Students’ Background Information
Dolan and Hall (2001) have demonstrated that students arrive in class with varying capabilities, learning disabilities, and learning styles. According to Ellis and Worthington (1994), to effectively provide instructions when teaching mathematics, it is important for the teacher to differentiate instructions based on the students’ background information, which is a critical basis for providing appropriate instructions to students taking mathematics in English as a second language.
It is important as research has shown that the professional teacher first understands the background of the students because it helps in differentiating the students when providing instructions in English (Meyer & Rose 1998; Oaksford & Jones 2001).
Professional teachers needs to be culturally sensitive and aware of the customs and traditions of the students they teach, which enables the students to be confortable in class and the teacher to deliver instructions effectively.
Research has shown that culturally sensitive teachers involve the student’s family in the academic progress of the student because they are able to use appropriate phrases in English when teaching the students (VanTassel-Baska & Stambaugh, 2005).
Another criterion that provides appropriate teachers with the best methods of differentiating instructions for the students is to review students’ records and their scores to enable appropriate planning for subsequent lessons based on the learning needs of each student (Vaughn, Linan-Thompson, Kouzekanani, Bryant, Dickson & Blozis, 2003).
Tomlinson (2001) has shown that for the professional teacher to comprehensively understand and plan on the best instructional delivery method for students with English as the second language, the teacher should reflect on the cultural behavior of the student, as it forms a strong basis for learning about corrective and proactive methods to design the best approach to use.
ESL students sometimes try to avoid eye contact with the cultural explanation being to show respect for the teacher because some cultures regard direct eye contact as showing disrespect. Sometimes students smile while disagreeing with an issue being discussed as a gesture of respect. Other cultural issues include failure by the student to read quietly, reluctance to participate in debates, lack of respect in the side of the student, and lack of active listening behavior (Sizer, 2001).
Language Acquisition
According to studies by VanTassel-Baska and Stambaugh (2005), when students are given tasks to perform, it gives them the opportunities to conduct detailed investigations to understand mathematical concepts. Examples include when finding the perimeter and area of a two dimensional figure by developing the formula for calculating the area and perimeter of the figure by using formulas that they have participated in developing.
In this case, it is important for students to work in groups. Working in groups gives the students the opportunities to share their experiences and skills in not only developing the formulas but giving each the opportunity to learn the English language associated with each of the steps involved (Rose & Meyer, 2002). In addition, working in groups promotes a low anxiety environment and enhances every opportunity for authentic conversations.
When working in groups, students freely takes the opportunity to ask their peers questions and promotes cooperative learning, which gradually improves each student’s attitude toward learning mathematics in class.
That leads the students taking English as the second language to develop visible language proficiencies that are used in the common mathematical expressions from the hidden cognitive academic language proficiency. The learning process further benefits the student in enhancing the conscious linguistic behavior toward a task like solving a problem involving the usage of words in mathematics (Pettig, 2000).
The teacher ensures that students as a first step are able to provide the meaning of each of the shapes, which are added to a word wall which consists of a collection of pictures, words, and definitions. It is important at this point in the learning process to add and interpret words in the context of mathematics.
The words included are random, field, point, set, sum, even, breadth, length, and area.it is important for the location and use of words including hypotenuse, length, width, and diagonal to be clearly indicated on the word board. There should be a mathematics register as well which shows the style and meaning of the words used and the role each word play in the learning process (Reis, Kaplan, Tomlinson, Westbert, Callahan & Cooper, 2001).
Rose and Meyer (2000a) assert that in the language acquisition and learning process, the students are required to write down the area and perimeter of the figures they have used in the process and to write the general formulas they have used to calculate the area of figures.
The teacher uses manipulative techniques to teach the mathematics concepts used to enable the student understand the meaning in English and to apply the concepts in class. Other requirements include asking the students to find the largest area and the smallest area of different shapes (Rose, 2001).
A similar process to the first one can be done working with different shapes. In this case, the students are asked to define the shapes by talking with peers in English, provide comprehensive inputs from other students in different groups. In each of the tasks performed, the teacher should reflect on the instructions provides to assess if it has been differentiated enough to understand by students using English as a second language (Troxclair, 2000).
Teaching academic vocabulary
Finn, Julian and Petrilla (2006) have demonstrated that instructions in English as a second language should be done professionally by teachers to be effective in offering math instructions. The difference in the use of words in different fields and in mathematics comes out clearly when math specific terms are taught and the difference explained as applicable in each area.
A typical example includes words like “decimal” and “percent”. In this case, the teacher should demonstrate that the vocabulary can have multiple meanings, which helps the student understand how to use the words precisely in the mathematics context (Beck, McKeown & Kucan, 2002).
Learning is about supporting each other in groups. The teacher should encourage students to offer bilingual support because research has demonstrated that students understand better the materials offered to them when they explain to each other. In addition, using graphical presentations and pictures and giving students the opportunity to teach with images and objects and the use of manipulative offers students the opportunity to learn the meaning of symbols in English (Berninger & Fayol, 2008).
The Objectives
The purpose of differentiating the mathematical instructions for the English language learners is to make the lesson of mathematics comprehensible for all students in the class (Tomlinson, 1999). That is because students come from varying learning capabilities, educational and cultural backgrounds, language preferences, learning interests, and level of responsiveness (VanTassel-Baska & Stambaugh, 2005).
Differentiated learning provides mixed students with an appropriate learning environment to optimize each student’s learning capabilities. In addition, the approach is to maximize the learning process and help the student to succeed in their knowledge acquisition (Tomlinson, 2003).
Through this concept, the students are supposed to achieve the needed mathematical concepts despite their language barriers. As a result, the teacher is supposed to ensure that the students express the numbers or concept used to solve a certain mathematical expression in writing or orally. This involves ensuring that the lesson is not given as it is written in the books but rather is made for the students (Glencoe, 2005).
To be effective in creating an environment that supports differentiated learning, the teacher needs to identify the components and the features associated with differentiated learning ((Tomlinson, 1999). Differentiated teaching and learning provides the best solution to students in mixed classes as it provides each student with the opportunities to be taught based on their abilities, cultural backgrounds, and linguistic capabilities.
Content
There is need to identify all the materials that are critical and necessary in supporting instructional content. The elements included are attitude toward math learning, skills, concepts, acts, and generalization principles (Glencoe, 2005). Access to the content used to learn by the student is critical in supporting the level of success for the student.
In addition, there is need to align goals with the learning objectives when the designers of differentiated instructions are developing content. Assessment of the goals are done by the tests conducted using quality tests and administered frequently based on standardized measures (Simon, 2006).
It is critical for the curriculum designers to write the objectives in incremental steps to produce a continuum of skills building tasks. It is important to note that the instructional steps used in teaching mathematics based on differentiated methods provide the basis for using objectives that have been aligned to the content (Simon, 2006).
It is important to make the instructional concepts to be focused and driven by the underlying differentiated instructions principles. The objectives should capture a broad based instructional concept without considering the minute details and unlimited facts. Teachers implementing differentiated instructional methods should factor student contributions with the level of complexity adjusted to suit the needs of each student in the diverse group (Silver & Stein, 1996).
Products
Solomon (1989) established that there is an intrinsic need to conduct an ongoing assessment of the student to provide meaningful differentiation based on pre-assessment and ongoing assessment of the student. That enables the student and the teacher to access and provide a scaffold of varying needs based on formal or informal assessment methods that include performance assessment evaluation techniques and procedures (Skemp, 1976).
It is important to differentiate the expectations and requirements for the responses provided by the students. Here, the students express their level of knowledge and understanding of the subject in different ways (Stenmark, 1991).
Process
There is need to use differentiated methods of instruction by the use of flexible grouping methods. Flexible grouping allows students to interactively work together and share their knowledge and understanding in the process of developing new content (Stuart, 2000). The teacher undertakes to provide introductory lessons for the whole class, followed by subdividing the students into smaller groups that are not fixed.
It is important to ensure that differentiated teaching is dynamic and making the grouping and regrouping process dynamic. In each case, grouping and regrouping plays a significant role in in the ongoing evaluation process as the changes go along with the changes in content (Buswell, Schaffner & Seyler, 1999).
There is need to ensure classroom management is designed to benefit the teacher in instructional delivery and the student in the acquisition of the skills and knowledge in mathematics using English as a second language. The teacher should carefully select the instructional delivery method and the organization of the content to deliver to the students (Council of Chief State School Officers, 2006).
Content delivery effectiveness
The delivery of content should be effective by ensuing that the content delivered content is clearly expressed and generalized to enable and make the students understand that the future relies on an understanding of the concepts of differentiated teaching.
It is important to use “assessment as a tool for the purpose of extending instruction rather than merely for measuring the accuracy of the design” (VanTassel-Baska & Stambaugh, 2005). Assessment should “always be done in before and instruction episode, during and after the session by posing questions to optimize learning and student needs” (Scholastic Instructor, 2010).
It is essential to engage learners by developing and structuring lessons which motivate learners and with different needs in a differentiated class.
Networks appropriate teaching methods
A differentiated environment provides students with abilities to support recognition networks. In context, the network provides multiple examples with each critical feature integrated into the network. It is critical to support the background context, support different strategic networks, such as models for skills based performance, feedback, leaning opportunities, and choice of learning contents.
Assessment Methods
Assessment is critical in differentiated teaching as it is a source of knowledge and information that is essential for decision making for teachers when planning instructional and learning activities. Planning provides a sound foundation for the teacher to create an organizational structure that enable the teacher to mold the students according to the learning goals and objectives.
It is critical to understand that assessment supports to a significant extent the teacher’s quest to understand the needs of each of the students and to create an instruction and content delivery according to the needs of the student. It is therefore worth understanding the role differentiated assessment plays in providing differentiated instruction.
It is critical to note that differentiated assessment provides the teacher with information about the differentiated need and information about each student. Differentiated assessment provides information about the needs of each student and their strengths in relation to the desired outcome.
The interdependence of differentiated instruction and assessment is that differentiated instruction provides teachers with the opportunity to learn the expected outcomes using diverse tools and strategies that are appropriate for measuring differentiated assessment. Here, differentiated instruction leads to differentiated assessment which informs differentiated instruction.
The importance of the teacher playing a critical role in working toward differentiated assessment is based on the rationale of facilitating issues such as metacognition.
Metacognition calls for teachers to understand and help students to develop inherent capabilities to diagnose any deficiencies in their learning progress. In this case, the student, under the leadership of the teacher is able to recognize metacognition, which includes setting individualized learning goals, making their own choices, and the ability to conduct their own reflections and self-assessment.
Planning for assessment
Before implementing differentiated teaching before, when, during, and after implementing the strategies involved in the learning process, the teacher is supposed to make an assessment of the class and students in order to identify the needs of the students. There are several methods that can be used.
The first method is examination of the records. In this case, the teacher is supposed to carefully examine or review the test score of the students in previous mathematical tests. He or she is also supposed to check the daily assignments and the wording used in the students’ books. Assessment should be done at the beginning of the term or the period the teacher has taken over.
Assessments can also be done through a one-on-one talk with the student in case the class is small. In addition, assessment can also be done through testing a learning style inventory that can work best to the students. This is possible through ascertaining the topic that best suits the students (American Institutes for Research, 2010). For this case, the students should be given topics, such as algebra and statistics.
Students should also be assessed for their progress. This should be done through the different skills levels, learning style and thinking skills among many other issues. At the end of every period, the teacher should give the students some projects and evaluate the same to see the extent to which they have grasped the concept (Baker, Gersten, & Lee, 2002).
In addition, once the student needs have been identified and integrated into the teaching plan, it is important for the teacher to use daily warm up activities to assess if the student has developed mastery of the mathematics concepts.
A number of assessment method have been prosed by researchers. The assessment methods appropriate for a differentiated environment include teaching and learning include performance assessments and the reading and writing assessments, which can either be formative or informative. It is important for the teacher to ensure that teaching and learning tasks are rich in language integrating standard based instructions.
Examples, which are discussed elsewhere, include journal writing, open ended tasks, reflection, and explanations. Teachers have the obligation of monitoring the progress of their students in the acquisition of skills and usage of English language. Language development and content are important components to use in the assessment process.
The teachers effect assessment through a formative process where the assessment occurs in class and enables the teacher to determine the conceptual understanding and language proficiency of the students. It has been established that formative assessments of the students cannot be used as a tool to measure the grading of students but is crucial in determining the progress of the student in class based on feedback from the students.
The assessment process includes students being encouraged and taught on how to create concept maps, semantic webs, and show how they can create relationships between different ideas in mathematics. Monitoring the progress of the student to determine the student’s usage of vocabularies and content knowledge is always based on an assessment of the student’s abilities to respond to questions, explanations on the reasoning behind the process, anecdotal records, portfolios, and homework logs.
Performance assessment
The assessment method is designed to accommodate different student capabilities especially for students who study using English as a second language. The inclinations of the student, learning profile, interest, and student needs to improve the method of delivering instructions to the students.
The performance assessment process requires that the teacher be able to identify the process a student undertakes to solve a mathematics problem and not just the results from a task. It is important to adopt performance measurement to students still learning English by making appropriate adaptations, and a comprehensive understanding of the language needs of the student. In this case, students might be required to show what they know, a study based on alternative assessment.
Based on alternative assessment, students show what they know by using written correspondence based on authentic techniques such as determining the rationale for solving a problem, what the student task requires and how to solve the problem.
In addition, the student should show evidence of reading the required materials by writing journals of the problems solved and the skills employed, using graphic organizers among other tools. The need for students to write on how the solved the problem is critical for students who use English as a second language.
It has been established in research that improved performance assessments for minority English speakers provides the students with ample opportunities to express their knowledge in a meaningful way.
Performance assessment enables teachers to provide students with new tasks to make the assessment process authentic using open ended techniques and accommodate varied learning styles. It is important for teachers to understand the English language proficiency developed in the students as and the effect on the way they respond to different activities.
Reading and writing
Reading and writing provides the teacher with the opportunities to understand the level of proficiency the student has acquired by demonstrating their skills and conceptual understanding of the use of language to solve problems in mathematics.
It is important for the teachers to inquire from students if they understand explanations of solving a problem provided by their peers. It is important for teachers to encourage students to speak and paraphrase what they have learnt in class in their own words, and to clearly relate ideas to different mathematical problems.
The Strategies
The strategies of delivering mathematical instructions students who take English as the second language are varied. Included in the strategies are thematic instructions, inquiry and problem solving, cooperative learning, scientific inquiry, mathematical problem solving, vocabulary development, classroom discourse, and affective influence.
Thematic instructions
Thematic instructions require that the teacher makes preparations of delivering theme based instructions consisting of thematic units of key concepts in mathematics. The approach enables students take more time to become proficient and used to the language used to explain the key mathematics concepts.
The approach is important for new learners of English because it enables the student to connect their knowledge with what is contained in the curriculum of the teacher. It has been proven important that teachers should design and place the thematic units in the mathematics context of the new learner and everyday life.
In this case, it is important for the concepts to be inclusive of mathematical problems and how to seek mathematical solutions for the problems. The teacher is always aware that the student has to connect their learning experience with the real life way of solving problems using mathematical expressions. The expressions include role play, physical activities, rephrasing of expressions, using the correct language and providing the correct questions, and incorporating learning, acquisition, and writing skills.
Inquiry and problem solving
The tasks confronting students being instructed in mathematics using English as a second language is cognitive factors where the leaner has to develop conceptual knowledge of the use of English to express mathematical solutions based on the language.
Another problem experienced by speakers of English as a second language is the affective factor or self-confidence to use and express mathematical problems and solutions using English as a second language. It is important for the teacher to ensure that students who speak English as a second language develop individual problem solving skills and as they develop proficiency in the use of English as an instruction delivery language.
According to the curriculum of charter and public schools, it is important for the student under the instructions provided by the teacher to coordinate previous experience, intuition, and knowledge without direct procedures. According to the assumptions integrated into the problems solving strategy is for the student to understand the problem clearly, device a strategy to solve the pro0blems, and do some reflection on the outcome of the strategy.
For speakers of English as a second language, the student should use heuristics in understanding mathematical problems by stating any problem in mathematics in their own words, determining the unknown, and establishing what is required to solve the problem.
Research has established that problem solving strategies, inquiry, and second language acquisition often progresses to more abstract reasoning based on concrete strategies. It is important for students at the inquiry and problem solving stage to clearly state the inquiry of the meaning of words, how to solve mathematical problems, and report the findings from the inquiry.
The benefits associated with inquiry and problem solving strategies for English speakers as a second language include the ability of the student to learn and develop functional, aesthetic, and logical ways of solving mathematical problems.
In addition, some students might have individual learning disabilities such as the inability to speak, understand, and write in English effectively. It is important for the teacher to provide students with tasks that are sound with mathematics solvable problems, and problems related to the student’s background.
The tasks are required to engage the intellect of the student, develop the skills of the student in understanding the language, promote effective communication of mathematical expressions, and ensure real life activities are part of the learning process in developing the student’s disposition to do mathematics.
Both the student and the teacher each have roles to play in the acquisition process. For the teacher, it is essential to pose tasks and questions that stimulate engagement of the mind of the student toward the problem to seek for a logical answer by engaging the mind.
In addition, the teacher should take the initiative to listen to the students’ ideas, encouraging and asking the students to communicate orally and in written, and monitoring and encouraging students for being active when learning mathematics in English as a second language. On the other hand, the student is required to question one another and respond to the questions by the teacher and individual students. It is important for the students to initiate problems, conjure up solutions, and assess the validity of the solutions
Cooperative learning
Cooperative learning which has its foundation on the theory of social interdependence, behavioral learning, and cognitive development has been shown to provide the basis for achieving positive development in teaching mathematics to students in a mixed environment. Findings indicate that when peers discuss in small groups, they are able to assist one another as they discuss lesson materials in English.
Students use the second language skills they have developed with time in authentic discourse, enabling them understand instructions based on the complex language structures which they continually refine by expressing mathematical problems and solutions which are negotiated through talk. As mentioned, students integrate the concept of problem solving through groups to improve the reasoning capabilities and by enabling language minority students to contribute meaningfully to the group.
It is crucial to note that cognitive growth is the fundamental element that precedes cooperation to attain the goal of solving problems in mathematics. Students in such a situation, students should be grouped according to needs, color, and using a racially integrated class. In addition to learning mathematics using English as a second language, students in a mixed environment should be taught interaction skills to communicate with peers and the teacher in performing assigned tasks.
Mathematical problem solving
One of the strategies teachers use to help students acquire the linguistic capabilities demanded for learning mathematics is the use of discussions that involve vocabularies in English about the situational context of mathematical problems. The approach is important in enabling students perform linguistic and conceptual mathematical tasks by breaking problems into grammatical phrases.
The contextual meaning and mathematical relationship provides the basis for solving mathematical problems by students in mixed classes. Typically, it involves the coordination of different and complex skills which the student reliably implements using a particular problem solving procedure with the underlying English language syntax to express the problem.
Teachers who deliver instructions to students in English integrate the cognitive part of the multi-strategy intervention with metacognitive components and to learn and understand in English the explicit procedure to analyses and provide solutions to the mathematical problem.
The student under the instructional assistance of the teacher should read and understand the problem as a metacognitive component. The student shows development of skills in understanding mathematical problems in English and the method of solving the problem.
Making Expressions Banks
The strategy consists in making the use of diagrams that show expressions and phrases that are helpful in the English language learners’ (ELLs) study of mathematics. This occurs because when the words used by a teacher are accompanied by diagrams and illustrations, they help the ELLs understand various mathematical concepts and have the memory stick accordingly.
The Use of Manipulative Tools
These are gadgets that a teacher should employ in the course of teaching in order to ease understanding. These manipulative tools are made to help the students come up with physical illustrations which comprise the mathematical expressions. Having a student come up with a physical mathematical model will boost his or her confidence and motivate them to understanding the mathematical concept easily and qucikly (Scholastic Instructor, 2010).
Modify a Teacher Talk and Practice Wait Time
The teacher should not engage in a lot of talking without giving time to ask questions. Also, when asking a question, sometime in order to generate answers should be given to the students in the class. Writing the question on the board helps a lot as well as it helps to stress the most major concepts in the mathematical language (Scholastic Instructor, 2010).
Eliciting Nonverbal Responses
The English language learners are in most cases used to nonverbal communication. As such, the teacher should be keen to notice their understanding of concepts by simply observing their behavior and reactions while teaching (Scholastic Instructor, 2010).
The Use of Sentence Frames
The English language learners understand sentence frames quite well in their English language. Therefore, the use of such statements while expressing mathematical concept will foster the students’ understanding.
Design Different Questions and Prompts at Each Proficiency Level
Asking question gives students a chance to express and confirm their understanding of the subject. Also, it helps the teacher know if the concepts taught in the class has been grasped or not.
The Use of Prompts to Support Student’s Responses
The use of prompts to support a student’s responses entails giving a certain way of answering a question to the English language learners. Such prompts help them to be confident while expressing their answers during the lesson.
Consider Language and Math Skills When Grouping Students
Interacting in a group level gives students the opportunity to learn new ideas as well as overcome difficulties which they might have in understanding some mathematical concepts. Therefore, grouping students with different abilities together helps their learning to a great extent.
The people who support education for ELL suggest that common and core academic standards should be implemented with the aim of raising achievement for the English learners. Education sector should pay more attention to the non-performers to improve their performance in all subject areas of study.
Screening the students’ performance to identify their weaknesses could contribute positively to their performance in the end (Finn, Julian & Petrilla, 2006). The Arizona system of assessment should also be evaluated to improve its effectiveness on the assessment of the students’ performance. Since the study identified that the non-ELL performed better in math than non-ELL, more emphasis should be put on their system of education and the curriculum to equalize the performance of both groups.
Utilize Partner Talk
In the course of teaching, the teacher should allow discussions between the neighboring students, which breaks the monotony of the teacher talking alone and also contributes to building trust between the students, being very vital in the process of studying in class.
Encourage Choral Responses from Students
To encourage choral responses from students helps a sector of learners who hardly speak out to answer a question or ask one. In a choral response, therefore, they are able to gain confidence as well as get the right pronunciation of the mathematical concepts (Scholastic Instructor, 2010).
Implementation of the Plan
It is important for the teacher to prepare well in advance before setting the stage for the delivery of instructions. The teacher should begin by selecting collaborative objectives for teaching the mathematics for the target learning students, develop a well thought out plan for each of the mathematics activities, identify methods to use to enhance the acquisition of mathematics skills in English language, create the roles each of the students are to play, and create the groups where each of the students will belong.
The implementation plan involves a process that is procedurally factored into the entire differentiation process. It is important for the teachers involved in the implementation process to ensure that they are well prepared through workshops involving teachers interested in the process.
Based on the knowledge the students have acquired, the teachers should prepare differentiated units that are conceptualized to provide effective feedback to the teacher on the progress of the student. In addition, the teachers should work collaboratively in developing differentiated units and lessons. It is important for the teacher to recall and use previous materials when implementing the plan before starting the process (Gamoran, 2004).
The implementation process involves breaking instructions into small units at the beginning to ensure the units and subunits serve the purpose of the students. The teacher should ensure that there are other teachers that they can collaborate with, and the process should be started by involving staff with a small number of groups and units.
The process should be student driven with appropriate resources made available for each defined target group that reflects the curriculum content based on previous curriculum materials before shifting to the current materials. It is important that the teacher identifies weaknesses and strengths of the student at an early stage to formulate techniques and strategies to take corrective actions in the process.
It is important to involve and plan flexible groupings for each of the student groups and units that have been created. Planning of the groups and units must occur under strict adherence to an identification and classification process for the students. The students involved have varying capabilities and involves multiple-intelligence.
It is important at this stage for the teacher to ensure that the students are able to identify what they need to learn and how they want the instructions to be delivered to them. In the process, the teacher should factor the differences in the language needs of the students and address the problem by providing them with the right learning experience. The strategy should involve small groups and whole group initiated instructions. The teacher should play an important role of being a facilitator for processing learning information.
When setting out the plan, the teacher is supposed to ensure that the room is well arranged in a way that it can quickly be rearranged for the next lesson. The teacher should then issue materials in a properly arranged manner to be used for the study. Materials such as drawings tools, computers, textbooks, and audio materials among many others should be provided (Allsopp, 2008). When everything is ready and arranged, the lesson should start. A typical implementation process involves a number of steps that can be drawn from
Leadership Principles
It is crucial for the teacher as a leader to ensure that they create a differentiated environment to ensure optimal learning occurs. The “environment is crucial in supporting or deterring the quest for a student’s affirmation” (Rose & Meyer, 2000b) in the classroom. The teacher has to ensure effective layout of the classroom, effective use of space, effective lighting, appropriate preparation and incorporation of environmental elements, a positive environment, and a supportive environment that is effective for learning in class.
It is crucial to ensure that the physical environment is structured to accommodate differentiated instructions delivery of math lessons in English as a second language. It is crucial for the teacher’s approach to integrate fairness and success for mutual growth and success. In addition, the environment should be differentiated effectively to ensure student readiness, learning profile, and interest. The teacher should provide instructions using easily understood methods, while ensuring minimum noise
The teacher is supposed to display some qualities or principles vital for the implementation of the plan. The first principle is patience. The teacher should be patient with the students and give everyone time to express their own ideas. Patience is core in encouraging students to promote, sustain, positive relationship with the students, and quality teaching.
Typically, leadership is a relational and not an individual phenomenon in delivering instructions in class. Patience, impartiality in dealing with the students without showing discrimination for other students, impartiality in understanding the diverse needs of the students, and politeness contribute positively to the development in the acquisition of mathematics skills based on an understanding of English language as a second language.
The next principle should be willingness. The teacher should develop a parental caring heart and be willing to always help his or her students any time. At the same time, the teacher should maintain professional methods and never deviate from the topic or give up on it because of the difficulties involved. When teaching, the teacher should be honest with his or her students and avoid showing divided favors.
Agenda
The teacher should enable the students to create personalized list of tasks to complete within a certain specified period. The agenda constitutes activities that vary from one student to the other in the differentiated class based on their needs. It is important for the teacher to develop an agenda that lasts the student sufficient time to complete and start a new agenda when the previous one is exhaustively completed.
The teacher provides the students with sufficient freedom to determine the order of completing the agendas. That enables the teacher to devote much of the time to assess the groups and create new subgroups according to the needs of the students and other group attributes that define the groups.
Tiered activities
As a leader, the teacher should formulate techniques and other methods to enable the students learn the same activity using the same skills, though they learn in a differentiated environment. The teacher has to use tiered activities to ensure equal opportunities are available for all students with differing learning capabilities and language backgrounds to learn and grasp the same ideas as other students.
Engage students actively
It is beneficial to the students in mixed classes to be engaged actively in the learning process (Rose & Meyer, 2000b). The opportunities available for learning include involving students to collect necessary materials and items that they are to use in the math lesson. Learning is a process that involves more than listening to the teachers delivering instructions, students memorizing formulas, and getting the correct answers.
When students reflect about what they have learnt, apply the knowledge they have acquired in real life experience, and relating what they have learnt to past experiences enhances the learning process. The teacher bears the responsibility of leading students by motivating them to want to learn, and to connect the content to areas of interest with the content they have learnt (Oaksford & Jones, 2001).
The teacher provides leadership and guidance to enable students to reflect on the steps and procedures for getting the correct answers to the mathematical problems. Students are advised to break into groups to solve problems with multiple paths and reflect on the methods they used to get the correct answer.
It is important to make the students apply open ended questioning methods and think about the problem. The teacher motivates the students to ask questions including how one could sort out a problem, the number of ways to find a solution to a problem, and the number of different ways to solve a problem. It is important for the teacher to ask questions that simulate mathematical thinking to enable the students develop strong conceptual frameworks which enable the teacher to understand what the student is thinking.
Surveys and questionnaires play an important part in collecting feedback and which shows the level of collaboration of group members and understand what the best strategy and elements for engaging math students.
The teacher ensures to share feedback with the students to show respect and motivation for the students. It is crucial to proactively engage the students and encourage them develop minds that are précises in thought, argument, language usage, and making sense out of conversations.
Self-reflection
It is important, according to studies done by Tomlinson and Allan (2000) on leadership for the teacher to take time, to assess and conduct self-reflection. Honest answers provide the teacher with honest results about the best corrective actions to take to improve the relationship with the student and improved delivery of instructional content.
Self-reflection involves an in-depth inquiry into quality attributes such as where the teacher had been successful and where the teacher had gone wrong in the delivery of content in mathematics (Rose, DSethuraman & Meo, 2000).
The teacher is able to reflect on the goals and the extent to which the goals have been attained. The self-assessment provides the teacher with appropriate information on the students they tend to ignore and the students who need more time to be spent on them.
Such an inquiry is important because the teacher understands all aspects of the profession that need improvement, methods to increase parental involvement, understanding of the resentments to resolve, what can be done to improve the teacher’s provocativeness in teaching and professional development, and continuous assessment of the impact of the content delivery to the students (Rose, DSethuraman & Meo, 2000).
Explicit
Torgesen (2002) argues that the teacher needs to be explicit about the curriculum content delivery by determining the skills and concepts in mathematics that the student needs to learn. The teacher provides leadership in determining the relationship between the mathematics concepts being delivered in English, and the best method to organize the skills, concepts, and facts in a logical manner (Reimer & Moyer, 2005).
The teacher as a leaders increases student involvement in instructional activities to enable them construct an understanding of the relationship between concepts and skills, with the teacher contributing to the efficiency of content and instruction delivery. Instructions given by the teacher should also be based on careful planning.
Keeping track
According to Pettig (2000), leadership is all about keeping track and reflecting on the progress made by the student in the differentiated class for mathematics. It has been proven essential for the teacher to ensure detailed records are kept of the progress of the student to ensure a well-developed planning guide is established (Rose & Meyer, 2000a).
Key players in the Plan
Since this is a school setting, various players should be involved for the success of the plan. First of all, the parents should be involved by all means. Parents make many decisions that affect the running of the school. The decisions weigh heavily on the ultimate influence and course of direction taken in the development of the kid.
Besides parents, other stakeholders are included in the hierarchy of stakeholders of the board which is made of elected or appointed board members. The founder has the sole responsibility of the method of selecting or electing the board members. On the other hand, the board is composed of members from diverse backgrounds who have and contribute different expertise on education, strategic planning, and personnel management among others.
The board is characterized by members with unwavering and passionate belief in the values stipulated in the school’s charter. In addition, a focus on results and a strong partnership between the school and the teachers, and an appropriate structure in the composition of teachers and other leaders in the school.
Charter schools receive only head funds from the government without any financial support for other facilities that are provided for in public schools. In addition, the schools attempt to provide curriculum that specializes in specific areas which is more cost efficient and based on state mandated exams.
Parents, teachers, or activists are supposed to provide the needed funds and materials for the success of the plan. Teachers should also be involved. They should mark the needs of the English language learners and be ready to be called for extra lessons. The teacher leaders should ensure that materials are availed on time. The staff should also be willing to help in any way possible. The students should be willing to be helped and always help each other (Allsopp, Kyger & Lovin, 2007).
Mathematics is often regarded as a foreign and quite hard subject to grasp to most students unlike the other subjects taught at school or college. Particularly, in the case of English Language Learners (ELLs), mathematics to them is a major challenge.
For a teacher, as a result, it is hard make the students fully understand the math language, as such; a lot of efforts are required to acquire math concepts in the oral and written form. To be effective in the delivery of specialized services, the schools have integrated into their models the accountability for student achievement.
The state
The state is also another player in the plan as it provides the funding to the charter schools. In context, charter schools can be public or private depending on who is applying for the charter. In such a situation, such schools are provided sponsorship by either universities, nonprofit institutions, or some government entities (Gill, Timpane, Ross, Brewer, & Booker, 2007). The underlying characteristics of the school are that they are nonprofit making entities.
Accountability for student achievement
The sole responsibility of student achievement is based on the laws and rules legislated, which define the school structure and which states the mission, goal and program of the school. Accountability of the charter school is the sole responsibility and obligation of the school to the parents, the local school board, university or any other entity to adhere to the charter contract (Goldring & Berends, 2009).
The need for the schools to remain open to any new leadership is emphasized in the charter contract, although the restructuring of such schools is limited. In addition, the schools operate on the concept that they provide quality education that cannot be rivaled by public schools. The education provides in such schools is unique and innovative and are always held accountable for the state mandates, scores, and other requirements by the law (Goldring & Cravens, 2008).
Operational autonomy
The waiver provided to the charter schools does not exempt them from the procedural requirements that bind public schools. Typically, charter schools operate as public schools with prescribed required autonomy ((Goldring & Cravens, 2008).
Research shows the criticality of autonomy for creating school culture and in helping teachers and the management to attain academic rigor, discipline, high expectations, and good relationship with the learner’s parents. It is critical to create a balanced charter in due consideration of the diversity of the students from different cultural and linguistic backgrounds (National Council of Teachers of Mathematics, 2000).
Organizing principles
A typical example is Minnesota which shows how the state laws illustrate different principles of organizing legislation and guidelines for charter schools. Among the components included are the performance expectations, the degree of autonomy, regulatory waivers, and the principles governor sponsorship for the charter schools and public schools.
Depending on the category of the laws applicable in the autonomy of the charter school, either strong or weak, the degree of autonomy is mandated by the bureaucracy and the labor management agreements. In that context, charter schools are authorized and allocated statewide funds based on the per pupil averages. The success of running differentiated schools lies on the organization of the schools independently without interference.
Funding
States are the main sources of information about the funding of chartered schools. Funding is critical in sustaining the schools in respect of the functional units and service delivery. In context, funding arrangements fall under the docket of the school district for resident school students by transferring funds to the respective schools.
The funding of charter schools as opposed to public schools which receive public funds is done by the government at reduced rates. Public schools get full funding from the government. Some schools are managed in ways that let corporates to provide funding for the running of the school activities. However, it is critical to note that the schools are nonprofit making entities with specialized curriculum.
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