Challenging Ways of Knowing - In English, Maths and Science

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It is perhaps most obvious that language varies according to content. Different words are used in mathematics than in science. But consider how different modalities present and enact meaning; for example, by writing rather than speaking, and how different wordings depending on the relationship of the speakers, for example, whether speaking one-on-one or with a small group.

The registers used respond to the contexts participated in, so shaping contexts to enable students to expand their linguistic repertoires is an important goal of instruction in all subjects; adding new registers and developing existing registers is a main goal of schooling. The notion of register helps point out how teachers can engage learners in activities that build from everyday ways of interacting toward more formal ways of presenting disciplinary meanings, as well as how learners can unpack disciplinary meanings into language that connects with the language and meanings they bring to the classroom.

Within the same classroom, different activities offer learners different affordances for drawing on language and the multicompetencies they already are comfortable with and for learning new ways of making meaning that are subject-specific. ELs who are less proficient in English may be most confident in participating when encouraged to use a range of modalities and work in a small group setting with peers, while those with greater proficiency may participate in imperfect but comprehensible English and interact in whole class settings.

While different participation structures present different challenges and affordances to particular students, language will develop as students have multiple opportunities to engage with the same content and concepts over a unit of study Haynes and Zacarian, The particular ways to talk and write discourse patterns about the content will not be the same across the unit. Introducing and working with a concept initially, students may use everyday language and informal vocabulary and sentence structure.

As they become more familiar with the technical aspects of the STEM concepts they are learning and the STEM practices they are engaging in, they move toward more disciplinary ways of talking about what they are learning, using technical language, sentence structure, and arguments more typical of written or formal discourse. For example, in a unit of instruction about division with fractions, the activities that 5th-grade students can engage in move from hands-on interaction to reporting on the interaction and then writing about what was learned. Table illustrates the variation in register that results as the children work to make sense of, represent, and discuss multiple solutions to a problem.

It presents hypothetical responses that could occur with any group of children as they engage in different participation structures across an activity sequence:. Sophia wants to make peach tarts for her friends. She needs two-thirds of a peach for each tart and she has 10 peaches. What is the greatest number of tarts that she can make with 10 peaches?

To divide a whole number by a fraction, multiply the whole number by the reciprocal of the fraction. In Context 1 , the children first interact in a small group using manipulatives that represent the peaches to explore this problem. Their language includes commands to each other to act, sentence fragments, and words like this and those that are meaningful only because of the shared context and the objects or manipulatives. This language and interaction is functional for finding and discussing solutions in a small group. This change in context leads to different language choices.

Instead of those , the student says the 10 peaches , as the shift in context requires the speaker to make explicit referents that could be pointed at when the group was interacting with the manipulatives. Instead of commands to act, the student uses past tense to say what the group did, and sequencing terms then to order the procedures they engaged in, and conjunctions so to draw conclusions. In Context 3 , the students work individually to write about their solutions, discuss which solution may be general, and finally settle on a general statement. The language choices are different as the students discuss multiple solutions and write a general statement about how to find the answer.

The audience is now distant, so everything that could be left implicit, known from the context, in Context 1, has to be made explicit. When the goal is to share a generalized description of the experience, instead of what we did , the writer would describe what a generalized you can do to make sense of and solve the problem, using simple present tense to present timeless generalizations. Words like since and phrases such as that means help the writers construct a cohesive description of what they did to solve the problem and words like because would be part of an explanation or justification for why they did what they did and why it works.

These students are shifting registers, drawing on language and other meaning-making resources in different ways as they engage with the same content and present it to audiences with which they have different relationships. A textbook, as in Context 4 , represents yet another register with which students must engage; this register presents a mathematical generalization about the meaning of division by fractions in a sentence that distills several concepts into technical language accompanied by an equation in mathematical symbolic language.

With textbooks, through which students are exposed to the written language of the disciplines, stylistic differences in language are also well-documented e. This understanding of language suggests important implications for providing instruction and supports that will engage and challenge ELs and. In Chapter 4 , the committee reports on what is known about how best to support high-quality instruction for ELs; with more evidence in science and mathematics than in technology and engineering. This understanding of language is also fundamental to preparing teachers to create learning environments and design STEM instruction that is effective with diverse learners, including ELs.

In this section, the committee describes contemporary views of STEM education with ELs that provide important background for understanding the current literature; specific instructional strategies and the research associated with these views are discussed in Chapter 4. Due to the imbalance of research in these disciplinary content areas, we acknowledge that science and mathematics are necessarily overrepresented. Based on extensive research on how children learn science in school National Research Council, , and in informal settings National Research Council, , the National Research Council report A Framework for K—12 Science Education: Practices, Crosscutting Concepts, and Core Ideas hereafter referred to as the Framework captures contemporary knowledge of what counts as science and engineering and provides a broad set of expectations for K—12 students see Box Recent years have witnessed parallel shifts toward promoting the social and sense-making nature of both science learning and second language development.

Because this approach to science learning involves using. In second-language development, whereas earlier theories saw it as the accumulation of discrete elements of vocabulary lexicon and grammar syntax to be internalized by learners, more recent thinking has taken a sociocultural turn, viewing language as a set of dynamic meaning-making practices learned through participation in social contexts Beckner et al. Because this approach to language learning involves using language for a particular purpose, it has been referred to as language-in-use e.

Knowledge-in-use in science education and language-in-use in second-language development complement each other, such that science instructional shifts promote language learning with ELs, while language instructional shifts promote science learning with ELs. Recognizing science and language instructional shifts as mutually supportive can lead to better and more coherent instructional approaches that promote both science and language learning with all students, especially ELs see the example in Box and more details in Chapter 4.

The importance of discourse processes in science education builds from longstanding research examining the multiple ways language supports the creation of knowledge. In particular, sociocultural approaches brought more focused attention to the role of cultural tools such as language in mediating the processes of individual learning and cultural production and change Nasir et al. This perspective offers an important opportunity to see how scientific knowledge accrues and changes over time as well as how knowledge is created and negotiated through social engagement and discussion in classroom settings.

As will be further articulated in the Mathematical Practices section below, classroom activities should be constructed to be developmentally appropriate approximations of scientific practices, as described in Box Research on science practices often focuses on the establishment and evaluation of knowledge claims. These epistemic practices are central to learning the disciplinary knowledge and ways of being for various science fields. Such practices vary across disciplinary communities, ways of knowing, and power dynamics that also operate in the presentation of cultures Knorr-Cetina, ; Watson-Verran and Turnbull, Those epistemic practices leading to generalized knowledge claims about nature tend to be legitimized in disciplinary communities in science and engineering Kelly,.

Chinn, Buckland, and Samarapungavan , drawing on work in the philosophy of science, suggested five focal areas: 1 epistemic aims and values, 2 structure of knowledge and other epistemic achievements, 3 sources of justification of knowledge, 4 epistemic virtues and vices, and 5 reliable and unreliable processes for achieving epistemic aims. These epistemic practices of science have been examined in a number of studies.

Studies of student uses of knowledge in problem solving also entail engagement in scientific practices. In each of these cases, examining student engagement in epistemic or scientific practices relies on a methodological focus on discourse processes because the ways that communities affiliate, build knowledge, and construct social practices are constructed in and through discourse Berland et al. Working in groups engages students in discourse through which they both construct knowledge and enact relationships, highlighting the social nature of science learning. By focusing on the ways that knowledge was constructed, negotiated, and valued, a number of studies identified key aspects of discourse for productive educational aims Duschl, ; Herrenkohl and Cornelius, A number of studies illustrated how access to scientific knowledge was negotiated through discourse processes and tied to the ongoing social practices and norms of the classrooms Alozie, Moje, and Krajcik, ; Barton and Tan, ; Oliveira, The alignment of evidence in disciplinary-specific and genre-specific forms of language has entered studies of science education as argumentation Duschl and Osborne, Studies of argumentation have explored different contexts, have drawn from multiple argumentation analytics for analysis, and.

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Argumentation has been applied across multiple science subject areas Herrenkohl and Cornelius, and entered into teacher education to prepare teachers to orchestrate uses of evidence among students Elby and Hammer, ; Sadler, ; Zembal-Saul, A second interpretation focuses on educational, or instructional, technology as a central tool for teaching and learning language and content both in and out of the classroom. Some influential educational technologies to date are personal computers as well as laptops, tablet computers, and smart-phones , the Internet including online resources and educational software , and cloud computing.

A third interpretation focuses on the tools used by practitioners of science, mathematics, engineering, and beyond. These tools include computers, software, sensors, and other data collection instruments. For all interpretations, there is limited research on technology and technology education with respect to ELs; nevertheless, we highlight what is known from the existing literature. Within K—12, the goal of technology education is to prepare students to make well-informed decisions about matters that influence technology or are influenced by technology National Academy of Engineering and National Research Council, Typically, aspects of technology education are incorporated into multiple disciplines e.

Yet, no explicit recommendations for supporting linguistically diverse students in meeting these standards have been outlined. For example, students were found to write more via computer compared to when given pen and paper, and computer-based collaborative activities encouraged more attentiveness to listening, speaking, reading, and writing Warschauer and Meskill, Moreover, these activities help students integrate language and culture, which led students to converse in English in more meaningful ways Garrett, ; Warschauer and Meskill, These findings have implications for how technology could support ELs in engaging in meaningful discourse beyond learning a language.

Likewise, educational technologies have also been shown to benefit ELs in learning science content Ryoo and Bedell, ; Zheng et al. In a year-long, quasi-experimental study involving linguistically diverse 5th-grade students, laptop use was found to be correlated with higher science scores for ELs on the California Standards Test compared to their counterparts in the control group Zheng et al. These visualization technologies were embedded in Web-based inquiry instruction in science, and EL and non-EL students were randomly assigned to either a static or dynamic visualization condition.

Compared to the students in the static group, ELs and non-ELs within the dynamic visualization group engaged in more discourse and used both text and visual representations to make sense of the scientific phenomena. Additionally, these students more successfully evaluated the range of ideas presented in order to develop coherent scientific explanations based on evidence from the visualizations.

These findings suggest that dynamic visualization technology can support the development of coherent scientific understanding for all students, including ELs Ryoo and Bedell, Related to the third interpretation, computational thinking is becoming increasingly essential for all students to become STEM professionals or participants in an information society. Despite the growing emphasis on computational thinking in STEM education, incorporating computational thinking in the school curriculum faces challenges. One major challenge involves lack of an agreement on what constitutes computational thinking National Research Council, , pp.

One approach emphasizes computer literacy, which generally involves using tools to create newsletters, Web pages, or multimedia presentations. A second approach emphasizes computer science by teaching students about programming in particular languages as a way to process, analyze, and interpret information with an emphasis on key computer science concepts such as abstraction, modularization, loops, and conditionals.

A fourth approach emphasizes learning to think computationally 4 as a fundamental analytical skill that everyone, not just computer scientists, can use to help solve problems, design systems, and understand human behavior. This approach mirrors the growing recognition that computational thinking and not just computation has begun to influence and shape thinking in STEM disciplines and beyond Weintrop et al. Few studies have examined instructional materials that enable teachers of STEM subjects to support ELs in developing computational thinking.

Engineering is a relatively recent addition to K—12 education Carr, Bennett, and Strobel, It traces some of its beginnings to CTE programs and technology education programs at the middle and high school levels, which traditionally involved a trade or job skills program, but over the past decade, have adopted a more academic program of study Park, Pearson, and Richardson, Over time, individual states introduced engineering in their CTE or science standards and some, such as Massachusetts, expanded to include engineering at the elementary level as well Massachusetts Department of Education, Such state-level efforts, coupled with a series of influential reports produced by the National Academy of Engineering National Academy of Engineering, ; National Academy of Engineering and National Research Council, , ,.

In , the Framework National Research Council, and the resulting NGSS articulated a new vision for three-dimensional learning by blending disciplinary core ideas, crosscutting concepts, and science and engineering practices that encompass both engineering and science. The inclusion of engineering in these documents was pivotal for efforts to integrate engineering into K—12 settings.

Many more schools and teachers across the country have begun to consider how to implement engineering in their classrooms. The introduction of a new discipline in classrooms offers a number of exciting opportunities with respect to ELs. Engineering design and analysis offer unique opportunities for ELs. Most age-appropriate engineering for elementary and middle school students focuses on producing a material product.

As they do so, students explore different materials and their properties and consider which ones are important to the functioning of their design. For example, creating a materials table, such as the one shown in Figure , not only stores such information, but also introduces students to a variety of descriptive properties to consider as they communicate.

As students construct and manipulate materials and design solutions, they can show their understandings with concrete models. Designs are tangible, possibilities and ideas demonstrated, and the performance of a design against a set of evaluative criteria observed. This materiality can invite participation of students with varying degrees of English proficiency—they can show what they know. Authentic engineering tasks are open-ended, permitting multiple solutions.

Thus, students can draw upon their own funds of knowledge see Positioning of ELs in the Classroom in Chapter 4 and creativity as they generate possible designs. As they engage in such meaningful, relevant, purposeful activity, they naturally use different registers to describe their unique ideas and convince others to consider their approaches.

The use of language is tied to and often follows from experiences with concrete materials, models, and designs—there is an interplay of concepts, words, language, and experiences Yocom de Romero, Slater, and DeCristofano, As students engage with a real problem, they build identity with the discipline and begin to consider it as a possible future Kelly, Cunningham, and Ricketts, Because the discipline is new at the precollege level, research studies of K—12 engineering education are nascent.

Although some studies of classroom engineering include students from culturally, linguistically, racially, ethnically, and economically diverse backgrounds Cunningham. The mathematics education community presents a contemporary view of mathematics instruction based on decades of research on mathematical proficiency and beliefs, and more recent research on mathematical practices, mathematical discourse, and the role of language in learning and teaching mathematics.

Research focusing on language and mathematical discussions blossomed in the past 30 years i. A view of academic literacy in mathematics Moschkovich, a that balances the three components—mathematics proficiency, practices, and discourse—is especially crucial for supporting ELs Moschkovich, a. These three aspects of mathematics instruction are based on mathematics education research and are evident in reforms initiated by the National Council of Teachers of Mathematics NCTM in the s.

A current description of mathematical proficiency National Research Council, shows five intertwined strands, meant to portray the successful mathematics learner:. Procedural fluency refers to computational fluency, strategic competence to problem-solving skills, and adaptive reasoning to justification. In particular, all strands of proficiency, not just procedural fluency, are developed through access to effective instruction, materials, and interactions.

If students are excluded from instructional interactions designed to foster conceptual understanding, strategic competence, adaptive reasoning, and productive disposition, their opportunity to develop proficiency will be limited to procedural fluency. For example, if teachers want their ELs to learn whole number multiplication, either as grade-level instruction in the early grades or as remediation in later grades, this does not mean their instruction should be focused principally or primarily on memorizing multiplication facts.

Such a narrow focus includes only procedural fluency while disregarding the other four components of mathematical proficiency. In particular, this narrow focus leaves out conceptual understanding, which supports accurate recall. Based on research on how to best teach multiplication for student understanding, as ELs learn whole number multiplication, instruction balances a focus on procedural fluency or drill with support for conceptual understanding by asking students to represent, apply, and connect the meaning of multiplication to other important mathematical ideas.

This balance can be accomplished, for example, by representing multiplication using arrays and area models, solving multidigit multiplication exercises by grouping and regrouping and making a connection to the distributive property, or solving multiplication word problems. It is crucial that teachers who work with ELs develop a contemporary view of what conceptual understanding is and how to teach mathematics for understanding. Conceptual understanding is fundamentally about the meanings that learners construct for mathematical solutions: knowing the meaning of a result i.

Another central aspect of conceptual understanding involves connecting representations e. Reasoning, logical thought, explanation, and justification are closely related to conceptual understanding. Student reasoning is evidence of conceptual understanding when a student explains why a particular result is the right answer or justifies a conclusion.

For example, multiplication involves many subtle issues: If multiplication of whole numbers is repeated addition,. Why is a negative times a negative positive? Why do we invert and multiply when dividing by a fraction? Teachers who develop a contemporary view of mathematics instruction that does not rigidly prescribe the sequence of mathematical topics are better positioned to provide challenging grade-level instruction to ELs.

An important result from research on mathematical proficiency is that students profit from exposure to advanced competencies as they build proficiency in less advanced competencies. For example, students who are still developing proficiency with whole number multiplication are not precluded from participating in instruction that supports algebraic thinking; proficiency with the first is not a rigid prerequisite for exposure to and progress toward proficiency in the second. Instruction that supports early algebraic thinking can be provided in the early grades or in parallel with instruction focusing on whole number operations Carpenter et al.

Lastly, teachers who develop a broader view of the role of communication are better positioned to work with ELs in mathematics; for these teachers, English proficiency is not seen as a prerequisite for doing more complex mathematics, because conceptual understanding and communication are closely related. Communicating about mathematics is important because it supports conceptual understanding.

The more opportunities a learner has to make connections among multiple representations, the more opportunities that learner has to develop conceptual understanding Grapin, ; Lemke, However, not all kinds of communication will support conceptual understanding in mathematics. Classroom communication that engages students in evidence-based arguments by focusing on explanations, arguments, and justifications builds conceptual understanding Moschkovich, whereas communication limited to just procedures or calculation may be inadequate.

Communication that includes multiple modes e. In summary, this view of mathematical proficiency has important implications for instruction for ELs. If, for example, ELs are building proficiency in procedural skills for whole number multiplication, instruction that bal-. The five strands of mathematical proficiency, described above, provide a cognitive account of mathematical activity focused on knowledge and beliefs. From a contemporary sociocultural perspective, mathematics students are not only acquiring mathematical knowledge, but also learning to participate in valued mathematical practices Moschkovich, , , The role of interaction with others will be central in understanding learning.

Work in mathematics education in the past 20 years has assumed that mathematics instruction in schools should parallel, at least in some ways, the practices of mathematicians e. These proposals emphasize classroom activities that are developmentally appropriate approximations of academic mathematical practices.

Students are expected to explore the nature of mathematical objects, make and test conjectures, and construct arguments, and instruction is expected to emphasize abstracting and generalizing as central mathematical practices. Bringing the practices of mathematicians into the classroom creates a common set of practices that parallel academic mathematical practices.

Students are expected to make conjectures, agree or disagree with the conjectures made by their peers or the teacher, and engage in public discussion and evaluation of claims and arguments made by others. This approach is intended to give students access to academic mathematical practices, such as the construction and presentation of mathematical proofs or arguments.

They are social, cultural, and discursive, because they arise from communities, mark membership in communities, and involve discourse. They are also semiotic, because they involve such semiotic systems as signs, tools, and their meanings. Academic mathematical practices can be understood in general as using language and other symbols systems to think, talk, and participate in the practices that are the objective of school learning. There is no single set of mathematical practices or one mathematical community see Moschkovich, Mathematical activity can involve different communities e.

Practices vary across communities of research mathematicians, traditional classrooms, and reformed classrooms. However, across these various communities and genres, there are common practices that can be labeled as academic mathematical practices see CCSS mathematical practices listed above. The sociocultural framing of mathematical practices described above has implications for connecting practices to discourse. Discourse is central to participation in many mathematical practices, as meanings are situated and constructed while participating in mathematical practices. Work on the language of disciplines e.

Mathematical discourse refers to the communicative competence necessary and sufficient for competent participation in mathematical practices Moschkovich, Mathematical discourse is not principally about formal or technical vocabulary Moschkovich, , Textbook definitions and formal ways of talking are only one aspect of school mathematical discourse. In classrooms, students use multiple resources, including everyday registers and experiences, to make sense of mathematics. It is thus important to avoid construing everyday and academic registers as opposites Moschkovich, Box provides a discussion of recent research with ELs on language practices during mathematical activity.

Attending to precision can also refer to deciding when and what kind of precision is necessary during a computation, including when an exact answer is or is not necessary, a mathematical practice that does not require a precise word. Attending to precision is also involved in making precise claims, a practice that is not at the word level but at the discourse level. Rather, the precision lies in specifying when the claim is true. We will have occasion to point out specific aspects of standards that have the.


In fact, the most recent standards and frameworks have articulated language demands that comprise considerable potential for literacy development Kibler, Walqui, and Bunch, if ELs are granted full curricular access. In addition, if ELs are to truly access rich academic content, assessments must be developed alongside the new frameworks and standards Bunch, Walqui, and Pearson, To engage effectively with disciplinary learning, students expand their repertoires of language skills developed during the early years of schooling and learn to recognize how language is used to make meaning, discuss ideas, present knowledge, construe value, and create specialized texts across disciplines.

Just as each discipline requires that students engage with a specialized body of knowledge and practices, each also requires that students engage with the specialized language through which the knowledge and practices are presented. And because practices vary across disciplines, these practices are best learned and taught within each discipline. STEM subjects are best learned with the help of teachers who can support ELs in engaging in the disciplinary practices through which both disciplinary concepts and disciplinary language are developed simultaneously.

Supporting language development across STEM disciplines requires that teachers develop both disciplinary concepts and practices, as well as knowledge about language and registers relevant to the discipline. This knowledge has been characterized in various ways: as literacy pedagogical content knowledge Love, , pedagogical language knowledge Bunch, ; Galguera, , or disciplinary linguistic knowledge Turkan et al. Teachers also need to effectively use their own. That is, they can be intentional in their linguistic pedagogies such as crafting STEM explanations in ways that make content most accessible to ELs without reducing the level of complexity of the content Bailey and Heritage, Alozie, N.

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Lerman Ed. Dordrecht: Springer. Herrenkohl, L. Journal of the Learning Sciences, 22 3 , — Hertel, J. The roles of engineering notebooks in shaping elementary engineering student discourse and practice. International Journal of Science Education , 39 9 , — The science teacher had a mix of English-only and more proficient ELs, whereas the ESL teacher had a class of relatively newcomer students who were beginning to acquire English. The newcomer ELs were predominantly users of Chinese as a first language. Both adopted a register approach to unpacking the language of science so that students could use all of their available linguistic resources to demonstrate their content knowledge.

Slater and Mohan b argued that oral explanations provide teachers with the requisite information they need to scaffold student learning. Moreover, these authors provided a clear example of formative assessment being ideally suited to EL pedagogy that integrates language and content learning; only by being engaged in an approach to formative assessment that requires oral discourse to generate evidence of science learning are teachers also able to build on what their students say contingently. This 3-year research-practice partnership assisted teachers in intentionally planning for and then putting into practice formative assessment with Spanish-dominant ELs by implementing three components of a formative assessment approach: 1 setting learning goals for science and language based on state science and ELD standards during lesson planning and using self-reflection guides; 2 making success criteria explicit to stu-.

This small-scale qualitative study can only be suggestive of the impacts of formative assessment implementation on science and language learning, but it revealed that, over time, formative assessment was more frequently adopted and enabled teachers to identify gaps between current levels of student science and language understanding and the desired learning goals, as well as documented increased student engagement and talk during science lessons over the same time period.

These discussions in turn provide opportunities for formative assessment of student scientific understanding. This review also highlights the close connections between science instruction and assessment when a formative approach is adopted. Bailey and Heritage provided several clinical examples of formatively assessing ELs in both mathematics and science among other content areas, also primarily with an emphasis on explanation as a cross-curriculum language practice.

Only with this simultaneous focus, the authors argued, can teachers effectively develop contingent teaching that takes account of the integration of content and language: that is, make in-the-moment decisions to either make modifications to any content misconceptions or language ambiguities to complete the formative feedback loop, or to move on to presenting students with a suitably calibrated subsequent challenge. The centrality of this feedback loop in formative assessment is discussed in the next section.

Generating feedback so that teachers know what to teach next or which pedagogical moves to choose and provide feedback to students about how their learning is progressing is central to formative approaches. Feedback that was effective was coupled with instruction-enhanced learning, whereas feedback that involved praise only was not effective for learning.

Effective feedback makes partners out of the student and the teacher, giving each a role in response to the same assessment information e. Students studied concepts and their definitions, and they were then tested on their knowledge and asked to self-assess their performances. Feedback was effective in improving the accuracy of their self-assessments. The authors even reported that initial age differences in selecting what aspects of their work needed restudying went away after students received feedback on how to improve their definitions.

These findings indicate that students used information from feedback to make themselves not only better self-evaluators but also better regulators of their own learning. For over a decade, there has been much interest within the assessment field in the development of learning progressions, also known as trajectories of learning in some STEM disciplines Shavelson, ; Wilson, Progressions have been used to guide classroom assessment, particularly formative approaches to assessment. Learning progressions are useful to formative approaches to assessment because they can provide the necessary details of how student thinking about a domain develops over time with instruction and experience with tasks and thus guide teachers in their choice of what next to teach and in their feedback to students on what next to learn.

When they are not empirically based, these ideas are based on logical analyses Ayala et al. If they are well devised and implemented, learning progressions can be a framework to integrate assessment both summative and formative with instruction and can take account of developmental theories of learning see National Research Council, ; Wilson and Toyama, However, the course of a progression is not developmentally inevitable for every student.

While most students will follow the different phases of the progression if it is well researched and designed, proponents of learning progressions point out that due to individual variation in student development and instructional experience, it is not expected that all students exhibit every growth point along the route to greater expertise e.

Indeed, learning progressions are descriptions of typical development of a domain and are not intended for students and teachers to follow lockstep through each phase if students have already progressed to more sophisticated levels of understanding and skill. The learning of ELs with strong literacy skills but still emerging oral English skills, the learning of newcomers with extensive schooling experiences in their first language, or the learning of ELs with interrupted schooling may all be better understood with a learning progression of a specific domain e.

These hypotheses are then tested empirically to assess how valid they are Does the hypothesized sequence describe a path most students actually experience given appropriate instruction? With notable exceptions in a recent volume on STEM and ELs Bailey, Maher, and Wilkinson, , few studies have expressly included ELs in their descriptions of learning progression development and implementation.

In that volume, Covitt and Anderson described a program of research in the science field that uses clinical interviews and written assignments with K—12 and university students in order to develop a comprehensive learning progression framework. Student oral and written performances in the genres of scientific discussion, namely explanation, argument, and prediction, show trajectories from less sophisticated informal discourse in these genres to more sophisticated scientific discourse.

The authors pointed out how ELs are faced with the challenge of acquiring not only a new language for day-to-day purposes, but also the characteristics of these different scientific genres.

Challenging Ways of Knowing - In English, Maths and Science

Also adopting a learning progression approach to describe alignment among science and literacy curriculum, instruction, and summative and formative assessment in the same volume, Wilson and Toyama articulated how the implementation of learning progressions with ELs may possibly differ from that of non-ELs.

First, ELs may follow the same learning progression as non-ELs but are systematically at lower anchoring points as measured by assessment items of tasks. Second, ELs may follow the same learning progression but assessment items behave differently for ELs i. Third, ELs may follow a different progression from non-ELs. Finally, Wylie and colleagues examined proportional reasoning in mathematics and language progressions in tandem.

See Box for an example of how an elementary teacher of a dual-language classroom had created her own tool to guide her next-steps pedagogical moves as a result of using the sentence structure progression. Wylie and colleagues placed written explanations of the mathematical reasoning of 6th- and 7th-grade students on both the proportional reasoning and language progressions to produce four interpretative quadrants of intersectional performance.

They noted that few non-EL students could convey high levels of mathematical understanding without corresponding high levels of written explanation abilities, which has implications for ELs as well. Although dual progressions for multiplication and language were also applied to the writing of a 6th-grade EL student as a proof of concept, the current state of research in this area is too much in its infancy to know how useful this technique will be for generating feedback to ELs and teachers on progress in the STEM disciplines and their related language learning.

A similar conclusion can be drawn from the review of available research on classroom assessments and assessment practices for evaluating the STEM preparation of K—12 ELs. With few exceptions e. The ideal of a comprehensive, coherent , and continuous assessment system National Research Council, has yet to be realized. Both summative and formative assessments could yield richer information when mutual links among ELD standards, math or.

Moreover, effective classroom summative and formative assessment will require robust teacher professional development for effective implementation Lyon, Several studies point to what this might take in terms of teacher preparation and continued professional supports. This support may come in the form of professional learning communities or communities of learning to create sustainable venues for teachers to discuss interpretations of assessment information, acquire knowledge of learning progression tied to formative assessment, and enhance strategies for addressing EL learning in terms of both their language and STEM content knowledge and skills e.

These studies also found that classroom assessment involves an investment in time. This is not simply time for teachers to build their familiarity with assessment techniques, but also sustained amounts of time to carry out assessment often with individual students. There are important criticisms of learning progressions and the role they can play in both effective instruction and formative assessment. These criticisms stem in part from concerns that learning progressions may be erroneously implemented as prescriptive sequences of acquisition rather than as descriptive guides to the general course of development of a domain e.

Learning may occur gradually, but it may not be a linear process. This may be especially true of language learning that occurs in the real-world context of the classroom rather than neatly falling along a simple-to-more complex continuum Velasco, Until more research is conducted on the validity of learning progressions in effective instruction and formative assessment approaches with ELs, the implementation of STEM and language learning progressions remain a promising practice with ELs. Teacher bias in assessment of students may also be of particular concern with classroom assessment of student learning.

Teachers also need to build expertise with data use as a result of generating the amounts of information yielded by classroom summative and formative assessment. Addressing teacher bias will be just one aspect of the validity of classroom assessments that needs to be established. Establishing the validity of formative assessment approaches will be particularly challenging given their more qualitative and informal nature.

However, Heritage b has suggested how formative assessment valid-. To be successfully implemented, any improvement in assessment practices for ELs needs to be supported by proper training for decision makers, school administrators, and educators. This training needs to address the heterogeneity of EL populations and the limitations of testing accommodations and accessibility resources as forms of support for ELs.

The preparation of teachers and the examinations required of those seeking credentials and certification need to be designed to support and evaluate teachers as they become critical assessment users, task designers, and interpreters of student performances.

Teachers also need greater familiarity with data use and support in becoming critical assessment users e. Teachers need to critically interpret and integrate information from assessment with other sources of information e. This would be tantamount to promoting enhanced teacher skills for the benefit of ELs through teacher certification examinations.

Existing limitations of teacher examinations and certification processes may stem from the fact that teachers of English as a foreign language and bilingual teachers are viewed as equivalent in their roles and responsibilities, and the requisite knowledge, skills, and abilities for effectively fulfilling these roles are considered equivalent. Incorporating the knowledge, skills, and abilities that enable teachers to provide socially and culturally responsive instruction to ELs would improve the examination and certification process for both kinds of teacher.

Teacher certification examinations of STEM have improved in their degree of coverage of important constructs, as well as in their integration of academic language and inclusion of EL instructional strategies. One such examination is the edTPA, which is a widely available teacher candidate assessment now used in most states American Association of Councils for Teacher Education, This examination is based on the former Performance Assessment for California Teachers PACT that has integrated a focus on mathematics, academic language, and EL students for all teacher.

Teacher certification examinations for STEM teaching could be reviewed to determine whether the examination content is up to date on EL assessment issues and knowledge, and whether they effectively capture the assessment literacy teachers will need, both in terms of interpreting the results of state-wide, large-scale STEM assessments, and at the local level in which they are implementing classroom summative and formative assessment approaches Bailey, Maher and Wilkinson, In order for these transformations to take place, revising existing practices is crucial.

Needed changes concern the methods used to address the characteristics of ELs, to develop STEM assessment instruments, to analyze and interpret information produced by tests, and to prepare teachers to effectively design and interpret STEM assessments in their classrooms. Although the move away from accommodations in favor of accessibility resources is viewed positively, the implementation of accommodations must also improve in those situations where accommodations are provided.

While there is evidence that formative assessment approaches, particularly those that encourage student self- and peer assessment, have positive outcomes for learning, this evidence comes from the area of literacy, not STEM, and has not systematically included EL students. Two key aspects of formative assessment emerge from the literature: the role of feedback for teachers and students and the use of learning progressions as an interpretive framework for student performance on tasks. Much of this work is conducted with non-EL students, and the few studies that do include EL students tend to be small scale or report clinical applications of formative assessment.

Nevertheless, formative assessment stands to become transformative assessment for EL students and their teachers that could lead to a greater degree of self-regulated learning for students who are engaged in self-assessment as a component of formative assessment. For teachers, learning progressions used as an interpretive framework for formative assessment have highlighted the need for greater STEM knowledge on the part of teachers to be able to work well with learning progressions used in formative assessment.

Lastly, although teacher certification exams have improved in recent years in their coverage of important constructs and the integration of academic language, their coverage of the knowledge, skills, and abilities to provide socially and culturally responsive instruction to ELs and of current EL classroom assessment is unclear. Abedi, J. Educational Researcher, 33 1 , 4— Research and recommendations for formative assessment with English language learners. Andrade and G.

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Number Series Reasoning Tricks - The Easy Way!

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Epub Challenging Ways Of Knowing In English Maths And Science

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Challenging Ways of Knowing - In English, Maths and Science Challenging Ways of Knowing - In English, Maths and Science
Challenging Ways of Knowing - In English, Maths and Science Challenging Ways of Knowing - In English, Maths and Science
Challenging Ways of Knowing - In English, Maths and Science Challenging Ways of Knowing - In English, Maths and Science
Challenging Ways of Knowing - In English, Maths and Science Challenging Ways of Knowing - In English, Maths and Science
Challenging Ways of Knowing - In English, Maths and Science Challenging Ways of Knowing - In English, Maths and Science
Challenging Ways of Knowing - In English, Maths and Science Challenging Ways of Knowing - In English, Maths and Science
Challenging Ways of Knowing - In English, Maths and Science Challenging Ways of Knowing - In English, Maths and Science
Challenging Ways of Knowing - In English, Maths and Science Challenging Ways of Knowing - In English, Maths and Science
Challenging Ways of Knowing - In English, Maths and Science

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