Connecting Writing to Reading... Why write?

In synthesizing the reading and writing processes, the importance of writing for English language learners (ELL) is integral to the development of fluency in their developing language system. Just as structured input activities--such as information gap activities--are crucial to the ELL who is learning how to manipulate the new (second language or L2) input that s/he is hearing and reading, so too must these learners engage in structured output activities. Output is any production of language, be it oral or written, and production of the second language requires multiple strategies and demands on the ELL. These production (or output) processes include accessing or retrieving of the correct forms, monitoring or editing one's speech/writing, and production strategies used for stringing forms and words together into sentences and connected discourse. All of these processes are affected by a variety of factors (see the research of Pienemann, 1998). The term "access" was first used for referring to retrieval by Terrell (1986, 1991) and is part of the binding process whereby an L2 learner binds a word or form with its meaning. According to Terrell's theory, production in an L2 involves two processes or abilities: (1) the ability to express a particular meaning using a particular form or structure, and (2) the ability to string together forms and structures in appropriate ways. The first process is what Terrell refers to as access and the second process is what Terrell defines as production strategies. Access involves retrieving the correct verb tense when attempting to express the associated concept temporally. What is important for teachers to keep in mind is that access does not automatically follow language acquisition. Simply because an ELL student has incorporated a particular form or structure into his or her developing L2 system does not mean that it can be easily accessed and thus produced (in oral or written output) automatically. It is important to to note that learners can acquire a great deal of grammatical information, but not be able to apply it in communicative situations. The ability to read a language, therefore, does not provide the opportunity to create output in that language. Hence, the importance of writing in the L2 in order to practice access as well as producing output which in turn increases accessing abilities. Output then serves as further input of the L2 as the learner writes, edits, and reads his or her work. Structuring output refers to sequencing the production activities to follow the input activities, creating coherent grammar lessons that take the student from processing a grammatical feature in the input (reading, listening) to accessing the feature from his or her developing language system, to creating the feature in his or her output (writing, speaking). Creating structured output activities for ELLs, the teacher should keep the learner's processes in mind, presenting one thing at a time, keeping meaning in focus (meaningful context), moving from sentences to connected discourse, using both written and oral output, and having others respond to the content of the output through grand discussion, group work, and instructor feedback. It is through writing that all learners use their developing grammar and vocabulary to communicate information, and writers need ample opportunities to express themselves. Only through writing and discussing writing do learners activate all the processes responsible for the development of language fluency and accuracy. Write on!

Teacher Activities of Before, During, and After phases of a Mathematics Lesson

Before:

Prepare students mentally for the task (i.e. the “pre-activity”):

I feel that this should be done first in order to activate students’ schemata which will allow them to proceed into the activity at hand by placing the concept into a meaningful context. I feel strongly about the mental preparation of any task, as this is an important tool that can be viewed as we would view differentiation. By activating each student’s schema and tapping into their previous experiences and prior knowledge, we bring engage the students mentally on an individual level that allows each student to see their own personal connection to the task at hand (differentiation, in a way!) as well as placing the task into a meaningful context (cultural universals) that will give purpose to the task.

The teacher will be providing some sort of a simple version of the task that will serve multiple purposes: (1) it will activate students’ schemata, (2) it will establish expectations as the teacher is modeling the simple version of the task, some of the strategies and procedures that the task (and lesson task) will demand, and (3) it provides the teacher an opportunity to define vocabulary, giving multiple possible entries into the problem, and/or brainstorming or modeling mental computation or estimation strategies. This pre-activity is the key to engaging students and providing the actual presentation of the task or problem, as well as serving as a pre-assessment to the teacher as to what his/her students already know and where and how s/he can connect to this knowledge in order to provide a basis for students to construct new knowledge upon and modify existing conceptual knowledge.

During:

Provide for students who finish early/quickly:

This is an important aspect of planning that I have often seen neglected in many classrooms that I have worked in, therefore, I am aware of the importance of this step in my planning. Providing for students who finish quickly must also be combined with listening actively, as active listening works as an embedded assessment that reveals the student’s thinking by asking “how” and “why” and encouraging the testing of ideas.

The teacher’s role is crucial in assisting the student who finishes quickly to go beyond the simple solution of the problem/task at hand and extend the task to make it more challenging to those students. This is also a differentiation aspect, as we are to meet the needs of all of our students. The teacher can encourage further exploration by scaffolding questions such as “What if you tried…?” or asking the student validate their solution by asking “Would the same idea/method work for…?”. The teacher can also encourage students who have completed the task early to try to define characteristics or rule construction: “Suppose that you tried to find…” or “Can you find another way to solve this?” These types of scaffolded inquiries work as “hooks” to re-engage the student to go further in their problem-solving task.

After:

Inclusion of all learners!

Summarizing ideas without passing judgment and listing hypotheses that have arisen from students’ discussions is my favorite “after” activity, for I feel that it is through discussion and multiple perspectives that we begin to construct our own ideas and understanding. The subsequent testing of hypotheses will then engage the students in the dynamic nature of mathematical investigation: the doing of mathematics!

All too often I find that elementary mathematics instruction conveys a didactic message of right or wrong ways of solving a problem and the great hunt for the “right answer”, leaving out the exploration of ideas and multiple approaches. This type of instruction inherently excludes a percentage of students in any given group: those who did not share the instructor’s viewpoint or other students’ methodology. I see this learning environment as detrimental to the creative thinking process which is the basis of learning. We not only exclude those students who have not grasped the teacher’s idea, but we simultaneously snuff out any spark of creative individual or group ideas.

It is through the active listening process and the acknowledging of multiple perspectives and strategies that we, as teachers, establish an atmosphere where students are willing to explore ideas and test problem-solving strategies without risking judgment or exclusion. This is the prerequisite learning environment that we must establish through our classroom management and modeling. Unfortunately, many of our students will have expectations of math instruction as being teacher-based and will be hesitant to feel free to fully explore their own problem-solving ideas. Instruction must be anchored in the students’ ideas and understanding. We explore what our students know in each unit’s introductory lessons, using these activities as embedded assessments for planning our problem-solving-based lessons and units. Thusly, students learning of mathematics is actively constructed via problem-solving and de-construction and re-construction of their existing conceptual knowledge and understanding. Teaching is then full integrated with the students’ learning process.

Technology as a Differentiation Tool...

Technology as a tool in second language acquisition and foreign language teaching is only in its infancy. Early software programs have fallen short of communicative language teaching pedagogy and goals, imitating the drills of audiolingual methodology of the 1950s and 60s. It has been a marketer’s dream of the magical ‘pill’ of foreign language mastery in an easy-to-learn, guaranteed-to-succeed set of CD-ROMs (guaranteed to succeed in making money for the publisher, that is!). I have begun to use blogging in my own French teaching at MSU, as well as multiple on-line language learning resources. The more variety of input mediums and contexts that I provide my diverse group of learners, the more chances I have of meeting their individual learning styles and processes. It is only through the use of multimedia in reading, listening, writing, and speaking, that I can truly begin to differentiate my teaching within a highly-structured departmental curriculum. Our 200-level textbook takes the role of ‘resource’ in the classroom. As the old adage goes, “A picture is worth a thousand words,” becomes the backdrop to a rich array of visual media (photographs, video clips, news footage, music videos…) that I can use to provide contextual meaning and activate schema and prior knowledge of my students. By using images within context, a second language learner can ‘bind’ new vocabulary directly to the action or object, without translating from their first language lexicon. This concept of binding is crucial to building contextual cognitive webs of lexicon, whereby new vocabulary words are ultimately associated directly with their meaning and not with a translation. Anchoring second language input is not limited to visuals, but visual representation of sentences and connected discourse can enhance auditive comprehension, simultaneously providing language input in two forms (seeing and hearing), and thus increasing the chances of a learner attending to a form or a task at hand. Technology is rapidly progressively towards being more and more interactive, which is mandatory for optimal foreign language teaching scenarios. Just as we would research and critique any new teaching approach or textbook, so do we need to be critical investigators and consumers of technology use in the classroom. If the focus of the task is based upon the activity and not the objectives, then we are no longer constructively using the technology. Do I believe that new literacies can help us with issues of equity and differentiation in our classrooms? You betcha!

Exploring New Literacies...

Emergent, developing, and fluent are very broad literacy evaluation labels that do not encompass habits and processes such as attitude, purpose, and use. I would label myself Developing in new literacies. I prioritize the new literacies and apply myself only to those that I find useful for second language teaching. Within each field of interest, there is a plethora of literacies and available media technologies. If, however, I do not find a new literacy constructive in multiple purposes and uses of my students’ language learning, then I do not feel that it is a good use of my time to integrate it into my curriculum. With our rapidly growing technologies, I feel that educators need to spend more time evaluating the merits of each development, with a critical eye towards possible applications in the field that will enhance the classroom experience. The one aspect of emergent readers and writers that I wish to maintain in my own developing new literacies exploration is their belief that learning is fun and exciting. This attitude is the intrinsic motivation to exploring digital literacies and incorporating multiple media resources in a language learning environment.

Discussing math concepts

I have always been fascinated by listening to young children explain concepts of regrouping and trying to grasp their understanding of our base ten system. Our readings, the video clips, and in-class discussion have all underscored the importance of the discussion of mathematical processes for me. I feel that way too much emphasis is put upon the omnipotent one and only correct answer, as opposed to the process itself. I feel that it is through our understanding of a student’s processes and conceptual knowledge that we can gain insight into misunderstanding and/or mis-connected ‘discrete’ concepts that underlie a student’s poor understanding of a big idea or concept. Hundreds of worksheet problems cannot tap into a conceptual misunderstanding or lack of understanding if the ‘right answers’ are all that are asked for by the assessment tool. Through conversation and dialogue, we negotiate our mathematical understanding and question the reasons why we need to find efficient problem-solving methods and tools. The process of sharing and comparing methods and ideas is the journey to a deeper, more integral understanding of a technique or concept. This personal realization leads me to question why we do not spend more time on this aspect of teaching elementary mathematics. By understanding exactly what our students’ conceptual understanding is based upon, we can then truly connect to their prior knowledge and build cognitive networks of mathematical meaning that make sense to them in a real-world context. Knowing how to calculate a correct answer using a traditional algorithm is not an accurate predictor of a student’s ability to apply a mathematical concept in their daily life. I wonder why we do not explore other number base systems and concepts at the elementary level in order to develop the ‘template’ of numerical base systems. It seems as though base systems are not explored until middle school and algebra-level coursework. Why do we wait so long to play with the concept of bases and pattern repetition?