Best Instructional Practices to Teach High-Level Mathematics to English Language Learners in the Middle Grades

Best Instructional Practices to Teach High-Level Mathematics to English Language Learners in the Middle Grades

A Launching the lesson Introducing a new mathematical concept or skill begin their exploration of critical concepts with concrete activities that model the featured concept and connect it to their prior knowledge. use manipulatives and drawings to model mathematical concepts and solve problems. use prior knowledge from their own lives to connect them to main mathematical concept. make choices in selecting the materials and strategies they use to solve math problems. has a clear idea of the big idea/ mathematical concept and can explain the idea (not the formula or procedure) in multiple ways provides many concrete examples of how the critical concept looks like in students daily lives. uses many different modalities - illustrations, body language, key vocabulary words to help explain and model the concept. asks all students to think of situations that can illustrate the critical concept. creates scenarios that include people and situations students know and care as setups for working on open ended problems that illustrate the main concept. provides a range of materials students can use to create models of the critical concept. requires students to choose the materials and the strategies they will use to illustrate a concept or a models the many different ways in which students can explore the concept or problem creating a model; drawing a picture; using body language, explaining in words; creating a table, graph or chart; working backwards; or starting from an easy version of the same does not give the formula, algorithm or procedure associated with the concept at this point in the lesson.

B Learning to think, create, problem solve and apply deep understanding in mathematics through speaking, listening, and responding spend a considerable amount of time working in small groups, taking turns explaining and clarifying their thinking to each other. speak to each other and every student responds through speaking, drawing or movement - no matter what their level of English acquisition. follow structured and timed protocols for speaking and listening; all students speak and all students listen actively. listen to each other and comment thoughtfully on each other s contributions. follow structured and timed protocols for speaking and listening; all students speak and all students listen actively. models how to listen and respond to every student by providing opportunities for all students to speak to the entire class. asks other students to respond to a student before giving any feedback. requires all students to explain why they are giving a particular response. asks questions and designs activities that are rich, requiring considerable thinking, provide for multiple entry points and methods of exploration. gives clear, well paced and well timed directions for every segment of the lesson. uses structured protocols for cooperative group work throughout the lesson and works on them until they are done well. tells students what to listen to when other students speak and models how they are expected to respond when it is their turn. spends considerable time listening carefully to students and intervening only when students are stuck or going too far off in a dead end direction. gives direct, explicit, personal and immediate feedback to specific student statements, supporting students in reaching deeper understanding gives explicit feedback and asks all students to provide thoughtful and explicit feedback. explicitly encourages reasoned risktaking and multiple ways of thinking through a listens to students far more than talks to students.

C Using higher order thinking questions as a key element of mathematical reasoning ask each other questions to help everyone develop more accurate and thoughtful answers to complex questions. ask each other higher order thinking questions without being asked to do so by the teacher. vary their questions to suit each student s response. ask good follow-up questions that push for deeper understanding and fuller explanations. asks open ended questions to probe all students thinking rather than telling them the answer or what steps to take. gives students lists of good kinds of questions they can use and models for them how and when to use them in specific situations. uses a question asking and responding protocol in small groups whenever students begin their work on a problem or rich activity. requires students to ask open ended questions as they work with each other on problems. requires students to write down several good questions to ask each other before the group begins responding. models using follow-up questions to probe for deeper understanding and multiple perspectives.

D Using the language of math as essential to mathematical reasoning and understanding know that math is a language and feel comfortable in using math language appropriately in the math classroom. use sentence stems modeled by their teacher when they speak and write. use math vocabulary and math syntax when they discuss mathematical concepts and solve problems. hold each other accountable for giving clear explanations of the concepts they are studying and the formulas and procedures they use to solve them. explains that math is a language and that the language of math must be used in a math classroom in order to understand and explain math. continually models what it sounds like and looks like to use the very exact and explicit language of math in the classroom. decides in advance what sentence stems and vocabulary words are appropriate for the students and models their use throughout the class. hands out written copies of the sentence stems and questions an/or posts them throughout the classroom. chooses a few key vocabulary to pre-teach in the context of introducing the targeted mathematical concept at the beginning of the lesson. uses the key vocabulary words throughout the lesson, explaining and demonstrating their use each time and providing good graphics that illustrate the words. requires students to use the key vocabulary words once students have had multiple opportunities to work with that concept through concrete activities, discussion, questions and problem solving. structures protocols so that students hold each accountable for coming up with clear explanations and accurate solutions. spends a considerable amount of time listening to the small group discussions and readjusting the class based on her assessment of students understandings and misconceptions.

E Being organized, methodical, exact, persistent, and inquisitive use graphic organizers to help organize their thinking. follow routines and rituals to help organize their thinking and recognize patterns. write to learn throughout a lesson: they write down their predictions, educated guesses and answers at every stage of the lesson. organize information and look for patterns whenever they approach a ask questions whenever they don t understand anything and see this as the best kind of learning. uses the gradual release of responsibility to introduce, practice and assess every student s ability to follow explicit directions, work in groups, and listen and respond attentively. spends a considerable amount of time modeling all of the routines, rituals, problem solving techniques and protocols that students will use. requires students to practice these techniques on relatively simple problems until they have mastered them. provides written directions for all routines and posts them using clear graphics. develops graphic tools for students to use as they learn to be organized, methodical in their math classes.

TEACHER.. F Using ongoing and multiple forms of assessment throughout the lesson are intensely engaged throughout the class and clearly enjoy learning math. can explain why they are learning a math concept or skill and how it can be applied to solve real problems in their families, communities and on job sites. can explain how a concept or skill they are learning relates to others they have already learned. know when and how to use a formula and algorithm accurately. develop and try out several different approaches to solve problems. check their understanding throughout a lesson as a way of making sure they are getting at the best solutions to the reflect on how they are solving a problem and why their answer makes sense, as they are working and when they arrive at their solution/s. has instilled in students a belief that they can learn math at a high level and has made sure that they have succeeded in doing so. has modeled for students how to write a clear and complete explanation of various types of mathematical solutions anticipates the misconceptions students might have about the concept and asks students questions that explicitly probe those misunderstandings. requires all students to explain why (give the reasons) they are giving a particular response, and how they arrived at it (not simply tell what they did). requires students to work until they reach a supportable solution and provides them with the specific scaffolding they need when they reach a roadblock. helps students see the connection between the problem, the underlying concept, the vocabulary and the skills, procedures and formula associated with it throughout the lesson and unit. asks students to apply the concept to a range of situations and develop problems using that concept. requires students to use several different strategies in working on the same

Prepared for Center for Collaborative Education/ Turning Points by Dr. Sara Freedman, Project director Dr. Dan Lynn Watt, Math consultant