Audio Script for TELLIT: Math Cognitive Learning Environment

Lesson 1.0 Course Overview

Welcome to the online course for Texas English Language Learner Instructional Tool (or TELLIT): Math Cognitive Learning Environment. During this course, you will learn how to address the cognitive needs of English Language Learners (or ELL students) in math. This course provides opportunities for you to build a repertoire of cognitive (or instructional) learning strategies that will enhance mathematics instruction and promote academic achievement for ELL students. Click the arrow to continue.

Let’s begin this lesson by accessing your prior knowledge about the cognitive learning environment for English Language Learners. Accessing prior knowledge will help link new concepts with previous instructional experiences you have had with your ELL students and connect these new concepts to the real world.

In the next activity you can work online or you can download the activity to work offline and save to your computer. Click the arrow to work online.

Click Agree or Disagree for each statement. Click the arrow to continue.

Click each item to learn why an anticipation guide is a good strategy to use for ELL students.

An anticipation guide is a series of statements, usually between five and ten. Students must respond individually to each statement before reading a certain text.
The statements are designed in such a way as to activate thoughts about particular events, ideas, plots or issues that will be introduced in the text about to be read.
Having students engage in these thoughts before reading prepares them to read as more active participants.
Students get a sense of the major ideas they will encounter in the text.
Students have an opportunity to reflect and respond to statements individually before being influenced by the group.

Vacca and Vacca, in their book titled Content Area Reading, observe that students become more attuned to their individual opinions about a variety of issues brought forward during reading and thus, are more apt to make personal connections to these issues as they read." Students are often asked to respond to the statements with True or False, and sometimes, teachers ask students to support their opinion through discussion or even in writing.

An anticipation guide can be most useful when students are asked to:

respond to text with an opinion that compares or contrasts characters, events, or concepts;
take a position or consider various perspectives after reading text that contains a potentially controversial issue; or
distinguish between popular myth and fact after reading about a certain topic.

There are several components to an effective cognitive learning environment that address the needs of English language learners. This course help you review each of these components by providing instructional strategies that are beneficial for English Language Learners.Click each item for a brief summary of each component.

Cognitive Learning Environment
Know your students
Establish clear content objectives
Build background knowledge
Model new concepts
Use cooperative groups
Use hands-on materials
Share multiple solution paths
Actively engage students.
Incorporate technology

Lesson 2.0 Know Your Students

Let's begin this lesson by reflecting on what you learned so far about the characteristics of English language proficiency. Review the video and consider what techniques might help this teacher to work with students in his classroom who do not speak English at all. Click Next to watch the video.

Review the cases of three ELL students. Click each name to review the student's English language proficiency level and sample of work. Read and listen to examples. Click a student’s name.

Select the appropriate instruction or assessment options for the student. Drag the numbers of appropriate activities into each box.

Olga: How to simplify 3 times x plus 2y, plus 5 times 2x minus y, plus 4y: Well first of all you multiply 3 for x and 2y then the answer put it on the bottom of the equation. Then on the other side you do the same thing. Multiply 5 for 2x and then for y. Then bring it to the bottom and also bring the plus and 4y. Then you put the pairs together, for example all the x’s with the numbers that have the x and all the y’s with the numbers that have the y. Then after that you add the pairs and the answers of both of them. Bring them to the bottom with the plus sign.

Nikolai : I love problem solving. In problem solving you need the t-chart. The u stands for understanding and p stands for plan. And s stands fo sove and E stands for evaluate then a lot of thingto do on math it is fun to do that evrthing fun for you

Lesson 3.0 Establish Clear Objectives

In the previous lesson, you learned about the value of getting to know your ELL students. In this lesson, we will examine content and language objectives. Lesson planning provides a guide for managing the learning environment. Considering lesson goals, content, and the English proficiency levels of students establish the foundation for implementing effective strategies for ELL students.

Similar to the TEKS, the ELPS are written using technical terms that may not be easily understandable to ELL students. Simplifying the language of the language objective also helps ELL students with different levels of English proficiency understand the expectations for their performance.Simplifying the English Language Proficiency Standard helps students understand the expectations for demonstrating what they have learned.

Content and language objectives should be displayed, discussed, supported, and assessed. Review the video and consider how the language objective is displayed and discussed with students. Click Next to watch the video.

As you watched the video there were several things you may have noticed about introducing objectives. Click each item to hear descriptions of things you may have noticed.

The teacher displays the expectation for the lesson in writing. The objective is written so that students with lower levels of English proficiency can understand the expectation.

Rather than reading the objective to the students, the teacher asks a student to read the objective to the class. This provides an opportunity for students to use and practice academic English in the classroom.

The teacher points out the academic terms that students will be expected to understand as they master the content objective. The teacher gives students multiple opportunities to explain what they already know about the objective.

This teacher uses an exit ticket strategy to assess the content objectives before ending the lesson. The teacher asks the students to write a summary of the problem-solving process used in the lesson. This ensures that the ELL student has met the both the content and language objective.

Click the page corner to review various objectives from Mr. Noriega’s portfolio flipbook.

In these samples, note how the teacher simplified the English Language Proficiency Standard into a language objective written in student-friendly language. The format may change over time as teacher becomes more experienced with ELPS.

In these samples, note how the teacher simplified the TEK into a content objective written in student-friendly language.

Lesson 4.0 Build Background Knowledge

In the previous lesson, you learned about the importance of establishing clear objectives. In this lesson, you will learn about building the background knowledge of ELL students.

Building background knowledge (or accessing prior learning) is essential for the success of ELL students.

Prior to the lesson, the teacher must assess what the student already knows, or has previously learned about the lesson.

One of the challenges of teaching ELLs is that students in the same class vary in the amount of prior knowledge they possess related to the topic. Christen and Murphy (1991) suggest that students generally fall into three categories: much, some, or little prior knowledge.

An ELL student may get “lost” in the content if they do not understand the context of the problem.

Class, today we are going to talk about stars. As you can see from the image, it is important for the teacher to assess what the student knows about the lesson prior to checking for misconceptions and making connections to the content objective. If these were ELL students in your class, what would you say or do next?

Review the video and consider how the teacher builds ELL students’ background knowledge about similar triangles. Click Next to watch the video.

As you watched the video there were several things you may have noticed about the ELL strategies used by the teacher. Click each item to hear descriptions of things you may have noticed in the video.

The teacher explains to the students that similar triangles apply to real world problems. The teacher makes connections of similar triangles to real world situations; hence, the new material becomes real, relevant and meaningful for students.
By displaying a picture of the University of Texas Tower , the teacher connected the math content to a location that is known to them.
The teacher not only provided a familiar example, but provided historical information students might find interesting.
The teacher captured the students’ attention by constructing a problem that was more personalized, using himself in the problem. Note that the problem reads as if this actually occurred.

Based a student’s background knowledge, the teacher makes decisions that help build an ELL student’s understanding of the lesson’s topic prior to the opening the lesson. Teachers may access students’ background knowledge visually, contextually, or linguistically. Teachers may differentiate instruction by teaching prerequisite skills, discussing lesson attributes, and providing multiple examples.

Through pictures, that are displayed or drawn
Through discussions of personal experiences related to the lesson topic
Through common vocabulary that is related to the lesson topic

Teacher may differentiate instruction by:

teaching foundational skills to scaffold learning for the target content objective
facilitating a brainstorming activity of the lesson topic to draw out background knowledge, and
providing multiple examples that introduce the lesson topic.

Lesson 5.0 Modeling for Students

In the previous lesson, you learned about the significance of building background knowledge. In this session, you will learn about modeling new concepts for students.

Modeling allows the ELL student to have a clearer understanding of what the math task in the lesson entails. The teacher models or demonstrates these expectations for students. Click each item to review the details of using the Teacher-Group-Student Approach for Modeling.

The teacher demonstrates how to use tools that help students solve math problems and derive solutions.
The teacher visually displays steps of the process for solving problems.
The teacher provides a sample of the expected outcome of student learning. Sentence stems or paragraph frames are commonly used for this purpose.
Oral directions should always be accompanied by written ones so students can refer to them as needed.
Students work in groups to discuss and construct new knowledge based on what the teacher modeled.
The groups replicate the steps that the teacher modeled
Each group produces a written or oral product, such as the solution to a problem or construction of a model.
Group discussions of the lesson contain common terms and academic vocabulary that enhance understanding of the lesson.
In some cases, groups can report to the class in an oral presentation or a written report about their work.
An ELL student can work independently to demonstrate new knowledge acquired from the lesson activities.
An ELL student can recall group activities to reproduce the process, solution or products of the lesson.
An ELL student can use scaffolds that the teacher provides to produce a written or oral product, such as the solution to a problem or construction of a model.

Review the video to see how the teacher uses the Teacher-Group-Student approach for modeling the use of manipulatives. Click Next to watch the video.

As you watched the video there were several things you may have noticed about modeling new concepts. Click each item to hear descriptions of things you may have noticed.

After the teacher explained the expectation, she demonstrated what the manipulatives represented and how to use the proportion rods to the entire class. If groups or individual students needed further assistance, the teacher modeled the process, again.

Students used the manipulatives as they worked to solve the assigned problems. Students constructed visual representations of the problem making the concept more concrete.

After each group had time to find the solutions to the problems, the teacher asked a representative from each group to explain how the group solved the problem. This strategy allows students opportunities to practice academic language and reinforce new concepts.

Lesson 5.0 Modeling for Students

In the previous lesson, you learned about modeling new concepts for students. In this lesson, you will learn about using cooperative grouping and hands-on materials.

Review the video and consider the benefits of cooperative grouping for ELL students in Math. Click Next to watch the video.

Cooperative grouping is a teaching strategy designed to imitate real-life learning and problem solving by combining teamwork with individual and group accountability.

Cooperative learning changes students' and teachers' roles in classrooms. The ownership of teaching and learning is shared by groups of students, and is no longer the sole responsibility of the teacher. The authority of setting goals, assessing learning, and facilitating learning is shared by all.

Along with improving academic learning, cooperative learning helps ELL students engage in thoughtful discourse and examine different perspectives. Students have more opportunities to actively participate in their learning, question and challenge each other, share and discuss their ideas, and internalize their learning. Cooperative grouping has been proven to increase students' self-esteem, motivation, and empathy.

Varying grouping configurations by moving from whole class, to small groups, or partners, provides ELL students with opportunities to learn new information, discuss this information, and process new concepts.

Using hands-on materials, such as math manipulatives, that students can touch, feel and move around helps the learning process. For ELL students, such hand-on materials give them the opportunity to demonstrate their understanding of the content visually, while learning how to express what they've learned in English.

Drag each tile to an empty space on the model to learn how manipulatives have positive effects on ELL students’ learning and understanding of Math.

Using manipulatives is an instructional strategy to help make abstract ideas become concrete, providing a visual approach for teaching ELL students.
Using manipulatives helps ELL students categorize new concepts that share common properties, characteristics, or patterns.
Manipulatives can be a means for an ELL students to demonstrate their understanding in tangible ways, regardless of their language level.
Manipulatives assists students who do not understand the language of instruction with a visual sense of the process. For example, manipulatives allow students who may forget algorithms to visualize the process in order to figure out a solution.
Using manipulatives takes planning, creativity, and organization. For beginning students, teachers may choose to utilize pictures as manipulatives because students may not have developed enough English vocabulary.

6.0 Cooperative Groups and Using Hands-On Materials

In the previous lesson you learned about the significance of using math manipulatives for ELL students. In this lesson you will learn about sharing and supporting multiple solution paths with students.

Presenting math problems to students that have multiple solutions is an excellent way to foster active participation in learning.

During groupwork or independent work, students may derive other solution for the same problem. The teacher functions as a facilitator helping students develop critical thinking skills. The teachers ask students to explain how they solved the problem by asking questions such as: What is…? How do you…? What might be a better approach…? Or How do you know that?

The cognitive learning environment is one in which multiple solution paths are supported and encouraged.

Supporting an approach in which multiple solutions are possible when solving math problems fosters various life-long reasoning skills for ELL students.