TEACHING MATHEMATICS

TO ENGLISH LANGUAGE LEARNERS

Diana Cagle

ELL Symposium 2014

LET’S GROUP OURSELVES

Choose a card from the front desk and without talking find your partners

Once you have found your group, take a few minutes to get to know them

We will share out afterwards

IMPORTANCE OF GROUPINGALL GROUPS SHOULD HAVE A PURPOSE

Academic Purpose Relationship Purpose

•Ability Grouping (same level or peer tutoring)

•Pick Their Own Group (Good for feeling of comfort but bad for social or behavior)

•Gender Grouping (female/female and male/male)

•Fun Grouping (pick cards, favorite foods, animal with sounds, etc)

•Behavior Grouping (some students just cannot learn together)

•Quiet With Loud (get those quiet students to build relationship with the loud ones)

WHAT KIND OF GROUPING DO YOU THINK THE ELLs WOULD LIKE AND WHY?

IMPORTANCE OF RELATIONSHIPS

Positive teacher-student, student-student, and teacher-family relationships are associated with:

• Increasing student feeling of safety at school • Increasing academic test scores • Increasing student understanding and meaningfulness of what is being taught • Reducing absenteeism • Decreasing student dropout • Decreasing student-student conflict

• Improving school climate • Improving transition to school • Decreasing risk-taking behavior • Developing language skills • Improving self-esteem • Decreasing incidences of depression

WHY WOULD THIS MATTER FOR OUR ELLs?(Slade, 2011)

JUST AN HELPFUL HINT THAT WILL HELP ENHANCE LEARNING IN YOUR

CLASSROOM

Use certain color markers for teaching Example: Write new content vocabulary

words always in blue, non-content vocabulary words in red, write problems in purple, and steps to solving it in orange, etc

IMPORTANCE OF VOCABULARYACADEMIC VOCABULARY

Function is a relation for which each value from the set; the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair

WHAT TROUBLE MIGHT ELLs HAVE WITH THIS DEFINITION?

IMPORTANCE OF VOCABULARYSOME MISTAKES YOU MAY HAVE NEVER THOUGHT OF

IMPORTANCE OF VOCABULARY Demonstrate that vocabulary can have multiple

meanings. Help students understand the different meanings of words such as "table" and "quarter," as well as how to use them correctly in a mathematical context.

Encourage students to offer bilingual support to each other. Students will understand material better if they explain it to another student, and the new student will benefit from hearing the explanation in their first language.

Provide visual cues, graphic representations, gestures, and pictures. Offer students the chance to work with objects and images in order to master vocabulary. If there aren't enough items for each student, use manipulatives on the ELMO or posted throughout the classroom, and demonstrate the vocabulary in front of the students.

Identify key phrases or new vocabulary to pre-teach. This strategy will help students decide which math function they should apply. Example: "more than" means "add.

(Robertson, 2009)

IMPORTANCE OF VOCABULARY

Math Word Wall (No matter what grade level you teach)

IMPORTANCE OF VOCABULARY

Frayer Model (Great for new vocabulary)

GROUPS TURN TO PRACTICE

Choose a math vocabulary word that your group can create a Frayer model with

Use the Frayer model that I have provided for you

We will share out afterwards

IMPORTANCE OF VOCABULARYNONACADEMIC VOCABULARY

WORD PROBLEM: Maria has 24 marbles which is 8 fewer than Pablo has. How many marbles does Pablo have?

WHAT ACADEMIC AND NONACADEMIC VOCABULARY WORD(s) MIGHT NEED TO BE INTRODUCED HERE FOR ELLs? HOW WOULD YOU INTRODUCE IT?

IMPORTANCE OF BUILDING BACKGROUND KNOWLEDGE Modify the linguistic complexity of language and

rephrase math problems. Students will understand the problem better if it is stated in shorter sentences and in language they understand.

Guide students to cross out the unnecessary vocabulary in word problems. Doing so allows students to focus on the math function required.

Build knowledge from real world examples. Try to reinforce concepts with examples that students can picture and talk students through the situation.

Use manipulatives purposefully. This is important at all grade levels.

(Robertson, 2009)

WORD PROBLEM PRACTICE

WORD PROBLEM:Laura has a blue rope and an orange rope. The blue rope is 14 meters shorter than the orange rope. Laura also has 6 meters of duct tape. The orange rope is 16 meters long. How many meters of rope does Laura have in all?

WHAT MIGHT YOU NEED TO HELP ELLs WITH IN THIS WORD PROBLEM?

IMPORTANCE OF BUILDING ACADEMIC LANGUAGE

Have students translate symbols into words, and write the sentence out. This helps students process the operations involved in the question and gives them an opportunity to think through how to solve it. It also gives students a chance to familiarize themselves with important vocabulary words.

Create a "sentence frame" and post it on the board. Write the format of the sentence you would like students to use in discussion and then hold them accountable for using it.

Have students share problem-solving strategies. This involves asking a simple question such as, "Did anyone else get the answer in a different way?" Then allow enough wait time so students can think through how their problem-solving process was similar or different to the one offered.

Allow students to discuss how they are thinking about math. This is a way of redirecting the lesson from teacher-to-student to student-to-student. Allow students to share how they think about the math concept and any tips they have for remembering the information.

Incorporate writing activities like math journals. This is an excellent way for students to process what they've learned and what questions they still have.

Challenge students to create their own math problems. By creating the problem and checking the answer they are reinforcing their own learning.

(Robertson,2009)

IMPORTANCE OF USING TECHNOLOGY

Teach students how to use a calculator. Based on background and prior educational experience, students might not be familiar with how to use a calculator nor some of the more sophisticated models, such as the graphing calculator.

Look for educational resources that accompany your school's technology tools and programs.

Look for interactive games that offer students a chance to practice their mathematical skills.

(Robertson, 2009)

WHAT IS DIFFERENTIATED INSTRUCTION?

Each group come up with one myth and one reality about differentiation.

Once you have one, come and put it up on the chart that is provided on the wall.

IMPORTANCE OF DIFFERENTIATED INSTRUCTION

MYTHS REALITY

Differentiation is another word for “individualization”

Differentiation is not a synonym for individualization

Teachers do not teach Teachers are the key to making all of this work

Differentiation is only for the very high students or the very low students

Differentiation is for all students

No fair way to grade Teachers grade based on mastery

Students will not be prepared for high-stakes testing

Students will be more prepared for high-stakes testing

Students receive unbalanced workloads

Students receive the same amount of workload based on their own ability

Teachers teach so students should learn.

Teachers must realize everyone learns differently

Teachers have no time Saves time in the long run

(Wormeli, 2006)

IMPORTANCE OF DIFFERENTIATED INSTRUCTION

Six ways to differentiate instruction 1. Process – how you teach2. Product – what the students will

produce3. Content – different skills4. Readiness – level the complexity of the

skill5. Interest – choice activities6. Learning Modality – auditory, hands-

on, etc

IMPORTANCE OF DIFFERENTIATED INSTRUCTION

( Lazzaro, 2010)

IMPORTANCE OF DIFFERENTIATING INSTRUCTIONDinner Menu Main Dish (Select 1)

Measure the length of the objects in the measurement container using any of the nonstandard units we have used in class.

Use the large paper clips to measure the pictures of the objects on the worksheet R 17.1

Complete the “Different Units of Measure” worksheet. Side Dishes (Select at least 2)

Read the book The Biggest Fish. Measure the length of the fish in the fishing net to the nearest inch. Then glue them onto a sentence strip from shortest to longest.

Complete the “What’s My Length?” activity. Use a ruler to draw and label lines for the following measurements: 10 inches, 5

inches, 3 centimeters, 15 centimeters, 1 foot, 1 inch, 3 inches, and 10 centimeters. Organize the pictures of the objects in order from smallest to largest. Complete the “How Far to the Dragon’s Lair?” activity sheet

Dessert (Optional- Select 1) Draw a map. Label 4 locations on your map with a large dot. Using you ruler draw

lines to connect these locations. Measure and label these lines on your map to the nearest inch. Write a story problem on an index card that can be solved using your map.

Read How Big is a Foot? Then pick 5 objects from the measurement container to measure using a small paper clip, an eraser, and a ruler. Complete the worksheet for this activity.

(Dill,2010)

IMPORTANCE OF DIFFERENTIATED INSTRUCTION

WHY WOULD CHOICE ACTIVITIES BE GOOD FOR ELLs?

IMPORTANCE OF DIFFERENTIATING INSTRUCTION Rotating Groups

20 minutes of direct instruction (vocabulary, modeling examples)

20 minutes of a technology group 20 minutes of a project/hands-on group 20 minutes of skill practice 5 minutes for transitions between groups (approx 1 minute each)5 minutes at the end for closure

Total: 90 minutes

IMPORTANCE OF DIFFERENTIATED INSTRUCTION

One-Step and Two-Step Equations Example: First 20 minutes: 1. Introduce new vocabulary associated with equations

(variables, equation, inverse operations, etc) 2. Model ways to solve one and two-step equations (using the

color method) Next 20 minutes and so on: 3. Activity on computer (mathxl, math-play, mathplayground,

quia, etc) 4. Worksheet solve and write steps in words 5. Cutting and gluing matching equations

Teacher walks around and facilitates learning. Providing group roles may help groups work together better.

WHY WOULD TEACHING LIKE THIS HELP ELLs?

GROUPS TURN TO PRACTICE

Think about a topic that your group would be able to use in differentiating groups

What activities would each group do? What vocabulary words would you have

to pull out for your ELLs? What things would you have to model

and how would you model it? Is there any other problems or questions

that ELLs might face in this section? Share with whole group afterwards

QUESTIONS AND ANSWERS

REFERENCES

Dill, J. (2010). Pinterest. Retrieved from Dinner Menu: http://www.pinterest.com/pin/245305510926405429/

Lazzaro, T. (2011). Pbworks. Retrieved from ThinkTacToe: http://2differentiate.pbworks.com/w/page/860118/ThinkTacToe

Robertson, K. (2009). Colorin Colorado. Retrieved from Math Instruction for English Language Learners: http://www.colorincolorado.org/article/30570/

Wormeli, R. (2006). Busting Myths about Differentiated Instruction. LookSmart, 1-5.