Teaching CLD/CLDE Students to Solve Word Problems in Math

Charlotte Tyler and James Walker

July 19, 2010

SED: 513 Bilingual Special Education

Teaching CLD/CLDE Students to Solve Word Problems in Math

• Mathematics is a universal language

Learning Objectives

• To expect CLD/CLDE students to gain a conceptual understanding of solving math problems using the schema-based instruction strategy, in order to apply it in every day life.

• To create a collaborative setting to promote multiple interaction in verbal communication and peer learning.

• To develop and build vocabulary skills to enhance language proficiency in English.

• To exhibit explicitness and comprehension through various activities and modeling concepts, to help students understand word problems.

Welcome to the World of Math

• Your mind will be renewed as you open the doors to:

• Strategy I Schema-Based Instruction

• Strategy 2 Cooperative Learning

• Strategy 3 Vocabulary/Reading

Come Aboard !!!!

Strategy 1 Schema-Based Instruction

Schema…… What’s That?

Strategy 1 Schema-Based Instruction

• Focuses upon the structure of problems, thus, using schematic diagrams that help the student to categorize the different problem types and to organize the information in determining an appropriate solution (Jitendra, George, Sood, & Price, 2010).

Strategy 1…. Major Components of Schema-Based Instruction

• Students engage in thinking and reasoning versus rote learning.

• It is an instructional technique in facilitating word problem solving for all students, especially students with disabilities.

• It is a self-motivating tool for students in preparation for transitioning from teacher-mediated instruction to independent living.

• It is a teacher-mediated instruction, followed by paired partner learning, then independent learning activities.

• It scaffolds student learning, using visual diagrams until the student becomes an independent learner.

• It incorporates explicit instruction in constructing models to demonstrate or represent situations (Jitendra, et al., 2010).

Strategy 1…. 4 Key Steps in Solving Problems using Schema

• Step 1 Student reads and paraphrases story problem for the known and unknown.

• Step 2 Student uses schematic diagram in organizing information in the problem.

• Step 3 Student selects appropriate operation (add, subtract) in solving for the unknown.

• Step 4 Student solves for the unknown in the math sentence (Jitendra et al., 2010).

According to Van de Walle, 2004, (cited in Jitendra, Sczesniak, Griffin, & Deatline-Buchman, 2007, p. 283 ), “Story problems are critical for helping children connect different meanings, interpretations, and relationships to mathematical operations.”

Strategy 1 SchemaProblem Types and Illustrations

Problem types associated with addition and subtraction:

Type Three vital parts

change beginning, change, ending

compare difference, compared, referent

group part, whole, relationships

Following are three illustrations of the 2 types

Schema Type of Problem

Jane had four video games. Then, her mother gave her three more video games for her birthday. Jane now has seven video games.

Change:

+3Video Games

4 Video Games7 Video Games

BeginningEnding

Change

(Jitendra, Sczesniak, Griffin, & Deatline – Bachman, 2007)

Schema Type of Problem

Joe is eight years older than Jill. Jill is age 7 years, and Joe is age 15 years.

Compare:

Joe

15

Years

Jill

7

Years

8 Years

Bigger Smaller Difference

(Jitendra, Sczesniak, Griffin, & Deatline – Bachman, 2007)

Schema Type of Problem

Group: Jenny saw 25 birds on a camping trip. She saw 17 sparrows and some owls. How many owls did Jenny see on her camping trip?

Sparrows

17

Owls

?

Birds

25

Smaller Sets Larger Set

(Jitendra,2002)

How Can Schema- Based Learning Help?

• Marlen, a 10th grade student, is progressing very well with her English.

• Her academic vocabulary is good, but her social vocabulary is lacking.

• Combining her academic vocabulary with graphic representation of word problems will help her recognize similar problems or concepts outside the classroom.

• The goal “is to facilitate conceptual understanding” (Jitendra, 2002), which is Marlen’s next step in learning English.

Strategy 2 Cooperative Learning Scholars’ Viewpoints

• Johnson and Johnson, 2002; Slavin,1995, (as cited in Gillies,2006, p.271),stated that “cooperative learning is now accepted as an important teaching-learning strategy that promotes positive learning outcomes for all students, including students with a range of diverse learning and adjustment needs.”

• Mercer, 1996, (as cited in Gillies, 2006, p. 272), argued that “talk is now recognized as more than a means of sharing thoughts: it is a social mode of thinking, a tool for the joint construction of knowledge by teachers and learners.”

Strategy 2…. Scholar’s Views Cooperative Learning

• Vygotsky’s theories were very supportive of cooperative learning, where children work harmoniously in helping one another learn.

• He believed that learning is taking place as children work within the “zone of proximal development” (tasks that children cannot do alone, but could with the help of a more competent peer). Moreover, peers can be models for one another where their thinking may be somewhat advanced.

• He also believed that learning took place when children hear each other “think out loud” (Slavin, 2009).

Strategy 2Cooperative Learning

• There is face-to-face interaction.

• It provides that social nature of learning.

• Groups/peers model appropriate ways of thinking.

• Students observe and listen to others’ strategies/ideas.

• It is a supportive learning environment.

How does this benefit CLD/CLDE students:

Strategy 2….Cooperative Learning

• It contributes to achievement and social harmony.• Interactions benefit both individuals.• It enables students to speak more openly.• Students work jointly together to build new

understanding.

Hertz-Lazarowitz,1992,(as cited in Gillies, 2006, p.272), stated that “in cooperative classrooms, teachers move among the group to monitor progress and provide specific assistance. In this role, the teacher is ‘the guide on the side, not the sage on the stage’, and the language used is more caring and personal as they work more closely with small groups.”

Strategy 2….Cooperative Learning

A Few Helpful Tips

Strategy 2…. Cooperative Learning Activity

The Silent Card Shuffle is a cooperative strategy that exemplifies several applications, sequencing, classifying ,matching, and mapping. The activity below is to introduce students to parts of speech.

In this activity, cards have been created representing nouns, verbs, adjectives, adverbs and articles, prepositions and pronouns. Cards are cut up, placed in envelopes, and given to each group. Six cards are in each of the seven categories. It consists of five steps. http://itc-us.businesscatalyst.com/silent

ITC Publications, 2009

Strategy 2…. Cooperative Learning

• Cooperative Activities For CLD/CLDE– Team Jigsaw

Assign each student in a team one fourth of a page to read from any text to memorize. Each student completes his /her assignment, then teaches the others or helps put together a team product.

– Round RobinPresent category (“names of plants”) for discussion.

Have students take turns going around the group and naming items that fit the category. (Colorin Colorado, 2007)

Strategy 2…. Cooperative Learning

How can Veronica benefit from this learning?• According to Veronica’s profile, she is a highly

resilient student, displays a consistent sense of locus of control, appears comfortable in cross-cultural interactions, but she doesn’t make much of an effort to interact with majority peers. Moreover, she appears shy, tends to isolate herself in class, and rarely speaks in class.

• The school environment here may differ from that in her country or maybe she is going through the acculturation cycle.

Strategy 2…. Cooperative Learning

Cooperative learning would enhance and build Veronica’s social skills in these areas:

• Social interaction with peers in diverse setting• Informal conversations and discussions• Face-to-face interaction• Working in pairs or groups• Dialogic exchanges

Strategy 2…. Cooperative Learning

What about Marlen?• Marlen displays some of the same behaviors as

Veronica. • Marlen, however, is not shy and displays a high

level of confidence, except in social interactions with her majority peers.

• She feels that her vocabulary needs to improve, but does not realize that she is currently capable of interacting fully with her majority peers.

Strategy 2…. Cooperative Learning

Cooperative learning would enhance and build Marlen’s social skills in these areas:

• She would realize that she is at or above the level of her peers in many areas.

• It would improve her comfort level in mixed population group activities.

• Peers would develop respect for Marlen.

The icing on the cake: Marlen’s vocabulary would improve due to total immersion in the language.

Strategy 3…. Vocabulary/Reading

Research Says:• Research has confirmed the importance of language

skills for understanding and solving mathematical problems in large-scale assessments (Martiniello, 2008).

• Language is an important component of students’ thinking as they engage in solving mathematical problems (Miller & Hudson, 2006).

• According to Bley and Thornton, 1995, (as cited in Miller & Hudson, 2006, p. 31), “when a teacher plans instruction intended to teach mathematical concepts, he or she should consider the students’ current vocabulary knowledge and their language abilities.”

Strategy 3…. Vocabulary/Reading

What classroom activities would help CLD/CLDE students build vocabulary/ reading skills?

• Read Aloud introducing and expanding vocabulary.

• Maps and Graphic Organizers mapping used for visually organizing information. teaching explicitly and modeling various concepts.

• Make word connections using personal experiences to make new connections to new

concepts/words. creating vocabulary notebooks with definitions.

Click map for ideas

Strategy 3 Vocabulary/Reading

• Use visual tools and learning techniques developing vocabulary, word recognition, and comprehension. using graphic organizers, integrating new knowledge.

http://www.inspiration.com

• Create Print- Rich Environment– using vocabulary display as reinforcement and class

reference during class assignment.

• Introducing association among words, synonyms and antonyms.– requiring students to list vocabulary words, write a brief

definition, draw pictures to illustrate meaning. (McCollin, O’Shea, & McQuiston, 2010)

Strategy 3 Vocabulary/Reading

• Concept Mapping

BearsColor

Circus

Berries

Cubs

Caves

Can be different

Live in

Dance in

Eat

Have one or two

1. Expands vocabulary.2. Displays organization. 3. Shows connection.

Squires Media Center, 2010

Strategy 3 Vocabulary/ReadingStrategy

• KWL Chart

What I Learned

Polar Bearslive whereit’s cold.

Bears have Cubs.

How old is a cub

before it is grown up?

What I KNOW

What I WANT

To Know

Fosters thinking before, during, and after reading.

Squires Media Center, 2010

Strategy 3 Vocabulary/Reading

• Vocabulary Word Wall

Math Story Reading

AdditionSubtractionMultiplicationDivisionFractionsMixed numbersPercentEquationsSolutions

AnimalAnnaBicycleBaseballCarryCatchChocolateDangerEarlierEnough

1. Builds and expands vocabulary.

2. Uses as a reference for classroom tasks.

3. Uses for purposes of reinforcement.

Strategy 3…. Vocabulary/Reading

Can vocabulary/reading help Veronica?• Veronica’s background history states that her

primary/native language proficiency is high, both in social and academic language. However, she appears to be at the emerging stage in English language proficiency.

• Vocabulary skills can help her build and develop new words using prior experiences to make connections to new concepts. Also, through explicit teaching and teacher’s modeling and demonstrating various concepts/words, she can improve her language proficiency skills. Thus, reading aloud can expand her vocabulary.

We Come to the End!

• In conclusion, Miller and Hudson, 2006, state that according to the National Council of Teachers of Mathematics (NCTM, 2000), the “need to understand and be able to use mathematics in everyday life and in the workplace has never been greater and will continue to increase.”

• Now, it is time for you to assess your knowledge! “What Did You Learn?”

1 2 3 4 5 6 7 8 9 0 % / + * - =

1. What are two types of word problems?

2. What is the stated goal of schema- based instruction?

3. How can vocabulary instruction help CLD/CLDE students with word problems, how can word problems help CLD/CLDE students with vocabulary?

4. How is cooperative learning uniquely beneficial for CLD/CLDE students?

5. Scenario:

Ivan, a Russian boy in his second year in the United States, is in a 9 th grade algebra class. His English skills are improving, but he still speaks in ‘broken sentences’ and can get through texts with occasional use of a translation dictionary. Ivan has been screened for special education services and has been found to be LD, with difficulties in reading comprehension. As Ivan’s teacher, how would you use the three topics covered (vocabulary, cooperative learning, and schema based instruction) to give him the best chance for success?

QUIZ TIME

You Are Finished

ReferencesColorin Colorado. (2007). Cooperative learning strategies. Retrieved from

http://www.colorincolorado.org/educators/content/cooperative

Gillies, R. M. (2006). Teachers’ and students’ verbal behaviours during cooperative and small-group learning. British Journal of Educational Psychology, 76(2),

271-287. doi:10.1348/000709905x52337

Inspiration Software,Inc. (2010). Inspiration grades 6-12: Kidspiration grades k-5. Retrieved from http://www.inspiration.com/kidspiration/whets-New

ITC Publications. (2009). Silent card shuffle. Retrieved from http://itc-us.businesscatalyst.com/silent_card_shuffle

Jitendra, A. (2002). Teaching students math problem-solving through graphic representations. Teaching Exceptional Children, 34(4), 34-38.

Jitendra, A. K., George, M.P., Sood, S., & Price, K. (2010). Schema-based instructions: Facilitating mathematical word problem solving for students with emotional and behavioral disorders. Preventing School Failure, 54(3), 145-151. doi:10.1080/10459880903493104

Jitendra, A .k., Sczesniak, E., Griffin, C.C., & Deatline-Buchman, A. (2007). Mathematical word problem solving in third-grade classrooms. Journal of Educational Research, 100(5), 283-302.

Martiniello, M. (2008). Language and the performance of English-language learners in math word problems. Harvard Educational Review, 78(2), 333-368.

Mc Collin, M., O’Shea, D.J., & Mc Quiston, K. (2010). Improving vocabulary and comprehension skills of secondary-level students from diverse backgrounds. Preventing School Failure, 54(2 ), 133-136.

Miller, S.P., & Hudson, P. J. (2006). Helping students with disabilities understand what mathematics means. Teaching Exceptional Children, 39(1), 28-35.

Slavin, R. E. (2009). Educational psychology: Theory and practice. Upper Saddle River, NJ: Pearson Education, Inc.

References

References

Squires Media Center. (2010). Task definition strategies. Retrieved from http://www.squires.fayette.k12.ky.us/library/research/problem5.htm