## Action Research

*This action research project, a collaboration between Elvira Vargas, Laura Quintanar, and Cora Prado, focused on ratios and proportions.*

Click here to download the report as a Word document.

**1. Identification of Problem area: Ratios and Proportions**

The CST is composed of 39 % of questions related to number sense (28 out of a total of 72 questions). Ratios and proportions are part of this category, as students are required to use multiple math skills to solve problems. Click to see the relevant standards:

1.2* Interpret and use ratios in different context (e.g., averages, miles per hour)

1.3* Use proportions to solve problems (e.g., determine the value of N)

1.4* Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned and tips.

2.2* Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.

2.3 Solve problems involving rates, average speed, distance and time.

Key Standards*1.3* Use proportions to solve problems (e.g., determine the value of N)

1.4* Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned and tips.

2.2* Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.

2.3 Solve problems involving rates, average speed, distance and time.

A. The teachers in grade 6 were able to use the LAUSD Quarter Assessment Data in order to identify the problem. The data was averaged by classroom and was divided in five scoring categories: Advanced 85-100%, Proficient 66-84%, Basic 48-65%, Below Basic 31-47% and FBB 0-30%. This assessment consisted of twenty multiple choice questions, thirteen of them or 65% were related to ratios and proportions.

The constructive response was not included in the data analysis. The data showed that some students continue to have difficulty understanding and successfully solving word problems related to ratios and proportions.

Teacher |
Number of Students who scored proficient or above |
Number of Students who scored basic or below |
Percentage Proficient |

Ms. Vargas | 14 | 12 | 54% |

Ms. Quintanar | 15 | 12 | 56% |

Ms. Prado | 16 | 8 | 67% |

B. Ratios and Proportions Pre-Test

The pre-test consisted of one word problem that required the students to identify the unit rate (cost of one acre) and then multiply by 15 acres. The students had to identify the cost of fifteen acres for $24,000.

Teacher |
Number of Students who passed |
Number of Students who did not pass |
Percentage Passed |

Ms. Vargas | 11 | 14 | 44% |

Ms. Quintanar | 9 | 18 | 33% |

Ms. Prado | 15 | 11 | 58% |

C. Student Work

Word problems related to ratios and proportions were given to students over a period of five weeks. The first week, students were given a set of word problems with sentence frames that helped identify what the end result should be. Students were required to read the instructions carefully, and to identify what they were being asked to solve.

Students were encouraged to continue with the use of sentence frames as a variable to facilitate understanding of word problems.

D. Ratios and Proportions Post-Test

Teacher |
Number of students who passed |
Number of students who did not pass |
Percentage who passed |

Ms. Vargas | 16 | 10 | 62% |

Ms. Quintanar | 15 | 9 | 63% |

Ms. Prado | 19 | 7 | 73% |

**3. Interpretation of Data:**

The data showed that students continued to have some level of difficulty solving word problems related to ratios and proportions. Some ELL students lacked the command of the English language necessary to master math contents. It was evident that ELL students had more difficulty understanding word problems. Thus, addressing the needs of ELL students was the next step.

**4. Action Based on Data:**

- Provide instruction in mathematics vocabulary (e.g., unit rate, ratio, proportion, per, each)
- Incorporate scaffolding activities to teach listening and speaking skills (e.g. sentence frames, graphic organizers and oral cloze)
- Approach ELD Coordinators, or intervention coaches, to offer ideas to implement in the classroom

**5. Possible Interventions to Achieve the Desired Outcomes:**

Who: Mainstream and ELL math students in grade 6 What: Inclusion of sentence frames as a variable to facilitate understanding of word problems Where: Classroom and small group intervention Why: Difficulty understanding and solving word problems

**6. Identified Problem(s):**One sixth grade class was closed in mid-February 2010. Twenty one students were dispersed into the three classes listed above. The majority of these students are ELD level 5 and have been unable to reclassify.

**7. Evaluate the Results:**

The sentence frames helped many students understand the question. However, when the sentence frame was removed some students continued to have difficulty understanding the word problem.

The analysis of student work showed the following:

- Students in grade six continue to have difficulty multiplying and dividing with decimal numbers.
- Students continue to have difficulty completing long division
- Students need to be reminded to underline the question
- Students need to make a habit of showing all the work when solving problems
- Students need to share with classmates various ways to solve problems
- Students need more math vocabulary exposure

- Practice multiplication with decimal numbers early in the year
- Practice long division more regularly
- Implement routines and procedures when solving word problems
- Reinforce the use of scratch paper to solve problems
- Introduce math vocabulary before teaching the content area
- Enhance oral communication in the classroom to share different ways to solve math problems among students
- Incorporate activities to teach listening and speaking skills across the curriculum
- Continue with the use of sentence frames as a variable to facilitate understanding of word problems from the inception of the school year.
- Repetitive modeling/use of the use of sentence frames

## Student Work

**sentence starters**were used by Claudia Morales in her Fifth Grade classroom at Ellen Ochoa Learning Center.

Teachers can use sentences frames to model grammatical structures. Students use sentence stems to support their effort to communicate their understanding of mathematics concepts during pair and group work.

By giving students specific words to use in their group and pair work, the teacher ensures that the students practice using mathematical words in meaningful communication.

A

Example: Instead of "I like_____ because it is nice.", We could give students a Communication Guide: "I enjoy _____ for two primary reasons. In the first place, ________ makes me think of..... And, secondly, ________ is a way to...."

Rationale: It is essential to that English learners have daily time for oral rehearsal of language before writing, then oral retelling/sharing after writing. A communication guide lends structure to this task, and enables the teacher to target academic language according to the needs of the students.

Sources: "Teacher's ELD Seminar Guide" (LAUSD, LAB, 2005); "Task Based Learning & Teaching" (Rod Ellis); A Focused Approach to Instruction for English Learners (Susana Dutro), "Rethinking English Language Instruction" (Dutro & Moran)

**communication guide**is a cognitive strategy. A cognitive strategy enables second language learners to learn, remember, and understand language input. So, a communication guide provides the**forms**of language we want students to practice - first orally, then in writing. It involves constructing meaningful sentences by putting together known elements in new ways, also called recombining.Example: Instead of "I like_____ because it is nice.", We could give students a Communication Guide: "I enjoy _____ for two primary reasons. In the first place, ________ makes me think of..... And, secondly, ________ is a way to...."

Rationale: It is essential to that English learners have daily time for oral rehearsal of language before writing, then oral retelling/sharing after writing. A communication guide lends structure to this task, and enables the teacher to target academic language according to the needs of the students.

Sources: "Teacher's ELD Seminar Guide" (LAUSD, LAB, 2005); "Task Based Learning & Teaching" (Rod Ellis); A Focused Approach to Instruction for English Learners (Susana Dutro), "Rethinking English Language Instruction" (Dutro & Moran)

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