# RtIIES provides multiple recommendations. Symphony Math meets all of them.

In their publication, “Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools,” the National Center for Education Evaluation and Regional Assistance (IES) summarized eight recommendations to address the challenges educators face when implementing RtI.

Symphony Math® – a web-enabled program with a visual and highly intuitive interface that helps students understand math at a conceptual level – aligns with each of the recommendations. As our intervention program fits the criteria outlined in the IES report, it can be a tremendous tool for teachers while helping students build the understanding and confidence they need for future success.

The complete IES report is available at http://ies.ed.gov.

### Overview of Recommendations

Recommendation | Symphony Math Alignment | |

1. | Screen all students and provide interventions to students identified as at-risk. | Several tools within the program identify at-risk students easily and quickly. |

2. | Instructional materials for students should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5. | The program provides an easy-to-implement solution for the understanding of whole number relationships and for developing foundational proficiencies at Tier 2 and Tier 3 levels. |

3. | Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review. | Visual models, auditory problems, and word problems provide explicit, systematic, and easy-to-grasp guided practice through the most important mathematical concepts. |

4. | Interventions should include instruction on solving word problems that is based on common underlying structures. | The scope and sequence contain word problems for all ‘Big Ideas’. |

5. | Intervention materials should include opportunities for students to work with visual representations. | A key program environment consists of virtual manipulatives that enable students to understand and solve math problems visually. |

6. | Interventions at all grade levels should devote about ten minutes in each session to building fluent retrieval of basic arithmetic facts. | The program includes timed practice and addresses the immediate recall of foundational number relationships in two unique ways. |

7. | Monitor the progress of students receiving supplemental instruction. | An online dashboard and ten reports allow teachers and administrators to easily track detailed student progress in real-time. |

8. | Include motivational strategies in Tier 2 and Tier 3 interventions. | The program motivates students by presenting math problems in an engaging puzzle-like format and reflects success back to the student through graphs and progress indicators. |

### Recommendation #1: Screen all students and provide interventions to students identified as at risk.

Symphony Math® provides multiple mechanisms to recognize specific issues and develop appropriate interventions.

- The Symphony Math Screener quickly identifies students who are at-risk for math failure.
- The Symphony Math Benchmarker confirms the student’s at-risk status, and tracks growth three times during each school year.
- The Symphony Math Student Program provides a rigorous intervention that focuses on the most important concepts that are necessary for math success.

For example, the following Symphony Math® report displays the progress of a third grade student who began the program in September as a Tier 1 supplement to the core curriculum. After not mastering a single concept by November, the student transitioned from Tier 1 to Tier 2 and intensity increased from three to five sessions per week. When the intensity increases (i.e., the blue dots become more frequent), the progress line begins trending upwards.

#### Common Roadblocks

The IES guide indicates that a common roadblock to RtI screening is that “districts and school personnel may face resistance in allocating time resources to the collection of screening data.”

Symphony Math® helps overcome this challenge by integrating the screening into the Tier I program.

### Recommendation #2: Instructional materials for students should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5.

Symphony Math® provides an easy-to-implement solution for the understanding of whole number relationships and for developing foundational proficiencies at Tier 2 and Tier 3 levels.

For example, Symphony Math® delivers a sequence of concepts that helps students develop in-depth mastery of the underlying big idea of parts-to-whole, which is a foundational math concept. The approach involves on-screen manipulatives, symbols, language, word problems, and fluency practice. This in-depth treatment of whole numbers not only fosters proficiency in addition and subtraction, it also establishes strong fundamentals for students to tackle more complex problems later.

Although some teachers may worry that the intervention program is not aligned with the core classroom instruction, the authors of the IES report are unequivocal on this matter:

The panel believes that alignment with the core curriculum is not as crucial as ensuring that instruction builds students’ foundational proficiencies. Tier 2 and tier 3 instruction focuses on foundational and often prerequisite skills that are determined by the students’ rate of progress. So, in the opinion of the panel, acquiring these skills will be necessary for future achievement. Additionally, because tier 2 and tier 3 are supplemental, students will still be receiving core classroom instruction aligned to a school or district curriculum (tier 1 ). (p. 20)

The table below displays the 26 stages of Symphony Math® and their underlying big ideas.

# | Stage Name | Example | Underlying Big Idea |

1 | The Number Sequence | 1,2,3,4,? | Quantity |

2 | More/Less/Same | Find ’1′ more than 6. | Parts-to-Whole |

3 | Add & Subtract to 5 | 3 + 2 = ? | Parts-to-Whole |

4 | Ten as a Unit | ? = 8 + 2 | Parts-to-Whole |

5 | Comparing Numbers | 13 = ? | Quantity |

6 | Add & Subtract to 20 | 9 + 8 = ? | Parts-to-Whole |

7 | Tens | Create ’80′. | Hierarchical Groupings |

8 | Add & Subtract with 10s | 20 + 3 = ? | Hierarchical Groupings with Parts-to-Whole |

9 | Hundreds | Make ’600′. | Hierarchical Groupings |

10 | Add & Subtract with 100s | ? = 200 + 30 | Hierarchical Groupings with Parts-to-Whole |

11 | Foundations for Multiplication | 2,4,6,8,? | Repeated Equal Groupings with Parts-to-Whole |

12 | Regrouping with 2- and 3-digits | 19 + 5 = ? | Hierarchical Groupings with Parts-to-Whole |

13 | Multiplication & Division | 2 x 4 = ? | Repeated Equal Groupings |

14 | Introduction to Fractions | Create ‘Thirds’. | Repeated Equal Groupings with Parts-to-Whole |

15 | Multiply & Divide to 100 | 5 x 12 = ? | Repeated Equal Groupings |

16 | Multiply & Divide with 1/10/100 | 1×7, 10×7, 100×7 | Repeated Equal Groupings |

17 | Add & Subtract Unit Fractions | 1/4 + 1/4 = ? | Repeated Equal Groupings with Parts-to-Whole |

18 | Non-Unit Fractions | 2/6 + 3/6 = ? | Repeated Equal Groupings with Parts-to-Whole |

19 | Decimals | 0.4, 0.5, 0.6, ? | Repeated Equal Groupings, Parts-to-Whole, Hierarchical Groupings |

20 | Improper Fractions | 5/3 = 2/3 + ? | Repeated Equal Groupings with Parts-to-Whole |

21 | Standard Algorithm: Addition and Subtraction | 238 + 165 = ? | Parts-to-Whole, Hierarchical Groupings |

22 | Expanded Mode Multiplication and Division | 23 x 68 = ? | Repeated Equal Groupings, Parts-to-Whole, Hierarchical Groupings |

23 | Multiplying Fractions and Whole Numbers | 1/4 x 32 = ? | Repeated Equal Groupings, Parts-to-Whole, Hierarchical Groupings |

24 | Magnitude and Place Value | 7.01 x 100 = ? | Repeated Equal Groupings, Parts-to-Whole, Hierarchical Groupings |

25 | Decimals to Thousandths | 4.09 + 3.4 = ? | Repeated Equal Groupings, Parts-to-Whole, Hierarchical Groupings |

26 | Expanded Mode *÷ with Decimals | 7 x 0.5 = ? | Repeated Equal Groupings, Parts-to-Whole, Hierarchical Groupings |

### Recommendation #3: Instruction during the intervention should be explicit and systematic. This includes

providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.

Visual models, auditory problems, and word problems provide explicit, systematic, and easy-to-grasp guided practice through the most important mathematical concepts.

With Symphony Math® students solve problems and receive corrective feedback specific to the nature of their mistakes. Instead of merely indicating that an answer is incorrect, the program leads the student towards the correct answer and to a better understanding of the concept.

For example, if a student answers 3 + ? = 6 with a 2, the program displays that a 3-dot card combined with a 2-dot card is not the same as a 6-dot card. This approach helps students deduce for themselves why an answer is incorrect. This also is preferred to saying, “That’s not right, try again,” which often leads to guessing and no meaningful understanding of why the response was incorrect.

#### Common Roadblocks

The IES panel identifies several roadblocks to this recommendation. For example, interventionists may be unfamiliar with how to provide the type of instruction necessary, while some may underestimate the amount of practice required.

Symphony Math® addresses these roadblocks by automating explicit and systematic instruction. The program also provides intensive, one-to-one practice so that students can work at their own pace and build stronger foundations before progressing to higher-level concepts.

### Recommendation #4: Interventions should include instruction on solving word problems that is based on common underlying structures.

The scope and sequence for Symphony Math® contain word problems for over 70 underlying structures.

Symphony Math® systematically challenges students to work with world problems that are organized by their underlying structure. If a student has difficulty with a specific structural word problem, she will continue to see those types of word problems in the program until she demonstrates mastery.

For example, some word problems for addition consist of two parts and a missing whole, while some for missing addends consist of a part, a whole, and a missing part. This approach helps students recognize and apply the appropriate operation to a wide range of word problems.

#### Common Roadblocks

The IES panel identifies a potential roadblock in that not all intervention materials classify word problems by their structural type.

Symphony Math® eliminates this challenge by providing word problems that are organized and tracked by their underlying structure.

### Recommendation #5: Intervention materials should include opportunities for students to work with visual representations.

A key program environment of Symphony Math® consists of virtual manipulatives that enable students to understand and solve math problems visually.

Symphony Math® highlights instructional activities that use visual problems to help emphasize the size of numbers and their relationships to each other.

For example, one environment explicitly challenges students to connect visual representations with the symbols they represent. This ensures that students understand what the symbols mean and how to build visual representations of number sentences.

#### Common Roadblocks

The IES panel identifies that some interventionists believe using visual manipulatives is too time intensive, while others may not understand how to represent math concepts visually.

Symphony Math® overcomes these roadblocks by facilitating the visual representations via an on-screen environment. This saves time, does not require the teacher to effectively represent every concept with manipulatives, and simplifies the process for larger student groups.

### Recommendation #6: Interventions at all grade levels should devote about ten minutes in each session to building fluent retrieval of basic arithmetic facts.

Symphony Math® includes timed practice and addresses the immediate recall of foundational number relationships in two unique ways.

First, Symphony Math® only requires students to work on number relationships for which they have demonstrated conceptual mastery (via manipulatives, symbols, language, and applications). This helps students avoid the common pitfall of memorizing concepts they do not fully understand.

Second, Symphony Math® enables students to work on more than mastering simple addition and multiplication facts. For example, students work to quickly recall answers to numbers sentences such as 4 + ? = 9 and 15 ÷ ? = 5. This supports understanding by emphasizing the relationship between numbers and operations.

#### Common Roadblocks

The IES panel identifies that fluency exercises and practice may be boring for students.

Symphony Math® overcomes this obstacle by presenting the fluency practice in an engaging, motivating video game format that gives students precise feedback on their progress.

### Recommendation #7: Monitor the progress of students receiving supplemental instruction.

An online dashboard and multiple reports allow teachers and administrators to easily track detailed student progress in real-time.

The Symphony Math® dashboard and detailed data views deliver instant progress snapshots between groups (i.e., class, grade, school, or district), throughout a specific group, and for individual students.

#### Common Roadblocks

The IES panel indicates a potential roadblock in tracking students across varied ability levels who require different interventions and RtI groups.

Symphony Math® resolves this issue by engaging each student at their developmental level, thus allowing advanced students to progress quickly and less developed students to spend more time at earlier stages. Moreover, the program’s easy-to-use dashboard and reports overcome another challenge by providing real-time monitoring and saving teachers significant time.

### Recommendation #8: Include motivational strategies in tier 2 and tier 3 interventions.

Symphony Math® motivates students by presenting math problems in an engaging puzzle-like format and reflecting success back to the student through graphs and progress indicators.

Symphony Math® recognizes the importance of providing motivational strategies for students in several ways. For example, the program provides students with feedback through a variety of progress meters and Symphony Mastery Points. These tools help students appreciate the progress they are making and encourage them to continue their achievements.

While the IES panel cautions that teachers can find motivational strategies time consuming to implement, Symphony Math® builds the strategies into the intervention and makes them easily available. Additionally, the program offers certificates that teachers can download and print out to recognize student accomplishments and effort.