The PMD Group

Curriculum Director, Massachusetts

With Symphony Math®, these problems are resolved.

A web-enabled program with a visual and highly intuitive interface, Symphony Math® helps students understand at a conceptual level. Instead of being overwhelmed by numbers, students move at their own speed and learn how math works.

Through every stage of Symphony Math®, students gain a strong foundation in underlying principles and become better equipped to take on basic and advanced subjects. Going far beyond rote math drills and practice tests, this special teaching solution illuminates the core of learning and produces confident, more capable students.

IDENTIFY AT-RISK STUDENTS EARLY IN THEIR EDUCATION

The Symphony Math Screener is a 5-minute automated test that can determine which students are at risk for math failure, and can be group-administered to all students in a district. These may be students who otherwise do not yet show any symptoms of a math learning difficulty. The Symphony Math Screener includes these features:

Designed for Younger Students

CCSS-Based Items

Instant Results

Designed for Younger Students

Symphony Math assessments are available for students in grades K-8, but they were designed to be used independently by younger students. This allows educators to identify students at risk for math failure in the first month of kindergarten, instead of waiting until grade 4 when end-of-year grade 3 results become available. Instructional supports can be implemented early in the student’s learning career, to close the gap with peers before it becomes unmanageably large.

Symphony Math conforms to the Common Core State Standards (CCSS), and adopts the same commitment to in-depth learning and understanding. By aligning its assessments to the CCSS, Symphony Math enables schools to focus on assessing a narrow range of target concepts, at the in-depth and rigorous level specified by the CCSS.

The Symphony Math Screener probes for in-depth understanding by using technology-enhanced test items. Symphony assessment problems challenge students to produce multiple correct solutions, demonstrate fluency, graph lines, use measurement tools, and solve for the exact answer, instead of providing only a simple, multiple choice. These technology-enhanced problems require students to demonstrate a deeper level of understanding to produce correct responses.

Results are immediately available to authorized personnel, from the classroom teacher all the way up to the district office. Reports show groups and individual students who are At-Risk, Borderline, or Not At-Risk for math failure.

The Symphony Math Benchmarker is a computer adaptive test that identifies the precise instructional level of each student, providing a base-line for intervention and progress monitoring. The Benchmarker allows more of an opportunity for students to demonstrate their knowledge and reject their at-risk or borderline status.

Targets Precise Mathematical Ability

Provides Baseline Diagnostic for RtI

Multiple Administrations Quantify Student Learning Over Time

Targets Precise Mathematical Ability

The Symphony Math Benchmarker adaptive testing engine dynamically locates each student on a standardized scale of mathematical ability. The test is based upon an item bank of 900 test items that were specifically designed to measure progress against the Common Core State Standards (CCSS) for Mathematics. Benchmarker test items have been calibrated and organized on a scale of low difficulty to high difficulty; the program applies Item Response Theory algorithms which move the student to an easier item after an incorrect response, and to a harder item after a correct response.

Each student begins the Benchmarker with an assessment item that is two years below the student’s enrolled grade level. Depending on the student’s pattern of correct and incorrect responses, the test items will become more or less difficult. A student may see between 18 and 24 assessment items during a Benchmarker session. Benchmarker ends the assessment after it has seen enough responses to determine the student’s location on the standardized scale of CCSS mathematics ability.

Symphony Math supports Response to Intervention, helping assess and develop indepth understanding of mathematics. Some screeners used for Response to Intervention only measure fluency, or focus on a single skill, and are not aligned to the depth and rigor of the Common Core State Standards. However, using Symphony Math minimizes the chance that an at-risk student might quickly learn a skill needed to pass the fluency screener (e.g. single digit addition) without acquiring the in-depth and rigorous understanding necessary to succeed in a CCSS curriculum.

Multiple Administrations Student Learning Over Time

All students receive a standardized score on a common vertical scale which reveals how the tested students performed in comparison to grade-specific national norms. Because Symphony Benchmarker scores are expressed on a vertical scale, students’ scores can be readily compared across grades. We all expect that most first-graders have learned more than most kindergartners, most second-graders have learned more than most first-graders, and so on. With Symphony’s scale scores, teachers can track performance regardless of assigned grade, allowing tracking of students across grades, thus supplying a detailed picture of their progress over time.

The Symphony Benchmarker is given in the beginning, middle, and end of each school year, and testing windows can be customized by Administrators so that students receive the assessments at appropriate times for the school and district.

SUPPORT STUDENTS WHO NEED HELP IN MATH

The best practices in developmental psychology and cognitive science are the cornerstones of Symphony Math®. Our uniquely designed delivery methods ensure that students – regardless of learning styles or knowledge levels – fully grasp fundamental mathematical ideas, even for difficult-to-explain and abstract concepts. The result is a solid foundation for acquiring higher math skills, as well as a positive learning experience.The primary elements in the Symphony Math® approach, which cover Common Core Math standards in grades K-5, include:

Conceptual Sequences

Multiple Ways of Knowing

Instructive Feedback

Active Scaffolding

In-Depth Problem Solving

Dynamic Branching

Guided Practice Offline Worksheets

Teacher Overviews

Conceptual Sequences of the Most Important Mathematical Ideas

A tightly connected progression forms the conceptual sequence of Symphony Math®. These underlying “big ideas” provide the foundation for mathematical learning. As students master each big idea before moving on to the next, they learn to succeed with more complicated math later on.

Six distinct activity environments provide multiple representations of each concept and integrate with the conceptual sequence.

By “seeing” mathematical concepts, students develop mental models for meaning. In the screen below, a student must place a card with 2 dots to show that 1 + 1 = 2 (the part-to-whole concept).

Students learn the meaning of the symbols by explicitly connecting them to visual representations. In the screen below, a student must use symbols to construct the number sentence, “4 = 1 + 3.”

Manipulatives automatically appear to help students working at this abstract level.

Story problems deliver real-life applications of the concepts and help students who learn better through narratives and examples.

This learning environment fosters fluency once a student has demonstrated understanding of a concept using manipulatives, symbols, language, and story problems.

Instructive feedback encourages independent thinking by revealing the nature of each incorrect response. For example, if a student answers 3 + 2 = ? with a 6, the program immediately shows that a 2 bar combined with a 3 bar is not the same length as a 6 bar.

This approach helps students deduce for themselves why an answer is incorrect. This also is preferred to saying, “That’s not quite right, try again,” which often leads to guessing and no meaningful explanation of why the response was incorrect.

Active Scaffolding

The “Help” button provides scaffolding that leads the student closer to the solution, but does not give the answer immediately.

For example, if a student is working on 8 + 1 = ?, she can press the “Help” button to activate scaffolding that will help her connect 8 + 1 with her knowledge of concepts and number relationships. Pressing the “Help” button again provides additional scaffolding. Hints include the addition of visuals onscreen, re-ordering of possible solutions, and inclusion of one of the elements of the correct solution.

As scaffolding does not directly provide correct answers, students develop long-lasting problem solving skills and reduce their dependence on technology for solutions.

In-Depth Problem Solving

Each stage in Symphony Math® features uniquely designed problems that emphasize comprehension and problem solving.

For example, to master place value concepts, students solve a series of problems to understand the base ten system. Students combine numbers of different place values, such as “30 + 400 + 7 = ?”. They also create number sentences for which the sum is provided but the addends are missing, such as “? + ? + ? = 286″. Each addend must correspond to the ones, tens, and hundreds place value (e.g. 200 + 80 + 6 = 286). At the most difficult level, students provide three different solutions to this type of problem.

Students also learn to problem solve by connecting current problems to similar easier ones they answered previously.

Dynamic Branching

The dynamic branching of Symphony Math® allows students to learn at their own levels. As the program illuminates an area of need, progress slows until the student achieves the necessary understanding.

For example, the graphs below represent the progress of two third grade students who used Symphony Math® for the same amount of time. The student on the left required relatively little practice to demonstrate mastery, whereas the student on the right needed more practice to fully grasp the concepts.

Offline Worksheets to Frame Conversations

Manipulatives

Bridge (to Symbols)

Symbols

Apply (Story Problems with models)

Help indicators in Symphony reports suggest Guided Practice by comparing student performance to a nationally representative sample. For every suggestion, a simple click allows easy access to Guided Practice worksheets. Links to Latest Award certificates have also been added so that you can celebrate student achievement in the Symphony Math program.

Teacher Overviews

A full description of the “Big Idea” for the Stage

Worksheet instructions

Answer Keys for student worksheets

Common Core State Standards reference

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