Yes, Symphony Math may be used with older students. The program is designed with an age neutral interface that does not use cute cartoon characters or childish themes that make older students feel the program is inappropriate for them. Symphony Math addresses fundamental math skills that struggling students need to master in order for mathematics to be meaningful for them. The program has been used with middle school and high-school students in remedial settings.

We recommend 15- to 20-minute sessions three to five times a week. We recommend that students not be permitted to use the program more than 20-minutes a day, five days a week. There is not a required minimum amount of time students must use the program.

Our research led us to use the blue and yellow bars instead of having a different color for each bar for two reasons. The first is that children who have color perception difficulties would not be able to easily use a program with 10 different colors on the computer screen. The second reason is that with bars that have a unique color for each bar we found that some students rely mostly on verbal memory of the color relationships of the bar and do not consider the length of the bars. The length of each bar is the important mathematical quality to which we want the students attending. We found that when we used only two colors students were far more focused on the relative lengths of the bars and thus focused on the key variable of quantity.

One of the key developmental barriers Symphony Math is designed to help students work through is the transition from solving math problems by counting-on, and solving math problems by number conceptualization. Most students first solve 5+3 by counting “1, 2, 3, 4, 5 . . .” and then counting on three more, “6, 7, 8.” Subtraction is handled in a similar way by counting down. This is an inefficient and unreliable strategy for older students, though it is an important developmental accomplishment in kindergarten. Unfortunately the sight of third and fifth graders still counting up and counting down is far too prevalent and poses a major barrier to their advancement in math learning. Number bars are one of the few concrete representations (or manipulatives) that help students develop number conceptualization. The number bars provide a model to students that five is “five.” Five is not “1, 2, 3, 4, 5”. Three is “three.” Five plus three is eight. It is not “1, 2, 3, 4, 5 . . . 6, 7, 8.” The counting chips and other discontinuous representations reinforce the counting strategy of math. The number bars introduce and reinforce the number conceptualization strategy of math which is far more efficient and required for effective math learning in the higher grades.

The answer to this question is similar to the one preceding it. We could put lines on the bars that would indicate each unit of the bar. The seven bar could have equally spaced lines along the bar that divide it into seven equal sections. This would help students see the quantity that the seven bar represents. Similarly, we could have added lines to the three bar to divide it into three equal sections. To solve the problem 3+7 the student would only need to count the 10 sections on the two bars to arrive at the answer. While this is an effective and important strategy at an early stage in math learning, Symphony Math is designed to help student move beyond the counting strategy to number conceptualization. With Symphony Bars the student combines the three and the seven bars and then finds the bar that is the same length. The students see qualitatively that three and seven equal ten without falling back on counting strategies.

Students are not required to use number bars in the classroom before using Symphony Math. The program provides scaffolding and automatic support to help students begin using the activity. Symphony Math has been field tested in schools across the country and students in grades as early as pre-school and kindergarten have shown they can get up and running with the program quickly.

We agree with math experts who advocate for a math curriculum that is rich with multiple representations of quantity. Weights on a balance scale, a number line, and dominoes are all examples of effective representations of quantity to help students with learning math. Symphony Math is a complementary math program that offers an additional representation of quantity and is not intended to be the only representation used in a comprehensive and rich math curriculum. Symphony Math allows students to see systematically how one representation can be used for learning many concepts, such as addition, subtraction, multiplication etc, with the same representation. By using the same representation for a variety of math concepts they can see a visual model that shows how these concepts are interconnected.

The Symphony Math philosophy is that children are innately curious about their world and if we design a learning environment that presents mathematical concepts in an interesting and developmentally appropriate way they will be interested by the patterns and relationships of math and will not need unrelated stories, characters or music to maintain their interest. We believe children are intrinsically motivated to learn about math and Symphony Math is designed to work with students in that way.

A “symphony” is something characterized by a harmonious combination of elements. Commonly this is associated with music. The combination of all of the different instruments in a symphony orchestra is one example. In the name Symphony Math the term refers to the goal of our design philosophy which is to integrate a variety of teaching approaches and methods into one harmonious learning experience for each student. Some students need to explore concepts. Some need to work on mastering their math facts. Others need to work on applying their concepts and facts knowledge. Symphony Math is designed to evaluate a student’s needs and coordinate a variety of learning environments and teaching strategies to provide the appropriate learning experience.

One of the most important skills in math is problem-solving. In order to be able to apply what they have learned and solve novel mathematical problems students must develop the disposition of active thinkers who identify problems and seek out their solutions. Many of the learning tasks in Symphony Math are presented as puzzles that need to be “figured out.” Students find satisfaction in making these connections without being told in advance exactly how to solve the puzzle. The program does provide scaffolding in the form of instructional feedback when errors are made and in the form of a help button that can be selected for a clue that may lead the student to the answer.