Redes de Acceso Convergentes (RoF)

Q I see that the topics taught in Symphony MathIntervention fall mostly within our kindergarten through grade four curriculum. However, some of the problems look very challenging and the concepts are taught to a deep level. Is it appropriate to use the program with older students who do not have a solid math foundation?

A Yes, Symphony MathIntervention 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. Symphony MathIntervention addresses fundamental math skills that struggling students need to master in order for mathematics to be meaningful. The program has been used with middle-school and high-school students in remedial settings.

Q For how long and how often do you recommend that a student use Symphony Math?

A 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 30 minutes in any one day.

Q I see that Symphony Math uses number bars. Why not use a different color for each number bar to help students distinguish them?

A 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 are not 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 size bar, we found some students rely mostly on verbal memory of the color relationships of the bar and do not consider the length of the bars.

For example, some students memorize the color combinations, so that when you ask them to find two

bars that equal ten, they know that yellow plus yellow equals orange, but they may not understand why. The length of each bar is the important mathematical property to which the student needs to at-

tend. We find that with the Symphony number bars students are more focused on the relative lengths

of the bars and thus focused on the key variable of quantity.

Q I find it interesting that you do not have any counting chips, or dots in your program to help students count their way through the numbers. Why is this?

A One of the key developmental barriers Symphony Math is designed to help students overcome is the transition from solving math problems by counting-on, to solving math problems by number concep-

tualization. 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 too prevalent and poses a major barrier to their advancement in math. Number bars are one of the few concrete representations (or manipulatives) that help students develop number conceptu-

alization. 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. The number bars introduce and

reinforce the number conceptualization strategy which is more efficient and helpful for effective math

learning in the higher grades, especially with fractions.

Q Why don’t the bars have lines marking off each unit?

A 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. 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 students 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 relying exclusively on counting strategies.

Q Do we have to use number bars in our classroom?

A Symphony Learning does not sell hands on versions of the blue and yellow numbers bars. It is not required for students to practice with blue and yellow bars in the classroom in order to progress with the program. We do recommend that students use a wide variety of concrete representations in their core curriculum.

Q I noticed the program only uses number bars. Why not use many different representations, such as cubes, ten frames, counting chips, etc?

A We agree with math experts who advocate a math curriculum that is rich with multiple representa- tions. Weights on a balance scale, a number line, and dominoes are all examples of powerful math- ematical representations to help students understand math. Symphony Math is a complementary pro- gram that offers an additional representation 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, multiplication, and fractions - with the same representation. By using the same representation for a variety of math concepts, students can see a visual model that shows how these concepts are connected.

Q I noticed that Symphony Math does not have the usual cartoon characters, music, and narratives that I have seen in other educational software. Won’t kids get bored without those cute multimedia experiences?

A 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 manner, they will be engaged by these patterns and relationships 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 tap into this capacity.

Q Why is the program called Symphony Math?

A A “symphony” is something characterized by a harmonious combination of elements. Commonly this

is associated with music. The integration 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 experi- ence for each student. Some students need to explore concepts. Some need to work on mastering number relationships. Others need to work on applying their conceptual knowledge. Symphony Math is designed to evaluate a student’s needs and coordinate a variety of learning environments and teaching strategies to provide an appropriate and enjoyable learning experience.

Q In other educational software programs our school has used, the instructions are more explicit and even show the student exactly what to do or how to solve the problem. All the student has to do is copy what they were shown. Why does Symphony Math not model and explain exactly what students are supposed to do?

A One of the most important skills in math is problem solving. In order to be able to apply what they have learned and to 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

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 will lead the student a step closer to the answer.

Q Why doesn’t Symphony MathIntervention teach all of the different math strands and benchmarks required by my state standards? Topics like time, money, and data do not seem to be taught in depth in Symphony Math.

A The pedagogical premise of Symphony Math is that many students struggle with mathematics because they do no have an in-depth understanding of the big ideas of mathematics (please see Chapters 1 and 2). Symphony MathIntervention is designed to provide students with understanding of the most important math concepts. Research has shown that an in-depth understanding of these big ideas of math leads to improved performance on a variety of math topics. Your students should continue to be taught all of the topics and benchmarks they are required to know. Concurrently they can receive extra practice with Symphony Math on some of the most important and difficult-to-master

foundational concepts.

Q Why do you recommend that students restart the program after summer vacation or other breaks? Won’t they have to repeat a lot of material they have already covered?

A We recommend that if a student has not used Symphony Math for four weeks or longer she start the program from the beginning. Chapter 3 of this guide details how to reset students accounts. We have found through our research that most students will progress more quickly overall if they start Symphony Math from the beginning instead of continuing where they left off. If a student truly has in-depth mastery of the concepts she worked on in Symphony Math the first time, then she will quickly

move through those concepts and return to her challenge level. However, if a student was merely beginning to make important connections but did not develop in-depth mastery, those weaknesses

will be identified as she moves through the program a second time.