**PERSONALISED LEARNING**

Symphony Math automatically identifies each students' levels of proficiency as they work on each task, and adjusts the online curriculum accordingly.

Student tasks are further randonmised so that students working through at the same pace, each still have a unique experience and different problems to work on.

**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 to the right represent the progress of two 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.

**SCAFFOLDED HELP**

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.

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

The scaffolding for 8 + 1 = ? is shown below.

Help Button Activation | Help Provided for the Problem 8 + 1 = ? | |

1st | Show a "near neighbour": 7 + 1 = 8 | |

2nd | Show a second "near neighbout": 9 + 1 = 10 | |

3rd | Show 8 + 1 using number bars | |

4th | Show that the 9 bar is equal in length to the 8 and 1 bar |

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**INSTRUCTIVE FEEDBACK**

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.

**IN-DEPTH PROBLEM SOLVING**

Each stage in Symphony Math® features uniquely designed problems that emphasise 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.