Multi-Step Algorithms/Impact of Attention, Memory, and Sequential and Spatial Organization

Algorithms provide us with a blueprint, or set of guidelines, for working with math problems. An algorithm is a set of specific steps used to compute a problem. The algorithm for long division, for example, consists of the repeating sequence: divide, multiply, subtract, and bring down. For some students, learning and applying algorithms can be a challenge.

For students to use algorithms, they must rely on many attention skills including the ability to sustain attention to detail, to plan a solution, and to self-monitor progress. In addition, students must be able to call up algorithms from long-term memory and to hold a number of steps in their minds while working through multi-step solutions.

Students must also keep in mind the fact that algorithms are sequential in nature, having an order in which steps must be completed. The order of operations algorithm, for example, states that rather than moving from left to right to solve an equation like 3 + 6 X 4, the equation must be solved in a specific order based on the operation involved (in this case, first the multiplication: 6 X 4, then the addition: 3+24). Students must remember and follow the correct sequence to solve the problem correctly.

In addition to attending to the sequential aspect of algorithms, students must use spatial abilities to apply many procedures. When working with column addition and subtraction, or multiple-digit multiplication, for example, students must keep numbers aligned and spaced correctly on the page to do the calculations effectively.

Students with weak skills in any of the above areas may have difficulty working with algorithms.

Here are some strategies to help develop and strengthen students’ use of multi-step algorithms in math.

Helpful Hints

  • Teach students to break multi-step problems (including equations with several computations, word problems, etc.) into smaller parts. For example, ask students to first look over the entire problem, then to break the problem into parts and identify which parts require the use of algorithm(s). Next, have them choose the algorithm to be applied for each part, and finally, ask them to solve the problem, reflecting on their answers at each step. Note: A checklist may come in handy for students to use to break down problems into stages.  
  • Encourage students to practice using a calculator and the computer, math tools that will be useful in their school and work careers. As students progress in their mathematical development, they can continue to explore the many capabilities of these tools.  
  • Incorporate mnemonics. Mnemonics are memory techniques, like making up words or rhymes, to help us remember things such as the steps in a process. Use mnemonics to help students remember steps to math algorithms. For example, Daddy, Mama, Sister, Brother can be used for the long division algorithm (Divide, Multiply, Subtract, Bring down).