Why do you think students gravitate toward using algorithms,

even when more sensible strategies have been taught?

Amy H.

St. Charles, MO

I think it is a bit of spin. Most adults are more comfortable with the school-based algorithms we were taught than with mental computation and number play. When helping children with homework, parents show the algorithm as the way they were taught or an “easier” way. Teachers sometimes see mental strategies as “extra” and the algorithm as the goal, instead of another computational choice. Consequently, algorithms are introduced and marketed as the eaiser or most important method. Procedural fluency is thought of as algorithmic fluency.

That said, the algorithm is a relatively efficient arithmetic anser-getting technique. If the steps are correctly completed it provides a correct answer each time. However, as you said it is not always the most efficient choice.

- For 2001 – 3, counting back 3, removing 1 and then 2 more, thinking of the year that was 3 years prior are all more efficient than regrouping across zeros using paper and pencil.
- For 62 – 29, subtracting 30 and adding back 1 is more efficient than regrouping AND no paper and pencil is needed.
- Thinking of 399 + 198 as 400 + 197 or 3.99 + 1.98 as 4 + 1.97 is more efficient than regrouping. In these cases, students are applying the Associative Property.

399 + 198 = 399 + (1 + 197)

= (399 + 1) + 197

3.99 + 1.98 = 3.99 + (.01 + 1.97)

= (3.99 + .01) + 1.97

- Thinking of 3 x 3.99 as 3 x 4 – 3 x .01 or 3 x (4 – .01) [Use the Distributive Property] is more efficient than pretending there is no decimal point, multiplying, and then counting the positions to the right of the decimal point to place it in the correct position in the answer (as I was taught). Is is also more conceptually sound.

The “sensible strategies” allow us to move from arithmetic approaches for computation to algebraic approaches.

### Change the “spin” on strategies

I wonder what would happen if we marketed these strategies as the easier ways to compute and the algorithm as the last not first choice. What if students saw themselves as doing mental algebra instead of spending time away from learning a paper and pencil procedure? What if we thought in terms of procedural flexibiliy, not just procedural fluency?

I think students do what they are trained to do and what is easiest for them at that moment. If they are only trained in a single algorithm as THE WAY, then they will follow that. They will reach the end of the algorithm thinking they have solved the problem but not understanding why or how their algorithm works. If they are trained to think flexibly and make sense of a problem first, if they learn an algorithm with the underlying comprehension of how it is connected to the context in which it is being used, then they can decide for themselves whether or not to use said algorithm. Building understanding in this way definitely takes more time but is exponentially more powerful long term for all students. It also gives continual opportunities for student to experience AHAs as they see connections between different concepts. It is the creation of the connections that is deepest and most powerful learning experience.