Multiplication tables.

  Although I allow students to use calculators for multiplication, I worry they have not developed the number sense to know if the answer is in the ball park.

I realize most people use calculators to find the solution.  Even in the movie "Hidden Figures", the women used a mechanical device to do the calculations but they'd learned their multiplication tables so they knew if their answers were reasonable.

Knowing their multiplication facts falls under the general topic of Math Fact Fluency.  It has been found students who are fluent, have also developed strategies and use them to solve these problems.   In addition, these students have more cognitive resources available to learn more complex concepts and complete complex tasks.

Furthermore, being fluent means students experience less anxiety and increases their confidence so they are willing to solve more complex tasks.  Math fact fluency means a student can spend more time solving the problem rather than struggling to work through basic computation.

It has been found, the best interventions have components of practice using modeling and drilling  so students see how to do it and practice doing it.  Modeling could either be student or teacher based but there are three interventions which come highly recommended.

1. Taped-Problems Intervention in which the problems are recorded in audio form with consistent pauses between the problem and the answer.  The idea is for the students to listen and answer on the accompanying worksheet before the recording gives the answer.  If they have not written an answer down by the time the audio answer is given, they write it down.  If their answer is incorrect, they cross it out and record the correct answer. 

It is suggestion, that as students become more proficient, the pause becomes longer so they have time to record the answer.  This method provides immediate feedback.  Be sure to create at least three different recordings.

2. Cut, Cover, and Compare has students look at worksheets with the problems and answers on the left hand side but with the right side blank.  They are to study the problem and answer on the left.  Once they think they know it, they cover it and write it on the right side before checking.  If the answer is correct, they move to the next problem.  If its incorrect, they study the problem again until they get it right.

3. Incremental Rehearsal - Assess which facts the student already knows by giving a short test or activity.  Create flash cards using 9 facts the student already knows and 10 facts the student does not know.  Show the student the first unknown and ask him or her to answer it.  If they answer incorrectly, give the answer, then give them a fact they know to answer.  Anytime he answers an unknown incorrectly, give them two known facts before having them attempt another unknown. 

Once a student can answer the unknown, it becomes known.  Repeat until they know all the facts and test again to find the next facts they need to learn.

These are three suggested ways for students to learn their multiplication facts but I see a great use for Cut, Cover, and Compare in High School Math.  I'll talk about it tomorrow.  Let me know what you think.