Teaching Multiplication Tables (approach I'm willing to fund)

When I taught in the inner city in Los Angeles, I found that both my high school and junior high school students did not know their multiplication tables.  The school system allowed them to use printed multiplication tables, but the students did not use them well.  They would run their finger along a line in the table and end up one row or column “off”, producing an incorrect answer.

Beyond the inaccuracy, I also do not think that our students should be dependent on a printed table.  I preferred that they learn basic multiplication facts via principles or other ways.

Therefore, I did not allow my students to use the multiplication tables.  Instead I put multiplication facts up on the wall as follows:

1)   All multiplication facts (from 1 x 1 =1 through 12 x 12 = 144) were on the wall.

2)   Each fact card was done in color.  Facts that would be close to each other on a multiplication table were different colors.  If the students remembered seeing 7 x 9 in red, I did not want them to also remember 56 having been in red.  So the colors were NOT randomly picked.

3)   Facts that would be close to each other on a multiplication table were far apart.  That is, if they learned by space localization, I did not want 7 x 7 = 49 to be close to 8 x 6 = 48.  So the placards were NOT randomly placed.  They were placed with intentional disorder.

One Spring day, standardized testing was scheduled.  So, I came to school early and covered each multiplication fact with a piece of paper.

When the students came in, they protested vociferously.  I took a chance and claimed that they did not need to see the cards because they already knew what was on each card.  I then pointed to a blank piece of paper that had a card behind it and asked the students to tell me the underlying multiplication fact.  A chorus of correct answers responded.  We tested several cards, with correct choruses each time.  The students seemed quite surprised.

Note:    I did not check that each student knew the answers.

            I did not do any testing to see if they remembered these facts the next year, etc.

            I can't demonstrate improved math skills.  I did not receive before and after test results.

            This is a nice anecdote, but proves nothing.

Nonetheless, I am convinced that this idea has merit and is worth testing.  So I’d like to fund the cost of testing it further.