Learning basic facts through tricks or a mnemonic song leads students down a path of memorization, not understanding. I previously discussed the idea of conceptual development here. When students practice their multiplication facts, they’re expected to move from concrete to abstract too quickly. This takes time!!!

Moving too quickly forces memorization and avoids any possibility of multiplicative thinking. First students are asked to model 3 rows of 6 using colored tiles…

Then after a day or two of exploring arrays, students are magically expected to remember that…

**3 x 6 = 18**

Intensions are good but strategy development is the key underpinning of automaticity. In the past I’ve asked myself the following questions:

*When do students practice multiplication that’s not written as AxB? (for the purpose of automaticity)**When/how is multiplicative reasoning fostered?**When do multiplication strategies become automatized?**When do number strategies become number knowledge?*

My answer to all 4 questions….I use multiplication subitizing cards with my daughter whose in 2nd grade so I figured I’d videotape and share.

<<<Download an updated version of the multiplication subitizing cards here>>>

My takeaways:

- It’s easy to identify which facts she’s comfortable with and has automatized.
**At 1:15**– she demonstrates how she used multiplicative thinking for 6×6.**At 2:00-**she could use her understanding of the commutative property for multiplication to build fluency. She was quickly is able to recognize that 7×5=35 at*1 minute*, but it took some time to figure out 5×7. She owns this strategy for addition so I’m waiting for it to click with multiplication….no rush:-)**At 2:20**– I missed a fact when she was wrong (doh!)- At
**2:48**and**3:55**she explains her multiplicative reasoning.

5 minutes spent purposefully building fluency and I gained so much information about my daughter. The great thing is that it works for every 8 year old…even the ones in your school.

Hmmm,

If you mean providing context to the numbers we practice with, then I would agree with you. Graham would too. He spends at least two hours of his k-2 foundations course talking about just that.

Jumping from that to numerals seems a leap however. My understanding of the research is that moving from the concrete to the representational to the abstract would be the way to go. These cards seem very representational to me.

Current research suggests that tying numbers to visual representations is likely far more effective than what is being done here. In fact some of this may be a huge waste of time compared to straight numeral representations.