Hello fellow parents!

Here’s a quick question:  What does 4×5 equal?  How did you come up with your answer?  Did you skip count by 5, did you double 5 and then doubled it again? Or did you just recall it from your memory?  Most of us rely on our memory for math facts, because we’ve learned them a long time ago at school and thus don’t have to spend time calculating the answer every time we need it.  And you probably expect schools nowadays to teach our children the same skill, right?  Surprisingly, this may not be the case anymore in California.

Despite huge public opposition, the CA math framework adopted in 2023 does not require students to become fluent with multiplication facts until the end of 5th grade.  And over 60% of kids in California entering middle school still aren’t fluent!  Experts agree that it is going to hold students back in understanding more complex math tasks and executing multi step math procedures they are supposed to learn in middle school.

Learning multiplication tables by heart is just like learning to read common words by sight.  Imagine reading a book and every single time you see the word "the", you have to stop and sound out "T-H-E" again?  It would be incredibly slow and frustrating and you’d never get to enjoy a story or understand it because all your brainpower would be spent on the task that should be automatic.  The same happens with math.

Teachers share that nowadays middle schoolers are whipping out their calculators to multiply 3 times 7 while working on exponents such as (x³)⁷.  We had a 7th grader in our class asking to use a calculator to divide 100 by 4. These kids are bright, and it’s not their fault they aren’t taught to be fast with multiplication.  This is a shortcoming of our education system, so what can we do?

As concerned citizens, we should try to change the situation by joining petitions, writing letters to those responsible for the educational process, and making ourselves heard in any other legal way.  But as parents, we can and should make sure that our own children are learning what they should learn! 

Dr. Holl's light and easy flashcard practice tips

There are multiple ways to boost your child's math fact fluency such as with addition or multiplication, but if you happen to follow the time tested tradition of flashcards, then I have a few tips that have worked well for tutoring over the years for greasing wheels while avoiding any fiery brimstone and gnashing of teeth.

The tips:

• Make a game of it!  The game is: If they get the answer right on their first try, then they keep the flashcard as a point, so they’re not practicing with that card anymore that day.  If they don’t get it right, that’s okay!  Just smile, share the answer with them, and put the card back into the rear of the deck, so they’ll get another chance when it comes up again.

  • As the deck gets shorter, the tougher cards will come up more often, so their short term memory will have an easier chance of recalling.  Keep the humor alive even down to the last one or two cards.  For example, if their last card is 7×8 (which is notoriously tricky!) and they happen to get it wrong, then after showing them the backside answer of 56, pretend to put the card back in the deck, but oh wait, it is the only card left, so smilingly ask them what is 7×8 again.  They ought to get it now.  ;-)

  • When they’ve won all the cards as points, declare victory for the day, and give them whatever rewards are most motivating for them.  Depending on the child, rewards range anywhere from tons of verbal praise with hugs and smiles, to video game time, a tasty dessert, or world domination for the especially ambitious children.  🙂
    
    

• Kids make their own flashcards.  This serves 2 purposes.

  • When first writing a card such as 4×5, that is a great time to ask them to figure out what that answer is,using whatever technique works for them such as repeated addition 5+5+5+5=20 or 4+4+4+4+4=20.  When they see this card again in the future, they’ll know that this fact didn’t come from some book, but it came from them!  That at some point, their brilliant mind already computed this answer, so it is well within their super powers to just recall their own clever answer.  So the first purpose is longterm motivation:  If the flashcards ever seem daunting, you can remind them of their own brilliance.

  • The second purpose to making their own flashcards is that some kids need very tactile or visual learning approaches, and they’re free to use blocks or make drawings to come up with the answers to each card.
    
    

• Keep it short.  When first introducing the flashcards, have them make and try only 5 to 10 new cards per day.  On the next day, repeat the previous day’s cards, and add a few new ones at a time as they get faster with the older cards.

  • When first going through new cards, let them have as much time as they need to think or even re-figure out what the answer is.  After a few days, they ought to get faster at most of the cards, but a few cards may still stump them.  In some of the practices, try giving them only the tougher cards and skip most of the easier ones.  This keeps practice time short to prevent burnout.

  • As they begin to master all the relevant cards, every once or twice a week, test them with all the cards, so that they still get occasional practice with the easier math facts.  If needed, maybe make their reward roughly proportional to the number of cards they practiced with each day.

• In the long run, go for speed!  When starting out, let them take plenty of time to think and get the answer right, and over time, their speed should gradually increase.  Our target goal is attaining a recall time of 1 to 2 seconds per flashcard which corresponds to solving 30 to 60 simple problems per minute.  This is math fact fluency, and it will greatly aid them as they progress in their academics.

• Don't forget to celebrate!  When they're reliably whizzing through the deck at 1 to 2 seconds per card, then go for a bigger reward than usual.  It was a long journey, and you both deserve it.
  
  

• Advanced technique:

  • When they’re first making their flashcards: On one side of each card, write the problem, such as 5+4 or 9×2, and on the other side, only write the answer.  Don’t include the 9×2=18 on the back, especially for multiplication cards.  This will come in handy later.  ;-)

  • Later once they master the cards, try playing a new game where you show them the answer side of the card, such as 14, and they tell you what numbers would multiply to make that number.  This will give a huge advantage for mastering long division, simplifying fractions, and factoring polynomials later on.

  • This practice is also a fun excuse for giving them more positive rewards for their effort.  :-)

  • On a finer point, some numbers such as 24 will have multiple flashcards.  If your child says 4×6 then congratulate them and ask if they can think of another pair of numbers, in this case 3×8.  And for bigger numbers like 48, focus on the flashcard’s other side such as “6x8” and don’t bother asking for 2×24 or 3×16.  As they get more advanced with time, they may start giving these answers as well, but 48=6x8 and 56=7x8 should be fine enough.

While understanding how multiplication works (like repeated addition or groups) is vital, it needs to be paired with quick recall. Working on fluency is building a strong foundation for your kids' future math progress.  While most kids would rather not spend their time learning math facts, mastering that skill will make their journey through elementary, middle, and high school math much smoother and more enjoyable!