Thoughtful Thursday Week 5 – Speed vs. Depth

Did you grow up hating math or loving it? I grew up liking math. I made good grades in it, but I never thought I was a “math person” per se.

It turns out, there is no such thing as a “math person.” Everybody is capable of learning math. And everyone should have the chance of being introduced to math in a creative, fun way. Math should not be a series of mindless drills and repetition exercises. Math facts – especially the ones in arithmetic, or the early grades – should be understood.

Thoughtful Thursday

Which is why we chose to switch to Right Start Mathematics, a Montessori-inspired math program put together by Dr. Joan Cotter. I was getting a bit bored of this curriculum, not to mention confused – because it is so different, when… I discovered an MOOC by Stanford University called How to Learn Math – For Students. It totally reassured me Right Start Math is the right way to introduce my children to math concepts.

Oh, what a treasure trove of brain research and busted myths about mathematics I found in this Stanford course. It took me about two hours over two days (three sessions total) to finish all the lessons. My children came and hovered over my shoulder for a bit, as I watched the videos and answered the quizzes. Not sure they got much out of it, but some things sounded more interesting than others, I suppose. They stayed longer for some sessions. 

I thoroughly recommend you spend time and take this course. It’s free and it only takes a couple of hours here and there. Quit housework and Facebook for an hour today and one tomorrow. You will be glad you did. It will give you so much confidence to teach math in creative ways.

If you think that:

  • some kids are “mathy” and others aren’t
  • speed shows good skills in math
  • mistakes in math are bad and should be avoided at all cost
  • children should be encouraged by being told they are smart
  • math is a solitary activity
  • there is no creativity in solving math problems
  • math is a set of fixed facts

no offense, my friend, but you are wrong!

This course from Stanford de-bunks the above myths by quoting research after research study. Here are some true statements about math.

Everybody can learn math if they are taught math the right way.  When it comes to math skills, speed has no meaning. Depth has meaning. Do you understand math deeply? Then you have math skills. The fact that you can solve something fast does not necessarily mean you have a thorough understanding of mathematical concepts.

When somebody makes mistakes while solving a math problem, their brain is growing. Synapses are firing and connections are made. Learning takes place. Therefore, we should welcome mistakes because that is when our brains are growing.

Children should be encouraged by being told they work hard. Next time somebody tells your child, “What a smart boy you are!” immediately erase that with “He works hard every day.” I have had to do that a lot, since my son amazes many people with his advanced skills. But most of these people are old school: they know they should lavish praise, but they don’t know what kind of praise.

When you tell somebody they are smart, they actually want to be perceived as smart for the rest of their life. Therefore, they choose easier and easier routes, because they do not want to fail and they do not want to lose the label of smartness.

On the contrary, if you tell a child he is a hard worker, he will choose challenging paths because he knows he is a hard worker and trusts in his own efforts. He continues to grow because he welcomes challenges.

Math is not a solitary activity. In fact, upper level math should be studied in groups – apparently, the conversation keeps everybody motivated and concepts get absorbed better in a group setting. Something to keep in mind as my children get older. That does not mean I want to put them in a school setting for 35+ hours per week though. It just means that maybe once a week they should get together in a Math Club with a bunch of homeschoolers and solve really cool equations together.

Math problems can be solved in many different ways. If I asked you to solve 12×5, you would probably come up with a way that is different from other people’s. You could go 12 x 5 = 2 x 6 x 5 = 2 x 30 = 60 or 12 x 5 = 10 x 5 + 2 x 5 =  50 + 10 = 60 or any other way, right? Math methods abound. Number flexibility should be your greatest ally, something you cannot achieve if you just simply memorize facts.

Math is not a set of fixed facts. Math is a bundle of relationships.

This is just a foretaste of what you might expect through this MOOC from Stanford. Hope I have inspired you to try it out and keep yourself in tip-top shape for teaching your little ones the wonderful science of mathematics.

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