I also strongly disagree with your assertion that the only option is to teach multiplication facts in lieu of other number sense items. It may be happening in some places but the two are not mutually exclusive. Building a good foundation in place value and the grouping strategies you talk about (2 groups of 3) is critical to understanding math. These are the circling groups of butterflies and pencils that we did in the early grades before states mandated that preschoolers know how to read. When students understand these concepts than the algorithm method simply becomes an application of these concepts. Your chunking method in which you turn 12 x 9 into a matrix of 3-3′s x 4-3′s is simply a waste of cycles and confuses multiplication more than it makes it clear. If that is suppose to be a tool for students to use in doing everyday math, they better plan on taking a legal pad every time they go to a grocery store or need to figure out change. A person who knows their multiplication facts would have been done with that problem and 10 others while the student who doesn’t is still struggling to draw the box. And then if that student doesn’t know 3 x 3, now what? Or which is easier and makes more number sense place-value and facts 9 x 10 =90 and 2 x 9 =18 and 90 + 18 = 108 or using a matrix that ends up with 12 nines that have to be added together. By the way, poor math students can’t add 12, 9′s either, they don’t have enough fingers. Heck, skip the matrix altogether and say 12 x 9 = 9 added 12 times now do it if you want to go the addition route. I don’t care what the standard says, we can come up with 100′s of ways to look at a problem, that doesn’t mean they are all worth knowing. I imagine most of us have a very few ways that we solve particular problems and do not waste our time trying to figure out 4 or 5 ways to look at a problem differently.

I often think in our quest to help students understand we think the old must be thrown out and some new cute and clever must be found. Looking at something 10 different ways does not guarantee understanding, it typically only causes 10 different confusions. Rote memorization (with a good foundation) is not a bad thing. There I said it! Problem solving skills are paramount, but you can’t get beyond the numbers if you don’t have a solid foundation in computational skills. Kids who know their facts are simply better mathematicians and they have greater confidence in their math skills. Give me 100 mathematicians and I will bet you a dollar to a doughnut that those who know their math facts will outclass those who don’t by a large margin. Now if you are saying some students have physiological or cognitive issues with learning their multiplication facts, well just say that is whole other can of worms.

Just my counter opinion.

Respectfully,.

]]>I love how you mention adults and their problems with mathematics. When we hear so much negativity in regards to “new methods” from parents and the media, I wonder whether they are bashing simply because they do not feel comfortable with a variety of methods/strategies/approaches.

This recent article in the Huffington Post has a parent claiming he has Bachelor of Science and cannot understand how to do the problem herself. The kicker is that the parents claim “the problem takes a simple one-step subtraction problem and turns it into a complex endeavour with a series of unnecessary steps, including counting by 10s and 100s.” My immediate wondering is which strategy is more complex for a young student to understand; a memorized algorithm or a strategy that gives an entry point for anyone who understands what it means to subtract. You mentioned that “when things go wrong we fall back on what we are comfortable with or what we know” and I think this particular article clearly demonstrates this. The parent claims it is a simple subtraction problem, but fails to mention that it would only be simple to someone who is comfortable with that strategy.

Perspective is everything. It hasn’t been long since we began the journey down the constructivist pathway and therefore it will take time for us to become comfortable with implementing some of the great ideas that we know to be true about learning.

Thanks for the comment!

]]>If we shift our focus to students (namely those struggling with math), they will likely be better served with strategies to see what is really happening. Through a “variety of” strategies and tools, I’m sure that the eventual memorization of multiplication tables will come. Students are all unique, coming to the table with different assets (and liabilities) that can make memorization of multiplication tables a strategy that will – or will not – work for them.

I just worry that the argument to memorize multiplication tables comes from those who know their multiplication tables and have been surrounded by that belief their entire lives. Out of those who argue for memorization of multiplication tables, how many would consider themselves successful in math? How many of those who were unsuccessful in math are **not** represented in this debate? Would they agree that memorizing multiplication tables helped them or would they suggest that it discouraged them from engaging in math class?

Just some thoughts to consider…

]]>Given our proximity to the US media from our location in Essex County, there are lots of opportunity for mental calculations that I don’t think are exploited enough. Converting temperatures or car mileage or… the list goes on and on.

And, it’s too bad. Mathematics can be an art, a life skill, and fun. If every mathematics challenge (let’s lose the term mathematics problem) was seen as a puzzle, the approach might be different. Perhaps it’s the environment that I grew up in, but I’ve always enjoyed a good mathematics challenge.

I recall advice given to me at university that rang true then and I think rings true today. If a child has an aptitude for baseball, what do they do? Practice, Practice, Practice. If a child has an aptitude for music, what do they do? Practice, Practice, Practice. If a child has an aptitude for mathematics, what do they do? Go home and do the odd numbered questions on page 37 and then go outside and play baseball.

Could a change in attitude make everyone a math athlete?

]]>I have the paperback of Freakonomics and read about half… after reading this post, can you guess where? On vacation! When I got back home, the book went on the dresser and I haven’t touched it since. I actually really enjoyed the book, but just haven’t found the time to get back to it. Should I add it to my Audible list? Not a bad idea!

What platform are you using for audiobooks?

]]>Planet Money – Economics made interesting (http://www.npr.org/blogs/money/)

Freakonomics Radio – Crazy economics made interesting (http://freakonomics.com/radio/)

More of Less – picking apart numbers in the media (http://www.bbc.co.uk/programmes/b006qshd)

Science Friday – mostly about science but sometimes about math (http://www.sciencefriday.com/)

RadioLab – mostly about science but sometimes about math. spectacular production values (http://www.radiolab.org/series/podcasts/)

And as for audio books. I am currently listening to The Signal and the Noise by Nate Silver. And throw in Freakonomics and Superfreakonomics. All a must for any Data Management teacher.

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