Friday, October 25, 2013

Common Core Math Standards Ignore the Role of Pattern

I still cannot decide if I think the new Common Core Math Standards (CCMSs) are the best thing since sliced bread, just abother phase in the development of American Education or an imminent disaster. I've just spent three days at the ATMNE (Association of Teachers of Mathematics of New England) conference listening to a variety of speakers and presenters sharing their ideas and strategies for implementing the standards in classrooms througout New England. What concerns me most is that all the people I respect in the field of maths education all seem to have different views about the CCMSs. Most are passionately against or passionately for them; there seem to be few indifferent opinions. 

The focus on the math practice standards is probably a good change although the recognition of the importance of finding patterns in mathematics seems to be completely missing. Yes, finding structure is included as a practice standard but this is not the same.

For example in one of the presentations on misconceptions in fractions the presenter used an example of comparing the fractions 5/6 and 6/7 I think it was. Children, apparently, gave all soprts of answers and predominantly said they were the same because there was only 1 difference between the numerator and denominator in each fraction. Most teachers suggested converting to decimals or finding the common denominators.

But, if we taught children all about the inherent patterns in math they would be able to compare them easily. 

Look at this pattern; 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10. Numerators and denominators increase by 1 and each fraction is getting progressively closer to 1. In other words the bit left out of 1 not included in the fraction is getting smaller; 1/10 is smaller than 1/2, We can use models to show this.

Look at this pattern; 1/2, 2/4, 3/6, 4/8, 5/10, 6/12. All are other names for a half. In each one the numerator is half the denominator; the numeraotr increase by 1 and the denominators increase by 2.

Now look at this pattern; 1/3, 2/6, 3/9, 4/12, 5/15, 6/18. All are other names for 1/3 and in each the numerator is a third of the denominator with numerators increasing y 1 and denominators increasing by 3.

Just for fun, look at the half pattern again and find a fraction between 1/2 and 2/4. How about one and a half thirds? 11/2 is between 1 and 2, and 3 is between 2 and 4. It's actually 3/6.  Now try the fraction between 2/4 and 3/6.   

Monday, October 7, 2013

Maths Should Be Fun?

For some reason we seem to be going through a phase in our culture where math has to be fun. Judging by the incredible number of websites that have sprung up with mindless activities that you can play on-line and be subjected to a barrage of ads, or buy at great cost the business world has discovered there's money to be had with people's current dissatisfaction with public education. One such company IXL seems to appear everywhere and has probably the most useless activities of any to be found on-line.

Of course math should not be the incredible tedium it once was and still is in some places but neither should it be fun. It should be CAPTIVATING, INTERESTING, MEANINGFUL, RELEVANT and above all else, IT SHOULD MAKE SENSE. If everything in life was fun we would not know what fun was. Fun is something we have to relax and enjoy ourselves when we are not working. Learning math is work, it is something that, hopefully, is all of the things in CAPS above but it cannot be fun; not all the time. There are some things like muliplication facts that just have to be learned.

There are times of course when what we learn in math can lead to fun, When we are playing games that involve math knowledge and understanding such as cards, board games and many of the tech-based games that children play. Have you ever thought about how much math there is involved in playing Wii or the DS games? (Wii Play Together). There are also some great Apps for the Ipad2 that help children learn math facts and concepts in a motivating way.

OK, so there are some fun games for helping children remember their math facts but these should only be used after children have developed strategies for remembering their facts. Here's my current favorite on-line math activity. It's called Arcademics. Have fun, er, I mean, be captivated and try to
remember your facts.