Friday, August 12, 2016

A.R.C.H. - Coaching for Academics - Math

There is so much to say about coaching academics. I just touched the surface with handwriting and reading and now we dive into math.

First, take a deep breath.  Did you know that children who delay formal math until 7th grade learn it easily. quickly and with less stress (lots more about it here)?  Of course you do regular math around the house (counting, page numbers, reading the clock, cooking).  As we will see this is because math is logical and abstract - something that is not a strength of your average 6 and 7 year old.

Of course, waiting that long is not an option.  When you think about great math programs many people praise Montessori math.  I spent a year as a teaching assistant in a 3 to 6 year old Montessori classroom and math is the very last area children are allowed to use. Most children don't start math with numerals until 5 or 6 (this is a school that starts reading at 4). Why? Because math is a very abstract concept. The reason why Montessori does math so well is that it uses manipulatives to make math tactile and less abstract.  When you lay out the 1,000 bead chain (exactly what it sounds like) you get a real sense of how big 1,000 truly is.

3 Modes of Math Learning 

Beechick explains that there are 3 modes for math and uses Piaget's development theory to support her claims:

manipulation mode - using physical objects to aid with math problems (until at least 6 or 7)
mental image mode - imagine objects in our head - four people in our family and one guest equals 5 people (until about 12 or 13)
abstract mode - use numbers without thinking of images (twelve years old and up) 

As always, some children will move through these stages more quickly - but this is the average.  Do you see why delaying formal math instruction might relieve stress? Is this shocking to you?   

Children can't move forward until they are developmentally ready to do so (sound familiar).  Beechick encourages us to "know which mode of thinking the child does best, and take advantage of that strong mode. This way you teach more arithmetic."   So, the reason why Montessori is so successful is that it ALWAYS starts in the manipulative mode and allows the student to decide when they are ready to move unto the next mode.  Beechick explains that many math books try to move through all 3 modes in one page or lesson.  They start with a presentation using physical objects in the class, move to pictures on the page and then at the bottom of the worksheet expect children to just use numbers (4+3).  This is TOO fast for many kids.

Use Manipulatives 

I encourage you to do what Beechick calls "taking the long view" - basically allow children to use manipulatives for as long as they need to do so (like Montessori).  When a child is ready to move to the "mental image mode" using the manipulatives will take SO MUCH longer that they will want to leave them behind.  If this is an area that your child struggles with I highly recommend The Three R's by Ruth Beechick.

Montessori math gets expensive fast and can be hard to use at home; however, you could get some beads during sales.  The cheaper option is buying cuisinaire rods.   Miquon math (here is the scope and sequence) is a whole program (cheap workbooks) built around using the rods.  My oldest son hardly touched the rods to do Miquon because he moved quickly into the mental image stage (after being in a Montessori setting); I expect my number 2 will need to use the rods more.

There are FREE videos at Education Unboxed with great ideas about how to use rods to teach simple concepts all the way up to division, fractions and square roots. So, if your child is struggling with a concept let them "see" it with the rods (or beads) and play with it so that they can get it.  Please collaborate with your child's teacher on this issue so that your child can feel successful in math.  

Math and Handwriting 

Honestly, older math books expected all math to be done with pictures and orally until children were about 8 years old.  Dominoes were often used to introduce all of the number bonds and were repeated until they became rote.  Learning to do math in your head (figures) was a large part of early math education. Another barrier for some children at this young age is actually writing the numbers. Yet another reason math was done orally.  Why let handwriting stand in the way of your math development?  Honestly, like spelling words, if your child is struggling with handwriting you might have him tell you the answer out loud - you write it down on a separate sheet of paper and then allow him to copy it onto his worksheet.  Again, this won't help with tests but having the numbers modeled correctly will allow him to focus on the math.  (Montessori was genius at separating tasks so that students only worked on one skill at a time).

Another way to make math fun is through board games (more and more) that introduce basic mathematical concepts.  I can't wait to get my hands on Prime Climb.  My kids have no idea what complicated math, strategy and problem solving skills they are learning while having fun.  Here is a 70 page PDF that includes a ton of math games that support all types of math operations using a basic deck of cards.  It's a great way for my husband to interact with them as well.  There are also many books that touch on math concepts, the Sir Cumference series is pretty fun.

Puzzles, pattern blocks, regular blocks, tangrams and similar toys help kids develop their spatial abilities.  Cooking with kids is also a great way to introduce fractions.  I have been meaning to read the book Ratio which is all about the patterns of cooking.  Bedtime Math provides different levels of math problems each day to help you think differently about math.

We all want our children to be successful.  Allowing our children to learn these academic skills at their own pace, knowing which concepts they have mastered and which ones they should attempt next can make a huge difference in their confidence.  In the end, we want them to have the WILL and the SKILL.  If we push and compare them to others they will lose confidence in themselves and lose the will to master these difficult skills.

Next week we tackle the last part of our A.R.C.H. - Habit formation.

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