The MOST Important Decision You Can Make in Math Education

 

Math. It is often met with either cheers of excitement or groans of utter pain. As homeschool mammas we could spend HOURS researching the countless math programs, reading the pros and cons and the testimonials of parents just like us. We could spend hundreds of dollars trying out different programs from year to year. But I have a secret to share with you. The most important decision to make when it comes to math isn't which program to use, it's HOW to teach the program you have. There is one method of teaching math that has proved tremendously successful in certain parts of the world. And in other parts of the world (like North America) where this method isn't being used, math scores are in a sad state.

 

So here is the method to success: Teach math using the concrete, pictorial, abstract method. There are math programs that specifically follow this method, such as Singapore Math or Math in Focus. But no matter what math program you are using, you can apply this teaching method to create an environment of success and understanding in math.  

 

So how does this method work? It's quite simple actually! When introducing a new concept you start with concrete materials - materials your child can touch and manipulate - AKA manipulatives. For a child learning to add or subtract you could use animal counters, jelly beans, or an abacus. For a child learning to divide you could use cookies divided onto plates (and of course eat some after!). For a child learning fractions you could use a pie, Lego, or pool noodles cut into fractions.

 

You might be thinking, "But I'm not creative enough to come up with these ideas for EVERY math concept!" Don't fret because a quick search on Pinterest is bound to give you countless ideas of concrete materials you can use to teach any math concept. A word of advice, if you aren't having success searching with the words 'concrete materials', just swap it out for the word 'manipulatives' and you are sure to find what you are looking for! Of course, if you are using a math program that follows the concrete, pictorial, abstract method it will tell you exactly what concrete materials you can use. 

 

After your child has had plenty of exposure to these concrete materials it is time to move onto the next step - pictorial. This is where you will be taking those physical objects and substituting them for pictures. There are still NO written numbers involved or abstract symbols such as an addition sign or equals sign.

 

Let me give you an example. If you are teaching your child to add, starting with the concrete stage, you could start out with colourful dot counters. You would give your child three and give yourself three then say, "I have three counters and you have three counters. If we put them together, how many would we have?" When you move onto the pictorial stage, you would draw the counters. You would draw three counters and put a rectangle around them, draw another three with a rectangle around them, and then say, "Here is a group of three counters and here is another group of three counters. How many counters are there altogether?" After your child counts and says there are six counters altogether, you would draw a third rectangle, in line with the first two rectangles, with six counters in it. After spending time on the pictorial stage you can then move onto the abstract stage. 

 

The abstract stage is where you will introduce the numbers and symbols that go along with the pictures you have been talking about. Those two rectangles with three counters drawn in them, can now have the number 3 written above each of them. You can add a plus sign in between the two rectangles with three counters in each. You can add an equals sign between the second rectangle with three counters and the third rectangle with six counters. Now you are starting to create a number sentence using abstract symbols. Continue using both the pictures and the abstract symbols (numbers, addition sign, equal sign) together until your child seems very comfortable with it. Then, and only then, transition to just abstract symbols. On the paper you are now going to write 3+3=6. Your child is going to clearly understand what this number sentence means and represents because she has touched and seen the abstract concept prior to the abstract step of learning. 

 

It may seem rather obvious with addition to go through the steps of concrete, pictorial, and abstract. But I can't stress enough that following this teaching method with ALL math concepts will greatly increase your child's comprehension and success in math. 

 

When I look at the research it is abundantly clear that Singapore is consistently at the top or very near to the top in math scores worldwide. Here in North America, our students are scoring MUCH lower. The logical next step then, is to look at how math is approached in Singapore compared to how it is approach in North America. It only takes a two minute search online to discover that Singapore follows this concrete, pictorial, abstract approach. They are having tremendous success teaching math this way!

 

When I discovered Singapore math five years ago, before I started homeschooling, I was immediately convicted that I wanted my children to learn math this way. It just made sense! When I started homeschooling two years later, I jumped right in using the concrete, pictorial, abstract method. I have never had a moment of regret and I would never change what we are doing! It might be different than how you learned math as a child and it might take a little more prep, but the payoff in laying a solid foundation of understanding and seeing your child succeed is well worth the investment of time and effort. 

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