If I told you math had a third language - would you a) weep, b) brace yourself or c) jump for joy?

Yup, it's the language of Pictures!

Help your child with math w/o knowing the math.

Hey Math Parents,

If I told you math had a third language, would you a) weep, b) brace yourself or c) jump for joy? Choose c) jump for joy!!! Choose c) as it’s where the math makes sense!

The third and last language of math?

Pictures! Yup, think of a visual, image, diagram, maps, plots, drawings - the saying a picture is worth a thousand words becomes apt when is comes to math.

And more than the Word or Symbol, it is the ‘Picture’ that is the saving grace for students. It brings the math alive, it makes it real, relatable. How?

1) Many students are visual learners!
2) Pictures are relatable, closer to real life.
3) A Picture makes more sense, and
4) ‘Makes sense’ is a key part in remembering math.
5) Visuals make math easier.
6) And when you recognize that the Picture takes the math Words and Symbols and their meanings and wraps it up into a nice, neat package (i.e. shortens it into one visual), and again that proverbial ‘picture is worth a thousand words’ comes home to math. The Picture literally replaces a ton of math.

That’s six benefits of doing math visually, oh, and here’s another two:

7) Every math question can be done with a Picture - mind-blowing when you think about that.
8) It gives your child a second way to do a question – e.g., forgot the rule to add fractions, then do the question with a Picture! Yay! Yahoo!! Bring on the math!!!

Here’s the thing … doing math with pictures is the easiest way to understand math!

That’s good news about learning with Pictures, but I’ll balance that with a not-so-good math announcement. As students get older and move into higher grades, math is taught less and less with pictures and more with symbols. Yes, visuals still exist, but the ‘dominant’ two languages become Words and Symbols.

Pictures get tossed and relegated! So, the one way that would make sense to a struggling student gets shown the exit door. And that’s like asking a right-hander to write with their left hand. They can try it but,
1) Won’t want to,
2) Will question, “Why do I need to do this?” and
3) It will slowly eat away at any enthusiasm they once had for math.
And, yeah, I know my example of right to left hand is crazy foolish, but that’s my point! Why take away a strength?

To put all of this in context, ask your child, “What’s a rectangle?” They will draw a picture of it pronto, speedily, before you can say 1-2-3 go! It’s quick, and that picture sums up the meaning of all words associated with what a rectangle means*. It’s brilliant!

1. *A rectangle is a four sided figure ✅

2. Opposite sides are parallel ✅

3. Opposite sides are equal in length ✅

4. All angles are at 90 degrees✅

But ask them what a rectangle is or means - as in, “How would you explain this to me without drawing a picture?” that’s not easy for them – it should be, but it isn’t. And the reason it’s not easy-peasy is two-fold:

#1 They may not have realized the importance of having the skill to translate/change that picture back to words, and
#2 They don’t know the meanings of math words - yes, it always goes back to that most critical part of math.

Here’s the definition of a rectangle using language a grade 6 student (age 11) could understand from the picture they drew:

1. It’s a two-dimensional shape with four lines*

2. Opposite sides are parallel, opposite sides have equal length, has four angles, and all angles are ninety degrees.

That’s 13 math words in the sentence I just wrote, 13! Thirteen words to describe what a drawn rectangle solved in seconds! And that gives you a sense of the plus in knowing the picture - it’s quicker.  
**Note: The correct math word is ‘line segments’, as lines go on forever.

But here’s the catch-22:

Teaching with Symbols is quicker to teach and quicker for the student to do, but for the pupil, it’s much quicker to forget 😔. And the flip is correct, as teaching with pictures takes longer to teach, but the student will remember it longer 😀.

The catch 22: Teaching with Symbols is quicker to teach and quicker for the learner to do, but for the pupil, it’s quicker to forget.

Consider the math word question: 

A ninety-degree triangle has side lengths of three centimetres and four centimetres (or with Imperial units, lengths of three inches and four inches). Find the length of the third side. 

If I give that to grade 6 or 7 students (age 11 or 12) they’ll have more success on it than some students in grade 8 or 9 (age 13 or 14). That doesn’t make sense, as in no other endeavour should younger students be doing questions better than older students.

The question, of course, is why?

The gr 8/9 student would sketch a rectangle (or think it) and try to do it with Symbols (using a memorized rule they were taught – the Pythagorean Theorem). But some will not think about the rule or mix up the rule or forget it. The grade 6 or 7s, well they’d rock it - by drawing the Picture with a ruler and measure the approximate length of the third side with a ruler, and voila …. PROBLEM SOLVED! The problem for the older students is that learning it visually gets dropped, and they’ve forgotten doing it with symbols. Actually, I think the belief is more “You were taught it, so you should remember it.” 

How to use Pictures to help your child?  

1. Tell them every math question can be done with pictures. They’ll love to hear that.

2. Have them understand that math is taught three different ways, with Words, Symbols and Pictures. All can mean the same thing, and like pieces of a jigsaw puzzle, they depend on each other.

3. Play a game with your child and ask them what a rectangle*** means. The odds are high they’ll draw a picture of a rectangle. Now ask them to tell you what a rectangle is without them drawing anything, and you’re going to follow their instructions. What you’re hoping for is that you, the parent recreate a rectangle based on their verbal instructions.
   You can have ‘fun’ with this as I do with my students: if your child says, “Well, it has four-lines”, you draw four random lines, and they’ll say, “no-no, not like that …”, and then they’ll start to think! The big advantage in this is they’ve had success to start - they know the picture! And success breeds success and self-belief, so when asked to explain that visual in words, well, their thinking cap gets put on. And thinking is a good learning habit to create in math, as it’s the seed of problem-solving.

   ***You can choose any math word (e.g., Triangle, Pentagon, Area, Add, Fraction, Ratio, Rate). And if your child is older and in high school where the words are not as familiar to you (e.g. Relation, Domain, Factor, Quadratic), then choose words from their past as many will keep coming up in their courses (e.g. Triangle, Pentagon, Area, Add, Fraction, Ratio, Rate). 

   then ask them to ‘teach’ you what the math word means, and you will follow their teachings to make a picture.

   A fun game of math awaits. Try it you’ll like it

And should the day come when your child gets stymied on a question or asks you, “Parent, why does the memorized math rule tell me that I need the same denominator when adding fractions?”. Just respond, “Picture it!” That’s your gift to them that will keep on giving. Two words that will empower them, Picture it!

Pictures are a part of learning!

Best with your pictures,
Edison

Edison Hopkinson BSc Mech Eng, B.Ed., OCT
Math Learning Strategist
Strategies to use when the usual isn’t working!