Thank You, Dan, for pushing me to make this a real thing. A book sounded scary and impossible but a tweet from you and a lot of help from the community turned a messy google doc into a typeset document. This crowd is amazing and I can’t wait to see what we come up with next!

Nix the Tricks is dead on. Tricks are how I “learned” in school and why TEACHING 4th and 5th grade math conceptually finally taught how math works.

As soon as memorization replaces conceptual development, all math is built upon a baseless foundation and therefore, crumbles.

Expediency and calculator usage increase a teacher’s reliance on tricks and shortchange students.

At this point, deviation from tricks will never happen. Teachers have too much pressure to perform and knowing their job is on the line with test scores will increase, not decrease tricks in math.

Thanks so much for putting this together! I have to admit my guilt in using some of these tricks, but it is good to be aware of them and I will try to avoid using them!

Once when tutoring a student from another school, I noticed she was using the distance formula and attempting to just memorize it. I pointed out to her that it was simply Pythagoras and she stared at me with utter amazement. We graphed the line segment, drew the sides of the right triangle and calculated the length using Pythagoras. Her teacher had never even mentioned the connection.

Here in the Caribbean we are driven to teach to the exam. Everything hinges on passing exams, one at the end of Grade 6 and the most important one at the end of Form 5 (grade 11) Teachers rely on tricks because they feel the pressure to cover all of the exam topics. There is just not enough time. Algorithms are taught and students are just expected to memorize them without any real thinking or understanding.

The system as it stands is not working. Only about 30% of the students pass the CSEC exam given at the end of Form 5. The college professors complain that even those students who passed have no real understanding or the ability to reason logically.

There are those who are trying to address the problems and it has been realized that change must start at the primary level.

I will share your document with other teachers, and I am sure it will generate a great deal of discussion!

Thanks again for putting it together.

Love it! Lots of good theory in there and I like the look at how Cardone explains these concepts to her students.

If I may have a soapbox moment, in discussing order of operations and why it’s exponents then multiplication, then division, Cardone writes “The most powerful operations should be completed first – exponents increase at a greater rate than multiply, which increases at a greater rate than addition.” This is actually just a mnemonic device as well, as it isn’t the reason that the operations are in the order they are in. The real reason is that exponents are repeated multiplication, so
7 x 2^3 = 7 x 2 x 2 x 2 = 56 which is what we get if we do the exponent first. If we did the multiplication first, we’d instead get 7 x 2^3 = 2744, which is inconsistent with exponentiation’s definition as a repeated multiplication.

Similarly, addition is repeated multiplication, so:
4 + 5 x 3 = 4 + 5 + 5 + 5 =/= 9 + 9 + 9 = (4+5) x 3

The very definitions of exponentiation and multiplication as repetitions of multiplication and addition requires them to have higher priority.

Apologies – number 8 is a disagreement with number 7.