We are reflective teachers who embrace the CCSS Standards for Mathematical Practice. We are committed teachers who want to take the magic out of mathematics and focus on the beauty of sense-making. We wish for teachers everywhere to seek coherence and connection rather than offer students memorized procedures and short-cutting tricks. Students are capable of rich conceptual understanding; don't rob them of the opportunity to experience the discovery of new concepts.
We acknowledge that this is hard, that students will have to think and they will say they don't want to. We recognize that students (and parents and tutors) will need to readjust their expectations; but we believe it is in the best interest of students everywhere to make the focus of mathematics critical thinking.
“But it’s just to help them remember - I taught them the concept!”
SOH CAH TOA is a mnemonic device. There is no underlying reason why sine is the ratio of opposite to hypotenuse, it is a definition. Kids can use this abbreviation without losing any understanding.
FOIL is a trick. There is a good reason why we multiply binomials in a certain way, and this acronym circumvents understanding the power of the distributive property. If you teach the distributive property, have students develop their own shortcut and then give it a name, that’s awesome. However, we’d rather you use the phrase “each by each” since it doesn’t imply that a certain order is necessary (my honors PreCalc students were shocked to hear OLIF would work just as well as FOIL) and reminds students what they are doing. Many students will wait for the shortcut and promptly forget the reason behind it if the trick comes too soon.
Read through these pages with an open mind. Consider how you can empower students to discover a concept and find their own shortcuts (complete with explanations!). Ask questions, make suggestions, share and discuss with your colleagues