# Why Learn to do Math by Hand?

There’s a connection between pencil, paper and brain.

My chairman who is 20 years my junior has lit upon an old idea: help students understand Math without the crutch of a calculator.  This summer, I will teach arithmetic along with algebraic and geometric skills to rising college freshmen to boost their analytical skills, critical thinking and mathematical breadth.  One of the goals is to help students see how much understanding the times tables contributes to the knowledge and skills for high school and college Math.

After teaching Math for Elementary Educators for over 10 years, I can appreciate how the classroom can differ without the use of technology.    This is like going back home as I am from the last millenium aka BC Before Calculators.

Some of the topics we will cover include multiplication and division in various formats, adding and multiplying fractions, finding equivalent fractions for repeating decimals as well as using the “educated guess and check” method for computing square roots.  I may also dust off my knowledge of square roots by hand and share this division-related topic.

So how would you do 1472 divided by 5?  If you answered “With a calculator.”, you may find that most efficient but doing it by hand can help build estimation and computational skills while promoting Math facts and self-reliance.  In a tech-filled world, it can be wonderful to think independently without a calculator or Siri or Alexa or Google Assistant etc.

So sharpen your pencils and try my 3 favorite division problems on paper — yes please write these down and then close your laptop and/or power down your phone til it’s just you and the Math:

70 divided by 5
365 divided by 7
1000 divided by 8.

# Get the Math and Points: CC Algebra I June 2016 Regents #16 plus Metacognition

Inspired by this tweet:

Looking at our latest Algebra I Regents, here in NY, here is a great example of the use of a graphing calculator and compare/contrast/use metacognition:

All 4 answer choices have a 3 but in different and important places!!
First question, does this xy table look like it is for a linear function?
We can look at the equations and see which f(x) = mx + b
We can also use the TI-84 and check the table to see if it matches the table above!
Let’s go to the graphing calculator:
Answer choice (1)  below: this is linear and is clearly not a match especially since the rate of change is always 3 (every time x goes up by 1 y goes up by 3)

Answer choice (2) below is also linear as it has  a constant rate of change…not a match:

Answer choice (3) is shown below and, well, we’re still lookin’: