Category Archives: Teaching Philosophy

Why Learn to do Math by Hand?

            Division Jluy 2019       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.


Easy Medium Hard Regents Questions

From the Jan 2016 Common Core Algebra I Regents:

The level of challenge on the Regents like any exam varies quite a bit.
After posting about #1-19 of the Jan 2016 Common Core Algebra I Regents, challenge level is being added to each problem.
Please comment if you feel a problem is misclassified as I am only right about 80% of the time.  Most importantly, students need to know what they find easy medium hard (often abbreviated as EMH)

that was easyc

click on the word easy for blog posts for Jan 2016 1 3 4 5 8 9 12 15 16
click on the word medium for blog posts for Jan 2016 2 7 13 14 17 18 19
click on the word hard for blog posts for Jan 2016 6 10 11 20

Increasing the Math Willingness of Students

Embedded image permalink

Boosting Math Confidence is most of what I do in the classroom and one-on-one.  I named my website Math Confidence as it is the opposite of Math Anxiety.   Grouping students may increase classroom discussion although sometimes the sharper students will just tell the reluctant students.

Here are some things I do to encourage participation:
Note: this may not lead to everyone being part of the whole class discussion but at
least it makes the more reluctant students do Math 😉 and it gives the teacher a lot of material from which to lead the discussion.

Independent Work

5 or so mins of independent work (the room is slient) so I can walk around and work with s’s one on one.  This could include comparison type questions, matching, or other low-intensity tasks.

Surveying without Student Names

low tech: index cards or Post Its
high tech: Nearpod, Poll Everywhere or Kahoot (disclaimer: I have not used Kahoot yet but plan to next year)

blind voting:  everyone puts their head on their desk and votes (I can see but fellow
students cannot!)

Increase Self-Awareness

A lot of Math mistakes are “fuzzy errors” rather than conceptual errors.  A lot of the questions I ask are self-reflective, metacognitive questions such as “Is it bigger or less than 1/2? Why?”, “Easy, Medium or Hard?” and “Is that your final answer?”.  And for reluctant students, building confidence often comes from being ok with making mistakes and correcting them.

Allowing/Requiring Open Book/ Open Note Exams
Math is not about memorization and I have the great fortune of being able to allow students to use their notes/textbooks during quizzes and tests.  This boosts confidence for many students that they do not have to memorize but instead figure it out!!
I also share that iif they write nothing then their score will be nothing and talk to students about reading over the entire exam before they get started and figuring out their “Easy, Medium or Hard?”.