Author: congruentthoughts

Mathematics Vocabulary Activities

It’s nearly impossible to separate mathematics and language.  We can’t teach math and students can’t ‘do’ math without naming mathematical objects and concepts and without language to express mathematical ideas.  In the October, 2020 issue of Mathematics Teacher: Learning and Teaching PK–12, the authors of the article, Developing and Writing Language Objectives, state “the role … Continue reading Mathematics Vocabulary Activities

Not a Math Person

Not a Math Person? Do you hear this, in one form or another, from your students?  Or, do you think that about yourself?  If so, I suggest you read the following - Living Proof: Stories of Resilience Along the Mathematical Journey which is a free download from the Mathematical Association of America.  The book … Continue reading Not a Math Person


First of all, most of the courses I teach are fully online, and most of my students are graduate students who ‘attend’ our university while juggling their full-time jobs as teachers and about half are parents too.  Expecting them to place my courses as their highest priority every day is unrealistic Most of these K-12 … Continue reading THOUGHTS ON THE NEW SCHOOL YEAR – 2020

Sense-making and reasoning in the time of Corona Part II

In a recent blog post I urged teachers to focus on developing students’ sense-making and reasoning skills rather than adding new content.  I shared some personal favorites tools for doing this and today I would like to share a few more. is a teacher run blog that asks students to solve visual puzzles such … Continue reading Sense-making and reasoning in the time of Corona Part II


When I taught my first class in the 1960’s, my methods instructor and assigned classroom teacher gave me few directions, so I taught as I remember being taught when I was in high school. I lectured, I thought telling/showing was teaching, and I assigned lots of homework problems. Times have changed, thank goodness.  Brain and … Continue reading Mindset