Thank you for taking the time to explore this page of ColbyMath.com. I have created it as a resource to foster understanding of our approach to math instruction at Trinity. When I first joined the Trinity faculty, many of the methods used by Trinity teachers were unfamiliar to me. I was surprised to find that traditional algorithms for multiplication and division were not taught until the later grades. I was even more surprised (shocked in fact) to learn that we don't teach order of operations (PEMDAS).
I quickly learned, with the help of my fellow teachers, that PEMDAS is unnecessary for students who have developed a deep understanding of terms, like terms and an ability to read mathematical expressions. Likewise, the traditional algorithm for multiplication and long division are not necessary for students who have developed a deep understanding of mathematical properties.
The understandings I have described above form a strong foundation of support for students as they enter Algebra and every other advanced mathematics course they will take at Trinity, high school, and college. Students who have been speaking the language of like terms, association, and distribution from the earliest grades have no trouble extending these understandings to the variable expressions they will encounter in Algebra and beyond. I have included many references below for you to read and view. I have also included, at the bottom of the page, documents detailing the syllabus and curriculum for this year's 5th grade math class. Please let me know if you have any questions or feedback.
Please click on the PDF on the right to view a presentation created by learning specialists and math instructors at Trinity. (I was not involved with the production of this presentation.) It offers an excellent explanation of our approach which promotes thinking and understanding over step by step procedures.
Common Core Math frustration
The PDF on the left is a letter from a blog. It was written to parents who have experienced frustration with the common core math standards. This is another excellent comparison of instructional methods that favor a procedural approach versus an approach that promotes understanding, creativity, and a love of mathematics.
I created the three videos below in the summer of 2013 before I had ever taught a class at Trinity. I was excited about these new ways of teaching math that I had been learning from my colleagues. I was looking for a way to share with parents my enthusiasm for these approaches to teaching math. I wish this was the way I had been taught and I am overjoyed to have the privilege to teach your children in this way.
Please click on the picture below to view the 5th grade math syllabus.
Please click on the picture below to view the understandings students will construct in 5th grade math listed by common core standards. You will see standards from 4th grade all the way through 8th grade listed.
30 minute rule for homework
Please click the video to the right to hear Mr. Colby explain the 30 minute homework rule. Thank you!