How many of the products in a 12 by 12 times table are odd numbers? This is a question we rarely ask in paper-based math classrooms, yet it is an important and a very interesting question. We ask students to explore it, learning to Show and Hide rows and columns in their spreadsheet at the …
“Today, it seems as if nearly everyone agrees that high school mathematics needs to change. For far too long high school mathematics has not worked for far too many students: too many students leave high school unprepared for college or a career, particularly a STEM career; too many students do not see how math is …
Counting-By introduces multiplication. Counting-by or skip-counting is, we believe, the best way to help students build their multiplication facts, and though they will live in an age of ubiquitous spreadsheets and calculators, they still need to have mastered their multiplication facts to do any interesting math in their heads. Here they learn to build rules …
Typical algebra courses start with equations and solving equations and then move to graphing and functions. We start with functions and use them to solve equations. We treat an equation as the equality of two functions, graph each one and then look at their intersection. This is a powerful way to think about solving equations …
We take that great old problem of the inventor of chess and the ruler of India and use it to see how powers of 2 grow in size. We start out with a chessboard and look at doubling each successive number. Then we seek a method of representing this doubling in a formula and introduce …
I just looked at a wonderful short video by Sir Ken Robinson on creativity at https://youtu.be/63NTB7oObtw in which he describes creativity as a process that produces something original that has value. At What if Math we seek to make learning a creative experience, a process that enables every student to produce something original that has …
Spreadsheet Resources for the Learning and Doing of Mathematics The spreadsheet is a tool that presents opportunities for learners of all ages and abilities to engage in learning and doing mathematics in a novel way. A selection of spreadsheet labs that challenge learners to think and problem solve creatively will be presented, with a focus …
This is the graduation exercise for the basic use of spreadsheets. We combine rules and addressing to have students build their own hundreds table in the fewest steps. There are many ways of doing this and students can be as creative and exploratory as they want. Nor should they feel limited to tables that start …
It was forty years ago this September that I started my career as a high school mathematics teacher, a career that spanned 36+ continuous years. I continued some teaching and other classroom work over the last few years, but this will be the first September I do not find myself preparing to greet some new …
In a magazine published for college trustees, a recent short article captured the latest statistics from the ACT and SAT tests. The downward trend was notable especially in math. For example, “Forty-nine percent of the class of 2018 that took the SAT (2 million students) showed a strong chance of getting at least a C …
