My previous posts were intended to establish the following.
- Student proficiency, as measured by National and International tests, is far below any reasonable expectation. This indicates Mathematics education should be revised.
- Recent advances in cognitive science have revealed much better methods of teaching and learning. This indicates there is a better alternative to how we teach Mathematics.
- It has long been agreed by many that early Algebra courses should introduce the student to the use of abstraction, generalization, deductive reasoning, creativity, and critical thinking while exploring the patterns and relationships of a variety of algebraic entities including, but not limited to, equations, inequalities, algebraic fractions, polynomials, and functions. This indicates Mathematics education should turn away from training in computational skills and return to teaching true mathematics content.
- Twenty-first century technology (computer and phone apps) make it less important that people will need to do common mundane computational tasks which have become the focus of most early Algebra courses. This indicates that content of early Algebra classes should address problem solving skills rather than training in computational skills.
I am firmly convinced that change in what and how we teach mathematics is long overdue. In the next series of posts I will present my view of early mathematics classes in the twenty-first century. I ask that you approach these posts with an open mind. Some ideas will be radical in comparison to today’s methods but that is expected because we have made virtually no positive change in the last 150 years.