The problems students see in class are usually only those that can be solved by the methods they have been taught. Too many students conclude that algebra can solve anything! But the reality is that if you just wrote an equation at random, it probably could not be solved algebraically. When students ask us about …
Numerical Approximation Methods: When Algebra Doesn’t Work Read More »
(A new question of the week) A recent question about an old puzzle leads to multiple references to our archive.
(An archive question of the week) Last time I looked at reasons for learning to estimate. In searching for answers on that topic, I ran across a question that touches not just on reasons for estimation, but on other ways to check an answer, and on some of the specific ideas we will be looking …
Many questions we have received have been about various aspects of estimation. Often this topic has been downplayed, because we tend to think of math as being all about precision; but it is essential in many applications, sometimes because there is nothing else to do, and other times because exactness wastes effort. I am starting …
Many students who write to us are involved in math competitions. They don’t always say that explicitly, but we can tell when the problems they ask about may be far beyond ordinary homework, requiring deeper problem-solving skills. The three questions I’ll look at today are from students asking how to prepare for these competitions, or …
Last time, we looked at some discussions we’ve had about motivation to study math. We’ve also had a few questions asking for help with study skills, and some of those answers, too, can be found in our archive. Let’s take a look.
As fall approaches, and the beginning of a new school year for many, let’s take a look at some of our past discussions of how to study math. We’ll start with some perspectives on being motivated to study, since you are not likely to do well if you hate math (as so many students tell …
I want to close out this series on multiplication with a very different kind of question. We have seen that multiplication of natural numbers can be modeled as a repeated sum of the multiplicand, taken the number of times indicated by the multiplier; and that the terms “multiplier” and “multiplicand” reflect only this model, not …
Last time we looked at the roles of multiplier and multiplicand from several perspectives. This time, I want to focus on one extended discussion about how children should be taught to think of multiplication.
We have received many questions over the years about the meaning of multiplication. When we multiply , what are we really doing? This can confuse not only students and their parents, but also teachers. The next couple posts will deal with various aspects of this question.