153 views

Viewing arithmetical operations as processes-possibly wrong and detrimental to long term math performance of the students [duplicate]

I think that the standard practice in the first grades when addition (or other operation) is taught as a "process" may be not so good. I always wondered why so many children lose interest in math ...
2k views

How to cure students from the idea that root and squaring are identity operators?

I tutor high school algebra and I’ve noticed that a lot of my students don’t seem to understand what they’re doing when they “convert” between different ways of writing numbers involving perfect ...
3k views

When should we first teach variables in school math? And how?

From a pedagogical point of view, when is the "right" moment to introduce letters and variables to school children? Let's say we taught arithmetic, the four operations, did computation exercises, or ...
675 views

What deficiencies are present in Precalculus curricula that causes so many students to fail Calculus I?

At our university we now require one semester of Pre-calculus instead of one semester of Algebra and one semester of Trigonometry before you take Calculus I (for those who do not test into Cal I). ...
553 views

How students write their work, and learning outcomes

While teaching students mathematics, I have noticed that some seem sloppy in the way that they write down their work. For example, a student is given a question: What is the area of the rectangle? <...
512 views

Teaching Completing the Square

I'm trying to teach some secondary school students on how to complete the square. The goal is to rewrite: $$y = ax^2 + bx + c \ \ \Rightarrow \ \ y = a(x-h)^2 + k$$ The first thing I did was to ask ...
509 views

Multiple students writing $y\frac{d}{dx}$ rather than $\frac{d}{dx}y$ — why?

I'm currently teaching a couple of courses that have a calculus prerequisite, and within the last week I've had two students make notational mistakes that amount to writing $y\frac{d}{dx}$ rather than ...
391 views

A more rigorous approach to Precalculus

I am a pure mathematics PhD student and graduate teaching assistant at a major state university. During the summers here, teaching assistants are typically appointed to teach an entire course, rather ...