Categories
Science Online resources Virtual Manipulative

What Causes Tides?

I’ll admit it – besides “knowing” that tides were caused by the moon’s gravitational pull, I had no idea why tides existed. A science teacher training class forced me to confront this ignorance starting with the simple question – if the moon’s gravitational pull causes tides, why do we have two high tides and two low tides in a day? (the moon’s orbit around the earth takes roughly a month, so tides should basically be dictated by the earth’s rotation – i.e. take 24 hours to go from one high tide to the next).

Digging deeper into the matter, I became pretty frustrated – online resources typically introduced another force (centrifugal force) to explain why the ocean “bulges” towards the moon (and sun, which is another layer in this topic), but it was hard to develop an intuition of how this all works together from the material that I found. Fortunately, people like Ingo Berg exist. His website has an application that finally helped me visualize the forces that shape tides – it might also help your students who need to construct visuals to understand concepts.

Categories
Mathematics Methods Algebraic Thinking

The “Growing Dots” Problem

Many of us probably memorized the slope intercept formula (y=mx+b) in middle school without fully understanding how the formula represents linear growth. I was not able to visualize how the formula translated into lines until 11th or 12th grade.

It turns out that, in Japan, some teachers give students an open ended (but supported) problem called the “growing dot” problem to try and build conceptual knowledge that relates to the slope intercept formula. Check out the slideshow below (adapted from a presentation for a Math and Technology class at Boston College) to see how one teacher applied this method to his middle-school students.

Source: Goldsmith, L. T., and Seago, N. M. (2013). Examining mathematics practice through classroom artifacts. 88-96, Boston. MA: Pearson