*By Melissa Schumacher, Curriculum Writer*

Which is more important for students to have: conceptual understanding or procedural fluency? Does one have to be taught before the other can emerge?

*By Melissa Schumacher, Curriculum Writer*

Which is more important for students to have: conceptual understanding or procedural fluency? Does one have to be taught before the other can emerge?

By William McCallum

*What are extraneous solutions?*

A while ago I wrote a blog post about solving equations where I talked about seeing the steps in solving equations as logical deductions. Thus the steps

\begin{align*}3x + 2 &= 5\\3x &= 3\\x &= 1\\ \end{align*}

are best thought of as a sequence of if-then statements: If $x$ is a number such that $3x + 2 = 5$, then $3x = 3$; if $3x = 3$, then $x = 1$. Continue reading “Truth and Consequences Revisited”