In the recent past, I've come across a pedagogical strategy for teaching/learning algebra that is sometimes called "Indicated Arithmetic" or "Delayed Evaluation". However, I've been unable to find any literature on it, and only know it by name from a former colleague. I've searched resources and have come up empty. Is this a term anyone is familiar with, and if so, do you have any source materials?
In the interest of clarity, here is an example where Indicated Arithmetic (or Delayed Evaluation) is used.
- Rommel brought $15 to a school fundraiser and spent it all on hot dogs and game tickets. Game tickets were 25 cents each, and hot dogs were 3 dollars each.
A number of standard algebraic questions can be asked following this set up, but they all generally get to the desire for an algebraic equation which describes the situation. A valuable tool for students who struggle with finding this equation is Indicated Arithmetic. The key attribute in IA is writing out all operations to be performed, but not performing any binary operations. Combined with the ideas of trying some explicit values, keeping track of your work with a table of values, and organizing your work, you might be able to create a visual like this.
The right column of the table builds towards the algebraic expression, and it is easy to see in this organized way, what different roles the different numbers play in the scenario and the expression. It is much easier for struggling students to see pattern that the $h$ variable follows, rather than trying to find a pattern in the sequence of values 0, 3, 6, 9, 12, 15.
In my searching I found a footnote:
The term “indicated arithmetic” was shared by Nicholas Branca in 2004. It is used to be explicit about making used work visual so that emerging patterns can be captured.
Branca was teaching at San Diego State University until his passing in 2008. Still, this doesn't quite satisfy my needs. If anyone has more information, I'd be forever indebted.