I just got back from attending a Response to Intervention conference and came back with some really awesome things. The one thing that stood out and agrees with a recent comment from the NCTM is simply we need to have students learn to communicate how did the problem. Not just using the mechanical means but using writing or verbal explanations. They highly recommended complex tasks or performance tasks that give a scenario like you have dogs and chicken for a total of 40 heads. Each dog has 4 legs and each chicken has 2 legs, how many dogs are there? This type of question is open in terms of how they will solve it but it can help us as teachers figure out misconceptions. This website talks about misconceptions that students have and these are the same ones I've seen my own students have. I may try this exercise in class later this week to see what my students have to do.
As for apps, I discovered on that uses algebraic tiles at a high school level. So far, I am finding that it is frustrating for me when I try it and I know the answer is correct but the app tells me I have the incorrect tiles. Its a math app called Algebraic tiles from the center for algebraic thinking. It uses tiles but until I can figure out how to use it fully I cannot have my students use it or they will get frustrated. The other thing is when I tried the factoring choice, the x^2 square was the same size as the x and the constants so the students are unable to see how the x^2 is different from x and it is something they need. I will get back to you all on this app.