By definition, any series of steps that is taught is an algorithm (pick a dictionary). A new method, an old method, any series of steps reaching a conclusion is an algorithm.
Please stop spreading this nonsense that one algorithm is “Good” and another is “Bad”. The method that gets you to the right answer and you understand is the best one. For some students, the old method is best and for others new methods may be better.
“Number sense” is still an algorithm. Students must mentally take steps to come to a conclusion. This is what makes math so great… a toolbox of different algorithms to solve problems.
Parent’s are struggling to understand these new methods. Schools want parents to be active, engaged and involved and schools are failing them by teaching new methods without giving them tools to understand these new methods. If you are going to teach the kids something new and you want the parents help you are going to have to teach them too. I am pretty certain that most teachers neither have the time or resources to double their class loads. This is why you are seeing a back lash from parents and the few staf that are brave enough to speak out.