It is important starting around entry to first grade, IMHO, for children to: a) have memorized the patterns of basic arithmetic equations, and to b) understand how more complex problems can break down into simpler step-by-step arithmetic. Doing this in a way that promotes right-minded learning (pattern recognition) is vital. I’ve done my best attempting this for my daughter with my app – mathflashapp – and her performance through the third grade suggest this is the right track.
I have lots to say here and struggled with whether to say it in the comments or on the main part of the blog. So forgive me if this gets too detailed.
The post in question was really about the relationship between research findings and a child’s development. I wasn’t expressing a belief or an opinion in that post, nor a philosophy. I was using the example to make the research come alive.
This points to a more general principle here on the blog. I am interested in examples (whether my own or others’) when they either:
(1) Present a puzzling case that needs explaining, or
(2) Illustrate research findings,
and when they
(3) Are offered with enough detail that others may propose alternate interpretations or hypotheses.
In Boolean algebra, I strive for (puzzling OR illustrative) AND detailed.
Claims of the sort, “It worked for me and I’m OK” or “I did this with my class; they seem to be unharmed” are not particularly helpful to the cause of each of us learning something.
I have no beef with fact memorization, nor with apps that help students to memorize these facts. But we have good research evidence that far more time is spent on low level rule recitation, practice and review in American mathematics classrooms than in other countries with more successful mathematics education programs.
One of the agendas of this blog (there are many) is to explore what other possibilities are within our grasp at a variety of levels. So I’m never going to devote much space to techniques for memorizing arithmetic facts. There’s no new ground for me to cover there. Yes, an app makes it more efficient and gives instantaneous feedback. It’s a marginally better training device than flashcards would be. I have no problem with that.
But I don’t think we learn much from it as a field.
On the other hand, I know for sure that few people outside of the hard-core elementary math education circles know anything substantive about CGI. We have a lot to learn from that project. Examples can help bring the findings to life, and can help people understand the importance of these findings.
Selling a group of math teachers on the proposition that it would be nice if more students knew their addition and multiplication facts? That is not a particularly difficult challenge.
Helping them (and me) to understand the thinking that’s going on in kids’ minds as they learn new stuff? That’s a life’s work.
See also my post on setting norms.