Tag Archives: research

An interesting story about research and assumptions

Nature v. nurture. Age-old debate on relative importance. Not gonna settle it here. Not even in the limited context of factors influencing mathematics success.

There is lots of interesting research going on, of course. I want to tell you a quick story about a very small subset of that research.

A few years back, a group of educational psychology researchers published a study that phys.org headlined, “Math ability is inborn“.

The study investigated the ability of 4-year olds to choose the larger of two sets of dots when these sets were viewed briefly (too briefly to allow for counting).

They found that children who were better at this task also knew more about numeration and counting.

A quote from one of the researchers, Melissa Libertus:

“Previous studies testing older children left open the possibility that differences in instructional experience is what caused the difference in their number sense; in other words, that some children tested in middle or high school looked like they had better number sense simply because they had had better math instruction. Unlike those studies, this one shows that the link between ‘number sense’ and math ability is already present before the beginning of formal math instruction.”

Read more at: http://phys.org/news/2011-08-math-ability-inborn.html#jCp

Let’s pause for a moment to think, shall we?

If a child has not had formal instruction in mathematics, is the only remaining possibility that her mathematical performance is due to innate skill?

Of course it isn’t.

There is also the possibility that the child has absorbed some mathematical knowledge from her environment, and that different environments might provide differential input.

Maybe the child who is better at discerning the larger set has more practice doing just that. Maybe that child’s parents have been asking her how many? how much? and which is more? for the last two or three years.

Maybe that child’s parents have been Talking Math with Their Kids.

Pushing back on some pushback

New comment in one of my Tabitha posts, from Steve Prosser (who, not coincidentally, has an app he’d like to sell you),

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.

Smart Boards excepted, right?

From EdTechResearcher by way of Audrey Watters at Hack Education:

In general, our findings cohere with 30 years of educational technology research. There are a handful of teachers who make remarkable use of new technologies, but for the most part, when teachers adopt new technologies, they use them to extend existing practices rather than to develop innovative practices.

As a dear colleague of mine once noted in a Smart Board session, “It’s just like the chalkboard; it’s the teacher’s worksheet.”

Your Daily Wu: Research

Wu on making claims about teaching and learning that are based on even a shred of research evidence

What i think he’s saying

Despite strong research evidence to the contrary, and despite the well-known historical trajectory of the development of the ideas that now comprise elementary school mathematics (including operations on both fractions and integers), the human mind is unfailingly logical.

Because all mathematical ideas can (post facto) be put into a logico-developmental framework, they must be. Anything else lacks rigor and misrepresents the nature of the field of mathematics.

These truths are self-evident. By definition, they do not require substantiation.