Teaching mathematics for understanding

Edward A. Silver, Vilma M. Mesa, Katherine A. Morris, Jon R. Star and Babette M. Benken have written an article that was published in the most recent issue of American Educational Research Journal. The article is called Teaching Mathematics for Understanding: An Analysis of Lessons Submitted by Teachers Seeking NBPTS Certification. Here is the abstract of their article:
The authors present an analysis of portfolio entries submitted by candidates seeking certification by the National Board for Professional Teaching Standards in the area of Early Adolescence/Mathematics. Analyses of mathematical features revealed that the tasks used in instruction included a range of mathematics topics but were not consistently intellectually challenging. Analyses of key pedagogical features of the lesson materials showed that tasks involved hands-on activities or real-world contexts and technology but rarely required students to provide explanations or demonstrate mathematical reasoning. The findings suggest that, even in lessons that teachers selected for display as best practice examples of teaching for understanding, innovative pedagogical approaches were not systematically used in ways that supported students’ engagement with cognitively demanding mathematical tasks.


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Anonymous said...

My suggestion is you look more deeply into the studies than print the abstracts. Silver has been a prominent supporter of the DOE's math programs - his findings will reflect the bias of the textbook authors.

US educators are being scapegoated for poorly written, poorly conceived textbooks.

How else would you explain a nation-wide lowering of test scores, putting US students 4-6 years behind Korean and Singapore students?

I would like to see more research done on what the Finns are doing to educate their Swedish-speaking minority. Like the Canadians, the Finns appear to have acknowledged that academic success must include teaching language minorities.

Reidar said...

Thanks a lot for both of your comments!

To the last commenter: I know Ed Silver, and I have great respect for him. I would also have liked to look more deeply into these studies, rather than just mention them and print their abstracts. The thing is, I am doing this in my spare time, and it actually takes quite a lot of time already. My aim is to do as you suggest, but I simply don't have the time to do that at the moment. The reason why I started to write this blog was to help myself keep up to date on what's happening within my field of research. I think that this blog is helping me in my own research, and I'm happy that other people might find it helpful too!

On a side note, I don't think poorly written and/or poorly conceived textbooks are the only reasons why US students get so low scores on the international tests. I am quite certain that it is a little more complex than that :-)

I think it is also very much a matter of cultural issues involved. For instance: why is the teacher profession so popular and highly regarded in Finland? They don't get paid very well. I think this is related to some cultural issues that are hard to "insert" into any other country just like that...


Anonymous said...

If you and Dr. Silver have reasoned that cultural issues are NCTM's justification for US students' lack of success, then you probably both disagree with the National Math Panel's findings that only a small fraction (<1%) of the 16,000 studies they reviewed actually met professional research standards.

As I said before, what were Dr. Silver's assumptions for the data he collected. Was there data dropping or not? How would you suggest we validate his findings? I don't know, do you?

Perhaps one reason teachers are held in higher regard in other countries is that students and parents are satisfied with the textbooks they have been given. That's hardly a cultural issue.

Reidar said...

I think cultural issues are part of the picture, but certainly not the entire answer. If there was a simple answer, which I knew the one and only answer to, I would be quite famous by now, I think :-)

The Math Panel had their criteria for evaluating research, and I do not completely agree with them. People (and researchers) have different opinions about what good research is. In the Nordic countries, for instance, a large amount of researchers in mathematics education place themselves within a sociocultural research paradigm, and they believe in qualitative research. Many of them are quite critical towards measurements, and the type of research that would fit within the standards of the Math Panel. I am leading a project where we try to adapt and use the MKT measures (developed by a research team at the University of Michigan) in Norway, and I know that several of my Nordic colleagues are highly critical towards such an approach. I don't think measurements will ever give us all the answers we are searching for, but I also think we need to go beyond what I often refer to as "a world championships in case-study research". I think we need to combine methods and approaches, and I think we need to have a critical approach towards any kind of research method we are involved with, because there is no such thing as one perfect research method!

When it comes to Dr. Silver's research, and the interpretations of that, I think it would be better to ask him rather than me. Being faced with a researcher like Ed Silver, I feel like a novice, and I am not going to pretend that I know how to evaluate his approach, or say what he did right or wrong.

I guess satisfaction with textbooks could be part of the story, but I certainly do not think that adopting some kind of textbook is the holy grail here! Still, if people's view of, or satisfaction with, a textbook differs from one country to another, I would say that this might be a cultural issue. Culture in this respect would mean a different thing from what a musician or an actor would tell you...