kitchen table math, the sequel: Defense of the Sage on the Stage

Thursday, May 15, 2014

Defense of the Sage on the Stage

The joy of lecturing--With a critique of the romantic tradition of education writing (Appendix to How to Teach Mathematics by S.G. Krantz, 2nd edition, Amer. Math. Soc. 1999, pp. 261-271) (Appendix to How to Teach Mathematics by S.G. Krantz, 2nd edition, Amer. Math. Soc. 1999, pp. 261-271) by H. Wu.


"It appears to me that this rejection of the sage-on-the-stage method of instruction is unjustified. There are situations where lectures are very effective, and in fact there are even circumstances which make this method of instruction mandatory..."


Hainish said...

Wu writes:

"For example, if the amount of material to be covered in a course can be greatly reduced (thereby violating (iii)) and students are expected to spend 8 years in college (thereby violating (ii)), then we can all safely abandon the lecture format and engage in a wholesale application of the guide-on-the-side philosophy in our teaching."

[(ii) being the constraint on number of years of schooling and (iii) being the competence attained from it]

Though I fully agree, I think Wu underestimates the willingness of GotS proponents to do away with coverage of content in lieu of "deep, conceptual" understanding. For them, learning half as much is not a problem - if the way it is learned promotes "life-long learning" in the student's future. (Besides which, you can just Google anything you may need to know.) So, while his argument works for those who agree with his basic premises, it will not for those who de-prioritize content. The de-valuation of knowledge is what we're up against.

SteveH said...

It's also an issue of competence. Does whatever they do get the job done? They like balance, but do students know the times table in fifth grade? Can they reliably manipulate simple fractions in seventh grade? Too many turn to the IQ excuse without applying any sort of common sense judgment. I tell parents that I had to work with my son at home to ensure that he mastered the basics. This was a serious issue for us in grades 3-5. Many don't quite believe me. They think I spent time with my son on fancy problem solving techniques. I tell them that I was NOT a guide-on-the-side. I used worksheets.

I always stress that this is not some sort of battle between two equal, but different pedagogical approaches. The real difference is low versus high expectations.

Anonymous said...

Note Wu wrote it 15 years ago now.
So I think 15 years ago, he might still have been correct, but having lost the battle, yes, the willingness to accept that classrooms do less became the norm. Not so shockingly, CC asks them to do more again, so we are now back to new ways to do less--like abandoning assessments.

palisadesk said...

Hmmm. I wonder if this isn't another area where there is a big discrepancy between what happens in middle class/upper SES schools and what happens in the low-income schools.

For example, I haven't seen much if any "discovery learning" emphasis outside of Kindergarten for 15 years or so, and the primary approach is definitely teacher-centric. Not so much "lecture" -- attention spans of young children are limited, so an interactive direct teaching model is more effective -- but definitely not "guide on the side." I've been in 4 low-SES schools in that time, one of them high-performing, but have seen similar instructional emphases in all of them. The quality of the instruction certainly varies (my current colleagues are almost all very effective but in other schools there was a wider spread of teaching ability).

However, I've never seen the attitude that seems to prevail in upper-SES schools, even in my district, where responsibility for kids' learning the basics is offloaded to the home. It was hammered into me from the get-go that it was MY responsibility to teach kids the things they needed to learn, not the parents' responsibility (which in many cases they did not have the resources to do anyway). It helps that the families in general support a more instructivist stance and expect us to be hammering the foundation skills. We allocate 20 minutes daily across the grades to structured practice of math skills. Counting, math facts, metric conversions, fractions, formulae -- depending on the grade. Our math results are better than those in some of the middle-class schools, which I find interesting. We are doing something right.

Even so it is an uphill struggle because many kids need far more instructional time than we can provide, and issues like absenteeism, frequent moves, family crises and hunger do affect kids' learning no matter how well we can teach them. But I haven't seen the following in any of my schools for over a decade:
1) movies shown during instructional time
2) "art" projects in reading or math.No dioramas, foldables, posters etc.
3) "discovery" learning."Guided discovery" is a bit different -- in a science activity, students might be led through a series of steps to "discover" something (really, to observe it) and detail their observations, but they aren't turned loose with stuff and expected to "discover" something.
4)"group" work with the exception of leveled groups for reading and math; when not directly taught by the teacher the groups will have individualized seatwork or follow-up assignments.

I think it may be a very different ethos in the low-SES schools. Three of my four were schools (large, with around 600-700 kids) with NO middle-income families among them. The curriculum is, supposedly, the same, but how it is delivered is very, very different.

It's a matter of where the locus of responsibility is believed to be. I and many of my colleagues believe the kids' academic progress is OUR responsibility. Perhaps in better-off neighborhoods this "locus of responsibility" is not the same. Certainly many parents here (and on some of my listservs) have shared stories that suggest it is not.

Hainish said...

Palisadek, if you are correct, then low-SES students in high-SES-area schools should be worse off than those in low-SES schools. Teachers could then point to out-of-school factors as being the cause of discrepancies in achievement.

Anonymous said...

Here in the Twin Cities, we are experiencing multiple and opposing forces at the same time.

Hainish, I see some low-SES kids in private schools here that are worse off than if they were in high performing low SES schools. The rest of the school is barreling along doing discovery math, and these kids have no chance to learn. High SES kids are eventually tutored privately, but low SES kids aren't. It is more noticeable in reading, where these kids get no phonics instruction, but the high SES kids eventually get IEPs and massive services to support terrible reading comprehension.

But, they are better off than being in Minneapolis public schools, where they would get no phonics and TERC investigations.

Plenty of low SES charters here are a total disaster. they may not be quite "guide on the side" but the teachers largely have no idea content matters. So there are no drills in math, no sense of what must be known year to year. No urgency.

Another big factor I see here is the "school expects home to teach math facts, but forgets to tell home that." A typical example for me is parents are shocked to find out their 4th grader is not competent at multiplication, and teacher is recommending summer school. They come to me to ask what is going wrong, and how do they help their child. Among other things, I suggest they ask teacher "how many minutes a day is spent on math facts in class?" They do, and receive the response "none".

Meanwhile, I see other schools where the parents are involved but to negative effect. In another typical example, the parents provide a steady steam of complaints if their child is not getting an A. This encourages group work and discovery learning, rather than tests that can be graded.

palisadesk said...

"Palisadek, if you are correct, then low-SES students in high-SES-area schools should be worse off than those in low-SES schools."

I think this may well be true, for several reasons. As Allison explained, the low-SES kids don't have the outside tutoring/afterschooling etc. that higher-income families routinely provide, and they tend (this is a generalization) to respond poorly to unstructured learning situations, which much "group work" and "exploratory learning" seems to be. They haven't got the resources at home or school to do artsy projects, may not have access to a computer or the Internet (or even a telephone!) at home, may have other responsibilities after school, not be able to afford field trips and school clubs/sports etc.

A previous school I worked at was in a neighborhood separated by a large city park from a very wealthy area of manicured million-dollar homes. The school for that neighborhood served these very affluent families, who comprised most of the enrollment, but on the edge of the neighborhood, bordering a freeway, there was a smallish public housing project. The children there also attended this school. So you had the very poor and the extremely rich. The school got allocated some extra special education staff for the "project" kids, but both socially and academically those children were isolated and tended to be academically unsuccessful. A top teacher from my school transferred there a few years ago and tells me that the great divide is still present, and the school does not have the kind of supports low-SES kids need.

For example, at my school the library has been kept open after school for parents and children to come in and use the computers for research, skill practice, homework and so on. Even though math facts are taught, many children need much more practice than can be given in class; we recommend some online sites for practice and pay for some sites where children can practice reading skills online (about 40% of our students have internet at home). Teachers also provide tutoring and support over the lunch hour and run academic clubs like math clubs and spelling clubs to reinforce basics in an engaging way.

Upper-income schools don't, in my experience, provide this kind of thing. Their students are leaving after school for Little League, swimming, horseback riding and gymnastics. Our students are leaving to care for younger siblings or help mom and dad at the bakery.

Adding to the difficulty is the fact that the lower-SES parents feel uncomfortable in a milieu of affluence (less so if it is a mix of working poor and working class), so parents aren't as involved in the school as they would be in one that was more reflective of their own social station.

One benefit, we do get away with a lot of direct teaching (phonics included) even though it is less than optimal. I compared my school's test results with those of one near my home, which has a median family income of 250K (I live on the poor side of the highway, LOL). My school roundly trounced this school, despite being 60% ESL and 95% nonwhite. Test results are only one indicator, but it does show that our kids are learning and we hope they will have a chance to make their way in the world.

Catherine Johnson said...

oh my gosh -- I've never seen this!

Thank you!

Catherine Johnson said...

HAINISH wrote: low-SES students in high-SES-area schools should be worse off than those in low-SES schools

This has been a theme on ktm for years --

Ed and I always had the following thought experiment: what would happen if you did a student-body swap, my high school for a high school in Yonkers.

I think achievement for my town's kids would be the same; achievement for the Yonkers kids would collapse.

Catherine Johnson said...

I mentioned in another post that middle-school teachers here are apparently loading on hours of HW in the run-up to the CC tests.

Basically, teachers are having their students cram for the teachers' scores.

Teachers in low-SES schools couldn't do that.

Teachers in low-SES schools probably couldn't even imagine doing that.

Catherine Johnson said...

PALISADESK wrote: Our math results are better than those in some of the middle-class schools, which I find interesting. We are doing something right.

That reminds me: I've been meaning to post a white paper on technology in the schools, which found that underprivileged kids were using educational software to drill math facts.

The white paper saw that as a bad thing.

(Have to remember which paper it was....)