Jo Boaler went to England for three years and studied two schools, Amber Hill and Phoenix Park. Both schools served working class populations and began with equal test scores.
Amber Hill taught a traditional curriculum:
All the mathematics teachers were well-qualified specialists, and all of them...believed that the most efficient and effective way to teach mathematics was to impart knowledge of different mathematical procedures,using the chalkboard, and then get students to practice these procedures individually. The teachers believed that if they explained mathematical methods clearly, the students would gain an understanding of them. The teachers also believed that students needed to do a large number of similar exercises because the act of repeating a procedure they had learned would make students remember it. The teachers' belief in this didactic model of teaching meant that their main concern as teachers was to cover all of the necessary mathematical content.
Amber Hill was more than just traditional, though. These folks drilled, and drilled hard. They never taught conceptual math--literally, never. They focused exclusively on procedures without any real look at the broader context of math. The teachers actively discouraged students from using their own methods or from trying to gain a broader understanding.
Picture the worst way of teaching math with a blackboard and chalk. That's what Amber Hill was doing. The teachers often said that this was all they thought the students were capable of.
Phoenix Park is a progressive school.
...the students worked on open-ended projects in every lesson. During this time, the students were taught in mixed ability groups. Projects usually lasted for about 3 weeks. The teachers introduced students to a product or a theme, which the students explored using their own ideas and mathematical knowledge. The projects were usually extremely open, amounting to little more than a challenging statement.
...
At Phoenix Park, the teachers gave out projects and left students to develop them and use their own ideas. The teachers were available to help students, but the students could not rely on this help because there was only one teacher in each room. Students were encouraged to work together and help each other as part of their work, and most students did this.
Phoenix Park teachers didn't grade until year-end. They often "treated students as if they were adults". They would occasionally introduce a method or concept to an individual or group without introducing it to the class.
So for three years the students worked in this open-ended fashion, from the equivalent (I think) of eighth through tenth grade. Then they revert to traditional for a while (less than a year, I think) to study for exams. (O or A levels, I assume).
I don't want to accuse Boaler of bias. She doesn't misrepresent her findings and I'm certain she's not cherrypicking her quotes or her data.
But.
It's always gray in Amber Hill. The teachers. The uniforms. The weather. The students' lives, miserable and oppressed.
Conversely, the sun always shines at Phoenix Park. The teachers are young, the students are vibrant and live lives of fulfillment and purpose.
But then, there's this fascinating little bit about the progressive nirvana:
In every mathematics lesson...between three and six students would do little work and spend much of their time disrupting others....These students had been given the same starting points as everybody else, but for some reason seemed unwilling to think of ways to work on the activities without the teacher telling them what to do The students who did not work in lessons were no less able than other students; they did not come from the same middle school and they were socioeconomically diverse.....The only aspect that seemed to unite the students was their behavior and the fact that most of them were boys...Martin Collins believed that more of the boys experienced difficulty with the approach because they were less mature and less willing to take responsibility for their own learning than girls.(emphasis mine)
So in this little haven of happiness where all colors are primary and the rain never falls, around 10% of the students don't do lessons, disrupt class, aren't learning math--and do so with apparently complete impunity because the paradigm allows the kids to chose.
And notice that to Boaler, this failure is entirely the students' fault. At no point does she wonder if maybe the teachers should be engaging these students. At no point does she wonder if perhaps this is a failing of the progressive method. No. According to Boaler, students who aren't "willing" to "take responsibility for their own learning" are defective. There's something wrong with them. They aren't a normal part of the population and thus, any problems they have don't reflect a problem with the progressive approach.
We discussed this in groups of four (G--my student teacher partner, C, and D are the other three). D said "I wonder what the test results are?"
I laughed, because that was my first and only reaction to the reading, and not because I was curious.
I said "I will bet cash money that the results show relatively little difference in the mean achievement of students for math knowledge, and that Amber Hill's low is much higher than Phoenix Park's low."
D said "Yeah, that wouldn't surprise me."
C said "But don't you think that student happiness and satisfaction is a valid metric?"
Me: "I dunno. Phoenix Park had nicer everything, younger everything, and teachers steeped in the whole progressive/project/guide mode, and they're hard to find. If it turns out that for all that, they end up learning the same amount of math, what does that say about happiness and satisfaction?"
G: "But can you really believe that the Amber Hill kids learned more math?"
Me: "At the lower achievement levels? Yes. Boaler makes that clear, even though she blames it all on the students, not the fabulous progressive teaching methods that make the sun shine and the uniforms bright." (D snorfles.)
So group discussion ends and the section leader gives a presentation where, eventually, the test results are mentioned:
I give myself the terrorist dap. Yes! I was right!
Note how Boaler splits up "procedural" vs. "conceptual". Note also how the chart doesn't mention what the overall results were, once procedural and conceptual are combined. But you can guess, for two reasons. First, "conceptual" is usually a smaller percentage of the overall test. Second, if Phoenix Park had trounced Amber Hill in overall test results, Boaler would have trumpeted the news. So I suspect that the schools' overall results look like the procedural results.
Which were pretty much what I predicted: the mean's the same, but the low end kids do much better at Amber Hill. As for the conceptual results, certainly they reveal that just focusing on procedures without giving kids any time on conceptual issues--or, more importantly, problem solving--is going to result in kids with a weak grasp on concepts.
But the real shocker, of course, is that the utopian Phoenix Park didn't result in spectacularly higher test scores. Worse, the kids in the lower ability range were actively hurt by their years in nirvana.
Really, there's almost no evidence that progressive tenets actually translate into more effective education.