Knowledge-Based Grades (Who'da Thunk?!?)

Although Out in Left Field blogged first, I couldn't keep from mentioning it here, too. This recent New York Times article describes a new trend in grading--basing grades on what students have learned. New? Yes. Grades are almost always based on a mix of what students know and how they act--whether they complete homework, hand in assignments on time, raise their hand in class. In other words, grades reflect how well students please the teacher as well as how well they have mastered the material. This dual function of grading shows up when students take standardized exams, in which no amount of people-pleasing will help:

About 10 percent of the students who earned A’s and B’s in school stumbled during end-of-the-year exams. By contrast, about 10 percent of students who scraped along with C’s, D’s and even F’s — students who turned in homework late, never raised their hands and generally seemed turned off by school — did better than their eager-to-please B+ classmates.

One district in New York State changed to knowledge-based grading, which didn't sit so well with some parents:

“Does the old system reward compliance? Yes,” she said. “Do those who fit in the box of school do better? Yes. But to revamp the policy in a way that could be of detriment to the kids who do well is not the answer.” In the real world, she points out, attitude counts. 

Of course, when the system was set up to work to detriment of bright nonconformists, no one complained quite as loudly.

Katharine Beals terms this favoritism toward the eager-sociable, grade reversal, and cites the larger culture's embrace of right-brain thinking as a (the?) cause. I'm not so sure; I see different mechanisms to point a finger at.

One is the selection process for public school educators and administrators. As a whole, education majors are not as academically inclined as graduates of other programs. They also seem (and I am speculating here) to have been more challenged by analytical, academic tasks than by things like motivation, organization, and "fitting in." It is natural that they would value what they excel at and redefine achievement to be more in line with their own strengths.

The second mechanism is what I call parentism, and it deserves a post all to itself.

Middle Schools Matter, Too (And Not in a Good Way)

OK, so I guess curriculum isn't the only thing that matters.

In this Education Next article, Jonah Rockoff and Benjamin Lockwood show that structure matters too. They looked at students who transitioned to a 6-8 middle school in either grade 6, grade 7, or not at all (i.e., went to a k-8 school). Students experience a marked drop in achievement beginning the year they move to the middle school, and continuing through the middle school years. This drop happens whether they transition in grade 6 or 7. It does not happen at all with the k-8 educated students.

Read the whole thing. It's scary.

The authors do not pinpoint a reason for the decline, but the results are consistent with my (and many parents' and students') observations about middle schools. The teaching is often horrendous, and the large number of kids in that age range leads to a chaotic atmosphere.

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Jay Matthews also blogs about middle school math, and one of the comments really stood out for me. Slackermom writes:

Middle school isn't much different from elementary school. Teachers are still somewhat intimidated by mathematics; thus, the same topics are taught over and over again without much depth. There are still what I used to call 'holding' years (I remember 8th grade being such a year). These are the years where you learn absolutely nothing new in math classes. Nothing. [emphasis added]

I remember that same 8th grade year when I learned absolutely nothing in math. I remember being so bored I almost walked out (I only regret that I didn't).

So not only do U.S. schools retard students in math, but they do it actively and on purpose.

Whaddayaknow? In Math, Curriculum Matters!

Since this blog is ostensibly about science curriculum, it may seem odd that I am blogging about math. After all, other blogs out there already cover math well enough.

But be patient. We're getting there.

First, let me present another piece of the (math) curriculum puzzle.

A recent Mathematica Policy Institute study looked at four different math curricula used in the early elementary grades and found that (you guessed it!) curriculum matters. Some, like Saxon Math, led to higher student achievement than others, such as TERC investigations. Schools were randomly assigned to different math curricula. The full report comes out next summer.

This was a federally funded study, and it is heartening to see some attention being paid to curriculum effects. It makes this blogger glad.

National Math Curriculum: A Lesson from TIMSS

2002 was, by all appearances, a banner year for discussion of curriculum issues by the AFT. In A Coherent Curriculum: The Case of Mathematics, researchers compare the breadth and depth of math curricula in the "A+" countries that achieved top rankings in the TIMSS with those of 21 U.S. states. They found that the A+ countries covered fewer topics per year, focused in-depth on more topics per year, and taught each topic over fewer years than states in the U.S.

(For a quick overview, download the pdf United States vs. International Standards from this Education Week article.)

It is tempting to think that the effects of what is actually taught pale in comparison with other factors, such as teacher quality, school funding, or the socioeconomic status of the student body. But the fact is that what you teach is what you get.

One of the most important findings from TIMSS is that the differences in achievement from country to country are related to what is taught in different countries. In other words, this is not primarily a matter of demographic variables or other variables that are not greatly affected by schooling. What we can see in TIMSS is that schooling makes a difference. Specifically, we can see that the curriculum itself—what is taught—makes a huge difference.

So what lessons can we draw from this study?

First, the A+ countries had something of a consensus about when topics should be introduced. For example, none of the A+ curricula covered polygons and circles before grade 4. In contrast, 100% of the 21 state curricula specified that this topic be taught starting in grade 1. And so on.... For a total of 32 mathematics topics examined, all but five were introduced later in the top-achieving countries than in the U.S. states.

Second, the A+ countries had a sense that some topics should be mastered before children move on to more advanced topics. As such, a clear sequence emerges of early-elementary, late-elementary, early-middle, and late-middle grade content. In contrast, in the U.S. states,

Prerequisite knowledge doesn’t come first. For example, properties of whole number operations (such as the distributive property) are intended to be covered in first grade, the same time that children are beginning to study basic whole-number operations. This topic is first typically introduced at grade four (and not earlier than grade three) in the top-achieving countries.

In contrast, 100% of the 21 state curricula examined featured this topic in all of the grades from 1-7, and >83% also covered it in grade 8. That's a lot of polygons and a lot of circles! While the A+ countries introduced and taught each topic to mastery in a relatively short time, the U.S. covered...and covered...and covered...and covered the same topics, ad infinitum. The authors state:

The longer topic coverage combined with the absence of the three-tier structure suggest that state standards are developed from a laundry-list approach to mathematics that lacks any sense of the logic of mathematics as a discipline. For many of the individual states it seems that almost all topics are intended to be taught to all students at all grades. [emphasis added]

The report gives us a glimpse of what a coherent curriculum would look like, and I encourage you to read the whole thing (pdf), including the related articles (there is one by E.D. Hirsch).

Lack of a Set Curriculum Hurts Teachers

Lack of curriculum is not a new problem, as evidenced by this AFT article from 2002. In Lost at Sea: Without a Curriculum, Navigating instruction Can Be Tough--Especially for New Teachers, the authors describe the challenges of make-it-up-as-you-go teaching.

Despite what some would have you believe, teachers want a set curriculum...as long as they are not constrained to it. So, being required to follow a script would be a no-go, but having a script to fall back on, use, improve, and modify is something that teachers desire:

We expected that new teachers in this context might feel constrained and frustrated by the rigidity of the curricula they encountered. Instead, we found that despite Massachusetts' detailed system of standards and accountability measures, most new teachers we interviewed received little or no guidance about what to teach or how to teach it. [...] Left to their own devices, they struggled day-to-day to prepare content and materials instead of developing a coherent plan to address long-term objectives. Rather than lamenting a lack of freedom or expressing a need to assert their autonomy, they longed for greater specification of their curriculum—both what to teach and how to teach it. [Emphasis added]

Has anything changed in the past 8 years?

I know that since 2002, some for-profit companies have developed bespoke curricula (daily lesson plans, scripts, the whole nine yards) at the behest of specific districts. Of course, these are not made public and they are not scrutinized by teachers at large, so their impact is limited.

What would an effective solution to the curriculum problem look like?

First off, lesson planning materials would have to be open-source. Any teacher should be allowed to access them and to modify them as they see fit. They must be able to give feedback on the lessons and post their modifications back into the curriculum bank. The curriculum should benefit from teacher expertise as well as guide it.

Second, one or more scope-and-sequence specs would have to be developed, and they would have to be aligned to existing science standards. With talk of national science standards, this may soon become a lot easier. While there might not be a single right sequence to teach the topics, there are surely one or more ways that work better than others.


If you are a teacher, what would you like to see in a curriculum?